packages feed

hmt 0.16 → 0.20

raw patch · 213 files changed

Files

− Music/Theory/Array.hs 
@@ -1,90 +0,0 @@-module Music.Theory.Array where--import Data.List {- base -}-import qualified Data.Array as A {- array -}--import qualified Music.Theory.List as T {- hmt -}---- * Association List (List Array)--larray_bounds :: Ord k => [(k,v)] -> (k,k)-larray_bounds = T.minmax . map fst--larray :: A.Ix k => [(k,v)] -> A.Array k v-larray a = A.array (larray_bounds a) a---- * List Table---- | Append a sequence of /nil/ (or default) values to each row of /tbl/--- so to make it regular (ie. all rows of equal length).-make_regular :: t -> [[t]] -> [[t]]-make_regular k tbl =-    let z = maximum (map length tbl)-    in map (T.pad_right k z) tbl---- * Matrix Indices---- | Matrix dimensions are written (rows,columns).-type Dimensions i = (i,i)---- | Matrix indices are written (row,column) & are here _zero_ indexed.-type Ix i = (i,i)---- | Translate 'Ix' by row and column delta.------ > ix_translate (1,2) (3,4) == (4,6)-ix_translate :: Num t => (t,t) -> Ix t -> Ix t-ix_translate (dr,dc) (r,c) = (r + dr,c + dc)---- | Modulo 'Ix' by 'Dimensions'.------ > ix_modulo (4,4) (3,7) == (3,3)-ix_modulo :: Integral t => Dimensions t -> Ix t -> Ix t-ix_modulo (nr,nc) (r,c) = (r `mod` nr,c `mod` nc)---- | Given number of columns and row index, list row indices.------ > row_indices 3 1 == [(1,0),(1,1),(1,2)]-row_indices :: (Enum t, Num t) => t -> t -> [Ix t]-row_indices nc r = map (\c -> (r,c)) [0 .. nc - 1]---- | Given number of rows and column index, list column indices.------ > column_indices 3 1 == [(0,1),(1,1),(2,1)]-column_indices :: (Enum t, Num t) => t -> t -> [Ix t]-column_indices nr c = map (\r -> (r,c)) [0 .. nr - 1]---- | All zero-indexed matrix indices, in row order.  This is the order--- given by 'sort'.------ > matrix_indices (2,3) == [(0,0),(0,1),(0,2),(1,0),(1,1),(1,2)]--- > sort (matrix_indices (2,3)) == matrix_indices (2,3)-matrix_indices :: (Enum t, Num t) => Dimensions t -> [Ix t]-matrix_indices (nr,nc) = concatMap (row_indices nc) [0 .. nr - 1 ]---- | Corner indices of given 'Dimensions', in row order.------ > matrix_corner_indices (2,3) == [(0,0),(0,2),(1,0),(1,2)]-matrix_corner_indices :: Num t => Dimensions t -> [Ix t]-matrix_corner_indices (nr,nc) = [(0,0),(0,nc - 1),(nr - 1,0),(nr - 1,nc - 1)]---- | Parallelogram corner indices, given as rectangular 'Dimensions' with an--- offset for the lower indices.------ > parallelogram_corner_indices ((2,3),2) == [(0,0),(0,2),(1,2),(1,4)]-parallelogram_corner_indices :: Num t => (Dimensions t,t) -> [Ix t]-parallelogram_corner_indices ((nr,nc),o) = [(0,0),(0,nc - 1),(nr - 1,o),(nr - 1,nc + o - 1)]---- | Apply 'ix_modulo' and 'ix_translate' for all 'matrix_indices',--- ie. all translations of a 'shape' in row order.  The resulting 'Ix'--- sets are not sorted and may have duplicates.------ > concat (all_ix_translations (2,3) [(0,0)]) == matrix_indices (2,3)-all_ix_translations :: Integral t => Dimensions t -> [Ix t] -> [[Ix t]]-all_ix_translations dm ix =-    let f z = ix_modulo dm . ix_translate z-    in map (\dx -> map (f dx) ix) (matrix_indices dm)---- | Sort sets into row order and remove duplicates.-all_ix_translations_uniq :: Integral t => Dimensions t -> [Ix t] -> [[Ix t]]-all_ix_translations_uniq dm = nub . map sort . all_ix_translations dm
− Music/Theory/Array/CSV.hs 
@@ -1,189 +0,0 @@--- | Regular matrix array data, CSV, column & row indexing.-module Music.Theory.Array.CSV where--import qualified Data.Array as A {- array -}-import Data.List {- base -}--import qualified Text.CSV.Lazy.String as C {- lazy-csv -}--import qualified Music.Theory.Array.Cell_Ref as T {- hmt -}-import qualified Music.Theory.IO as T {- hmt -}-import qualified Music.Theory.List as T {- hmt -}-import qualified Music.Theory.Tuple as T {- hmt -}---- * TABLE---- | When reading a CSV file is the first row a header?-type CSV_Has_Header = Bool---- | Alias for 'Char', allow characters other than @,@ as delimiter.-type CSV_Delimiter = Char---- | Alias for 'Bool', allow linebreaks in fields.-type CSV_Allow_Linebreaks = Bool---- | When writing a CSV file should the delimiters be aligned,--- ie. should columns be padded with spaces, and if so at which side--- of the data?-data CSV_Align_Columns = CSV_No_Align | CSV_Align_Left | CSV_Align_Right---- | CSV options.-type CSV_Opt = (CSV_Has_Header,CSV_Delimiter,CSV_Allow_Linebreaks,CSV_Align_Columns)---- | Default CSV options, no header, comma delimiter, no linebreaks, no alignment.-def_csv_opt :: CSV_Opt-def_csv_opt = (False,',',False,CSV_No_Align)---- | Plain list representation of a two-dimensional table of /a/ in--- row-order.  Tables are regular, ie. all rows have equal numbers of--- columns.-type Table a = [[a]]---- | CSV table, ie. a 'Table' with 'Maybe' a header.-type CSV_Table a = (Maybe [String],Table a)---- | Read 'CSV_Table' from @CSV@ file.-csv_table_read :: CSV_Opt -> (String -> a) -> FilePath -> IO (CSV_Table a)-csv_table_read (hdr,delim,brk,_) f fn = do-  s <- T.read_file_utf8 fn-  let t = C.csvTable (C.parseDSV brk delim s)-      p = C.fromCSVTable t-      (h,d) = if hdr then (Just (head p),tail p) else (Nothing,p)-  return (h,map (map f) d)---- | Read 'Table' only with 'def_csv_opt'.-csv_table_read_def :: (String -> a) -> FilePath -> IO (Table a)-csv_table_read_def f = fmap snd . csv_table_read def_csv_opt f---- | Read and process @CSV@ 'CSV_Table'.-csv_table_with :: CSV_Opt -> (String -> a) -> FilePath -> (CSV_Table a -> b) -> IO b-csv_table_with opt f fn g = fmap g (csv_table_read opt f fn)---- | Align table according to 'CSV_Align_Columns'.------ > csv_table_align CSV_No_Align [["a","row","and"],["then","another","one"]]-csv_table_align :: CSV_Align_Columns -> Table String -> Table String-csv_table_align align tbl =-    let c = transpose tbl-        n = map (maximum . map length) c-        ext k s = let pd = replicate (k - length s) ' '-                  in case align of-                       CSV_No_Align -> s-                       CSV_Align_Left -> pd ++ s-                       CSV_Align_Right -> s ++ pd-    in transpose (zipWith (map . ext) n c)---- | Pretty-print 'CSV_Table'.-csv_table_pp :: (a -> String) -> CSV_Opt -> CSV_Table a -> String-csv_table_pp f (_,delim,brk,align) (hdr,tbl) =-  let tbl' = csv_table_align align (T.mcons hdr (map (map f) tbl))-      (_,t) = C.toCSVTable tbl'-  in C.ppDSVTable brk delim t---- | 'T.write_file_utf8' of 'csv_table_pp'.-csv_table_write :: (a -> String) -> CSV_Opt -> FilePath -> CSV_Table a -> IO ()-csv_table_write f opt fn csv = T.write_file_utf8 fn (csv_table_pp f opt csv)---- | Write 'Table' only (no header) with 'def_csv_opt'.-csv_table_write_def :: (a -> String) -> FilePath -> Table a -> IO ()-csv_table_write_def f fn tbl = csv_table_write f def_csv_opt fn (Nothing,tbl)---- | @0@-indexed (row,column) cell lookup.-table_lookup :: Table a -> (Int,Int) -> a-table_lookup t (r,c) = (t !! r) !! c---- | Row data.-table_row :: Table a -> T.Row_Ref -> [a]-table_row t r = t !! T.row_index r---- | Column data.-table_column :: Table a -> T.Column_Ref -> [a]-table_column t c = transpose t !! T.column_index c---- | Lookup value across columns.-table_column_lookup :: Eq a => Table a -> (T.Column_Ref,T.Column_Ref) -> a -> Maybe a-table_column_lookup t (c1,c2) e =-    let a = zip (table_column t c1) (table_column t c2)-    in lookup e a---- | Table cell lookup.-table_cell :: Table a -> T.Cell_Ref -> a-table_cell t (c,r) =-    let (r',c') = (T.row_index r,T.column_index c)-    in table_lookup t (r',c')---- | @0@-indexed (row,column) cell lookup over column range.-table_lookup_row_segment :: Table a -> (Int,(Int,Int)) -> [a]-table_lookup_row_segment t (r,(c0,c1)) =-    let r' = t !! r-    in take (c1 - c0 + 1) (drop c0 r')---- | Range of cells from row.-table_row_segment :: Table a -> (T.Row_Ref,T.Column_Range) -> [a]-table_row_segment t (r,c) =-    let (r',c') = (T.row_index r,T.column_indices c)-    in table_lookup_row_segment t (r',c')---- * Array---- | Translate 'Table' to 'Array'.  It is assumed that the 'Table' is--- regular, ie. all rows have an equal number of columns.------ > let a = table_to_array [[0,1,3],[2,4,5]]--- > in (bounds a,indices a,elems a)------ > > (((A,1),(C,2))--- > > ,[(A,1),(A,2),(B,1),(B,2),(C,1),(C,2)]--- > > ,[0,2,1,4,3,5])-table_to_array :: Table a -> A.Array T.Cell_Ref a-table_to_array t =-    let nr = length t-        nc = length (t !! 0)-        bnd = (T.cell_ref_minima,(toEnum (nc - 1),nr))-        asc = zip (T.cell_range_row_order bnd) (concat t)-    in A.array bnd asc---- | 'table_to_array' of 'csv_table_read'.-csv_array_read :: CSV_Opt -> (String -> a) -> FilePath -> IO (A.Array T.Cell_Ref a)-csv_array_read opt f fn = fmap (table_to_array . snd) (csv_table_read opt f fn)---- * Irregular--csv_field_str :: C.CSVField -> String-csv_field_str f =-    case f of-      C.CSVField _ _ _ _ s _ -> s-      C.CSVFieldError _ _ _ _ _ -> error "csv_field_str"--csv_error_recover :: C.CSVError -> C.CSVRow-csv_error_recover e =-    case e of-      C.IncorrectRow _ _ _ f -> f-      C.BlankLine _ _ _ _ -> []-      _ -> error "csv_error_recover: not recoverable"--csv_row_recover :: Either [C.CSVError] C.CSVRow -> C.CSVRow-csv_row_recover r =-    case r of-      Left [e] -> csv_error_recover e-      Left _ -> error "csv_row_recover: multiple errors"-      Right r' -> r'---- | Read irregular @CSV@ file, ie. rows may have any number of columns, including no columns.-csv_load_irregular :: (String -> a) -> FilePath -> IO [[a]]-csv_load_irregular f fn = do-  s <- T.read_file_utf8 fn-  return (map (map (f . csv_field_str) . csv_row_recover) (C.parseCSV s))---- * Tuples--type P5_Parser t1 t2 t3 t4 t5 = (String -> t1,String -> t2,String -> t3,String -> t4,String -> t5)-type P5_Writer t1 t2 t3 t4 t5 = (t1 -> String,t2 -> String,t3 -> String,t4 -> String,t5 -> String)--csv_table_read_p5 :: P5_Parser t1 t2 t3 t4 t5 -> CSV_Opt -> FilePath -> IO (Maybe [String],[(t1,t2,t3,t4,t5)])-csv_table_read_p5 f opt fn = do-  (hdr,dat) <- csv_table_read opt id fn-  return (hdr,map (T.p5_from_list f) dat)--csv_table_write_p5 :: P5_Writer t1 t2 t3 t4 t5 -> CSV_Opt -> FilePath -> (Maybe [String],[(t1,t2,t3,t4,t5)]) -> IO ()-csv_table_write_p5 f opt fn (hdr,dat) = csv_table_write id opt fn (hdr,map (T.p5_to_list f) dat)
− Music/Theory/Array/CSV/Midi/MND.hs 
@@ -1,203 +0,0 @@--- | Functions for reading midi note data (MND) from CSV files.--- This is /not/ a generic text midi notation.--- The defined commands are @on@ and @off@, but others may be present.--- Non-integral note number and key velocity data are allowed.-module Music.Theory.Array.CSV.Midi.MND where--import Data.List.Split {- split -}-import Data.List {- base -}-import Data.Maybe {- base -}-import Data.Word {- base -}--import qualified Music.Theory.Array.CSV as T {- hmt -}-import qualified Music.Theory.Math as T {- hmt -}-import qualified Music.Theory.Read as T {- hmt -}-import qualified Music.Theory.Time.Seq as T {- hmt -}---- | If /r/ is whole to /k/ places then show as integer, else as float to /k/ places.-data_value_pp :: Real t => Int -> t -> String-data_value_pp k r =-    if T.whole_to_precision k r-    then show (T.real_floor_int r)-    else T.real_pp k r---- | Channel values are 4-bit (0-15).-type Channel = Word8---- | The required header field.-csv_mnd_hdr :: [String]-csv_mnd_hdr = ["time","on/off","note","velocity","channel","param"]--type Param = (String,Double)--param_parse :: String -> [Param]-param_parse str =-    let f x = case splitOn "=" x of-                [lhs,rhs] -> (lhs,read rhs)-                _ -> error ("param_parse: " ++ x)-    in if null str then [] else map f (splitOn ";" str)--param_pp :: Int -> [Param] -> String-param_pp k =-    let f (lhs,rhs) = concat [lhs,"=",T.real_pp k rhs]-    in intercalate ";" . map f---- | Midi note data, the type parameters are to allow for fractional note & velocity values.--- The command is a string, @on@ and @off@ are standard, other commands may be present.------ > unwords csv_mnd_hdr == "time on/off note velocity channel param"-type MND t n = (t,String,n,n,Channel,[Param])--csv_mnd_parse :: (Read t,Real t,Read n,Real n) => T.CSV_Table String -> [MND t n]-csv_mnd_parse (hdr,dat) =-    let err x = error ("csv_mnd_read: " ++ x)-        f m = case m of-                [st,msg,mnn,vel,ch,pm] ->-                    (T.reads_exact_err "time:real" st-                    ,msg-                    ,T.reads_exact_err "note:real" mnn-                    ,T.reads_exact_err "velocity:real" vel-                    ,T.reads_exact_err "channel:int" ch-                    ,param_parse pm)-                _ -> err "entry?"-    in case hdr of-         Just hdr' -> if hdr' == csv_mnd_hdr then map f dat else err "header?"-         Nothing -> err "no header?"--load_csv :: FilePath -> IO (T.CSV_Table String)-load_csv = T.csv_table_read (True,',',False,T.CSV_No_Align) id---- | Midi note data.------ > let fn = "/home/rohan/cvs/uc/uc-26/daily-practice/2014-08-13.1.csv"--- > m <- csv_mnd_read fn :: IO [MND Double Double]--- > length m == 17655--- > csv_mnd_write 4 "/tmp/t.csv" m-csv_mnd_read :: (Read t,Real t,Read n,Real n) => FilePath -> IO [MND t n]-csv_mnd_read = fmap csv_mnd_parse . load_csv---- | Writer.-csv_mnd_write :: (Real t,Real n) => Int -> FilePath -> [MND t n] -> IO ()-csv_mnd_write r_prec nm =-    let un_node (st,msg,mnn,vel,ch,pm) =-            [T.real_pp r_prec st-            ,msg-            ,data_value_pp r_prec mnn-            ,data_value_pp r_prec vel-            ,show ch-            ,param_pp r_prec pm]-        with_hdr dat = (Just csv_mnd_hdr,dat)-    in T.csv_table_write id T.def_csv_opt nm . with_hdr . map un_node---- * MND Seq forms---- | (p0=midi-note,p1=velocity,channel,param)-type Event n = (n,n,Channel,[Param])---- | Translate from 'Tseq' form to 'Wseq' form.-midi_tseq_to_midi_wseq :: (Num t,Eq n) => T.Tseq t (T.Begin_End (Event n)) -> T.Wseq t (Event n)-midi_tseq_to_midi_wseq = T.tseq_begin_end_to_wseq (\(n0,_,c0,_) (n1,_,c1,_) -> c0 == c1 && n0 == n1)--midi_wseq_to_midi_tseq :: (Num t,Ord t) => T.Wseq t x -> T.Tseq t (T.Begin_End x)-midi_wseq_to_midi_tseq = T.wseq_begin_end---- | Ignores non on/off messages.-mnd_to_tseq :: Num n => [MND t n] -> T.Tseq t (T.Begin_End (Event n))-mnd_to_tseq =-    let mk_node (st,msg,mnn,vel,ch,pm) =-            case msg of-              "on" -> Just (st,T.Begin (mnn,vel,ch,pm))-              "off" -> Just (st,T.End (mnn,0,ch,pm))-              _ -> Nothing-    in mapMaybe mk_node---- | 'Tseq' form of 'csv_mnd_read', channel information is retained, off-velocity is zero.-csv_mnd_read_tseq :: (Read t,Real t,Read n,Real n) => FilePath -> IO (T.Tseq t (T.Begin_End (Event n)))-csv_mnd_read_tseq = fmap mnd_to_tseq . csv_mnd_read---- | 'Tseq' form of 'csv_mnd_write', data is .-csv_mnd_write_tseq :: (Real t,Real n) => Int -> FilePath -> T.Tseq t (T.Begin_End (Event n)) -> IO ()-csv_mnd_write_tseq r_prec nm sq =-    let f (t,e) = case e of-                    T.Begin (n,v,c,p) -> (t,"on",n,v,c,p)-                    T.End (n,_,c,p) -> (t,"off",n,0,c,p)-    in csv_mnd_write r_prec nm (map f sq)---- * MNDD (simplifies cases where overlaps on the same channel are allowed).---- | Message should be @note@ for note data.-csv_mndd_hdr :: [String]-csv_mndd_hdr = ["time","duration","message","note","velocity","channel","param"]---- > unwords csv_mndd_hdr == "time duration message note velocity channel param"-type MNDD t n = (t,t,String,n,n,Channel,[Param])--csv_mndd_parse :: (Read t,Real t,Read n,Real n) => T.CSV_Table String -> [MNDD t n]-csv_mndd_parse (hdr,dat) =-    let err x = error ("csv_mndd_read: " ++ x)-        f m =-            case m of-              [st,du,msg,mnn,vel,ch,pm] ->-                  (T.reads_exact_err "time" st-                  ,T.reads_exact_err "duration" du-                  ,msg-                  ,T.reads_exact_err "note" mnn-                  ,T.reads_exact_err "velocity" vel-                  ,T.reads_exact_err "channel" ch-                  ,param_parse pm)-              _ -> err "entry?"-    in case hdr of-         Just hdr' -> if hdr' == csv_mndd_hdr then map f dat else err "header?"-         Nothing -> err "no header?"---- | Midi note/duration data.-csv_mndd_read :: (Read t,Real t,Read n,Real n) => FilePath -> IO [MNDD t n]-csv_mndd_read = fmap csv_mndd_parse . load_csv---- | Writer.-csv_mndd_write :: (Real t,Real n) => Int -> FilePath -> [MNDD t n] -> IO ()-csv_mndd_write r_prec nm =-    let un_node (st,du,msg,mnn,vel,ch,pm) =-            [T.real_pp r_prec st,T.real_pp r_prec du,msg-            ,data_value_pp r_prec mnn,data_value_pp r_prec vel-            ,show ch-            ,param_pp r_prec pm]-        with_hdr dat = (Just csv_mndd_hdr,dat)-    in T.csv_table_write id T.def_csv_opt nm . with_hdr . map un_node---- * MNDD Seq forms---- | Ignores non note messages.-mndd_to_wseq :: [MNDD t n] -> T.Wseq t (Event n)-mndd_to_wseq =-    let mk_node (st,du,msg,mnn,vel,ch,pm) =-            case msg of-              "note" -> Just ((st,du),(mnn,vel,ch,pm))-              _ -> Nothing-    in mapMaybe mk_node---- | 'Wseq' form of 'csv_mndd_read'.-csv_mndd_read_wseq :: (Read t,Real t,Read n,Real n) => FilePath -> IO (T.Wseq t (Event n))-csv_mndd_read_wseq = fmap mndd_to_wseq . csv_mndd_read---- | 'Wseq' form of 'csv_mndd_write'.-csv_mndd_write_wseq :: (Real t,Real n) => Int -> FilePath -> T.Wseq t (Event n) -> IO ()-csv_mndd_write_wseq r_prec nm =-    let f ((st,du),(mnn,vel,ch,pm)) = (st,du,"note",mnn,vel,ch,pm)-    in csv_mndd_write r_prec nm . map f---- * Composite---- | Parse either MND or MNDD data to Wseq, CSV type is decided by header.-csv_midi_parse_wseq :: (Read t,Real t,Read n,Real n) => T.CSV_Table String -> T.Wseq t (Event n)-csv_midi_parse_wseq (hdr,dat) = do-  case hdr of-    Just hdr' -> if hdr' == csv_mnd_hdr-                 then midi_tseq_to_midi_wseq (mnd_to_tseq (csv_mnd_parse (hdr,dat)))-                 else if hdr' == csv_mndd_hdr-                      then mndd_to_wseq (csv_mndd_parse (hdr,dat))-                      else error "csv_midi_read_wseq: not MND or MNDD"-    _ -> error "csv_midi_read_wseq: header?"--csv_midi_read_wseq :: (Read t,Real t,Read n,Real n) => FilePath -> IO (T.Wseq t (Event n))-csv_midi_read_wseq = fmap csv_midi_parse_wseq . load_csv
− Music/Theory/Array/Cell_Ref.hs 
@@ -1,228 +0,0 @@--- | Cell references & indexing.-module Music.Theory.Array.Cell_Ref where--import qualified Data.Array as A {- array -}-import Data.Char {- base -}-import Data.Function {- base -}-import Data.Maybe {- base -}-import Data.String {- base -}---- | @A@ indexed case-insensitive column references.  The column--- following @Z@ is @AA@.-data Column_Ref = Column_Ref {column_ref_string :: String}--instance IsString Column_Ref where fromString = Column_Ref-instance Read Column_Ref where readsPrec _ s = [(Column_Ref s,[])]-instance Show Column_Ref where show = column_ref_string-instance Eq Column_Ref where (==) = (==) `on` column_index-instance Ord Column_Ref where compare = compare `on` column_index--instance Enum Column_Ref where-    fromEnum = column_index-    toEnum = column_ref--instance A.Ix Column_Ref where-    range = column_range-    index = interior_column_index-    inRange = column_in_range-    rangeSize = column_range_size---- | Inclusive range of column references.-type Column_Range = (Column_Ref,Column_Ref)---- | @1@-indexed row reference.-type Row_Ref = Int---- | Zero index of 'Row_Ref'.-row_index :: Row_Ref -> Int-row_index r = r - 1---- | Inclusive range of row references.-type Row_Range = (Row_Ref,Row_Ref)---- | Cell reference, column then row.-type Cell_Ref = (Column_Ref,Row_Ref)---- | Inclusive range of cell references.-type Cell_Range = (Cell_Ref,Cell_Ref)---- | Case folding letter to index function.  Only valid for ASCII letters.------ > map letter_index ['A' .. 'Z'] == [0 .. 25]--- > map letter_index ['a','d' .. 'm'] == [0,3 .. 12]-letter_index :: Char -> Int-letter_index c = fromEnum (toUpper c) - fromEnum 'A'---- | Inverse of 'letter_index'.------ > map index_letter [0,3 .. 12] == ['A','D' .. 'M']-index_letter :: Int -> Char-index_letter i = toEnum (i + fromEnum 'A')---- | Translate column reference to @0@-index.------ > :set -XOverloadedStrings--- > map column_index ["A","c","z","ac","XYZ"] == [0,2,25,28,17575]-column_index :: Column_Ref -> Int-column_index (Column_Ref c) =-    let m = iterate (* 26) 1-        i = reverse (map letter_index c)-    in sum (zipWith (*) m (zipWith (+) [0..] i))---- | Column reference to interior index within specified range.  Type--- specialised 'Data.Ix.index'.------ > map (Data.Ix.index ('A','Z')) ['A','C','Z'] == [0,2,25]--- > map (interior_column_index ("A","Z")) ["A","C","Z"] == [0,2,25]------ > map (Data.Ix.index ('B','C')) ['B','C'] == [0,1]--- > map (interior_column_index ("B","C")) ["B","C"] == [0,1]-interior_column_index :: Column_Range -> Column_Ref -> Int-interior_column_index (l,r) c =-    let n = column_index c-        l' = column_index l-        r' = column_index r-    in if n > r'-       then error (show ("interior_column_index",l,r,c))-       else n - l'---- | Inverse of 'column_index'.------ > let c = ["A","Z","AA","AZ","BA","BZ","CA"]--- > in map column_ref [0,25,26,51,52,77,78] == c------ > column_ref (0+25+1+25+1+25+1) == "CA"-column_ref :: Int -> Column_Ref-column_ref =-    let rec n = case n `quotRem` 26 of-                  (0,r) -> [index_letter r]-                  (q,r) -> index_letter (q - 1) : rec r-    in Column_Ref . rec---- | Type specialised 'pred'.------ > column_ref_pred "DF" == "DE"-column_ref_pred :: Column_Ref -> Column_Ref-column_ref_pred = pred---- | Type specialised 'succ'.------ > column_ref_succ "DE" == "DF"-column_ref_succ :: Column_Ref -> Column_Ref-column_ref_succ = succ---- | Bimap of 'column_index'.------ > column_indices ("b","p") == (1,15)--- > column_indices ("B","IT") == (1,253)-column_indices :: Column_Range -> (Int,Int)-column_indices =-    let bimap f (i,j) = (f i,f j)-    in bimap column_index---- | Type specialised 'Data.Ix.range'.------ > column_range ("L","R") == ["L","M","N","O","P","Q","R"]--- > Data.Ix.range ('L','R') == "LMNOPQR"-column_range :: Column_Range -> [Column_Ref]-column_range rng =-    let (l,r) = column_indices rng-    in map column_ref [l .. r]---- | Type specialised 'Data.Ix.inRange'.------ > map (column_in_range ("L","R")) ["A","N","Z"] == [False,True,False]--- > map (column_in_range ("L","R")) ["L","N","R"] == [True,True,True]------ > map (Data.Ix.inRange ('L','R')) ['A','N','Z'] == [False,True,False]--- > map (Data.Ix.inRange ('L','R')) ['L','N','R'] == [True,True,True]-column_in_range :: Column_Range -> Column_Ref -> Bool-column_in_range rng c =-    let (l,r) = column_indices rng-        k = column_index c-    in k >= l && k <= r---- | Type specialised 'Data.Ix.rangeSize'.------ > map column_range_size [("A","Z"),("AA","ZZ")] == [26,26 * 26]--- > Data.Ix.rangeSize ('A','Z') == 26-column_range_size :: Column_Range -> Int-column_range_size = (+ 1) . negate . uncurry (-) . column_indices---- | Type specialised 'Data.Ix.range'.-row_range :: Row_Range -> [Row_Ref]-row_range = A.range---- | The standard uppermost leftmost cell reference, @A1@.------ > Just cell_ref_minima == parse_cell_ref "A1"-cell_ref_minima :: Cell_Ref-cell_ref_minima = (Column_Ref "A",1)---- | Cell reference parser for standard notation of (column,row).------ > parse_cell_ref "CC348" == Just ("CC",348)-parse_cell_ref :: String -> Maybe Cell_Ref-parse_cell_ref s =-    case span isUpper s of-      ([],_) -> Nothing-      (c,r) -> case span isDigit r of-                 (n,[]) -> Just (Column_Ref c,read n)-                 _ -> Nothing--is_cell_ref :: String -> Bool-is_cell_ref = isJust . parse_cell_ref--parse_cell_ref_err :: String -> Cell_Ref-parse_cell_ref_err = fromMaybe (error "parse_cell_ref") . parse_cell_ref---- | Cell reference pretty printer.------ > cell_ref_pp ("CC",348) == "CC348"-cell_ref_pp :: Cell_Ref -> String-cell_ref_pp (Column_Ref c,r) = c ++ show r---- | Translate cell reference to @0@-indexed pair.------ > cell_index ("CC",348) == (80,347)--- > Data.Ix.index (("AA",1),("ZZ",999)) ("CC",348) == 54293-cell_index :: Cell_Ref -> (Int,Int)-cell_index (c,r) = (column_index c,row_index r)---- | Inverse of cell_index.------ > index_to_cell (80,347) == (Column_Ref "CC",348)--- > index_to_cell (4,5) == (Column_Ref "E",6)-index_to_cell :: (Int,Int) -> Cell_Ref-index_to_cell (c,r) = (column_ref c,r + 1)--parse_cell_index :: String -> (Int,Int)-parse_cell_index = cell_index . parse_cell_ref_err---- | Type specialised 'Data.Ix.range', cells are in column-order.------ > cell_range (("AA",1),("AC",1)) == [("AA",1),("AB",1),("AC",1)]------ > let r = [("AA",1),("AA",2),("AB",1),("AB",2),("AC",1),("AC",2)]--- > in cell_range (("AA",1),("AC",2)) == r------ > Data.Ix.range (('A',1),('C',1)) == [('A',1),('B',1),('C',1)]------ > let r = [('A',1),('A',2),('B',1),('B',2),('C',1),('C',2)]--- > in Data.Ix.range (('A',1),('C',2)) == r-cell_range :: Cell_Range -> [Cell_Ref]-cell_range ((c1,r1),(c2,r2)) =-    [(c,r) |-     c <- column_range (c1,c2)-    ,r <- row_range (r1,r2)]---- | Variant of 'cell_range' in row-order.------ > let r = [(AA,1),(AB,1),(AC,1),(AA,2),(AB,2),(AC,2)]--- > in cell_range_row_order (("AA",1),("AC",2)) == r-cell_range_row_order ::  Cell_Range -> [Cell_Ref]-cell_range_row_order ((c1,r1),(c2,r2)) =-    [(c,r) |-     r <- row_range (r1,r2)-    ,c <- column_range (c1,c2)]-
+ Music/Theory/Array/Csv/Midi/Cli.hs view
@@ -0,0 +1,47 @@+module Music.Theory.Array.Csv.Midi.Cli where++import qualified Music.Theory.Array.Csv.Midi.Mnd as T {- hmt -}+import qualified Music.Theory.Time.Seq as T {- hmt -}++usage :: [String]+usage =+  ["concat {r} -o output-file input-file..."+  ,"mnd-to-mndd {i|r} precision:int input-file output-file"+  ,"mndd-transpose precision:int n:int input-file output-file"]++read_wseq_i :: FilePath -> IO (T.Wseq Double (T.Event Int))+read_wseq_i = T.csv_midi_read_wseq++read_wseq_r :: FilePath -> IO (T.Wseq Double (T.Event Double))+read_wseq_r = T.csv_midi_read_wseq++mnd_to_mndd_i :: Int -> FilePath -> FilePath -> IO ()+mnd_to_mndd_i p i_fn o_fn = do+  m <- read_wseq_i i_fn+  T.csv_mndd_write_wseq p o_fn m++mndd_transpose_r :: Int -> Double -> FilePath -> FilePath -> IO ()+mndd_transpose_r p k i_fn o_fn = do+  m <- read_wseq_r i_fn+  let f (t,(mnn,vel,ch,pr)) = (t,(mnn + k,vel,ch,pr))+  T.csv_mndd_write_wseq p o_fn (map f m)++csv_midi_concat_r :: FilePath -> [FilePath] -> IO ()+csv_midi_concat_r o_fn i_fn = do+  i <- mapM read_wseq_r i_fn+  T.csv_mndd_write_wseq 4 o_fn (T.wseq_concat i)++csv_midi_cli :: [String] -> IO ()+csv_midi_cli arg =+  case arg of+    "concat":"r":"-o":o_fn:i_fn -> csv_midi_concat_r o_fn i_fn+    ["mnd-to-mndd","i",p,i_fn,o_fn] -> mnd_to_mndd_i (read p) i_fn o_fn+    ["mndd-transpose","r",p,k,i_fn,o_fn] -> mndd_transpose_r (read p) (read k) i_fn o_fn+    _ -> putStrLn (unlines usage)++{-+fn = "/home/rohan/uc/invisible/heliotrope/csv/rough/00.csv"+mnd_to_mndd_i 4 fn "/tmp/t-mndd.csv"+mndd_transpose_r 4 (-12) fn "/tmp/t-trs.csv"+-}+
+ Music/Theory/Array/Csv/Midi/Mnd.hs view
@@ -0,0 +1,270 @@+{- | Functions for reading midi note data (Mnd) from Csv files.++This is /not/ a generic text midi notation.+The required columns are documented at `Mnd` and `Mndd`.+The defined commands are @on@ and @off@, but others may be present.+Non-integral note number and key velocity data are allowed.+-}+module Music.Theory.Array.Csv.Midi.Mnd where++import Data.Function {- base -}+import Data.List {- base -}+import Data.Maybe {- base -}++import Data.List.Split {- split -}++import qualified Music.Theory.Array.Csv as T {- hmt-base -}+import qualified Music.Theory.Math as T {- hmt-base -}+import qualified Music.Theory.Read as T {- hmt-base -}+import qualified Music.Theory.Show as T {- hmt-base -}++import qualified Music.Theory.Time.Seq as T {- hmt -}++-- * Param ; Sound.SC3.Server.Param++type Param = [(String,Double)]++param_parse :: (Char,Char) -> String -> Param+param_parse (c1,c2) str =+    let f x = case splitOn [c2] x of+                [lhs,rhs] -> (lhs,read rhs)+                _ -> error ("param_parse: " ++ x)+    in if null str then [] else map f (splitOn [c1] str)++param_pp :: (Char,Char) -> Int -> Param -> String+param_pp (c1,c2) k =+    let f (lhs,rhs) = concat [lhs,[c2],T.double_pp k rhs]+    in intercalate [c1] . map f++-- * Mnd++-- | If /r/ is whole to /k/ places then show as integer, else as float to /k/ places.+data_value_pp :: Real t => Int -> t -> String+data_value_pp k r =+    if T.whole_to_precision k r+    then show (T.real_floor_int r)+    else T.real_pp k r++-- | Channel values are 4-bit (0-15).+type Channel = Int++-- | The required header (column names) field.+csv_mnd_hdr :: [String]+csv_mnd_hdr = ["time","on/off","note","velocity","channel","param"]++{- | Midi note data, the type parameters are to allow for fractional note & velocity values.++The command is a string, @on@ and @off@ are standard, other commands may be present.+note and velocity data is (0-127), channel is (0-15), param are ;-separated key:string=value:float.++> unwords csv_mnd_hdr == "time on/off note velocity channel param"++> all_notes_off = zipWith (\t k -> (t,"off",k,0,0,[])) [0.0,0.01 ..] [0 .. 127]+> csv_mnd_write 4 "/home/rohan/sw/hmt/data/csv/mnd/all-notes-off.csv" all_notes_off+-}+type Mnd t n = (t,String,n,n,Channel,Param)++csv_mnd_parse_f :: (Read t,Real t,Read n,Real n) => (n -> m) -> T.Csv_Table String -> [Mnd t m]+csv_mnd_parse_f cnv (hdr,dat) =+    let err x = error ("csv_mnd_read: " ++ x)+        f m = case m of+                [st,msg,mnn,vel,ch,pm] ->+                    (T.reads_exact_err "time:real" st+                    ,msg+                    ,cnv (T.reads_exact_err "note:real" mnn)+                    ,cnv (T.reads_exact_err "velocity:real" vel)+                    ,T.reads_exact_err "channel:int" ch+                    ,param_parse (';','=') pm)+                _ -> err "entry?"+    in case hdr of+         Just hdr' -> if hdr' == csv_mnd_hdr then map f dat else err "header?"+         Nothing -> err "no header?"++csv_mnd_parse :: (Read t,Real t,Read n,Real n) => T.Csv_Table String -> [Mnd t n]+csv_mnd_parse = csv_mnd_parse_f id++load_csv :: FilePath -> IO (T.Csv_Table String)+load_csv = T.csv_table_read (True,',',False,T.Csv_No_Align) id++-- | Midi note data.+--+-- > let fn = "/home/rohan/cvs/uc/uc-26/daily-practice/2014-08-13.1.csv"+-- > let fn = "/home/rohan/sw/hmt/data/csv/mnd/1080-C01.csv"+-- > m <- csv_mnd_read fn :: IO [Mnd Double Int]+-- > length m -- 1800 17655+-- > csv_mnd_write 4 "/tmp/t.csv" m+csv_mnd_read :: (Read t,Real t,Read n,Real n) => FilePath -> IO [Mnd t n]+csv_mnd_read = fmap csv_mnd_parse . load_csv++-- | Writer.+csv_mnd_write :: (Real t,Real n) => Int -> FilePath -> [Mnd t n] -> IO ()+csv_mnd_write r_prec nm =+    let un_node (st,msg,mnn,vel,ch,pm) =+            [T.real_pp r_prec st+            ,msg+            ,data_value_pp r_prec mnn+            ,data_value_pp r_prec vel+            ,show ch+            ,param_pp (';','=') r_prec pm]+        with_hdr dat = (Just csv_mnd_hdr,dat)+    in T.csv_table_write id T.def_csv_opt nm . with_hdr . map un_node++-- * Mnd Seq forms++-- | (p0=midi-note,p1=velocity,channel,param)+type Event n = (n,n,Channel,Param)++-- | mnn = midi-note-number+event_mnn :: Event t -> t+event_mnn (mnn,_,_,_) = mnn++-- | ch = channel+event_ch :: Event t -> Channel+event_ch (_,_,ch,_) = ch++-- | Are events equal at mnn field?+event_eq_mnn :: Eq t => Event t -> Event t -> Bool+event_eq_mnn = (==) `on` event_mnn++-- | Are events equal at mnn and ch fields?+event_eq_ol :: Eq t => Event t -> Event t -> Bool+event_eq_ol = (==) `on` (\(mnn,_,ch,_) -> (mnn,ch))++-- | Apply (mnn-f,vel-f,ch-f,param-f) to Event.+event_map :: (t -> u,t -> u,Channel -> Channel,Param -> Param) -> Event t -> Event u+event_map (f1,f2,f3,f4) (mnn,vel,ch,param) = (f1 mnn,f2 vel,f3 ch,f4 param)++-- | Apply /f/ at mnn and vel fields.+event_cast :: (t -> u) -> Event t -> Event u+event_cast f = event_map (f,f,id,id)++-- | Add /x/ to mnn field.+event_transpose :: Num a => a -> Event a -> Event a+event_transpose x = event_map ((+) x,id,id,id)++-- | Translate from 'Tseq' form to 'Wseq' form.+midi_tseq_to_midi_wseq :: (Num t,Eq n) => T.Tseq t (T.Begin_End (Event n)) -> T.Wseq t (Event n)+midi_tseq_to_midi_wseq = T.tseq_begin_end_to_wseq (\(n0,_,c0,_) (n1,_,c1,_) -> c0 == c1 && n0 == n1)++midi_wseq_to_midi_tseq :: (Num t,Ord t) => T.Wseq t x -> T.Tseq t (T.Begin_End x)+midi_wseq_to_midi_tseq = T.wseq_begin_end++-- | Ignores non on/off messages.+mnd_to_tseq :: Num n => [Mnd t n] -> T.Tseq t (T.Begin_End (Event n))+mnd_to_tseq =+    let mk_node (st,msg,mnn,vel,ch,pm) =+            case msg of+              "on" -> Just (st,T.Begin (mnn,vel,ch,pm))+              "off" -> Just (st,T.End (mnn,0,ch,pm))+              _ -> Nothing+    in mapMaybe mk_node++-- | 'Tseq' form of 'csv_mnd_read', channel information is retained, off-velocity is zero.+csv_mnd_read_tseq :: (Read t,Real t,Read n,Real n) => FilePath -> IO (T.Tseq t (T.Begin_End (Event n)))+csv_mnd_read_tseq = fmap mnd_to_tseq . csv_mnd_read++-- | 'Tseq' form of 'csv_mnd_write', data is .+csv_mnd_write_tseq :: (Real t,Real n) => Int -> FilePath -> T.Tseq t (T.Begin_End (Event n)) -> IO ()+csv_mnd_write_tseq r_prec nm sq =+    let f (t,e) = case e of+                    T.Begin (n,v,c,p) -> (t,"on",n,v,c,p)+                    T.End (n,_,c,p) -> (t,"off",n,0,c,p)+    in csv_mnd_write r_prec nm (map f sq)++-- * Mndd (simplifies cases where overlaps on the same channel are allowed).++-- | Message should be @note@ for note data.+csv_mndd_hdr :: [String]+csv_mndd_hdr = ["time","duration","message","note","velocity","channel","param"]++-- | Midi note/duration data.+-- The type parameters are to allow for fractional note & velocity values.+-- The command is a string, @note@ is standard, other commands may be present.+--+-- > unwords csv_mndd_hdr == "time duration message note velocity channel param"+type Mndd t n = (t,t,String,n,n,Channel,Param)++-- | Compare sequence is: start-time,channel-number,note-number,velocity,duration,param.+mndd_compare :: (Ord t,Ord n) => Mndd t n -> Mndd t n -> Ordering+mndd_compare x1 x2 =+  case (x1,x2) of+    ((t1,d1,"note",n1,v1,c1,p1),(t2,d2,"note",n2,v2,c2,p2)) ->+      compare (t1,c1,n1,v1,d1,p1) (t2,c2,n2,v2,d2,p2)+    _ -> compare x1 x2++csv_mndd_parse_f :: (Read t,Real t,Read n,Real n) => (n -> m) -> T.Csv_Table String -> [Mndd t m]+csv_mndd_parse_f cnv (hdr,dat) =+    let err x = error ("csv_mndd_read: " ++ x)+        f m =+            case m of+              [st,du,msg,mnn,vel,ch,pm] ->+                  (T.reads_exact_err "time" st+                  ,T.reads_exact_err "duration" du+                  ,msg+                  ,cnv (T.reads_exact_err "note" mnn)+                  ,cnv (T.reads_exact_err "velocity" vel)+                  ,T.reads_exact_err "channel" ch+                  ,param_parse (';','=') pm)+              _ -> err "entry?"+    in case hdr of+         Just hdr' -> if hdr' == csv_mndd_hdr then map f dat else err "header?"+         Nothing -> err "no header?"++-- | Pars midi note/duration data from Csv table.+csv_mndd_parse :: (Read t,Real t,Read n,Real n) => T.Csv_Table String -> [Mndd t n]+csv_mndd_parse = csv_mndd_parse_f id++-- | 'csv_mndd_parse' of 'load_csv'+csv_mndd_read :: (Read t,Real t,Read n,Real n) => FilePath -> IO [Mndd t n]+csv_mndd_read = fmap csv_mndd_parse . load_csv++-- | Writer.+csv_mndd_write :: (Real t,Real n) => Int -> FilePath -> [Mndd t n] -> IO ()+csv_mndd_write r_prec nm =+    let un_node (st,du,msg,mnn,vel,ch,pm) =+            [T.real_pp r_prec st,T.real_pp r_prec du,msg+            ,data_value_pp r_prec mnn,data_value_pp r_prec vel+            ,show ch+            ,param_pp (';','=') r_prec pm]+        with_hdr dat = (Just csv_mndd_hdr,dat)+    in T.csv_table_write id T.def_csv_opt nm . with_hdr . map un_node++-- * Mndd Seq forms++-- | Ignores non note messages.+mndd_to_wseq :: [Mndd t n] -> T.Wseq t (Event n)+mndd_to_wseq =+    let mk_node (st,du,msg,mnn,vel,ch,pm) =+            case msg of+              "note" -> Just ((st,du),(mnn,vel,ch,pm))+              _ -> Nothing+    in mapMaybe mk_node++-- | 'Wseq' form of 'csv_mndd_read'.+csv_mndd_read_wseq :: (Read t,Real t,Read n,Real n) => FilePath -> IO (T.Wseq t (Event n))+csv_mndd_read_wseq = fmap mndd_to_wseq . csv_mndd_read++-- | 'Wseq' form of 'csv_mndd_write'.+csv_mndd_write_wseq :: (Real t,Real n) => Int -> FilePath -> T.Wseq t (Event n) -> IO ()+csv_mndd_write_wseq r_prec nm =+    let f ((st,du),(mnn,vel,ch,pm)) = (st,du,"note",mnn,vel,ch,pm)+    in csv_mndd_write r_prec nm . map f++-- * Composite++-- | Parse either Mnd or Mndd data to Wseq, Csv type is decided by header.+csv_midi_parse_wseq_f :: (Read t,Real t,Read n,Real n,Num m, Eq m) => (n -> m) -> T.Csv_Table String -> T.Wseq t (Event m)+csv_midi_parse_wseq_f cnv (hdr,dat) = do+  case hdr of+    Just hdr' -> if hdr' == csv_mnd_hdr+                 then midi_tseq_to_midi_wseq (mnd_to_tseq (csv_mnd_parse_f cnv (hdr,dat)))+                 else if hdr' == csv_mndd_hdr+                      then mndd_to_wseq (csv_mndd_parse_f cnv (hdr,dat))+                      else error "csv_midi_read_wseq: not Mnd or Mndd"+    _ -> error "csv_midi_read_wseq: header?"++csv_midi_parse_wseq :: (Read t,Real t,Read n,Real n) => T.Csv_Table String -> T.Wseq t (Event n)+csv_midi_parse_wseq = csv_midi_parse_wseq_f id++csv_midi_read_wseq :: (Read t,Real t,Read n,Real n) => FilePath -> IO (T.Wseq t (Event n))+csv_midi_read_wseq = fmap csv_midi_parse_wseq . load_csv
+ Music/Theory/Array/Csv/Midi/Skini.hs view
@@ -0,0 +1,57 @@+-- | Functions (partial) for reading & writing Skini data files.+--+-- <https://ccrma.stanford.edu/software/stk/skini.html>+module Music.Theory.Array.Csv.Midi.Skini where++import Data.List {- base -}++import qualified Music.Theory.Array.Csv.Midi.Mnd as T {- hmt -}+import qualified Music.Theory.Time.Seq as T {- hmt -}++-- | Skini allows delta or absolute time-stamps.+data Time t = Delta t | Absolute t++-- | Skini data type of (message,time-stamp,channel,data-one,data-two)+type Skini t n = (String,Time t,T.Channel,n,n)++mnd_msg_to_skini_msg :: String -> String+mnd_msg_to_skini_msg msg =+  case msg of+    "on" -> "NoteOn"+    "off" -> "NoteOff"+    _ -> error "mnd_msg_to_skini_msg"++mnd_to_skini_f :: (t -> Time t) -> T.Mnd t n -> Skini t n+mnd_to_skini_f f mnd =+  case mnd of+    (t,msg,d1,d2,ch,[]) -> (mnd_msg_to_skini_msg msg,f t,ch,d1,d2)+    _ -> error "mnd_to_skini"++mnd_to_skini_abs :: T.Mnd t n -> Skini t n+mnd_to_skini_abs = mnd_to_skini_f Absolute++midi_tseq_to_skini_seq :: (Num t,Eq n) => T.Tseq t (T.Begin_End (T.Event n)) -> [Skini t n]+midi_tseq_to_skini_seq =+  let f e =+        case e of+          (t,T.Begin (d1,d2,ch,[])) -> ("NoteOn",Delta t,ch,d1,d2)+          (t,T.End (d1,d2,ch,[])) -> ("NoteOff",Delta t,ch,d1,d2)+          _ -> error "midi_tseq_to_skini_seq"+  in map f . T.tseq_to_iseq++time_pp :: Real t => Int -> Time t -> String+time_pp k t =+  case t of+    Delta x -> T.data_value_pp k x+    Absolute x -> '=' : T.data_value_pp k x++skini_pp_csv :: (Real t,Real n) => Int -> Skini t n -> String+skini_pp_csv k (msg,t,ch,d1,d2) =+  let f = T.data_value_pp k+  in intercalate "," [msg,time_pp k t,show ch,f d1,f d2]++-- > let fn = "/home/rohan/sw/hmt/data/csv/mnd/1080-C01.csv"+-- > m <- T.csv_mnd_read_tseq fn :: IO (T.Tseq Double (T.Begin_End (T.Event Int)))+-- > skini_write_csv 4 "/tmp/t.skini" (midi_tseq_to_skini_seq m)+skini_write_csv :: (Real t,Real n) => Int -> FilePath -> [Skini t n] -> IO ()+skini_write_csv k fn = writeFile fn . unlines . map (skini_pp_csv k)
Music/Theory/Array/Direction.hs view
@@ -41,7 +41,7 @@ derive_vec (c1,r1) (c2,r2) = (c2 - c1,r2 - r1)  unfold_path :: Num n => LOC n -> [VEC n] -> [LOC n]-unfold_path l p = scanl apply_vec l p+unfold_path = scanl apply_vec  -- * DIRECTION (non-diagonal)
− Music/Theory/Array/MD.hs 
@@ -1,108 +0,0 @@--- | Regular array data as markdown (MD) tables.-module Music.Theory.Array.MD where--import Data.List {- base -}--import qualified Music.Theory.Array as T {- hmt -}-import qualified Music.Theory.List as T {- hmt -}-import qualified Music.Theory.String as T {- hmt -}---- | Optional header row then data rows.-type MD_Table t = (Maybe [String],[[t]])---- | Join second table to right of initial table.-md_table_join :: MD_Table a -> MD_Table a -> MD_Table a-md_table_join (nm,c) (hdr,tbl) =-    let hdr' = fmap (\h -> maybe h (++ h) nm) hdr-        tbl' = map (\(i,r) -> i ++ r) (zip c tbl)-    in (hdr',tbl')---- | Add a row number column at the front of the table.-md_number_rows :: MD_Table String -> MD_Table String-md_number_rows (hdr,tbl) =-    let hdr' = fmap ("#" :) hdr-        tbl' = map (\(i,r) -> show i : r) (zip [1::Int ..] tbl)-    in (hdr',tbl')---- | Markdown table, perhaps with header.  Table is in row order.--- Options are /pad_left/ and /eq_width/.------ > let tbl = [["a","bc","def"],["ghij","klm","no","p"]]--- > putStrLn$unlines$"": md_table_opt (True,True," · ") (Nothing,tbl)-md_table_opt :: (Bool,Bool,String) -> MD_Table String -> [String]-md_table_opt (pad_left,eq_width,col_sep) (hdr,t) =-    let c = transpose (T.make_regular "" (maybe t (:t) hdr))-        nc = length c-        n = let k = map (maximum . map length) c-            in if eq_width then replicate nc (maximum k) else k-        ext k s = if pad_left then T.pad_left ' ' k s else T.pad_right ' ' k s-        jn = intercalate col_sep-        m = jn (map (flip replicate '-') n)-        w = map jn (transpose (zipWith (map . ext) n c))-        d = map T.delete_trailing_whitespace w-    in case hdr of-         Nothing -> T.bracket (m,m) d-         Just _ -> case d of-                     [] -> error "md_table"-                     d0:d' -> d0 : T.bracket (m,m) d'--md_table' :: MD_Table String -> [String]-md_table' = md_table_opt (True,False," ")---- | 'curry' of 'md_table''.-md_table :: Maybe [String] -> [[String]] -> [String]-md_table = curry md_table'---- | Variant relying on 'Show' instances.------ > md_table_show Nothing [[1..4],[5..8],[9..12]]-md_table_show :: Show t => Maybe [String] -> [[t]] -> [String]-md_table_show hdr = md_table hdr . map (map show)---- | Variant in column order (ie. 'transpose').------ > md_table_column_order [["a","bc","def"],["ghij","klm","no"]]-md_table_column_order :: Maybe [String] -> [[String]] -> [String]-md_table_column_order hdr = md_table hdr . transpose---- | Two-tuple 'show' variant.-md_table_p2 :: (Show a,Show b) => Maybe [String] -> ([a],[b]) -> [String]-md_table_p2 hdr (p,q) = md_table hdr [map show p,map show q]---- | Three-tuple 'show' variant.-md_table_p3 :: (Show a,Show b,Show c) => Maybe [String] -> ([a],[b],[c]) -> [String]-md_table_p3 hdr (p,q,r) = md_table hdr [map show p,map show q,map show r]--{- | Matrix form, ie. header in both first row and first column, in-each case displaced by one location which is empty.--> let h = (map return "abc",map return "efgh")-> let t = md_matrix "" h (map (map show) [[1,2,3,4],[2,3,4,1],[3,4,1,2]])-->>> putStrLn $ unlines $ md_table' t-- - - - --  e f g h-a 1 2 3 4-b 2 3 4 1-c 3 4 1 2-- - - - ----}-md_matrix :: a -> ([a],[a]) -> [[a]] -> MD_Table a-md_matrix nil (r,c) t = md_table_join (Nothing,[nil] : map return r) (Nothing,c : t)---- | Variant that takes a 'show' function and a /header decoration/ function.-md_matrix_opt :: (a -> String) -> (String -> String) -> ([a],[a]) -> [[a]] -> MD_Table String-md_matrix_opt show_f hd_f nm t =-    let t' = map (map show_f) t-        nm' = T.bimap1 (map (hd_f . show_f)) nm-    in md_matrix "" nm' t'---- | MD embolden function.-md_embolden :: String -> String-md_embolden x = "__" ++ x ++ "__"---- | 'md_matrix_opt' with 'show' and markdown /bold/ annotations for header.--- the header cells are in bold.-md_matrix_bold :: Show a => ([a],[a]) -> [[a]] -> MD_Table String-md_matrix_bold = md_matrix_opt show md_embolden
+ Music/Theory/Array/Square.hs view
@@ -0,0 +1,198 @@+-- | Square arrays, where the number of rows and columns are equal.+module Music.Theory.Array.Square where++import Data.List {- base -}+import Data.Maybe {- base -}++import qualified Data.Map as Map {- containers -}+import qualified Data.List.Split as Split {- split -}++import qualified Music.Theory.Array as T {- hmt-base -}+import qualified Music.Theory.Array.Text as T {- hmt-base -}+import qualified Music.Theory.List as T {- hmt-base -}++import qualified Music.Theory.Math.Oeis as T {- hmt -}++-- | Square as list of lists.+type Square t = [[t]]++-- | Squares are functors+sq_map :: (t -> t) -> Square t -> Square t+sq_map f = map (map f)++-- | 'sq_map' of '*' /n/+sq_scale :: Num t => t -> Square t -> Square t+sq_scale n = sq_map (* n)++-- | /f/ pointwise at two squares (of equal size, un-checked)+sq_zip :: (t -> t -> t) -> Square t -> Square t -> Square t+sq_zip f = zipWith (zipWith f)++-- | 'sq_zip' of '*'+sq_mul :: Num t => Square t -> Square t -> Square t+sq_mul = sq_zip (*)++-- | 'sq_zip' of '+'+sq_add :: Num t => Square t -> Square t -> Square t+sq_add = sq_zip (+)++-- | 'foldl1' of 'sq_add'+sq_sum :: Num t => [Square t] -> Square t+sq_sum = foldl1 sq_add++-- | Predicate to determine if 'Square' is actually square.+sq_is_square :: Square t -> Bool+sq_is_square sq = nub (map length sq) == [length sq]++-- | Square as row order list+type Square_Linear t = [t]++-- | Given degree of square, form 'Square' from 'Square_Linear'.+sq_from_list :: Int -> Square_Linear t -> Square t+sq_from_list = Split.chunksOf++-- | True if list can form a square, ie. if 'length' is a square.+--+-- > sq_is_linear_square T.a126710 == True+sq_is_linear_square :: Square_Linear t -> Bool+sq_is_linear_square l = length l `T.elem_ordered` T.a000290++-- | Calculate degree of linear square, ie. square root of 'length'.+--+-- > sq_linear_degree T.a126710 == 4+sq_linear_degree :: Square_Linear t -> Int+sq_linear_degree =+    fromMaybe (error "sq_linear_degree") .+    flip T.elemIndex_ordered T.a000290 .+    length++-- | Type specialised 'transpose'+sq_transpose :: Square t -> Square t+sq_transpose = transpose++{- | Full upper-left (ul) to lower-right (lr) diagonals of a square.++> sq = sq_from_list 4 T.a126710+> sq_wr $ sq+> sq_wr $ sq_diagonals_ul_lr sq+> sq_wr $ sq_diagonals_ll_ur sq+> sq_undiagonals_ul_lr (sq_diagonals_ul_lr sq) == sq+> sq_undiagonals_ll_ur (sq_diagonals_ll_ur sq) == sq++> sq_diagonal_ul_lr sq == sq_diagonals_ul_lr sq !! 0+> sq_diagonal_ll_ur sq == sq_diagonals_ll_ur sq !! 0++-}+sq_diagonals_ul_lr :: Square t -> Square t+sq_diagonals_ul_lr = sq_transpose . zipWith T.rotate_left [0..]++-- | Full lower-left (ll) to upper-right (ur) diagonals of a square.+sq_diagonals_ll_ur :: Square t -> Square t+sq_diagonals_ll_ur = sq_diagonals_ul_lr . reverse++-- | Inverse of 'diagonals_ul_lr'+sq_undiagonals_ul_lr :: Square t -> Square t+sq_undiagonals_ul_lr = zipWith T.rotate_right [0..] . sq_transpose++-- | Inverse of 'diagonals_ll_ur'+sq_undiagonals_ll_ur :: Square t -> Square t+sq_undiagonals_ll_ur = reverse . sq_undiagonals_ul_lr++-- | Main diagonal (upper-left -> lower-right)+sq_diagonal_ul_lr :: Square t -> [t]+sq_diagonal_ul_lr sq = zipWith (!!) sq [0 ..]++-- | Main diagonal (lower-left -> upper-right)+sq_diagonal_ll_ur :: Square t -> [t]+sq_diagonal_ll_ur = sq_diagonal_ul_lr . reverse++{- | Horizontal reflection (ie. map reverse).++> sq = sq_from_list 4 T.a126710+> sq_wr $ sq+> sq_wr $ sq_h_reflection sq++-}+sq_h_reflection :: Square t -> Square t+sq_h_reflection = map reverse++-- | An n×n square is /normal/ if it has the elements (1 .. n×n).+sq_is_normal :: Integral n => Square n -> Bool+sq_is_normal sq =+  let n = genericLength sq+  in sort (concat sq) == [1 .. n * n]++-- | Sums of (rows, columns, left-right-diagonals, right-left-diagonals)+sq_sums :: Num n => Square n -> ([n],[n],[n],[n])+sq_sums sq =+  (map sum sq+  ,map sum (sq_transpose sq)+  ,map sum (sq_diagonals_ul_lr sq)+  ,map sum (sq_diagonals_ll_ur sq))++-- * PP++sq_opt :: T.Text_Table_Opt+sq_opt = (False,True,False," ",False)++sq_pp :: Show t => Square t -> String+sq_pp = unlines . T.table_pp_show sq_opt++sq_wr :: Show t => Square t -> IO ()+sq_wr = putStrLn . ('\n' :) . sq_pp++sq_pp_m :: Show t => String -> Square (Maybe t) -> String+sq_pp_m e = unlines . T.table_pp sq_opt . map (map (maybe e (T.pad_left '·' 2 . show)))++sq_wr_m :: Show t => String -> Square (Maybe t) -> IO ()+sq_wr_m e = putStrLn . sq_pp_m e++-- * Square Map++-- | (row,column) index.+type Square_Ix = T.Ix Int++-- | Map from Square_Ix to value.+type Square_Map t = Map.Map Square_Ix t++-- | 'Square' to 'Square_Map'.+sq_to_map :: Square t -> Square_Map t+sq_to_map =+    let f r = zipWith (\c e -> ((r,c),e)) [0..]+    in Map.fromList . concat . zipWith f [0..]++-- | Alias for 'Map.!'+sqm_ix :: Square_Map t -> Square_Ix -> t+sqm_ix = (Map.!)++-- | 'map' of 'sqm_ix'.+sqm_ix_seq :: Square_Map t -> [Square_Ix] -> [t]+sqm_ix_seq m = map (sqm_ix m)++-- | Make a 'Square' of dimension /dm/ that has elements from /m/ at+-- indicated indices, else 'Nothing'.+sqm_to_partial_sq :: Int -> Square_Map t -> [Square_Ix] -> Square (Maybe t)+sqm_to_partial_sq dm m ix_set =+    let f i = if i `elem` ix_set then Just (m Map.! i) else Nothing+    in Split.chunksOf dm (map f (T.matrix_indices (dm,dm)))++-- * TRS SEQ++sq_trs_op :: [(String,Square t -> Square t)]+sq_trs_op =+    [("≡",id)+    ,("←",sq_h_reflection)+    ,("↓",sq_transpose)+    ,("(← · ↓)",sq_h_reflection . sq_transpose)+    ,("(↓ · ← · ↓)",sq_transpose . sq_h_reflection . sq_transpose)+    ,("(↓ · ←)",sq_transpose . sq_h_reflection)+    ,("(← · ↓ · ←)",sq_h_reflection . sq_transpose . sq_h_reflection)+    ,("↘",sq_diagonals_ul_lr)+    ,("↙ = (↘ · ←)",sq_diagonals_ul_lr . sq_h_reflection)+    ,("↗ = (← · ↙)",sq_h_reflection . sq_diagonals_ul_lr . sq_h_reflection)+    ,("↖ = (← · ↘)",sq_h_reflection . sq_diagonals_ul_lr)+    ]++sq_trs_seq :: Square t -> [(String,Square t)]+sq_trs_seq sq = map (\(nm,fn) -> (nm,fn sq)) sq_trs_op+
− Music/Theory/Bits.hs 
@@ -1,38 +0,0 @@--- | Bits functions.-module Music.Theory.Bits where--import Data.Bits {- base -}--bit_pp :: Bool -> Char-bit_pp b = if b then '1' else '0'--bits_pp :: [Bool] -> String-bits_pp = map bit_pp---- | Generate /n/ place bit sequence for /x/.-gen_bitseq :: FiniteBits b => Int -> b -> [Bool]-gen_bitseq n x =-    if finiteBitSize x < n-    then error "gen_bitseq"-    else map (testBit x) (reverse [0 .. n - 1])---- | Given bit sequence (most to least significant) generate 'Bits' value.------ > :set -XBinaryLiterals--- > pack_bitseq [True,False,True,False] == 0b1010--- > pack_bitseq [True,False,False,True,False,False] == 0b100100--- > 0b100100 == 36-pack_bitseq :: Bits i => [Bool] -> i-pack_bitseq =-    last .-    scanl (\n (k,b) -> if b then setBit n k else n) zeroBits .-    zip [0..] .-    reverse---- | 'bits_pp' of 'gen_bitseq'.------ > :set -XBinaryLiterals--- > 0xF0 == 0b11110000--- > gen_bitseq_pp 8 (0xF0::Int) == "11110000"-gen_bitseq_pp :: FiniteBits b => Int -> b -> String-gen_bitseq_pp n = bits_pp . gen_bitseq n
Music/Theory/Bjorklund.hs view
@@ -9,37 +9,39 @@  import qualified Music.Theory.List as T -type STEP a = ((Int,Int),([[a]],[[a]]))+-- | Bjorklund state+type BJORKLUND_ST a = ((Int,Int),([[a]],[[a]])) -left :: STEP a -> STEP a-left ((i,j),(xs,ys)) =+-- | Bjorklund left process+bjorklund_left_f :: BJORKLUND_ST a -> BJORKLUND_ST a+bjorklund_left_f ((i,j),(xs,ys)) =     let (xs',xs'') = splitAt j xs     in ((j,i-j),(zipWith (++) xs' ys,xs'')) -right :: STEP a -> STEP a-right ((i,j),(xs,ys)) =+-- | Bjorklund right process+bjorklund_right_f :: BJORKLUND_ST a -> BJORKLUND_ST a+bjorklund_right_f ((i,j),(xs,ys)) =     let (ys',ys'') = splitAt i ys     in ((i,j-i),(zipWith (++) xs ys',ys'')) -bjorklund' :: STEP a -> STEP a-bjorklund' (n,x) =+-- | Bjorklund process, left & recur or right & recur or halt.+bjorklund_f :: BJORKLUND_ST a -> BJORKLUND_ST a+bjorklund_f (n,x) =     let (i,j) = n     in if min i j <= 1        then (n,x)-       else bjorklund' (if i > j then left (n,x) else right (n,x))+       else bjorklund_f (if i > j then bjorklund_left_f (n,x) else bjorklund_right_f (n,x))  {- | Bjorklund's algorithm to construct a binary sequence of /n/ bits with /k/ ones such that the /k/ ones are distributed as evenly as possible among the (/n/ - /k/) zeroes.  > bjorklund (5,9) == [True,False,True,False,True,False,True,False,True]-> map xdot (bjorklund (5,9)) == "x.x.x.x.x"+> map xdot_ascii (bjorklund (5,9)) == "x.x.x.x.x" -> let {es = [(2,[3,5]),(3,[4,5,8]),(4,[7,9,12,15]),(5,[6,7,8,9,11,12,13,16])->           ,(6,[7,13]),(7,[8,9,10,12,15,16,17,18]),(8,[17,19])->           ,(9,[14,16,22,23]),(11,[12,24]),(13,[24]),(15,[34])]->     ;es' = concatMap (\(i,j) -> map ((,) i) j) es}-> in mapM_ (putStrLn . euler_pp') es'+> let es = [(2,[3,5]),(3,[4,5,8]),(4,[7,9,12,15]),(5,[6,7,8,9,11,12,13,16]),(6,[7,13]),(7,[8,9,10,12,15,16,17,18]),(8,[17,19]),(9,[14,16,22,23]),(11,[12,24]),(13,[24]),(15,[34])]+> let es' = concatMap (\(i,j) -> map ((,) i) j) es+> mapM_ (putStrLn . euler_pp_unicode) es'  > > E(2,3) [××·] (12) > > E(2,5) [×·×··] (23)@@ -85,12 +87,12 @@     let j = j' - i         x = replicate i [True]         y = replicate j [False]-        (_,(x',y')) = bjorklund' ((i,j),(x,y))+        (_,(x',y')) = bjorklund_f ((i,j),(x,y))     in concat x' ++ concat y'  -- | 'T.rotate_right' of 'bjorklund'. ----- > map xdot' (bjorklund_r 2 (5,16)) == "··×··×··×··×··×·"+-- > map xdot_unicode (bjorklund_r 2 (5,16)) == "··×··×··×··×··×·" bjorklund_r :: Int -> (Int, Int) -> [Bool] bjorklund_r n = T.rotate_right n . bjorklund @@ -102,40 +104,37 @@  -- | Unicode form, ie. @×·@. ----- > euler_pp' (7,12) == "E(7,12) [×·××·×·××·×·] (2122122)"-euler_pp' :: (Int, Int) -> String-euler_pp' = euler_pp_f xdot'+-- > euler_pp_unicode (7,12) == "E(7,12) [×·××·×·××·×·] (2122122)"+euler_pp_unicode :: (Int, Int) -> String+euler_pp_unicode = euler_pp_f xdot_unicode  -- | ASCII form, ie. @x.@. ----- > euler_pp (7,12) == "E(7,12) [x.xx.x.xx.x.] (2122122)"-euler_pp :: (Int, Int) -> String-euler_pp = euler_pp_f xdot+-- > euler_pp_ascii (7,12) == "E(7,12) [x.xx.x.xx.x.] (2122122)"+euler_pp_ascii :: (Int, Int) -> String+euler_pp_ascii = euler_pp_f xdot_ascii  -- | /xdot/ notation for pattern. ----- > map xdot (bjorklund (5,9)) == "x.x.x.x.x"-xdot :: Bool -> Char-xdot x = if x then 'x' else '.'+-- > map xdot_ascii (bjorklund (5,9)) == "x.x.x.x.x"+xdot_ascii :: Bool -> Char+xdot_ascii x = if x then 'x' else '.'  -- | Unicode variant. ----- > map xdot' (bjorklund (5,12)) == "×··×·×··×·×·"--- > map xdot' (bjorklund (5,16)) == "×··×··×··×··×···"-xdot' :: Bool -> Char-xdot' x = if x then '×' else '·'+-- > map xdot_unicode (bjorklund (5,12)) == "×··×·×··×·×·"+-- > map xdot_unicode (bjorklund (5,16)) == "×··×··×··×··×···"+xdot_unicode :: Bool -> Char+xdot_unicode x = if x then '×' else '·'  -- | The 'iseq' of a pattern is the distance between 'True' values. -- -- > iseq (bjorklund (5,9)) == [2,2,2,2,1] iseq :: [Bool] -> [Int]-iseq =-    let f = split . keepDelimsL . whenElt-    in tail . map length . f (== True)+iseq = let f = split . keepDelimsL . whenElt in tail . map length . f (== True)  -- | 'iseq' of pattern as compact string. -- -- > iseq_str (bjorklund (5,9)) == "(22221)" iseq_str :: [Bool] -> String-iseq_str = let f xs = "(" ++ concatMap show xs ++ ")"-           in f . iseq+iseq_str = let f xs = "(" ++ concatMap show xs ++ ")" in f . iseq
Music/Theory/Braille.hs view
@@ -103,7 +103,7 @@ -- -- > braille_lookup_ascii 'N' == Just (0x4E,'N',[1,3,4,5],'⠝',"n") braille_lookup_ascii :: Char -> Maybe BRAILLE-braille_lookup_ascii c = find ((== (toUpper c)) . braille_ascii) braille_table+braille_lookup_ascii c = find ((== toUpper c) . braille_ascii) braille_table  -- | The arrangement of the 6-dot patterns into /decades/, sequences -- of (1,10,3) cells.  The cell to the left of the decade is the empty@@ -160,6 +160,7 @@     let f n = if n `elem` d then b else w     in map (map f) [[1,4],[2,5],[3,6]] +-- | 'lines' as rows and 'Char' as cells in HTML table. string_html_table :: String -> String string_html_table s =     let f x = "<td>" ++ [x] ++ "</td>"
− Music/Theory/Byte.hs 
@@ -1,55 +0,0 @@--- | Byte functions.-module Music.Theory.Byte where--import qualified Data.ByteString as B {- bytestring -}-import Data.Char {- base -}-import Data.List.Split {- split -}-import Data.Maybe {- base -}-import Numeric {- base -}--import qualified Music.Theory.Read as T {- hmt -}---- | Given /n/ in (0,255) make two character hex string.------ > mapMaybe byte_hex_pp [0x0F,0xF0,0xF0F] == ["0F","F0"]-byte_hex_pp :: (Integral i, Show i) => i -> Maybe String-byte_hex_pp n =-    case showHex n "" of-      [c] -> Just ['0',toUpper c]-      [c,d] -> Just (map toUpper [c,d])-      _ -> Nothing---- | Erroring variant.-byte_hex_pp_err :: (Integral i, Show i) => i -> String-byte_hex_pp_err = fromMaybe (error "byte_hex_pp") . byte_hex_pp---- | 'unwords' of 'map' of 'byte_hex_pp_err'.------ > byte_seq_hex_pp [0x0F,0xF0] == "0F F0"-byte_seq_hex_pp :: (Integral i, Show i) => [i] -> String-byte_seq_hex_pp = unwords . map byte_hex_pp_err---- | Read two character hexadecimal string.-read_hex_byte :: (Eq t,Num t) => String -> t-read_hex_byte s =-    case s of-      [_,_] -> T.reads_to_read_precise_err "readHex" readHex s-      _ -> error "read_hex_byte"--read_hex_byte_seq :: (Eq t,Num t) => String -> [t]-read_hex_byte_seq = map read_hex_byte . words---- | Load binary 'U8' sequence from file.-load_byte_seq :: Integral i => FilePath -> IO [i]-load_byte_seq = fmap (map fromIntegral . B.unpack) . B.readFile--store_byte_seq :: Integral i => FilePath -> [i] -> IO ()-store_byte_seq fn = B.writeFile fn . B.pack . map fromIntegral---- | Load hexadecimal text 'U8' sequence from file.-load_hex_byte_seq :: Integral i => FilePath -> IO [i]-load_hex_byte_seq = fmap (map read_hex_byte . words) . readFile---- | Store 'U8' sequence as hexadecimal text, 16 words per line.-store_hex_byte_seq :: (Integral i,Show i) => FilePath -> [i] -> IO ()-store_hex_byte_seq fn = writeFile fn . unlines . map unwords . chunksOf 16 . map byte_hex_pp_err
Music/Theory/Clef.hs view
@@ -5,11 +5,11 @@ import Music.Theory.Pitch.Name {- hmt -}  -- | Clef enumeration type.-data Clef_T = Bass | Tenor | Alto | Treble | Percussion+data Clef_Type = Bass | Tenor | Alto | Treble | Percussion               deriving (Eq,Ord,Show)  -- | Clef with octave offset.-data Clef i = Clef {clef_t :: Clef_T+data Clef i = Clef {clef_t :: Clef_Type                    ,clef_octave :: i}               deriving (Eq,Ord,Show) @@ -18,7 +18,7 @@ -- -- > map clef_range [Treble,Bass] == [Just (d4,g5),Just (f2,b3)] -- > clef_range Percussion == Nothing-clef_range :: Clef_T -> Maybe (Pitch,Pitch)+clef_range :: Clef_Type -> Maybe (Pitch,Pitch) clef_range c =     case c of       Bass -> Just (f2,b3)
− Music/Theory/Combinations.hs 
@@ -1,21 +0,0 @@--- | Combination functions.-module Music.Theory.Combinations where--import qualified Music.Theory.Permutations as T---- | Number of /k/ element combinations of a set of /n/ elements.------ > (nk_combinations 6 3,nk_combinations 13 3) == (20,286)-nk_combinations :: Integral a => a -> a -> a-nk_combinations n k = T.nk_permutations n k `div` T.factorial k---- | /k/ element subsets of /s/.------ > combinations 3 [1..4] == [[1,2,3],[1,2,4],[1,3,4],[2,3,4]]--- > length (combinations 3 [1..5]) == nk_combinations 5 3-combinations :: Int -> [a] -> [[a]]-combinations k s =-    case (k,s) of-      (0,_) -> [[]]-      (_,[]) -> []-      (_,e:s') -> map (e :) (combinations (k - 1) s') ++ combinations k s'
Music/Theory/Contour/Polansky_1992.hs view
@@ -10,10 +10,11 @@ import Data.Maybe {- base -} import Data.Ratio {- base -} -import qualified Music.Theory.List as T-import qualified Music.Theory.Ord as T-import qualified Music.Theory.Permutations.List as T-import qualified Music.Theory.Set.List as T+import qualified Music.Theory.List as T {- hmt-base -}+import qualified Music.Theory.Ord as T {- hmt-base -}++import qualified Music.Theory.Permutations.List as T {- hmt -}+import qualified Music.Theory.Set.List as T {- hmt -}  -- * Indices
− Music/Theory/DB/CSV.hs 
@@ -1,24 +0,0 @@--- | Keys are given in the header, empty fields are omitted from records.-module Music.Theory.DB.CSV where--import Data.Maybe {- base -}-import qualified Text.CSV.Lazy.String as C {- lazy-csv -}--import Music.Theory.DB.Common {- hmt -}-import qualified Music.Theory.IO as T {- hmt -}---- | Load 'DB' from 'FilePath'.-db_load_utf8 :: FilePath -> IO DB'-db_load_utf8 fn = do-  s <- T.read_file_utf8 fn-  let p = C.fromCSVTable (C.csvTable (C.parseCSV s))-      (h,d) = (head p,tail p)-      f k v = if null v then Nothing else Just (k,v)-  return (map (catMaybes . zipWith f h) d)--db_store_utf8 :: FilePath -> DB' -> IO ()-db_store_utf8 fn db = do-  let (hdr,tbl) = db_to_table (fromMaybe "") db-      (_,tbl') = C.toCSVTable (hdr : tbl)-      str = C.ppCSVTable tbl'-  T.write_file_utf8 fn str
− Music/Theory/DB/Common.hs 
@@ -1,130 +0,0 @@-module Music.Theory.DB.Common where--import Data.List {- base -}-import Data.Maybe {- base -}-import Safe {- safe -}--import qualified Music.Theory.List as T {- base -}-import qualified Music.Theory.Maybe as T {- base -}---- * Type--type Entry k v = (k,v)-type Record k v = [Entry k v]-type DB k v = [Record k v]--type Key = String-type Value = String-type Entry' = Entry Key Value-type Record' = Record Key Value-type DB' = DB Key Value---- * Record---- | The sequence of keys at 'Record'.-record_key_seq :: Record k v -> [k]-record_key_seq = map fst---- | 'True' if 'Key' is present in 'Entity'.-record_has_key :: Eq k => k -> Record k v -> Bool-record_has_key k = elem k . record_key_seq---- | 'T.histogram' of 'record_key_seq'.-record_key_histogram :: Ord k => Record k v -> [(k,Int)]-record_key_histogram = T.histogram . record_key_seq---- | Duplicate keys predicate.-record_has_duplicate_keys :: Ord k => Record k v -> Bool-record_has_duplicate_keys = any (> 0) . map snd . record_key_histogram---- | Find all associations for key using given equality function.-record_lookup_by :: (k -> k -> Bool) -> k -> Record k v -> [v]-record_lookup_by f k = map snd . filter (f k . fst)---- | 'record_lookup_by' of '=='.-record_lookup :: Eq k => k -> Record k v -> [v]-record_lookup = record_lookup_by (==)---- | /n/th element of 'record_lookup'.-record_lookup_at :: Eq k => (k,Int) -> Record k v -> Maybe v-record_lookup_at (c,n) = flip atMay n . record_lookup c---- | Variant of 'record_lookup' requiring a unique key.  'Nothing' indicates--- there is no entry, it is an 'error' if duplicate keys are present.-record_lookup_uniq :: Eq k => k -> Record k v -> Maybe v-record_lookup_uniq k r =-    case record_lookup k r of-      [] -> Nothing-      [v] -> Just v-      _ -> error "record_lookup_uniq: non uniq"---- | 'True' if key exists and is unique.-record_has_key_uniq :: Eq k => k -> Record k v -> Bool-record_has_key_uniq k = isJust . record_lookup_uniq k---- | Error variant.-record_lookup_uniq_err :: Eq k => k -> Record k v -> v-record_lookup_uniq_err k = T.from_just "record_lookup_uniq: none" . record_lookup_uniq k---- | Default value variant.-record_lookup_uniq_def :: Eq k => v -> k -> Record k v -> v-record_lookup_uniq_def v k = fromMaybe v . record_lookup_uniq k---- | Remove all associations for key using given equality function.-record_delete_by :: (k -> k -> Bool) -> k -> Record k v -> Record k v-record_delete_by f k = filter (not . f k . fst)---- | 'record_delete_by' of '=='.-record_delete :: Eq k => k -> Record k v -> Record k v-record_delete = record_delete_by (==)---- * DB---- | Preserves order of occurence.-db_key_set :: Ord k => DB k v -> [k]-db_key_set = nub . map fst . concat--db_lookup_by :: (k -> k -> Bool) -> (v -> v -> Bool) -> k -> v -> DB k v -> [Record k v]-db_lookup_by k_cmp v_cmp k v =-    let f = any (v_cmp v) . record_lookup_by k_cmp k-    in filter f--db_lookup :: (Eq k,Eq v) => k -> v -> DB k v -> [Record k v]-db_lookup = db_lookup_by (==) (==)--db_has_duplicate_keys :: Ord k => DB k v -> Bool-db_has_duplicate_keys = any id . map record_has_duplicate_keys--db_key_histogram :: Ord k => DB k v -> [(k,Int)]-db_key_histogram db =-    let h = concatMap record_key_histogram db-        f k = (k,maximum (record_lookup k h))-    in map f (db_key_set db)--db_to_table :: Ord k => (Maybe v -> e) -> DB k v -> ([k],[[e]])-db_to_table f db =-    let kh = db_key_histogram db-        hdr = concatMap (\(k,n) -> replicate n k) kh-        ix = concatMap (\(k,n) -> zip (repeat k) [0 .. n - 1]) kh-    in (hdr,map (\r -> map (\i -> f (record_lookup_at i r)) ix) db)---- * Collating duplicate keys.--record_collate' :: Eq k => (k,[v]) -> Record k v -> Record k [v]-record_collate' (k,v) r =-    case r of-      [] -> [(k,reverse v)]-      (k',v'):r' ->-          if k == k'-          then record_collate' (k,v' : v) r'-          else (k,reverse v) : record_collate' (k',[v']) r'---- | Collate adjacent entries of existing sequence with equal key.-record_collate :: Eq k => Record k v -> Record k [v]-record_collate r =-    case r of-      [] -> error "record_collate: nil"-      (k,v):r' -> record_collate' (k,[v]) r'--record_uncollate :: Record k [v] -> Record k v-record_uncollate = concatMap (\(k,v) -> zip (repeat k) v)
− Music/Theory/DB/JSON.hs 
@@ -1,67 +0,0 @@--- | JSON string association database.--- JSON objects do no allow multiple keys.--- Here multiple keys are read & written as arrays.-module Music.Theory.DB.JSON where--import qualified Data.Aeson as A {- aeson -}-import qualified Data.ByteString.Lazy as B {- bytestring -}-import qualified Data.Map as M {- containers -}--import qualified Music.Theory.DB.Common as DB---- | Load 'DB' from 'FilePath'.-db_load_utf8 :: FilePath -> IO DB.DB'-db_load_utf8 fn = do-  b <- B.readFile fn-  case A.decode b of-    Just m ->-        let f = DB.record_uncollate .-                map (fmap maybe_list_to_list) .-                M.toList-        in return (map f m)-    Nothing -> return []---- | Store 'DB' to 'FilePath'.------ > let fn = "/home/rohan/ut/www-spr/data/db.js"--- > db <- db_load_utf8 fn--- > length db == 1334--- > db_store_utf8 "/tmp/sp.js" db-db_store_utf8 :: FilePath -> DB.DB' -> IO ()-db_store_utf8 fn db = do-  let db' = let f = map (fmap list_to_maybe_list) . DB.record_collate-            in map f db-      b = A.encode (map M.fromList db')-  B.writeFile fn b---- * Maybe List of String--data Maybe_List_Of_String = S String | L [String] deriving (Eq,Show)--maybe_list_to_list :: Maybe_List_Of_String -> [String]-maybe_list_to_list m =-    case m of-      S s -> [s]-      L l -> l--list_to_maybe_list :: [String] -> Maybe_List_Of_String-list_to_maybe_list l =-    case l of-      [s] -> S s-      _ -> L l---- > A.toJSON (S "x")--- > A.toJSON (L ["x","y"])-instance A.ToJSON Maybe_List_Of_String where-    toJSON (S s) = A.toJSON s-    toJSON (L l) = A.toJSON l---- > :set -XOverloadedStrings--- > A.decode "\"x\"" :: Maybe Maybe_List_Of_String--- > A.decode "[\"x\",\"y\"]" :: Maybe Maybe_List_Of_String-instance A.FromJSON Maybe_List_Of_String where-    parseJSON v =-        case v of-          A.String _ -> fmap S (A.parseJSON v)-          A.Array _ -> fmap L (A.parseJSON v)-          _ -> error "parseJSON: Maybe_List_String"
− Music/Theory/DB/Plain.hs 
@@ -1,60 +0,0 @@--- | @key: value@ database, allows duplicate @key@s.-module Music.Theory.DB.Plain where--import Data.List {- base -}-import qualified Data.List.Split as Split {- split -}-import Data.Maybe {- base -}-import qualified Safe as Safe {- safe -}--import qualified Music.Theory.IO as IO {- hmt -}-import qualified Music.Theory.List as T {- hmt -}---- | (RECORD-SEPARATOR,FIELD-SEPARATOR,ENTRY-SEPARATOR)-type SEP = (String,String,String)--type Key = String-type Value = String-type Entry = (Key,[Value])-type Record = [Entry]-type DB = [Record]--sep_plain :: SEP-sep_plain = (['\n','\n'],['\n'],": ")---- > record_parse (";","=") "F=f/rec;E=au;C=A;K=P;K=Q"-record_parse :: (String,String) -> String -> Record-record_parse (fs,es) = T.collate_adjacent . mapMaybe (T.separate_at es) . Split.splitOn fs--record_lookup :: Key -> Record -> [Value]-record_lookup k = fromMaybe [] . lookup k--record_lookup_at :: (Key,Int) -> Record -> Maybe Value-record_lookup_at (k,n) = flip Safe.atMay n . record_lookup k--record_has_key :: Key -> Record -> Bool-record_has_key k = isJust . lookup k--record_lookup_uniq :: Key -> Record -> Maybe Value-record_lookup_uniq k r =-    case record_lookup k r of-      [] -> Nothing-      [v] -> Just v-      _ -> error "record_lookup_uniq: non uniq"--db_parse :: SEP -> String -> [Record]-db_parse (rs,fs,es) s =-    let r = Split.splitOn rs s-    in map (record_parse (fs,es)) r--db_sort :: [(Key,Int)] -> [Record] -> [Record]-db_sort k = T.sort_by_n_stage (map record_lookup_at k)--db_load_utf8 :: SEP -> FilePath -> IO [Record]-db_load_utf8 sep = fmap (db_parse sep) . IO.read_file_utf8---- > record_pp (";","=") [("F","f/rec.au"),("C","A")]-record_pp :: (String,String) -> Record -> String-record_pp (fs,es) = intercalate fs . map (\(k,v) -> k ++ es ++ v) . T.uncollate--db_store_utf8 :: SEP -> FilePath -> [Record] -> IO ()-db_store_utf8 (rs,fs,es) fn = IO.write_file_utf8 fn . intercalate rs . map (record_pp (fs,es))
+ Music/Theory/Db/Cli.hs view
@@ -0,0 +1,52 @@+module Music.Theory.Db.Cli where++import qualified Music.Theory.Db.Csv as Csv {- hmt -}+import qualified Music.Theory.Db.Common as Common {- hmt -}+--import qualified Music.Theory.Db.Json as Json {- hmt -}+import qualified Music.Theory.Db.Plain as Plain {- hmt -}++db_load_ty :: String -> FilePath -> IO (Common.Db String String)+db_load_ty ty fn =+    case ty of+      "plain" -> fmap (map Common.record_uncollate) (Plain.db_load_utf8 Plain.sep_plain fn)+      --"json" -> JSON.db_load_utf8 fn+      "csv" -> Csv.db_load_utf8 fn+      _ -> error "db_load_ty"++db_store_ty :: String -> FilePath -> Common.Db String String -> IO ()+db_store_ty ty fn =+    case ty of+      "plain" -> Plain.db_store_utf8 Plain.sep_plain fn . map Common.record_collate+      --"json" -> JSON.db_store_utf8 fn+      "csv" -> Csv.db_store_utf8 fn+      _ -> error "db_store_ty"++-- > convert ("plain","csv") ("/home/rohan/ut/www-spr/data/db.text","/tmp/t.csv")+-- > convert ("csv","json") ("/tmp/t.csv","/tmp/t.json")+convert :: (String,String) -> (FilePath,FilePath) -> IO ()+convert (input_ty,output_ty) (input_fn,output_fn) = do+  db <- db_load_ty input_ty input_fn+  db_store_ty output_ty output_fn db++-- > stat "plain" "/home/rohan/ut/inland/db/artists.text"+stat :: String -> FilePath -> IO ()+stat ty fn = do+  db <- db_load_ty ty fn+  let ks = Common.db_key_set db+  print ("#-records",length db)+  print ("#-keys",length ks)+  print ("key-set",unwords ks)++help :: [String]+help =+    ["convert input-type output-type input-file output-file"+    ,"stat type file-name"+    ,""+    ,"  type = csv | plain"] -- json++db_cli :: [String] -> IO ()+db_cli arg = do+  case arg of+    ["convert",i_ty,o_ty,i_fn,o_fn] -> convert (i_ty,o_ty) (i_fn,o_fn)+    ["stat",ty,fn] -> stat ty fn+    _ -> putStrLn (unlines help)
+ Music/Theory/Db/Common.hs view
@@ -0,0 +1,131 @@+-- | Database as [[(key,value)]]+module Music.Theory.Db.Common where++import Data.List {- base -}+import Data.Maybe {- base -}+import Safe {- safe -}++import qualified Music.Theory.List as T {- hmt-base -}+import qualified Music.Theory.Maybe as T {- hmt-base -}++-- * Type++type Entry k v = (k,v)+type Record k v = [Entry k v]+type Db k v = [Record k v]++type Key = String+type Value = String+type Entry' = Entry Key Value+type Record' = Record Key Value+type Db' = Db Key Value++-- * Record++-- | The sequence of keys at 'Record'.+record_key_seq :: Record k v -> [k]+record_key_seq = map fst++-- | 'True' if 'Key' is present in 'Entity'.+record_has_key :: Eq k => k -> Record k v -> Bool+record_has_key k = elem k . record_key_seq++-- | 'T.histogram' of 'record_key_seq'.+record_key_histogram :: Ord k => Record k v -> [(k,Int)]+record_key_histogram = T.histogram . record_key_seq++-- | Duplicate keys predicate.+record_has_duplicate_keys :: Ord k => Record k v -> Bool+record_has_duplicate_keys = any ((> 0) . snd) . record_key_histogram++-- | Find all associations for key using given equality function.+record_lookup_by :: (k -> k -> Bool) -> k -> Record k v -> [v]+record_lookup_by f k = map snd . filter (f k . fst)++-- | 'record_lookup_by' of '=='.+record_lookup :: Eq k => k -> Record k v -> [v]+record_lookup = record_lookup_by (==)++-- | /n/th element of 'record_lookup'.+record_lookup_at :: Eq k => (k,Int) -> Record k v -> Maybe v+record_lookup_at (c,n) = flip atMay n . record_lookup c++-- | Variant of 'record_lookup' requiring a unique key.  'Nothing' indicates+-- there is no entry, it is an 'error' if duplicate keys are present.+record_lookup_uniq :: Eq k => k -> Record k v -> Maybe v+record_lookup_uniq k r =+    case record_lookup k r of+      [] -> Nothing+      [v] -> Just v+      _ -> error "record_lookup_uniq: non uniq"++-- | 'True' if key exists and is unique.+record_has_key_uniq :: Eq k => k -> Record k v -> Bool+record_has_key_uniq k = isJust . record_lookup_uniq k++-- | Error variant.+record_lookup_uniq_err :: Eq k => k -> Record k v -> v+record_lookup_uniq_err k = T.from_just "record_lookup_uniq: none" . record_lookup_uniq k++-- | Default value variant.+record_lookup_uniq_def :: Eq k => v -> k -> Record k v -> v+record_lookup_uniq_def v k = fromMaybe v . record_lookup_uniq k++-- | Remove all associations for key using given equality function.+record_delete_by :: (k -> k -> Bool) -> k -> Record k v -> Record k v+record_delete_by f k = filter (not . f k . fst)++-- | 'record_delete_by' of '=='.+record_delete :: Eq k => k -> Record k v -> Record k v+record_delete = record_delete_by (==)++-- * Db++-- | Preserves order of occurence.+db_key_set :: Ord k => Db k v -> [k]+db_key_set = nub . map fst . concat++db_lookup_by :: (k -> k -> Bool) -> (v -> v -> Bool) -> k -> v -> Db k v -> [Record k v]+db_lookup_by k_cmp v_cmp k v =+    let f = any (v_cmp v) . record_lookup_by k_cmp k+    in filter f++db_lookup :: (Eq k,Eq v) => k -> v -> Db k v -> [Record k v]+db_lookup = db_lookup_by (==) (==)++db_has_duplicate_keys :: Ord k => Db k v -> Bool+db_has_duplicate_keys = any record_has_duplicate_keys++db_key_histogram :: Ord k => Db k v -> [(k,Int)]+db_key_histogram db =+    let h = concatMap record_key_histogram db+        f k = (k,maximum (record_lookup k h))+    in map f (db_key_set db)++db_to_table :: Ord k => (Maybe v -> e) -> Db k v -> ([k],[[e]])+db_to_table f db =+    let kh = db_key_histogram db+        hdr = concatMap (\(k,n) -> replicate n k) kh+        ix = concatMap (\(k,n) -> zip (repeat k) [0 .. n - 1]) kh+    in (hdr,map (\r -> map (\i -> f (record_lookup_at i r)) ix) db)++-- * Collating duplicate keys.++record_collate_from :: Eq k => (k,[v]) -> Record k v -> Record k [v]+record_collate_from (k,v) r =+    case r of+      [] -> [(k,reverse v)]+      (k',v'):r' ->+          if k == k'+          then record_collate_from (k,v' : v) r'+          else (k,reverse v) : record_collate_from (k',[v']) r'++-- | Collate adjacent entries of existing sequence with equal key.+record_collate :: Eq k => Record k v -> Record k [v]+record_collate r =+    case r of+      [] -> error "record_collate: nil"+      (k,v):r' -> record_collate_from (k,[v]) r'++record_uncollate :: Record k [v] -> Record k v+record_uncollate = concatMap (\(k,v) -> zip (repeat k) v)
+ Music/Theory/Db/Csv.hs view
@@ -0,0 +1,26 @@+-- | Keys are given in the header, empty fields are omitted from records.+module Music.Theory.Db.Csv where++import Data.Maybe {- base -}++import qualified Text.CSV.Lazy.String as C {- lazy-csv -}++import qualified Music.Theory.Io as T {- hmt-base -}++import Music.Theory.Db.Common {- hmt -}++-- | Load 'DB' from 'FilePath'.+db_load_utf8 :: FilePath -> IO Db'+db_load_utf8 fn = do+  s <- T.read_file_utf8 fn+  let p = C.fromCSVTable (C.csvTable (C.parseCSV s))+      (h,d) = (head p,tail p)+      f k v = if null v then Nothing else Just (k,v)+  return (map (catMaybes . zipWith f h) d)++db_store_utf8 :: FilePath -> Db' -> IO ()+db_store_utf8 fn db = do+  let (hdr,tbl) = db_to_table (fromMaybe "") db+      (_,tbl') = C.toCSVTable (hdr : tbl)+      str = C.ppCSVTable tbl'+  T.write_file_utf8 fn str
+ Music/Theory/Db/Plain.hs view
@@ -0,0 +1,61 @@+-- | @key: value@ database, allows duplicate @key@s.+module Music.Theory.Db.Plain where++import Data.List {- base -}+import Data.Maybe {- base -}++import qualified Data.List.Split as Split {- split -}+import qualified Safe {- safe -}++import qualified Music.Theory.Io as Io {- hmt-base -}+import qualified Music.Theory.List as T {- hmt-base -}++-- | (Record-, Field-, Entry-) separators+type Sep = (String, String, String)++type Key = String+type Value = String+type Entry = (Key, [Value])+type Record = [Entry]+type Db = [Record]++sep_plain :: Sep+sep_plain = (['\n','\n'],['\n'],": ")++-- > record_parse (";","=") "F=f/rec;E=au;C=A;K=P;K=Q"+record_parse :: (String,String) -> String -> Record+record_parse (fs,es) = T.collate_adjacent . mapMaybe (T.separate_at es) . Split.splitOn fs++record_lookup :: Key -> Record -> [Value]+record_lookup k = fromMaybe [] . lookup k++record_lookup_at :: (Key,Int) -> Record -> Maybe Value+record_lookup_at (k,n) = flip Safe.atMay n . record_lookup k++record_has_key :: Key -> Record -> Bool+record_has_key k = isJust . lookup k++record_lookup_uniq :: Key -> Record -> Maybe Value+record_lookup_uniq k r =+    case record_lookup k r of+      [] -> Nothing+      [v] -> Just v+      _ -> error "record_lookup_uniq: non uniq"++db_parse :: Sep -> String -> [Record]+db_parse (rs,fs,es) s =+    let r = Split.splitOn rs s+    in map (record_parse (fs,es)) r++db_sort :: [(Key,Int)] -> [Record] -> [Record]+db_sort k = T.sort_by_n_stage_on (map record_lookup_at k)++db_load_utf8 :: Sep -> FilePath -> IO [Record]+db_load_utf8 sep = fmap (db_parse sep) . Io.read_file_utf8++-- > record_pp (";","=") [("F","f/rec.au"),("C","A")]+record_pp :: (String,String) -> Record -> String+record_pp (fs,es) = intercalate fs . map (\(k,v) -> k ++ es ++ v) . T.uncollate++db_store_utf8 :: Sep -> FilePath -> [Record] -> IO ()+db_store_utf8 (rs,fs,es) fn = Io.write_file_utf8 fn . intercalate rs . map (record_pp (fs,es))
− Music/Theory/Directory.hs 
@@ -1,38 +0,0 @@--- | Directory functions.-module Music.Theory.Directory where--import Data.List {- base -}-import Data.Maybe {- base -}-import System.Directory {- directory -}-import System.FilePath {- filepath -}---- | Scan a list of directories until a file is located, or not.-path_scan :: [FilePath] -> FilePath -> IO (Maybe FilePath)-path_scan p fn =-    case p of-      [] -> return Nothing-      dir:p' -> let nm = dir </> fn-                    f x = if x then return (Just nm) else path_scan p' fn-                in doesFileExist nm >>= f--path_scan_err :: [FilePath] -> FilePath -> IO FilePath-path_scan_err p x =-    let err = (error ("path_scan: " ++ show p ++ ": " ++ x))-    in fmap (fromMaybe err) (path_scan p x)---- | Subset of files in /dir/ with an extension in /ext/.-dir_subset :: [String] -> FilePath -> IO [FilePath]-dir_subset ext dir = do-  let f nm = takeExtension nm `elem` ext-  c <- getDirectoryContents dir-  return (map (dir </>) (sort (filter f c)))---- | If path is not absolute, prepend current working directory.------ > to_absolute_cwd "x"-to_absolute_cwd :: FilePath -> IO FilePath-to_absolute_cwd x =-    if isAbsolute x-    then return x-    else fmap (</> x) getCurrentDirectory-
Music/Theory/Duration.hs view
@@ -1,7 +1,6 @@ -- | Common music notation duration model. module Music.Theory.Duration where -import Control.Monad {- base -} import Data.List {- base -} import Data.Maybe {- base -} import Data.Ratio {- base -}@@ -9,12 +8,16 @@ import qualified Music.Theory.List as T {- hmt -} import qualified Music.Theory.Ord as T {- hmt -} +type Division = Integer+type Dots = Int+ -- | Common music notation durational model-data Duration = Duration {division :: Integer -- ^ division of whole note-                         ,dots :: Integer -- ^ number of dots-                         ,multiplier :: Rational -- ^ tuplet modifier-                         }-                deriving (Eq,Show)+data Duration =+  Duration+  {division :: Division -- ^ division of whole note+  ,dots :: Int -- ^ number of dots+  ,multiplier :: Rational} -- ^ tuplet modifier+  deriving (Eq,Show)  -- | Are multipliers equal? duration_meq :: Duration -> Duration -> Bool@@ -52,48 +55,54 @@ no_dots (x0,x1) = dots x0 == 0 && dots x1 == 0  -- | Sum undotted divisions, input is required to be sorted.-sum_dur_undotted :: (Integer, Integer) -> Maybe Duration-sum_dur_undotted (x0, x1)-    | x0 == x1 = Just (Duration (x0 `div` 2) 0 1)-    | x0 == x1 * 2 = Just (Duration x1 1 1)+sum_dur_undotted :: Rational -> (Division, Division) -> Maybe Duration+sum_dur_undotted m (x0, x1)+    | x0 == x1 = Just (Duration (x0 `div` 2) 0 m)+    | x0 == x1 * 2 = Just (Duration x1 1 m)     | otherwise = Nothing --- | Sum dotted divisions, input is required to be sorted.------ > sum_dur_dotted (4,1,4,1) == Just (Duration 2 1 1)--- > sum_dur_dotted (4,0,2,1) == Just (Duration 1 0 1)--- > sum_dur_dotted (8,1,4,0) == Just (Duration 4 2 1)--- > sum_dur_dotted (16,0,4,2) == Just (Duration 2 0 1)-sum_dur_dotted :: (Integer,Integer,Integer,Integer) -> Maybe Duration-sum_dur_dotted (x0, n0, x1, n1)+{- | Sum dotted divisions, input is required to be sorted.++> sum_dur_dotted 1 (4,1,4,1) == Just (Duration 2 1 1)+> sum_dur_dotted 1 (4,0,2,1) == Just (Duration 1 0 1)+> sum_dur_dotted 1 (8,1,4,0) == Just (Duration 4 2 1)+> sum_dur_dotted 1 (16,0,4,2) == Just (Duration 2 0 1)+-}+sum_dur_dotted :: Rational -> (Division,Dots,Division,Dots) -> Maybe Duration+sum_dur_dotted m (x0, n0, x1, n1)     | x0 == x1 &&       n0 == 1 &&-      n1 == 1 = Just (Duration (x1 `div` 2) 1 1)+      n1 == 1 = Just (Duration (x1 `div` 2) 1 m)     | x0 == x1 * 2 &&       n0 == 0 &&-      n1 == 1 = Just (Duration (x1 `div` 2) 0 1)+      n1 == 1 = Just (Duration (x1 `div` 2) 0 m)     | x0 == x1 * 4 &&       n0 == 0 &&-      n1 == 2 = Just (Duration (x1 `div` 2) 0 1)+      n1 == 2 = Just (Duration (x1 `div` 2) 0 m)     | x0 == x1 * 2 &&       n0 == 1 &&-      n1 == 0 = Just (Duration x1 2 1)+      n1 == 0 = Just (Duration x1 2 m)     | otherwise = Nothing --- | Sum durations.  Not all durations can be summed, and the present---   algorithm is not exhaustive.------ > import Music.Theory.Duration.Name--- > sum_dur quarter_note eighth_note == Just dotted_quarter_note--- > sum_dur dotted_quarter_note eighth_note == Just half_note--- > sum_dur quarter_note dotted_eighth_note == Just double_dotted_quarter_note+{- | Sum durations.  Not all durations can be summed, and the present+     algorithm is not exhaustive.++> import Music.Theory.Duration+> import Music.Theory.Duration.Name+> sum_dur quarter_note eighth_note == Just dotted_quarter_note+> sum_dur dotted_quarter_note eighth_note == Just half_note+> sum_dur quarter_note dotted_eighth_note == Just double_dotted_quarter_note+-} sum_dur :: Duration -> Duration -> Maybe Duration sum_dur y0 y1 =-    let f (x0,x1) = if no_dots (x0,x1)-                    then sum_dur_undotted (division x0, division x1)-                    else sum_dur_dotted (division x0, dots x0-                                        ,division x1, dots x1)-    in join (fmap f (T.sort_pair_m duration_compare_meq (y0,y1)))+    let (m0,m1) = (multiplier y0,multiplier y1)+        f (x0,x1) = if m0 /= m1+                    then Nothing -- cannot sum durations with non-equal multipliers+                    else if no_dots (x0,x1)+                         then sum_dur_undotted m0 (division x0, division x1)+                         else sum_dur_dotted m0 (division x0, dots x0+                                                ,division x1, dots x1)+    in T.sort_pair_m duration_compare_meq (y0,y1) >>= f  -- | Erroring variant of 'sum_dur'. sum_dur_err :: Duration -> Duration -> Duration@@ -102,46 +111,52 @@         err = error ("sum_dur': " ++ show (y0,y1))     in fromMaybe err y2 --- | Standard divisions (from 0 to 256).  MusicXML allows @-1@ as a division (for @long@).-divisions_set :: [Integer]-divisions_set = [0,1,2,4,8,16,32,64,128,256]+{- | Standard divisions (from 1 to 256).+MusicXml allows 0 for breve and -1 for long.+Negative divisors can represent any number of longer durations, -2 be a breve, -4 a long, -8 a maximus, &etc.+-}+divisions_std_set :: [Division]+divisions_std_set = [1,2,4,8,16,32,64,128,256] --- | Durations set derived from 'divisions_set' with up to /k/ dots.  Multiplier of @1@.-duration_set :: Integer -> [Duration]-duration_set k = [Duration dv dt 1 | dv <- divisions_set, dt <- [0..k]]+divisions_musicxml_set :: [Division]+divisions_musicxml_set = -1 : 0 : divisions_std_set +-- | Durations set derived from 'divisions_std_set' with up to /k/ dots.  Multiplier of @1@.+duration_set :: Dots -> [Duration]+duration_set k = [Duration dv dt 1 | dv <- divisions_std_set, dt <- [0..k]]+ -- | Table of number of beams at notated division.-beam_count_tbl :: [(Integer,Integer)]-beam_count_tbl = zip (-1 : divisions_set) [0,0,0,0,0,1,2,3,4,5,6]+beam_count_tbl :: [(Division,Int)]+beam_count_tbl = zip divisions_musicxml_set [0,0,0,0,0,1,2,3,4,5,6]  -- | Lookup 'beam_count_tbl'. -- -- > whole_note_division_to_beam_count 32 == Just 3-whole_note_division_to_beam_count :: Integer -> Maybe Integer+whole_note_division_to_beam_count :: Division -> Maybe Int whole_note_division_to_beam_count x = lookup x beam_count_tbl  -- | Calculate number of beams at 'Duration'. -- -- > map duration_beam_count [Duration 2 0 1,Duration 16 0 1] == [0,2]-duration_beam_count :: Duration -> Integer+duration_beam_count :: Duration -> Int duration_beam_count (Duration x _ _) =     let err = error "duration_beam_count"         bc = whole_note_division_to_beam_count x     in fromMaybe err bc --- * MusicXML+-- * MusicXml --- | Table giving @MusicXML@ types for divisions.-division_musicxml_tbl :: [(Integer,String)]+-- | Table giving MusicXml types for divisions.+division_musicxml_tbl :: [(Division,String)] division_musicxml_tbl =     let nm = ["long","breve","whole","half","quarter","eighth"              ,"16th","32nd","64th","128th","256th"]-    in zip (-1 : divisions_set) nm+    in zip divisions_musicxml_set nm  -- | Lookup 'division_musicxml_tbl'. -- -- > map whole_note_division_to_musicxml_type [2,4] == ["half","quarter"]-whole_note_division_to_musicxml_type :: Integer -> String+whole_note_division_to_musicxml_type :: Division -> String whole_note_division_to_musicxml_type x =     T.lookup_err_msg "division_musicxml_tbl" x division_musicxml_tbl @@ -161,7 +176,7 @@ -- | Lookup 'division_unicode_tbl'. -- -- > map whole_note_division_to_unicode_symbol [1,2,4,8] == "𝅝𝅗𝅥𝅘𝅥𝅘𝅥𝅮"-whole_note_division_to_unicode_symbol :: Integer -> Char+whole_note_division_to_unicode_symbol :: Division -> Char whole_note_division_to_unicode_symbol x =     T.lookup_err_msg "division_unicode_tbl" x division_unicode_tbl @@ -175,8 +190,8 @@  -- * Lilypond --- | Give /Lilypond/ notation for 'Duration'.  Note that the duration--- multiplier is /not/ written.+-- | Give /Lilypond/ notation for 'Duration'.+-- Note that the duration multiplier is /not/ written. -- -- > map duration_to_lilypond_type [Duration 2 0 1,Duration 4 1 1] == ["2","4."] duration_to_lilypond_type :: Duration -> String@@ -191,11 +206,10 @@ <http://humdrum.org/Humdrum/representations/recip.rep.html>  > let d = map (\z -> Duration z 0 1) [0,1,2,4,8,16,32]-> in map duration_recip_pp d == ["0","1","2","4","8","16","32"]+> map duration_recip_pp d == ["0","1","2","4","8","16","32"]  > let d = [Duration 1 1 (1/3),Duration 4 1 1,Duration 4 1 (2/3)]-> in map duration_recip_pp d == ["3.","4.","6."]-+> map duration_recip_pp d == ["3.","4.","6."] -} duration_recip_pp :: Duration -> String duration_recip_pp (Duration x d m) =@@ -207,20 +221,40 @@  -- * Letter -whole_note_division_letter_pp :: Integer -> Maybe Char-whole_note_division_letter_pp x =-    let t = [(16,'s'),(8,'e'),(4,'q'),(2,'h'),(1,'w')]-    in lookup x t+{- | Names for note divisions.+Starting from 1/32 these names haev uniqe initial letters that can be used for concise notation.+-}+whole_note_division_name_tbl :: [(Division, String)]+whole_note_division_name_tbl =+  [(64,"sixtyfourth") -- hemidemisemiquaver+  ,(32,"thirtysecond") -- demisemiquaver+  ,(16,"sixteenth") -- semiquaver+  ,(8,"eighth") -- quaver+  ,(4,"quarter") -- crotchet+  ,(2,"half") -- minim+  ,(1,"whole") -- semibreve+  ,(0,"breve")+  ,(-1,"longa")+  ,(-2,"maxima")] --- > mapMaybe duration_letter_pp [Duration 4 0 1,Duration 2 1 1,Duration 8 2 1] == ["q","h'","e''"]--- > duration_letter_pp+whole_note_division_name :: Division -> Maybe String+whole_note_division_name = flip lookup whole_note_division_name_tbl++whole_note_division_letter_tbl :: [(Division, Char)]+whole_note_division_letter_tbl = map (\(d,n) -> (d,head n)) whole_note_division_name_tbl++  -- > mapMaybe whole_note_division_letter_pp [-2, -1, 0, 1, 2, 4, 8, 16, 32] == "mlbwhqest"+whole_note_division_letter_pp :: Division -> Maybe Char+whole_note_division_letter_pp = flip lookup (tail whole_note_division_letter_tbl)++-- > mapMaybe duration_letter_pp [Duration 4 0 1,Duration 2 1 1,Duration 8 2 1] == ["q","h.","e.."]+-- > mapMaybe duration_letter_pp [Duration 4 1 (2/3)] == ["q./2:3"] duration_letter_pp :: Duration -> Maybe String duration_letter_pp (Duration x d m) =-    let d' = genericReplicate d '\''+    let d' = genericReplicate d '.'         m' = case (numerator m,denominator m) of                (1,1) -> ""-               (1,i) -> '/' : show i-               (i,j) -> '*' : show i ++ "/" ++ show j+               (i,j) -> '/' : show i ++ ":" ++ show j     in case whole_note_division_letter_pp x of          Just x' -> Just (x' : d' ++ m')          _ -> Nothing
Music/Theory/Duration/Annotation.hs view
@@ -5,9 +5,10 @@ import Data.Ratio {- base -} import Data.Tree {- containers -} +import qualified Music.Theory.List as L {- hmt-base -}+ import Music.Theory.Duration-import Music.Theory.Duration.RQ-import qualified Music.Theory.List as L {- hmt -}+import Music.Theory.Duration.Rq  -- | Standard music notation durational model annotations data D_Annotation = Tie_Right@@ -57,7 +58,7 @@ da_tuplet (d,n) x =     let fn (p,q) = (p {multiplier = n%d},q)         k = sum (map (duration_to_rq . fst) x) / (d%1)-        ty = rq_to_duration_err (show ("da_tuplet",d,n,x,k)) k+        ty = rq_to_duration_err (show ("da_tuplet",d,n,x,k)) 2 k         t0 = [Begin_Tuplet (d,n,ty)]         ts = [t0] ++ replicate (length x - 2) [] ++ [[End_Tuplet]]         jn (p,q) z = (p,q++z)
− Music/Theory/Duration/CT.hs 
@@ -1,195 +0,0 @@--- | Functions to generate a click track from a metric structure.-module Music.Theory.Duration.CT where--import Data.Function {- base -}-import Data.List {- base -}-import Data.Maybe {- base -}--import qualified Music.Theory.Duration.RQ as T {- hmt -}-import qualified Music.Theory.List as T {- hmt -}-import qualified Music.Theory.Time_Signature as T {- hmt -}-import qualified Music.Theory.Time.Seq as T {- hmt -}---- | 1-indexed.-type Measure = Int---- | 1-indexed.-type Pulse = Int---- | Transform measures given as 'T.RQ' divisions to absolute 'T.RQ'--- locations.  /mdv/ abbreviates measure divisions.------ > mdv_to_mrq [[1,2,1],[3,2,1]] == [[0,1,3],[4,7,9]]-mdv_to_mrq :: [[T.RQ]] -> [[T.RQ]]-mdv_to_mrq = snd . mapAccumL T.dx_d' 0---- | Lookup function for ('Measure','Pulse') indexed structure.-mp_lookup_err :: [[a]] -> (Measure,Pulse) -> a-mp_lookup_err sq (m,p) =-    if m < 1 || p < 1-    then error (show ("mp_lookup_err: one indexed?",m,p))-    else (sq !! (m - 1)) !! (p - 1)---- | Comparison for ('Measure','Pulse') indices.-mp_compare :: (Measure,Pulse) -> (Measure,Pulse) -> Ordering-mp_compare = T.two_stage_compare (compare `on` fst) (compare `on` snd)---- * CT---- | Latch measures (ie. make measures contiguous, hold previous value).------ > unzip (ct_ext 10 'a' [(3,'b'),(8,'c')]) == ([1..10],"aabbbbbccc")-ct_ext :: Int -> a -> [(Measure,a)] -> [(Measure,a)]-ct_ext n def sq = T.tseq_latch def sq [1 .. n]---- | Variant that requires a value at measure one (first measure).-ct_ext1 :: Int -> [(Measure,a)] -> [(Measure,a)]-ct_ext1 n sq =-    case sq of-      (1,e) : sq' -> ct_ext n e sq'-      _ -> error "ct_ext1"---- | 'T.rts_divisions' of 'ct_ext1'.-ct_dv_seq :: Int -> T.Tseq Measure T.Rational_Time_Signature -> [(Measure,[[T.RQ]])]-ct_dv_seq n ts = map (fmap T.rts_divisions) (ct_ext1 n ts)---- | 'ct_dv_seq' without measures numbers.-ct_mdv_seq :: Int -> T.Tseq Measure T.Rational_Time_Signature -> [[T.RQ]]-ct_mdv_seq n = map (concat . snd) . ct_dv_seq n---- | 'mdv_to_mrq' of 'ct_mdv_seq'.-ct_rq :: Int -> T.Tseq Measure T.Rational_Time_Signature -> [[T.RQ]]-ct_rq n ts = mdv_to_mrq (ct_mdv_seq n ts)--ct_mp_lookup :: [[T.RQ]] -> (Measure,Pulse) -> T.RQ-ct_mp_lookup = mp_lookup_err . mdv_to_mrq--ct_m_to_rq :: [[T.RQ]] -> [(Measure,t)] -> [(T.RQ,t)]-ct_m_to_rq sq = map (\(m,c) -> (ct_mp_lookup sq (m,1),c))---- | Latch rehearsal mark sequence, only indicating marks.  Initial mark is @.@.------ > ct_mark_seq 2 [] == [(1,Just '.'),(2,Nothing)]------ > let r = [(1,Just '.'),(3,Just 'A'),(8,Just 'B')]--- > in filter (isJust . snd) (ct_mark_seq 10 [(3,'A'),(8,'B')]) == r-ct_mark_seq :: Int -> T.Tseq Measure Char -> T.Tseq Measure (Maybe Char)-ct_mark_seq n mk = T.seq_changed (ct_ext n '.' mk)---- | Indicate measures prior to marks.------ > ct_pre_mark [] == []--- > ct_pre_mark [(1,'A')] == []--- > ct_pre_mark [(3,'A'),(8,'B')] == [(2,Just ()),(7,Just ())]-ct_pre_mark :: [(Measure,a)] -> [(Measure,Maybe ())]-ct_pre_mark = mapMaybe (\(m,_) -> if m <= 1 then Nothing else Just (m - 1,Just ()))---- | Contiguous pre-mark sequence.------ > ct_pre_mark_seq 1 [(1,'A')] == [(1,Nothing)]--- > ct_pre_mark_seq 10 [(3,'A'),(8,'B')]-ct_pre_mark_seq :: Measure -> T.Tseq Measure Char -> T.Tseq Measure (Maybe ())-ct_pre_mark_seq n mk =-    let pre = ct_pre_mark mk-    in T.tseq_merge_resolve const pre (zip [1 .. n] (repeat Nothing))--ct_tempo_lseq_rq :: [[T.RQ]] -> T.Lseq (Measure,Pulse) T.RQ -> T.Lseq T.RQ T.RQ-ct_tempo_lseq_rq sq = T.lseq_tmap (ct_mp_lookup sq)---- | Interpolating lookup of tempo sequence ('T.lseq_lookup_err').-ct_tempo_at :: T.Lseq T.RQ T.RQ -> T.RQ -> Rational-ct_tempo_at = T.lseq_lookup_err compare---- | Types of nodes.-data CT_Node = CT_Mark T.RQ -- ^ The start of a measure with a rehearsal mark.-             | CT_Start T.RQ -- ^ The start of a regular measure.-             | CT_Normal T.RQ -- ^ A regular pulse.-             | CT_Edge T.RQ -- ^ The start of a pulse group within a measure.-             | CT_Pre T.RQ -- ^ A regular pulse in a measure prior to a rehearsal mark.-             | CT_End -- ^ The end of the track.-               deriving (Eq,Show)---- | Lead-in of @(pulse,tempo,count)@.-ct_leadin :: (T.RQ,Double,Int) -> T.Dseq Double CT_Node-ct_leadin (du,tm,n) = replicate n (realToFrac du * (60 / tm),CT_Normal du)---- | Prepend initial element to start of list.------ > delay1 "abc" == "aabc"-delay1 :: [a] -> [a]-delay1 l =-    case l of-      [] -> error "delay1: []"-      e:_ -> e : l--ct_measure:: T.Lseq T.RQ T.RQ -> ([T.RQ],Maybe Char,Maybe (),[[T.RQ]]) -> [(Rational,CT_Node)]-ct_measure sq (mrq,mk,pr,dv) =-    let dv' = concatMap (zip [1::Int ..]) dv-        f (p,rq,(g,du)) =-            let nm = if p == 1-                     then case mk of-                            Nothing -> CT_Start du-                            Just _ -> CT_Mark du-                     else if pr == Just ()-                          then CT_Pre du-                          else if g == 1 then CT_Edge du else CT_Normal du-            in (du * (60 / ct_tempo_at sq rq),nm)-    in map f (zip3 [1::Int ..] mrq dv')---- | Click track definition.-data CT = CT {ct_len :: Int-             ,ct_ts :: [(Measure,T.Rational_Time_Signature)]-             ,ct_mark :: [(Measure,Char)]-             ,ct_tempo :: T.Lseq (Measure,Pulse) T.RQ-             ,ct_count :: (T.RQ,Int)}-          deriving Show---- | Initial tempo, if given.-ct_tempo0 :: CT -> Maybe T.RQ-ct_tempo0 ct =-    case ct_tempo ct of-      (((1,1),_),n):_ -> Just n-      _ -> Nothing---- | Erroring variant.-ct_tempo0_err :: CT -> T.RQ-ct_tempo0_err = fromMaybe (error "ct_tempo0") . ct_tempo0---- > import Music.Theory.Duration.CT--- > import Music.Theory.Time.Seq--- > let ct = CT 2 [(1,[(3,8),(2,4)])] [(1,'a')] [(((1,0),T.None),60)] undefined--- > ct_measures ct-ct_measures :: CT -> [T.Dseq Rational CT_Node]-ct_measures (CT n ts mk tm _) =-    let f msg sq = let (m,v) = unzip sq-                   in if m == [1 .. n]-                      then v-                      else error (show ("ct_measures",msg,sq,m,v,n))-        msr = zip4-              (f "ts" (zip [1..] (ct_rq n ts)))-              (f "mk" (ct_mark_seq n mk))-              (f "pre-mk" (ct_pre_mark_seq n mk))-              (f "dv" (ct_dv_seq n ts))-    in map (ct_measure (ct_tempo_lseq_rq (ct_mdv_seq n ts) tm)) msr--ct_dseq' :: CT -> T.Dseq Rational CT_Node-ct_dseq' = concat . ct_measures--ct_dseq :: CT -> T.Dseq Double CT_Node-ct_dseq = T.dseq_tmap fromRational . ct_dseq'---- * Indirect--ct_rq_measure :: [[T.RQ]] -> T.RQ -> Maybe Measure-ct_rq_measure sq rq = fmap fst (find ((rq `elem`) . snd) (zip [1..] sq))--ct_rq_mp :: [[T.RQ]] -> T.RQ -> Maybe (Measure,Pulse)-ct_rq_mp sq rq =-    let f (m,l) = (m,fromMaybe (error "ct_rq_mp: ix") (findIndex (== rq) l) + 1)-    in fmap f (find ((rq `elem`) . snd) (zip [1..] sq))--ct_rq_mp_err :: [[T.RQ]] -> T.RQ -> (Measure, Pulse)-ct_rq_mp_err sq = fromMaybe (error "ct_rq_mp") . ct_rq_mp sq--ct_mp_to_rq :: [[T.RQ]] -> [((Measure,Pulse),t)] -> [(T.RQ,t)]-ct_mp_to_rq sq = map (\(mp,c) -> (ct_mp_lookup sq mp,c))
+ Music/Theory/Duration/ClickTrack.hs view
@@ -0,0 +1,216 @@+-- | Functions to generate a click track from a metric structure.+module Music.Theory.Duration.ClickTrack where++import Data.Bifunctor {- base -}+import Data.Function {- base -}+import Data.List {- base -}+import Data.Maybe {- base -}++import qualified Music.Theory.List as List {- hmt-base -}++import qualified Music.Theory.Duration.Rq as T {- hmt -}+import qualified Music.Theory.Time_Signature as T {- hmt -}+import qualified Music.Theory.Time.Seq as T {- hmt -}++-- | 1-indexed.+type Measure = Int++-- | 1-indexed.+type Pulse = Int++-- | Measures given as 'T.Rq' divisions, Mdv abbreviates measure divisions.+type Mdv = [[T.Rq]]++{- | Absolute 'T.Rq' locations grouped in measures.+     mrq abbreviates measure rational quarter-notes.+     Locations are zero-indexed.+-}+type Mrq = [[T.Rq]]++{- | Transform Mdv to Mrq.++> mdv_to_mrq [[1,2,1],[3,2,1]] == [[0,1,3],[4,7,9]]+-}+mdv_to_mrq :: Mdv -> Mrq+mdv_to_mrq = snd . mapAccumL List.dx_d' 0++{- | Lookup function for ('Measure','Pulse') indexed structure.+     mp abbreviates Measure Pulse.+-}+mp_lookup_err :: [[t]] -> (Measure,Pulse) -> t+mp_lookup_err sq (m,p) =+    if m < 1 || p < 1+    then error (show ("mp_lookup_err: one indexed?",m,p))+    else (sq !! (m - 1)) !! (p - 1)++-- | Comparison for ('Measure','Pulse') indices.+mp_compare :: (Measure,Pulse) -> (Measure,Pulse) -> Ordering+mp_compare = List.two_stage_compare (compare `on` fst) (compare `on` snd)++-- * Ct++{- | Latch measures (ie. make measures contiguous, hold previous value).+     Arguments are the number of measures and the default (intial) value.++> unzip (ct_ext 10 'a' [(3,'b'),(8,'c')]) == ([1..10],"aabbbbbccc")+-}+ct_ext :: Int -> t -> T.Tseq Measure t -> T.Tseq Measure t+ct_ext n def sq = T.tseq_latch def sq [1 .. n]++-- | Variant that requires a value at measure one (first measure).+ct_ext1 :: Int -> T.Tseq Measure t -> T.Tseq Measure t+ct_ext1 n sq =+    case sq of+      (1,e) : sq' -> ct_ext n e sq'+      _ -> error "ct_ext1"++-- | 'T.rts_divisions' of 'ct_ext1'.+ct_dv_seq :: Int -> T.Tseq Measure T.Rational_Time_Signature -> [(Measure,[[T.Rq]])]+ct_dv_seq n ts = map (fmap T.rts_divisions) (ct_ext1 n ts)++-- | 'ct_dv_seq' without measures numbers (which are 1..n)+ct_mdv_seq :: Int -> T.Tseq Measure T.Rational_Time_Signature -> [[T.Rq]]+ct_mdv_seq n = map (concat . snd) . ct_dv_seq n++-- | 'mdv_to_mrq' of 'ct_mdv_seq'.+ct_rq :: Int -> T.Tseq Measure T.Rational_Time_Signature -> [[T.Rq]]+ct_rq n ts = mdv_to_mrq (ct_mdv_seq n ts)++ct_mp_lookup :: [[T.Rq]] -> (Measure,Pulse) -> T.Rq+ct_mp_lookup = mp_lookup_err . mdv_to_mrq++ct_m_to_rq :: [[T.Rq]] -> [(Measure,t)] -> [(T.Rq,t)]+ct_m_to_rq sq = map (\(m,c) -> (ct_mp_lookup sq (m,1),c))++-- | Latch rehearsal mark sequence, only indicating marks.  Initial mark is @.@.+--+-- > ct_mark_seq 2 [] == [(1,Just '.'),(2,Nothing)]+--+-- > let r = [(1,Just '.'),(3,Just 'A'),(8,Just 'B')]+-- > in filter (isJust . snd) (ct_mark_seq 10 [(3,'A'),(8,'B')]) == r+ct_mark_seq :: Int -> T.Tseq Measure Char -> T.Tseq Measure (Maybe Char)+ct_mark_seq n mk = T.seq_changed (ct_ext n '.' mk)++-- | Indicate measures prior to marks.+--+-- > ct_pre_mark [] == []+-- > ct_pre_mark [(1,'A')] == []+-- > ct_pre_mark [(3,'A'),(8,'B')] == [(2,Just ()),(7,Just ())]+ct_pre_mark :: [(Measure,a)] -> [(Measure,Maybe ())]+ct_pre_mark = mapMaybe (\(m,_) -> if m <= 1 then Nothing else Just (m - 1,Just ()))++-- | Contiguous pre-mark sequence.+--+-- > ct_pre_mark_seq 1 [(1,'A')] == [(1,Nothing)]+-- > ct_pre_mark_seq 10 [(3,'A'),(8,'B')]+ct_pre_mark_seq :: Measure -> T.Tseq Measure Char -> T.Tseq Measure (Maybe ())+ct_pre_mark_seq n mk =+    let pre = ct_pre_mark mk+    in T.tseq_merge_resolve const pre (zip [1 .. n] (repeat Nothing))++ct_tempo_lseq_rq :: [[T.Rq]] -> T.Lseq (Measure,Pulse) T.Rq -> T.Lseq T.Rq T.Rq+ct_tempo_lseq_rq sq = T.lseq_tmap (ct_mp_lookup sq)++-- | Interpolating lookup of tempo sequence ('T.lseq_lookup_err').+ct_tempo_at :: T.Lseq T.Rq T.Rq -> T.Rq -> Rational+ct_tempo_at = T.lseq_lookup_err compare++-- | Types of nodes.+data Ct_Node = Ct_Mark T.Rq -- ^ The start of a measure with a rehearsal mark.+             | Ct_Start T.Rq -- ^ The start of a regular measure.+             | Ct_Normal T.Rq -- ^ A regular pulse.+             | Ct_Edge T.Rq -- ^ The start of a pulse group within a measure.+             | Ct_Pre T.Rq -- ^ A regular pulse in a measure prior to a rehearsal mark.+             | Ct_End -- ^ The end of the track.+               deriving (Eq,Show)++-- | Lead-in of @(pulse,tempo,count)@.+ct_leadin :: (T.Rq,Double,Int) -> T.Dseq Double Ct_Node+ct_leadin (du,tm,n) = replicate n (realToFrac du * (60 / tm),Ct_Normal du)++-- | Prepend initial element to start of list.+--+-- > delay1 "abc" == "aabc"+delay1 :: [a] -> [a]+delay1 l =+    case l of+      [] -> error "delay1: []"+      e:_ -> e : l++{- | Generate Ct measure.+     Calculates durations of events considering only the tempo at the start of the event.+     To be correct it should consider the tempo envelope through the event.+-}+ct_measure:: T.Lseq T.Rq T.Rq -> ([T.Rq],Maybe Char,Maybe (),[[T.Rq]]) -> [(Rational,Ct_Node)]+ct_measure sq (mrq,mk,pr,dv) =+    let dv' = concatMap (zip [1::Int ..]) dv+        f (p,rq,(g,du)) =+            let nm = if p == 1+                     then case mk of+                            Nothing -> Ct_Start du+                            Just _ -> Ct_Mark du+                     else if pr == Just ()+                          then Ct_Pre du+                          else if g == 1 then Ct_Edge du else Ct_Normal du+            in (du * (60 / ct_tempo_at sq rq),nm)+    in map f (zip3 [1::Int ..] mrq dv')++-- | Click track definition.+data Ct =+  Ct+  {ct_len :: Int+  ,ct_ts :: [(Measure,T.Rational_Time_Signature)]+  ,ct_mark :: [(Measure,Char)]+  ,ct_tempo :: T.Lseq (Measure,Pulse) T.Rq+  ,ct_count :: (T.Rq,Int)}+  deriving Show++-- | Initial tempo, if given.+ct_tempo0 :: Ct -> Maybe T.Rq+ct_tempo0 ct =+    case ct_tempo ct of+      (((1,1),_),n):_ -> Just n+      _ -> Nothing++-- | Erroring variant.+ct_tempo0_err :: Ct -> T.Rq+ct_tempo0_err = fromMaybe (error "ct_tempo0") . ct_tempo0++-- > import Music.Theory.Duration.Ct+-- > import Music.Theory.Time.Seq+-- > let ct = CT 2 [(1,[(3,8),(2,4)])] [(1,'a')] [(((1,1),T.None),60)] undefined+-- > ct_measures ct+ct_measures :: Ct -> [T.Dseq Rational Ct_Node]+ct_measures (Ct n ts mk tm _) =+    let f msg sq = let (m,v) = unzip sq+                   in if m == [1 .. n]+                      then v+                      else error (show ("ct_measures",msg,sq,m,v,n))+        msr = zip4+              (f "ts" (zip [1..] (ct_rq n ts)))+              (f "mk" (ct_mark_seq n mk))+              (f "pre-mk" (ct_pre_mark_seq n mk))+              (f "dv" (ct_dv_seq n ts))+    in map (ct_measure (ct_tempo_lseq_rq (ct_mdv_seq n ts) tm)) msr++ct_dseq' :: Ct -> T.Dseq Rational Ct_Node+ct_dseq' = concat . ct_measures++ct_dseq :: Ct -> T.Dseq Double Ct_Node+ct_dseq = T.dseq_tmap fromRational . ct_dseq'++-- * Indirect++ct_rq_measure :: [[T.Rq]] -> T.Rq -> Maybe Measure+ct_rq_measure sq rq = fmap fst (find ((rq `elem`) . snd) (zip [1..] sq))++ct_rq_mp :: [[T.Rq]] -> T.Rq -> Maybe (Measure,Pulse)+ct_rq_mp sq rq =+    let f (m,l) = (m,fromMaybe (error "ct_rq_mp: ix") (elemIndex rq l) + 1)+    in fmap f (find ((rq `elem`) . snd) (zip [1..] sq))++ct_rq_mp_err :: [[T.Rq]] -> T.Rq -> (Measure, Pulse)+ct_rq_mp_err sq = fromMaybe (error "ct_rq_mp") . ct_rq_mp sq++ct_mp_to_rq :: [[T.Rq]] -> [((Measure,Pulse),t)] -> [(T.Rq,t)]+ct_mp_to_rq sq = map (first (ct_mp_lookup sq))
+ Music/Theory/Duration/Hollos2014.hs view
@@ -0,0 +1,104 @@+-- | "Creating Rhythms" by Stefan Hollos and J. Richard Hollos+--    <http://abrazol.com/books/rhythm1/software.html>+module Music.Theory.Duration.Hollos2014 where++import Data.List {- base -}++import Music.Theory.List {- hmt-base -}++import Music.Theory.Permutations.List {- hmt -}+import Music.Theory.Set.List {- hmt -}++-- | Donald Knuth, Art of Computer Programming, Algorithm H+--   <http://www-cs-faculty.stanford.edu/~knuth/fasc3b.ps.gz>+--+-- > partm 3 6 == [[1,1,4],[2,1,3],[2,2,2]]+partm :: (Num a, Ord a) => a -> a -> [[a]]+partm i j =+  let f t m n =+        if m == 1 && t == n+        then [[t]]+        else if n < m || n < 1 || m < 1 || t < 1+             then []+        else [reverse (t : r) | r <- f t (m - 1) (n - t)] ++ (f (t - 1) m n)+  in f (j - i + 1) i j++-- | Generates all partitions of n.+--+-- > compUniq 4 == [[1,1,1,1],[1,1,2],[1,3],[2,2],[4]]+-- > compUniq 5 == [[1,1,1,1,1],[1,1,1,2],[1,1,3],[2,1,2],[1,4],[2,3],[5]]+part :: (Num a, Ord a, Enum a) => a -> [[a]]+part n = concatMap (\k -> partm k n) (reverse [1 .. n])++-- | Generates all partitions of n with parts in the set e.+--+-- > parta 8 [2,3] == [[2,2,2,2],[3,2,3]]+parta :: (Num a, Ord a, Enum a) => a -> [a] -> [[a]]+parta n e = filter (all (`elem` e)) (part n)++-- | Generate all compositions of n.+--+-- > comp 4 == [[1,1,1,1],[1,1,2],[1,2,1],[2,1,1],[1,3],[3,1],[2,2],[4]]+-- > length (comp 8) == 128+comp :: (Num a, Ord a, Enum a) => a -> [[a]]+comp = concatMap multiset_permutations . part++-- | Generates all compositions of n into k parts.+--+-- > compm 3 6 == [[1,1,4],[1,4,1],[4,1,1],[1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1],[2,2,2]]+-- > length (compm 5 16) == 1365+compm :: (Ord a, Num a) => a -> a -> [[a]]+compm k = concatMap multiset_permutations . partm k++-- | Generates all compositions of n with parts in the set (p1 p2 ... pk).+--+-- > compa 8 [3,4,5,6] == [[3,5],[5,3],[4,4]]+compa :: (Num a, Ord a, Enum a) => a -> [a] -> [[a]]+compa n e = filter (all (`elem` e)) (comp n)++-- | Generates all compositions of n with m parts in the set (p1 p2 ... pk).+--+-- > compam 4 16 [3,4,5]+compam :: (Num a, Ord a, Enum a) => a -> a -> [a] -> [[a]]+compam k n e = filter (all (`elem` e)) (compm k n)++-- | Generates all binary necklaces of length n.  <http://combos.org/necklace>+--+-- > neck 5 == [[1,1,1,1,1],[1,1,1,1,0],[1,1,0,1,0],[1,1,1,0,0],[1,0,1,0,0],[1,1,0,0,0],[1,0,0,0,0],[0,0,0,0,0]]+neck :: (Ord t, Num t) => Int -> [[t]]+neck n = concatMap multiset_cycles [replicate i 0 ++ replicate (n - i) 1 | i <- [0 .. n]]++-- | Generates all binary necklaces of length n with m ones.+--+-- > neckm 8 2 == [[1,0,0,0,1,0,0,0],[1,0,0,1,0,0,0,0],[1,0,1,0,0,0,0,0],[1,1,0,0,0,0,0,0]]+neckm :: (Num a, Ord a) => Int -> Int -> [[a]]+neckm n m = filter ((== m) . length . filter (== 1)) (neck n)++-- | Part is the length of a substring 10...0 composing the necklace.+--   For example the necklace 10100 has parts of size 2 and 3.+--+-- > necklaceParts [1,0,1,0,0] == [2,3]+-- > necklaceParts [0,0,0,0,0,0,0,0] == []+necklaceParts :: (Eq a, Num a) => [a] -> [Int]+necklaceParts l = d_dx (findIndices (== 1) l ++ [length l])++necklaceWithParts :: (Eq a, Num a) => [Int] -> [a] -> Bool+necklaceWithParts e l =+  let p = necklaceParts l+  in not (null p) && all (`elem` e) p++-- | Generates all binary necklaces of length n with parts in e.+--+-- > necka 8 [2,3,4] == [[1,0,1,0,1,0,1,0],[1,0,1,0,0,1,0,0],[1,0,1,0,1,0,0,0],[1,0,0,0,1,0,0,0]]+necka :: (Num a, Ord a) => Int -> [Int] -> [[a]]+necka n e = filter (necklaceWithParts e) (neck n)++-- | Generates all binary necklaces of length n with m ones and parts in e.+neckam :: (Num a, Ord a) => Int -> Int -> [Int] -> [[a]]+neckam n m e = filter (necklaceWithParts e) (neckm n m)++-- | Generates all permutations of the non-negative integers in the set.+--+-- > permi [1,2,3] == [[1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1]]+permi :: [a] -> [[a]]+permi = permutations_l
Music/Theory/Duration/Name.hs view
@@ -1,7 +1,7 @@ -- | Names for common music notation durations. module Music.Theory.Duration.Name where -import Music.Theory.Duration+import Music.Theory.Duration {- hmt -}  -- * Constants
Music/Theory/Duration/Name/Abbreviation.hs view
@@ -1,4 +1,4 @@--- | Abbreviated names for 'Duration' values when written as literals.+-- | Abbreviated names for 'Duration' values when written as Haskell literals. -- There are /letter/ names where 'w' is 'whole_note' and so on, and -- /numerical/ names where '_4' is 'quarter_note' and so on.  In both -- cases a @'@ extension means a @dot@ so that 'e''' is a double
− Music/Theory/Duration/RQ.hs 
@@ -1,173 +0,0 @@--- | Rational quarter-note notation for durations.-module Music.Theory.Duration.RQ where--import Data.Function {- base -}-import Data.List {- base -}-import Data.Maybe {- base -}-import Data.Ratio {- base -}--import Music.Theory.Duration {- hmt -}---- | Rational Quarter-Note-type RQ = Rational---- > rq_duration_tbl 2-rq_duration_tbl :: Integer -> [(Rational,Duration)]-rq_duration_tbl k = map (\d -> (duration_to_rq d,d)) (duration_set k)---- | Rational quarter note to duration value.  It is a mistake to hope--- this could handle tuplets directly since, for instance, a @3:2@--- dotted note will be of the same duration as a plain undotted note.------ > rq_to_duration (3/4) == Just dotted_eighth_note-rq_to_duration :: RQ -> Maybe Duration-rq_to_duration x = lookup x (rq_duration_tbl 2)---- | Is 'RQ' a /cmn/ duration.------ > map rq_is_cmn [1/4,1/5,1/8,3/32] == [True,False,True,False]-rq_is_cmn :: RQ -> Bool-rq_is_cmn = isJust . rq_to_duration---- | Variant of 'rq_to_duration' with error message.-rq_to_duration_err :: Show a => a -> RQ -> Duration-rq_to_duration_err msg n =-    let err = error ("rq_to_duration:" ++ show (msg,n))-    in fromMaybe err (rq_to_duration n)---- | Convert a whole note division integer to an 'RQ' value.------ > map whole_note_division_to_rq [1,2,4,8] == [4,2,1,1/2]-whole_note_division_to_rq :: Integer -> RQ-whole_note_division_to_rq x =-    let f = (* 4) . recip . (%1)-    in case x of-         0 -> 8-         -1 -> 16-         _ -> f x---- | Apply dots to an 'RQ' duration.------ > map (rq_apply_dots 1) [1,2] == [3/2,7/4]-rq_apply_dots :: RQ -> Integer -> RQ-rq_apply_dots n d =-    let m = iterate (/ 2) n-    in sum (genericTake (d + 1) m)---- | Convert 'Duration' to 'RQ' value, see 'rq_to_duration' for--- partial inverse.------ > let d = [half_note,dotted_quarter_note,dotted_whole_note]--- > in map duration_to_rq d == [2,3/2,6]-duration_to_rq :: Duration -> RQ-duration_to_rq (Duration n d m) =-    let x = whole_note_division_to_rq n-    in rq_apply_dots x d * m---- | 'compare' function for 'Duration' via 'duration_to_rq'.------ > half_note `duration_compare_rq` quarter_note == GT-duration_compare_rq :: Duration -> Duration -> Ordering-duration_compare_rq = compare `on` duration_to_rq---- | 'RQ' modulo.------ > map (rq_mod (5/2)) [3/2,3/4,5/2] == [1,1/4,0]-rq_mod :: RQ -> RQ -> RQ-rq_mod i j-    | i == j = 0-    | i < 0 = rq_mod (i + j) j-    | i > j = rq_mod (i - j) j-    | otherwise = i---- | Is /p/ divisible by /q/, ie. is the 'denominator' of @p/q@ '==' @1@.------ > map (rq_divisible_by (3%2)) [1%2,1%3] == [True,False]-rq_divisible_by :: RQ -> RQ -> Bool-rq_divisible_by i j = denominator (i / j) == 1---- | Is 'RQ' a whole number (ie. is 'denominator' '==' @1@.------ > map rq_is_integral [1,3/2,2] == [True,False,True]-rq_is_integral :: RQ -> Bool-rq_is_integral = (== 1) . denominator---- | Return 'numerator' of 'RQ' if 'denominator' '==' @1@.------ > map rq_integral [1,3/2,2] == [Just 1,Nothing,Just 2]-rq_integral :: RQ -> Maybe Integer-rq_integral n = if rq_is_integral n then Just (numerator n) else Nothing---- | Derive the tuplet structure of a set of 'RQ' values.------ > rq_derive_tuplet_plain [1/2] == Nothing--- > rq_derive_tuplet_plain [1/2,1/2] == Nothing--- > rq_derive_tuplet_plain [1/4,1/4] == Nothing--- > rq_derive_tuplet_plain [1/3,2/3] == Just (3,2)--- > rq_derive_tuplet_plain [1/2,1/3,1/6] == Just (6,4)--- > rq_derive_tuplet_plain [1/3,1/6] == Just (6,4)--- > rq_derive_tuplet_plain [2/5,3/5] == Just (5,4)--- > rq_derive_tuplet_plain [1/3,1/6,2/5,1/10] == Just (30,16)------ > map rq_derive_tuplet_plain [[1/3,1/6],[2/5,1/10]] == [Just (6,4)--- >                                                      ,Just (10,8)]-rq_derive_tuplet_plain :: [RQ] -> Maybe (Integer,Integer)-rq_derive_tuplet_plain x =-    let i = foldl lcm 1 (map denominator x)-        j = let z = iterate (* 2) 2-            in fromJust (find (>= i) z) `div` 2-    in if i `rem` j == 0 then Nothing else Just (i,j)---- | Derive the tuplet structure of a set of 'RQ' values.------ > rq_derive_tuplet [1/4,1/8,1/8] == Nothing--- > rq_derive_tuplet [1/3,2/3] == Just (3,2)--- > rq_derive_tuplet [1/2,1/3,1/6] == Just (3,2)--- > rq_derive_tuplet [2/5,3/5] == Just (5,4)--- > rq_derive_tuplet [1/3,1/6,2/5,1/10] == Just (15,8)-rq_derive_tuplet :: [RQ] -> Maybe (Integer,Integer)-rq_derive_tuplet =-    let f (i,j) = let k = i % j-                  in (numerator k,denominator k)-    in fmap f . rq_derive_tuplet_plain---- | Remove tuplet multiplier from value, ie. to give notated--- duration.  This seems odd but is neccessary to avoid ambiguity.--- Ie. is @1@ a quarter note or a @3:2@ tuplet dotted-quarter-note etc.------ > map (rq_un_tuplet (3,2)) [1,2/3,1/2,1/3] == [3/2,1,3/4,1/2]-rq_un_tuplet :: (Integer,Integer) -> RQ -> RQ-rq_un_tuplet (i,j) x = x * (i % j)---- | If an 'RQ' duration is un-representable by a single /cmn/--- duration, give tied notation.------ > catMaybes (map rq_to_cmn [1..9]) == [(4,1),(4,3),(8,1)]------ > map rq_to_cmn [5/4,5/8] == [Just (1,1/4),Just (1/2,1/8)]-rq_to_cmn :: RQ -> Maybe (RQ,RQ)-rq_to_cmn x =-    let (i,j) = (numerator x,denominator x)-        k = case i of-              5 -> Just (4,1)-              7 -> Just (4,3)-              9 -> Just (8,1)-              _ -> Nothing-        f (n,m) = (n%j,m%j)-    in fmap f k---- | Predicate to determine if a segment can be notated either without--- a tuplet or with a single tuplet.------ > rq_can_notate [1/2,1/4,1/4] == True--- > rq_can_notate [1/3,1/6] == True--- > rq_can_notate [2/5,1/10] == True--- > rq_can_notate [1/3,1/6,2/5,1/10] == False--- > rq_can_notate [4/7,1/7,6/7,3/7] == True--- > rq_can_notate [4/7,1/7,2/7] == True-rq_can_notate :: [RQ] -> Bool-rq_can_notate x =-    let x' = case rq_derive_tuplet x of-               Nothing -> x-               Just t -> map (rq_un_tuplet t) x-    in all rq_is_cmn x'
− Music/Theory/Duration/RQ/Division.hs 
@@ -1,91 +0,0 @@--- | 'RQ' sub-divisions.-module Music.Theory.Duration.RQ.Division where--import Data.List.Split {- split -}-import Data.Ratio--import Music.Theory.Duration.RQ-import Music.Theory.Duration.RQ.Tied-import Music.Theory.List-import Music.Theory.Permutations.List---- | Divisions of /n/ 'RQ' into /i/ equal parts grouped as /j/.--- A quarter and eighth note triplet is written @(1,1,[2,1],False)@.-type RQ_Div = (Rational,Integer,[Integer],Tied_Right)---- | Variant of 'RQ_Div' where /n/ is @1@.-type RQ1_Div = (Integer,[Integer],Tied_Right)---- | Lift 'RQ1_Div' to 'RQ_Div'.-rq1_div_to_rq_div :: RQ1_Div -> RQ_Div-rq1_div_to_rq_div (i,j,k) = (1,i,j,k)---- | Verify that grouping /j/ sums to the divisor /i/.-rq_div_verify :: RQ_Div -> Bool-rq_div_verify (_,n,m,_) = n == sum m--rq_div_mm_verify :: Int -> [RQ_Div] -> [(Integer,[RQ])]-rq_div_mm_verify n x =-    let q = map (sum . fst . rq_div_to_rq_set_t) x-    in zip [1..] (chunksOf n q)---- | Translate from 'RQ_Div' to a sequence of 'RQ' values.------ > rq_div_to_rq_set_t (1,5,[1,3,1],True) == ([1/5,3/5,1/5],True)--- > rq_div_to_rq_set_t (1/2,6,[3,1,2],False) == ([1/4,1/12,1/6],False)-rq_div_to_rq_set_t :: RQ_Div -> ([RQ],Tied_Right)-rq_div_to_rq_set_t (n,k,d,t) =-    let q = map ((* n) . (% k)) d-    in (q,t)---- | Translate from result of 'rq_div_to_rq_set_t' to seqeunce of 'RQ_T'.------ > rq_set_t_to_rqt ([1/5,3/5,1/5],True) == [(1/5,_f),(3/5,_f),(1/5,_t)]-rq_set_t_to_rqt :: ([RQ],Tied_Right) -> [RQ_T]-rq_set_t_to_rqt (x,t) = at_last (\i -> (i,False)) (\i -> (i,t)) x---- | Transform sequence of 'RQ_Div' into sequence of 'RQ', discarding--- any final tie.------ > let q = [(1,5,[1,3,1],True),(1/2,6,[3,1,2],True)]--- > in rq_div_seq_rq q == [1/5,3/5,9/20,1/12,1/6]-rq_div_seq_rq :: [RQ_Div] -> [RQ]-rq_div_seq_rq =-    let f i qq = case qq of-                  [] -> maybe [] return i-                  q:qq' -> let (r,t) = rq_div_to_rq_set_t q-                               r' = maybe r (\j -> at_head (+ j) id r) i-                           in if t-                              then let (r'',i') = separate_last r'-                                   in r'' ++ f (Just i') qq'-                              else r' ++ f Nothing qq'-    in f Nothing---- | Partitions of an 'Integral' that sum to /n/.  This includes the--- two 'trivial paritions, into a set /n/ @1@, and a set of @1@ /n/.------ > partitions_sum 4 == [[1,1,1,1],[2,1,1],[2,2],[3,1],[4]]------ > map (length . partitions_sum) [9..15] == [30,42,56,77,101,135,176]-partitions_sum :: Integral i => i -> [[i]]-partitions_sum n =-    let f p = if null p then 0 else head p-    in case n of-         0 -> [[]]-         _ -> [x:y | x <- [1..n], y <- partitions_sum (n - x), x >= f y]---- | The 'multiset_permutations' of 'partitions_sum'.------ > map (length . partitions_sum_p) [9..12] == [256,512,1024,2048]-partitions_sum_p :: Integral i => i -> [[i]]-partitions_sum_p = concatMap multiset_permutations . partitions_sum---- | The set of all 'RQ1_Div' that sum to /n/, a variant on--- 'partitions_sum_p'.------ > map (length . rq1_div_univ) [3..5] == [8,16,32]--- > map (length . rq1_div_univ) [9..12] == [512,1024,2048,4096]-rq1_div_univ :: Integer -> [RQ1_Div]-rq1_div_univ n =-    let f l = [(n,l,k) | k <- [False,True]]-    in concatMap f (partitions_sum_p n)
− Music/Theory/Duration/RQ/Tied.hs 
@@ -1,91 +0,0 @@--- | 'RQ' values with /tie right/ qualifier.-module Music.Theory.Duration.RQ.Tied where--import Data.Maybe-import Music.Theory.Duration.Annotation-import Music.Theory.Duration.RQ-import Music.Theory.List---- | Boolean.-type Tied_Right = Bool---- | 'RQ' with /tie right/.-type RQ_T = (RQ,Tied_Right)---- | Construct 'RQ_T'.-rqt :: Tied_Right -> RQ -> RQ_T-rqt t d = (d,t)---- | 'RQ' field of 'RQ_T'.-rqt_rq :: RQ_T -> RQ-rqt_rq = fst---- | 'Tied' field of 'RQ_T'.-rqt_tied :: RQ_T -> Tied_Right-rqt_tied = snd---- | Is 'RQ_T' tied right.-is_tied_right :: RQ_T -> Bool-is_tied_right = snd---- | 'RQ_T' variant of 'rq_un_tuplet'.------ > rqt_un_tuplet (3,2) (1,T) == (3/2,T)------ > let f = rqt_un_tuplet (7,4)--- > in map f [(2/7,F),(4/7,T),(1/7,F)] == [(1/2,F),(1,T),(1/4,F)]-rqt_un_tuplet :: (Integer,Integer) -> RQ_T -> RQ_T-rqt_un_tuplet i (d,t) = (rq_un_tuplet i d,t)---- | Transform 'RQ' to untied 'RQ_T'.------ > rq_rqt 3 == (3,F)-rq_rqt :: RQ -> RQ_T-rq_rqt n = (n,False)---- | Tie last element only of list of 'RQ'.------ > rq_tie_last [1,2,3] == [(1,F),(2,F),(3,T)]-rq_tie_last :: [RQ] -> [RQ_T]-rq_tie_last = at_last rq_rqt (\d -> (d,True))---- | Transform a list of 'RQ_T' to a list of 'Duration_A'.  The flag--- indicates if the initial value is tied left.------ > rqt_to_duration_a False [(1,T),(1/4,T),(3/4,F)]-rqt_to_duration_a :: Bool -> [RQ_T] -> [Duration_A]-rqt_to_duration_a z x =-    let rt = map is_tied_right x-        lt = z : rt-        f p e = if p then Just e else Nothing-        g r l = catMaybes [f r Tie_Right,f l Tie_Left]-        h = rq_to_duration_err (show ("rqt_to_duration_a",z,x)) . rqt_rq-    in zip (map h x) (zipWith g rt lt)---- | 'RQ_T' variant of 'rq_can_notate'.-rqt_can_notate :: [RQ_T] -> Bool-rqt_can_notate = rq_can_notate . map rqt_rq---- | 'RQ_T' variant of 'rq_to_cmn'.------ > rqt_to_cmn (5,T) == Just ((4,T),(1,T))--- > rqt_to_cmn (5/4,T) == Just ((1,T),(1/4,T))--- > rqt_to_cmn (5/7,F) == Just ((4/7,T),(1/7,F))-rqt_to_cmn :: RQ_T -> Maybe (RQ_T,RQ_T)-rqt_to_cmn (k,t) =-    let f (i,j) = ((i,True),(j,t))-    in fmap f (rq_to_cmn k)---- | List variant of 'rqt_to_cmn'.------ > rqt_to_cmn_l (5,T) == [(4,T),(1,T)]-rqt_to_cmn_l :: RQ_T -> [RQ_T]-rqt_to_cmn_l x = maybe [x] (\(i,j) -> [i,j]) (rqt_to_cmn x)---- | 'concatMap' 'rqt_to_cmn_l'.------ > rqt_set_to_cmn [(1,T),(5/4,F)] == [(1,T),(1,T),(1/4,F)]------ > rqt_set_to_cmn [(1/5,True),(1/20,False),(1/2,False),(1/4,True)]-rqt_set_to_cmn :: [RQ_T] -> [RQ_T]-rqt_set_to_cmn = concatMap rqt_to_cmn_l
+ Music/Theory/Duration/Rq.hs view
@@ -0,0 +1,239 @@+-- | Rational quarter-note notation for durations.+module Music.Theory.Duration.Rq where++import Data.Function {- base -}+import Data.List {- base -}+import Data.Maybe {- base -}+import Data.Ratio {- base -}++import qualified Music.Theory.List as T {- hmt-base -}++import Music.Theory.Duration {- hmt -}++-- | Rational Quarter-Note+type Rq = Rational++{- | Table mapping tuple Rq values to Durations.+     Only has cases where the duration can be expressed without a tie.+     Currently has entries for 3-,5-,6- and 7-tuplets.++> all (\(i,j) -> i == duration_to_rq j) rq_tuplet_duration_table == True+-}+rq_tuplet_duration_table :: [(Rq, Duration)]+rq_tuplet_duration_table =+  [(1/3,Duration 8 0 (2/3))+  ,(2/3,Duration 4 0 (2/3))+  ,(1/5,Duration 16 0 (4/5))+  ,(2/5,Duration 8 0 (4/5))+  ,(3/5,Duration 8 1 (4/5))+  ,(4/5,Duration 4 0 (4/5))+  ,(1/6,Duration 16 0 (2/3))+  ,(1/7,Duration 16 0 (4/7))+  ,(2/7,Duration 8 0 (4/7))+  ,(3/7,Duration 8 1 (4/7))+  ,(4/7,Duration 4 0 (4/7))+  ,(6/7,Duration 4 1 (4/7))+  ]++{- | Lookup rq_tuplet_duration_tbl.++> rq_tuplet_to_duration (1/3) == Just (Duration 8 0 (2/3))+-}+rq_tuplet_to_duration :: Rq -> Maybe Duration+rq_tuplet_to_duration x = lookup x rq_tuplet_duration_table++{- | Make table of (Rq,Duration) associations.+     Only lists durations with a multiplier of 1.++> map (length . rq_plain_duration_tbl) [1,2,3] == [20,30,40]+> map (multiplier . snd) (rq_plain_duration_tbl 1) == replicate 20 1+-}+rq_plain_duration_tbl :: Dots -> [(Rq,Duration)]+rq_plain_duration_tbl k = map (\d -> (duration_to_rq d,d)) (duration_set k)++rq_plain_to_duration :: Dots -> Rq -> Maybe Duration+rq_plain_to_duration k x = lookup x (rq_plain_duration_tbl k)++rq_plain_to_duration_err :: Dots -> Rq -> Duration+rq_plain_to_duration_err k x = T.lookup_err x (rq_plain_duration_tbl k)++{- | Rational quarter note to duration value.+     Lookup composite plain (hence dots) and tuplet tables.+     It is a mistake to hope this could handle tuplets directly in a general sense.+     For instance, a @3:2@ dotted note is the same duration as a plain undotted note.+     However it does give durations for simple notations of simple tuplet values.++> rq_to_duration 2 (3/4) == Just (Duration 8 1 1) -- dotted_eighth_note+> rq_to_duration 2 (1/3) == Just (Duration 8 0 (2/3))+-}+rq_to_duration :: Dots -> Rq -> Maybe Duration+rq_to_duration k x = lookup x (rq_tuplet_duration_table ++ rq_plain_duration_tbl k)++-- | Variant of 'rq_to_duration' with error message.+rq_to_duration_err :: Show a => a -> Dots -> Rq -> Duration+rq_to_duration_err msg k n =+    let err = error ("rq_to_duration:" ++ show (msg,n))+    in fromMaybe err (rq_to_duration k n)++-- | Is 'Rq' a /cmn/ duration (ie. rq_plain_to_duration)+--+-- > map (rq_is_cmn 2) [1/4,1/5,1/8,3/32] == [True,False,True,True]+rq_is_cmn :: Dots -> Rq -> Bool+rq_is_cmn k = isJust . rq_plain_to_duration k++-- | Convert a whole note division integer to an 'Rq' value.+--+-- > map whole_note_division_to_rq [1,2,4,8] == [4,2,1,1/2]+whole_note_division_to_rq :: Division -> Rq+whole_note_division_to_rq x =+    let f = (* 4) . recip . (% 1)+    in case x of+         0 -> 8+         -1 -> 16+         _ -> f x++-- | Apply dots to an 'Rq' duration.+--+-- > map (rq_apply_dots 1) [1,2] == [1 + 1/2,1 + 1/2 + 1/4]+rq_apply_dots :: Rq -> Dots -> Rq+rq_apply_dots n d =+    let m = iterate (/ 2) n+    in sum (genericTake (d + 1) m)++-- | Convert 'Duration' to 'Rq' value, see 'rq_to_duration' for partial inverse.+--+-- > let d = [Duration 2 0 1,Duration 4 1 1,Duration 1 1 1]+-- > map duration_to_rq d == [2,3/2,6] -- half_note,dotted_quarter_note,dotted_whole_note+duration_to_rq :: Duration -> Rq+duration_to_rq (Duration n d m) =+    let x = whole_note_division_to_rq n+    in rq_apply_dots x d * m++-- | 'compare' function for 'Duration' via 'duration_to_rq'.+--+-- > half_note `duration_compare_rq` quarter_note == GT+duration_compare_rq :: Duration -> Duration -> Ordering+duration_compare_rq = compare `on` duration_to_rq++-- | 'Rq' modulo.+--+-- > map (rq_mod (5/2)) [3/2,3/4,5/2] == [1,1/4,0]+rq_mod :: Rq -> Rq -> Rq+rq_mod i j+    | i == j = 0+    | i < 0 = rq_mod (i + j) j+    | i > j = rq_mod (i - j) j+    | otherwise = i++-- | Is /p/ divisible by /q/, ie. is the 'denominator' of @p/q@ '==' @1@.+--+-- > map (rq_divisible_by (3%2)) [1%2,1%3] == [True,False]+rq_divisible_by :: Rq -> Rq -> Bool+rq_divisible_by i j = denominator (i / j) == 1++-- | Is 'Rq' a whole number (ie. is 'denominator' '==' @1@.+--+-- > map rq_is_integral [1,3/2,2] == [True,False,True]+rq_is_integral :: Rq -> Bool+rq_is_integral = (== 1) . denominator++-- | Return 'numerator' of 'Rq' if 'denominator' '==' @1@.+--+-- > map rq_integral [1,3/2,2] == [Just 1,Nothing,Just 2]+rq_integral :: Rq -> Maybe Integer+rq_integral n = if rq_is_integral n then Just (numerator n) else Nothing++-- | Derive the tuplet structure of a set of 'Rq' values.+--+-- > rq_derive_tuplet_plain [1/2] == Nothing+-- > rq_derive_tuplet_plain [1/2,1/2] == Nothing+-- > rq_derive_tuplet_plain [1/4,1/4] == Nothing+-- > rq_derive_tuplet_plain [1/3,2/3] == Just (3,2)+-- > rq_derive_tuplet_plain [1/2,1/3,1/6] == Just (6,4)+-- > rq_derive_tuplet_plain [1/3,1/6] == Just (6,4)+-- > rq_derive_tuplet_plain [2/5,3/5] == Just (5,4)+-- > rq_derive_tuplet_plain [1/3,1/6,2/5,1/10] == Just (30,16)+--+-- > map rq_derive_tuplet_plain [[1/3,1/6],[2/5,1/10]] == [Just (6,4)+-- >                                                      ,Just (10,8)]+rq_derive_tuplet_plain :: [Rq] -> Maybe (Integer,Integer)+rq_derive_tuplet_plain x =+    let i = foldl lcm 1 (map denominator x)+        j = let z = iterate (* 2) 2+            in fromJust (find (>= i) z) `div` 2+    in if i `rem` j == 0 then Nothing else Just (i,j)++-- | Derive the tuplet structure of a set of 'Rq' values.+--+-- > rq_derive_tuplet [1/4,1/8,1/8] == Nothing+-- > rq_derive_tuplet [1/3,2/3] == Just (3,2)+-- > rq_derive_tuplet [1/2,1/3,1/6] == Just (3,2)+-- > rq_derive_tuplet [2/5,3/5] == Just (5,4)+-- > rq_derive_tuplet [1/3,1/6,2/5,1/10] == Just (15,8)+rq_derive_tuplet :: [Rq] -> Maybe (Integer,Integer)+rq_derive_tuplet =+    let f (i,j) = let k = i % j+                  in (numerator k,denominator k)+    in fmap f . rq_derive_tuplet_plain++-- | Remove tuplet multiplier from value, ie. to give notated+-- duration.  This seems odd but is neccessary to avoid ambiguity.+-- Ie. is @1@ a quarter note or a @3:2@ tuplet dotted-quarter-note etc.+--+-- > map (rq_un_tuplet (3,2)) [1,2/3,1/2,1/3] == [3/2,1,3/4,1/2]+rq_un_tuplet :: (Integer,Integer) -> Rq -> Rq+rq_un_tuplet (i,j) x = x * (i % j)++-- | If an 'Rq' duration is un-representable by a single /cmn/+-- duration, give tied notation.+--+-- > catMaybes (map rq_to_cmn [1..9]) == [(4,1),(4,3),(8,1)]+--+-- > map rq_to_cmn [5/4,5/8] == [Just (1,1/4),Just (1/2,1/8)]+rq_to_cmn :: Rq -> Maybe (Rq,Rq)+rq_to_cmn x =+    let (i,j) = (numerator x,denominator x)+        k = case i of+              5 -> Just (4,1)+              7 -> Just (4,3)+              9 -> Just (8,1)+              _ -> Nothing+        f (n,m) = (n%j,m%j)+    in fmap f k++{- | Predicate to determine if a segment can be notated+     either without a tuplet or with a single tuplet.++> rq_can_notate 2 [1/2,1/4,1/4] == True+> rq_can_notate 2 [1/3,1/6] == True+> rq_can_notate 2 [2/5,1/10] == True+> rq_can_notate 2 [1/3,1/6,2/5,1/10] == False+> rq_can_notate 2 [4/7,1/7,6/7,3/7] == True+> rq_can_notate 2 [4/7,1/7,2/7] == True+-}+rq_can_notate :: Dots -> [Rq] -> Bool+rq_can_notate k x =+    let x' = case rq_derive_tuplet x of+               Nothing -> x+               Just t -> map (rq_un_tuplet t) x+    in all (rq_is_cmn k) x'++-- * Time++-- | Duration in seconds of Rq given qpm+--+--   qpm = pulses-per-minute, rq = rational-quarter-note+--+-- > map (\sd -> rq_to_seconds_qpm (90 * sd) 1) [1,2,4,8,16] == [2/3,1/3,1/6,1/12,1/24]+-- > map (rq_to_seconds_qpm 90) [1,2,3,4] == [2/3,1 + 1/3,2,2 + 2/3]+-- > map (rq_to_seconds_qpm 90) [0::Rq,1,1 + 1/2,1 + 3/4,1 + 7/8,2] == [0,2/3,1,7/6,5/4,4/3]+rq_to_seconds_qpm :: Fractional a => a -> a -> a+rq_to_seconds_qpm qpm rq = rq * (60 / qpm)++-- | Qpm given that /rq/ has duration /x/, ie. inverse of 'rq_to_seconds_qpm'+--+-- > map (rq_to_qpm 1) [0.4,0.5,0.8,1,1.5,2] == [150,120,75,60,40,30]+-- > map (\qpm -> rq_to_seconds_qpm qpm 1) [150,120,75,60,40,30] == [0.4,0.5,0.8,1,1.5,2]+rq_to_qpm :: Fractional a => a -> a -> a+rq_to_qpm rq x = (rq / x) * 60+
+ Music/Theory/Duration/Rq/Division.hs view
@@ -0,0 +1,91 @@+-- | 'Rq' sub-divisions.+module Music.Theory.Duration.Rq.Division where++import Data.List.Split {- split -}+import Data.Ratio++import Music.Theory.Duration.Rq+import Music.Theory.Duration.Rq.Tied+import Music.Theory.List+import Music.Theory.Permutations.List++-- | Divisions of /n/ 'Rq' into /i/ equal parts grouped as /j/.+-- A quarter and eighth note triplet is written @(1,1,[2,1],False)@.+type Rq_Div = (Rational,Integer,[Integer],Tied_Right)++-- | Variant of 'Rq_Div' where /n/ is @1@.+type Rq1_Div = (Integer,[Integer],Tied_Right)++-- | Lift 'Rq1_Div' to 'Rq_Div'.+rq1_div_to_rq_div :: Rq1_Div -> Rq_Div+rq1_div_to_rq_div (i,j,k) = (1,i,j,k)++-- | Verify that grouping /j/ sums to the divisor /i/.+rq_div_verify :: Rq_Div -> Bool+rq_div_verify (_,n,m,_) = n == sum m++rq_div_mm_verify :: Int -> [Rq_Div] -> [(Integer,[Rq])]+rq_div_mm_verify n x =+    let q = map (sum . fst . rq_div_to_rq_set_t) x+    in zip [1..] (chunksOf n q)++-- | Translate from 'Rq_Div' to a sequence of 'Rq' values.+--+-- > rq_div_to_rq_set_t (1,5,[1,3,1],True) == ([1/5,3/5,1/5],True)+-- > rq_div_to_rq_set_t (1/2,6,[3,1,2],False) == ([1/4,1/12,1/6],False)+rq_div_to_rq_set_t :: Rq_Div -> ([Rq],Tied_Right)+rq_div_to_rq_set_t (n,k,d,t) =+    let q = map ((* n) . (% k)) d+    in (q,t)++-- | Translate from result of 'rq_div_to_rq_set_t' to seqeunce of 'Rq_Tied'.+--+-- > rq_set_t_to_rqt ([1/5,3/5,1/5],True) == [(1/5,_f),(3/5,_f),(1/5,_t)]+rq_set_t_to_rqt :: ([Rq],Tied_Right) -> [Rq_Tied]+rq_set_t_to_rqt (x,t) = at_last (\i -> (i,False)) (\i -> (i,t)) x++-- | Transform sequence of 'Rq_Div' into sequence of 'Rq', discarding+-- any final tie.+--+-- > let q = [(1,5,[1,3,1],True),(1/2,6,[3,1,2],True)]+-- > in rq_div_seq_rq q == [1/5,3/5,9/20,1/12,1/6]+rq_div_seq_rq :: [Rq_Div] -> [Rq]+rq_div_seq_rq =+    let f i qq = case qq of+                  [] -> maybe [] return i+                  q:qq' -> let (r,t) = rq_div_to_rq_set_t q+                               r' = maybe r (\j -> at_head (+ j) id r) i+                           in if t+                              then let (r'',i') = separate_last r'+                                   in r'' ++ f (Just i') qq'+                              else r' ++ f Nothing qq'+    in f Nothing++-- | Partitions of an 'Integral' that sum to /n/.  This includes the+-- two 'trivial paritions, into a set /n/ @1@, and a set of @1@ /n/.+--+-- > partitions_sum 4 == [[1,1,1,1],[2,1,1],[2,2],[3,1],[4]]+--+-- > map (length . partitions_sum) [9..15] == [30,42,56,77,101,135,176]+partitions_sum :: Integral i => i -> [[i]]+partitions_sum n =+    let f p = if null p then 0 else head p+    in case n of+         0 -> [[]]+         _ -> [x:y | x <- [1..n], y <- partitions_sum (n - x), x >= f y]++-- | The 'multiset_permutations' of 'partitions_sum'.+--+-- > map (length . partitions_sum_p) [9..12] == [256,512,1024,2048]+partitions_sum_p :: Integral i => i -> [[i]]+partitions_sum_p = concatMap multiset_permutations . partitions_sum++-- | The set of all 'Rq1_Div' that sum to /n/, a variant on+-- 'partitions_sum_p'.+--+-- > map (length . rq1_div_univ) [3..5] == [8,16,32]+-- > map (length . rq1_div_univ) [9..12] == [512,1024,2048,4096]+rq1_div_univ :: Integer -> [Rq1_Div]+rq1_div_univ n =+    let f l = [(n,l,k) | k <- [False,True]]+    in concatMap f (partitions_sum_p n)
+ Music/Theory/Duration/Rq/Tied.hs view
@@ -0,0 +1,101 @@+-- | 'Rq' values with /tie right/ qualifier.+module Music.Theory.Duration.Rq.Tied where++import Data.Maybe {- base -}++import Music.Theory.List {- hmt-base -}++import Music.Theory.Duration {- hmt -}+import qualified Music.Theory.Duration.Annotation as Annotation {- hmt -}+import Music.Theory.Duration.Rq {- hmt -}++-- | Boolean.+type Tied_Right = Bool++-- | 'Rq' with /tie right/.+type Rq_Tied = (Rq,Tied_Right)++-- | If Rq_Tied is not tied, get Rq.+rqt_to_rq :: Rq_Tied -> Maybe Rq+rqt_to_rq (rq,x) = if x then Nothing else Just rq++-- | Erroring variant of rqt_to_rq.+rqt_to_rq_err :: Rq_Tied -> Rq+rqt_to_rq_err = fromMaybe (error "rqt_to_rq") . rqt_to_rq++-- | Construct 'Rq_Tied'.+rqt :: Tied_Right -> Rq -> Rq_Tied+rqt t d = (d,t)++-- | 'Rq' field of 'Rq_Tied'.+rqt_rq :: Rq_Tied -> Rq+rqt_rq = fst++-- | 'Tied' field of 'Rq_Tied'.+rqt_tied :: Rq_Tied -> Tied_Right+rqt_tied = snd++-- | Is 'Rq_Tied' tied right.+is_tied_right :: Rq_Tied -> Bool+is_tied_right = snd++-- | 'Rq_Tied' variant of 'rq_un_tuplet'.+--+-- > rqt_un_tuplet (3,2) (1,T) == (3/2,T)+--+-- > let f = rqt_un_tuplet (7,4)+-- > in map f [(2/7,F),(4/7,T),(1/7,F)] == [(1/2,F),(1,T),(1/4,F)]+rqt_un_tuplet :: (Integer,Integer) -> Rq_Tied -> Rq_Tied+rqt_un_tuplet i (d,t) = (rq_un_tuplet i d,t)++-- | Transform 'Rq' to untied 'Rq_Tied'.+--+-- > rq_rqt 3 == (3,F)+rq_rqt :: Rq -> Rq_Tied+rq_rqt n = (n,False)++-- | Tie last element only of list of 'Rq'.+--+-- > rq_tie_last [1,2,3] == [(1,F),(2,F),(3,T)]+rq_tie_last :: [Rq] -> [Rq_Tied]+rq_tie_last = at_last rq_rqt (\d -> (d,True))++-- | Transform a list of 'Rq_Tied' to a list of 'Duration_A'.  The flag+-- indicates if the initial value is tied left.+--+-- > rqt_to_duration_a False [(1,T),(1/4,T),(3/4,F)]+rqt_to_duration_a :: Bool -> [Rq_Tied] -> [Annotation.Duration_A]+rqt_to_duration_a z x =+    let rt = map is_tied_right x+        lt = z : rt+        f p e = if p then Just e else Nothing+        g r l = catMaybes [f r Annotation.Tie_Right,f l Annotation.Tie_Left]+        h = rq_to_duration_err (show ("rqt_to_duration_a",z,x)) 2 . rqt_rq+    in zip (map h x) (zipWith g rt lt)++-- | 'Rq_Tied' variant of 'rq_can_notate'.+rqt_can_notate :: Dots -> [Rq_Tied] -> Bool+rqt_can_notate k = rq_can_notate k  . map rqt_rq++-- | 'Rq_Tied' variant of 'rq_to_cmn'.+--+-- > rqt_to_cmn (5,T) == Just ((4,T),(1,T))+-- > rqt_to_cmn (5/4,T) == Just ((1,T),(1/4,T))+-- > rqt_to_cmn (5/7,F) == Just ((4/7,T),(1/7,F))+rqt_to_cmn :: Rq_Tied -> Maybe (Rq_Tied,Rq_Tied)+rqt_to_cmn (k,t) =+    let f (i,j) = ((i,True),(j,t))+    in fmap f (rq_to_cmn k)++-- | List variant of 'rqt_to_cmn'.+--+-- > rqt_to_cmn_l (5,T) == [(4,T),(1,T)]+rqt_to_cmn_l :: Rq_Tied -> [Rq_Tied]+rqt_to_cmn_l x = maybe [x] (\(i,j) -> [i,j]) (rqt_to_cmn x)++-- | 'concatMap' 'rqt_to_cmn_l'.+--+-- > rqt_set_to_cmn [(1,T),(5/4,F)] == [(1,T),(1,T),(1/4,F)]+-- > rqt_set_to_cmn [(1/5,True),(1/20,False),(1/2,False),(1/4,True)]+rqt_set_to_cmn :: [Rq_Tied] -> [Rq_Tied]+rqt_set_to_cmn = concatMap rqt_to_cmn_l
Music/Theory/Duration/Sequence/Notate.hs view
@@ -1,7 +1,7 @@--- | Notation of a sequence of 'RQ' values as annotated 'Duration' values.+-- | Notation of a sequence of 'Rq' values as annotated 'Duration' values. -- -- 1. Separate input sequence into measures, adding tie annotations as--- required (see 'to_measures_ts').  Ensure all 'RQ_T' values can be+-- required (see 'to_measures_ts').  Ensure all 'Rq_Tied' values can be -- notated as /common music notation/ durations. -- -- 2. Separate each measure into pulses (see 'm_divisions_ts').@@ -17,53 +17,31 @@ -- 5. Ascribe values to notated durations, see 'ascribe'. module Music.Theory.Duration.Sequence.Notate where -import Control.Monad {- base -} import Data.List {- base -} import Data.List.Split {- split -} import Data.Maybe {- base -} import Data.Ratio {- base -} +import Music.Theory.Either {- hmt-base -}+import Music.Theory.Function {- hmt-base -}+import Music.Theory.List {- hmt-base -}+ import Music.Theory.Duration {- hmt -} import Music.Theory.Duration.Annotation {- hmt -}-import Music.Theory.Function {- hmt -}-import Music.Theory.Duration.RQ {- hmt -}-import Music.Theory.Duration.RQ.Tied {- hmt -}-import Music.Theory.List {- hmt -}+import Music.Theory.Duration.Rq {- hmt -}+import Music.Theory.Duration.Rq.Tied {- hmt -} import Music.Theory.Time_Signature {- hmt -}  -- * Lists --- | Variant of 'catMaybes'.  If all elements of the list are @Just--- a@, then gives @Just [a]@ else gives 'Nothing'.------ > all_just (map Just [1..3]) == Just [1..3]--- > all_just [Just 1,Nothing,Just 3] == Nothing-all_just :: [Maybe a] -> Maybe [a]-all_just x =-    case x of-      [] -> Just []-      Just i:x' -> fmap (i :) (all_just x')-      Nothing:_ -> Nothing+{- | Applies a /join/ function to the first two elements of the list.+     If the /join/ function succeeds the joined element is considered for further coalescing. --- | Variant of 'Data.Either.rights' that preserves first 'Left'.------ > all_right (map Right [1..3]) == Right [1..3]--- > all_right [Right 1,Left 'a',Left 'b'] == Left 'a'-all_right :: [Either a b] -> Either a [b]-all_right x =-    case x of-      [] -> Right []-      Right i:x' -> fmap (i :) (all_right x')-      Left i:_ -> Left i+> coalesce (\p q -> Just (p + q)) [1..5] == [15] --- | Applies a /join/ function to the first two elements of the list.--- If the /join/ function succeeds the joined element is considered--- for further coalescing.------ > coalesce (\p q -> Just (p + q)) [1..5] == [15]------ > let jn p q = if even p then Just (p + q) else Nothing--- > in coalesce jn [1..5] == map sum [[1],[2,3],[4,5]]+> let jn p q = if even p then Just (p + q) else Nothing+> coalesce jn [1..5] == map sum [[1],[2,3],[4,5]]+-} coalesce :: (a -> a -> Maybe a) -> [a] -> [a] coalesce f x =     case x of@@ -75,13 +53,13 @@  -- | Variant of 'coalesce' with accumulation parameter. ----- > coalesce_accum (\i p q -> Left (p + q)) 0 [1..5] == [(0,15)]+-- > coalesce_accum (\_ p q -> Left (p + q)) 0 [1..5] == [(0,15)] -- -- > let jn i p q = if even p then Left (p + q) else Right (p + i)--- > in coalesce_accum jn 0 [1..7] == [(0,1),(1,5),(6,9),(15,13)]+-- > coalesce_accum jn 0 [1..7] == [(0,1),(1,5),(6,9),(15,13)] -- -- > let jn i p q = if even p then Left (p + q) else Right [p,q]--- > in coalesce_accum jn [] [1..5] == [([],1),([1,2],5),([5,4],9)]+-- > coalesce_accum jn [] [1..5] == [([],1),([1,2],5),([5,4],9)] coalesce_accum :: (b -> a -> a -> Either a b) -> b -> [a] -> [(b,a)] coalesce_accum f i x =     case x of@@ -95,7 +73,7 @@ -- | Variant of 'coalesce_accum' that accumulates running sum. -- -- > let f i p q = if i == 1 then Just (p + q) else Nothing--- > in coalesce_sum (+) 0 f [1,1/2,1/4,1/4] == [1,1]+-- > coalesce_sum (+) 0 f [1,1/2,1/4,1/4] == [1,1] coalesce_sum :: (b -> a -> b) -> b -> (b -> a -> a -> Maybe a) -> [a] -> [a] coalesce_sum add zero f =     let g i p q = case f i p q of@@ -103,12 +81,6 @@                     Nothing -> Right (i `add` p)     in map snd . coalesce_accum g zero --- * Either---- | Lower 'Either' to 'Maybe' by discarding 'Left'.-either_to_maybe :: Either a b -> Maybe b-either_to_maybe = either (const Nothing) Just- -- * Separate  -- | Take elements while the sum of the prefix is less than or equal@@ -160,21 +132,21 @@                      Nothing -> Nothing       _ -> Nothing --- | Split sequence such that the prefix sums to precisely /m/.  The--- third element of the result indicates if it was required to divide--- an element.  Note that zero elements are kept left.  If the required--- sum is non positive, or the input list does not sum to at least the--- required sum, gives nothing.------ > split_sum 5 [2,3,1] == Just ([2,3],[1],Nothing)--- > split_sum 5 [2,1,3] == Just ([2,1,2],[1],Just (2,1))--- > split_sum 2 [3/2,3/2,3/2] == Just ([3/2,1/2],[1,3/2],Just (1/2,1))--- > split_sum 6 [1..10] == Just ([1..3],[4..10],Nothing)--- > fmap (\(a,_,c)->(a,c)) (split_sum 5 [1..]) == Just ([1,2,2],Just (2,1))--- > split_sum 0 [1..] == Nothing--- > split_sum 3 [1,1] == Nothing--- > split_sum 3 [2,1,0] == Just ([2,1,0],[],Nothing)--- > split_sum 3 [2,1,0,1] == Just ([2,1,0],[1],Nothing)+{- | Split sequence /l/ such that the prefix sums to precisely /m/.+     The third element of the result indicates if it was required to divide an element.+     Note that zero elements are kept left.+     If the required sum is non positive, or the input list does not sum to at least the required sum, gives nothing.++> split_sum 5 [2,3,1] == Just ([2,3],[1],Nothing)+> split_sum 5 [2,1,3] == Just ([2,1,2],[1],Just (2,1))+> split_sum 2 [3/2,3/2,3/2] == Just ([3/2,1/2],[1,3/2],Just (1/2,1))+> split_sum 6 [1..10] == Just ([1..3],[4..10],Nothing)+> fmap (\(a,_,c)->(a,c)) (split_sum 5 [1..]) == Just ([1,2,2],Just (2,1))+> split_sum 0 [1..] == Nothing+> split_sum 3 [1,1] == Nothing+> split_sum 3 [2,1,0] == Just ([2,1,0],[],Nothing)+> split_sum 3 [2,1,0,1] == Just ([2,1,0],[1],Nothing)+-} split_sum :: (Ord a, Num a) => a -> [a] -> Maybe ([a],[a],Maybe (a,a)) split_sum m l =     let (p,n,q) = take_sum m l@@ -186,24 +158,20 @@               [] -> Nothing               z:q' -> Just (p++[n],z-n:q',Just (n,z-n)) --- | Alias for 'True', used locally for documentation.-_t :: Bool-_t = True+{- | Variant of 'split_sum' that operates at 'Rq_Tied' sequences. --- | Alias for 'False', used locally for documentation.-_f :: Bool-_f = False+> t = True+> f = False --- | Variant of 'split_sum' that operates at 'RQ_T' sequences.------ > let r = Just ([(3,_f),(2,_t)],[(1,_f)])--- > in rqt_split_sum 5 [(3,_f),(2,_t),(1,_f)] == r------ > let r = Just ([(3,_f),(1,_t)],[(1,_t),(1,_f)])--- > in rqt_split_sum 4 [(3,_f),(2,_t),(1,_f)] == r------ > rqt_split_sum 4 [(5/2,False)] == Nothing-rqt_split_sum :: RQ -> [RQ_T] -> Maybe ([RQ_T],[RQ_T])+> r = Just ([(3,f),(2,t)],[(1,f)])+> rqt_split_sum 5 [(3,f),(2,t),(1,f)] == r++> r = Just ([(3,f),(1,t)],[(1,t),(1,f)])+> rqt_split_sum 4 [(3,f),(2,t),(1,f)] == r++> rqt_split_sum 4 [(5/2,False)] == Nothing+-}+rqt_split_sum :: Rq -> [Rq_Tied] -> Maybe ([Rq_Tied],[Rq_Tied]) rqt_split_sum d x =     case split_sum d (map rqt_rq x) of       Just (i,_,k) ->@@ -214,57 +182,61 @@                                   ,(q,z) : t)       Nothing -> Nothing --- | Separate 'RQ_T' values in sequences summing to 'RQ' values.  This--- is a recursive variant of 'rqt_split_sum'.  Note that is does not--- ensure /cmn/ notation of values.------ > let d = [(2,_f),(2,_f),(2,_f)]--- > in rqt_separate [3,3] d == Right [[(2,_f),(1,_t)]--- >                                  ,[(1,_f),(2,_f)]]------ > let d = [(5/8,_f),(1,_f),(3/8,_f)]--- > in rqt_separate [1,1] d == Right [[(5/8,_f),(3/8,_t)]--- >                                  ,[(5/8,_f),(3/8,_f)]]------ > let d = [(4/7,_t),(1/7,_f),(1,_f),(6/7,_f),(3/7,_f)]--- > in rqt_separate [1,1,1] d == Right [[(4/7,_t),(1/7,_f),(2/7,_t)]--- >                                    ,[(5/7,_f),(2/7,_t)]--- >                                    ,[(4/7,_f),(3/7,_f)]]-rqt_separate :: [RQ] -> [RQ_T] -> Either String [[RQ_T]]+{- | Separate 'Rq_Tied' values in sequences summing to 'Rq' values.+    This is a recursive variant of 'rqt_split_sum'.+    Note that is does not ensure /cmn/ notation of values.++> t = True+> f = False++> d = [(2,f),(2,f),(2,f)]+> r = [[(2,f),(1,t)],[(1,f),(2,f)]]+> rqt_separate [3,3] d == Right r++> d = [(5/8,f),(1,f),(3/8,f)]+> r = [[(5/8,f),(3/8,t)],[(5/8,f),(3/8,f)]]+> rqt_separate [1,1] d == Right r++> d = [(4/7,t),(1/7,f),(1,f),(6/7,f),(3/7,f)]+> r = [[(4/7,t),(1/7,f),(2/7,t)],[(5/7,f),(2/7,t)],[(4/7,f),(3/7,f)]]+> rqt_separate [1,1,1] d == Right r+-}+rqt_separate :: [Rq] -> [Rq_Tied] -> Either String [[Rq_Tied]] rqt_separate m x =     case (m,x) of       ([],[]) -> Right []-      ([],_) -> Left (show ("rqt_separate",x))+      ([],_) -> Left (show ("rqt_separate: lhs empty, rhs non-empty",x))       (i:m',_) ->           case rqt_split_sum i x of             Just (r,x') -> fmap (r :) (rqt_separate m' x')-            Nothing -> Left (show ("rqt_separate",i,m',x))+            Nothing -> Left (show ("rqt_separate: rqt_split_sum failed",(i,x),m')) -rqt_separate_m :: [RQ] -> [RQ_T] -> Maybe [[RQ_T]]+-- | Maybe form ot 'rqt_separate'+rqt_separate_m :: [Rq] -> [Rq_Tied] -> Maybe [[Rq_Tied]] rqt_separate_m m = either_to_maybe . rqt_separate m --- | If the input 'RQ_T' sequence cannot be notated (see+-- | If the input 'Rq_Tied' sequence cannot be notated (see -- 'rqt_can_notate') separate into equal parts, so long as each part -- is not less than /i/. ----- > rqt_separate_tuplet undefined [(1/3,_f),(1/6,_f)]--- > rqt_separate_tuplet undefined [(4/7,_t),(1/7,_f),(2/7,_f)]+-- > rqt_separate_tuplet undefined [(1/3,f),(1/6,f)]+-- > rqt_separate_tuplet undefined [(4/7,t),(1/7,f),(2/7,f)] -- -- > let d = map rq_rqt [1/3,1/6,2/5,1/10]--- > in rqt_separate_tuplet (1/8) d == Right [[(1/3,_f),(1/6,_f)]--- >                                         ,[(2/5,_f),(1/10,_f)]]+-- > in rqt_separate_tuplet (1/8) d == Right [[(1/3,f),(1/6,f)]+-- >                                         ,[(2/5,f),(1/10,f)]] -- -- > let d = [(1/5,True),(1/20,False),(1/2,False),(1/4,True)] -- > in rqt_separate_tuplet (1/16) d ----- > let d = [(2/5,_f),(1/5,_f),(1/5,_f),(1/5,_t),(1/2,_f),(1/2,_f)]+-- > let d = [(2/5,f),(1/5,f),(1/5,f),(1/5,t),(1/2,f),(1/2,f)] -- > in rqt_separate_tuplet (1/2) d -- -- > let d = [(4/10,True),(1/10,False),(1/2,True)] -- > in rqt_separate_tuplet (1/2) d-rqt_separate_tuplet :: RQ -> [RQ_T] -> Either String [[RQ_T]]+rqt_separate_tuplet :: Rq -> [Rq_Tied] -> Either String [[Rq_Tied]] rqt_separate_tuplet i x =-    if rqt_can_notate x+    if rqt_can_notate 2 x     then Left (show ("rqt_separate_tuplet: separation not required",x))     else let j = sum (map rqt_rq x) / 2          in if j < i@@ -274,10 +246,10 @@ -- | Recursive variant of 'rqt_separate_tuplet'. -- -- > let d = map rq_rqt [1,1/3,1/6,2/5,1/10]--- > in rqt_tuplet_subdivide (1/8) d == [[(1/1,_f)]--- >                                    ,[(1/3,_f),(1/6,_f)]--- >                                    ,[(2/5,_f),(1/10,_f)]]-rqt_tuplet_subdivide :: RQ -> [RQ_T] -> [[RQ_T]]+-- > in rqt_tuplet_subdivide (1/8) d == [[(1/1,f)]+-- >                                    ,[(1/3,f),(1/6,f)]+-- >                                    ,[(2/5,f),(1/10,f)]]+rqt_tuplet_subdivide :: Rq -> [Rq_Tied] -> [[Rq_Tied]] rqt_tuplet_subdivide i x =     case rqt_separate_tuplet i x of       Left _ -> [x]@@ -287,13 +259,13 @@ -- -- > let d = [(1/5,True),(1/20,False),(1/2,False),(1/4,True)] -- > in rqt_tuplet_subdivide_seq (1/2) [d]-rqt_tuplet_subdivide_seq :: RQ -> [[RQ_T]] -> [[RQ_T]]+rqt_tuplet_subdivide_seq :: Rq -> [[Rq_Tied]] -> [[Rq_Tied]] rqt_tuplet_subdivide_seq i = concatMap (rqt_tuplet_subdivide i)  -- | If a tuplet is all tied, it ought to be a plain value?! ----- > rqt_tuplet_sanity_ [(4/10,_t),(1/10,_f)] == [(1/2,_f)]-rqt_tuplet_sanity_ :: [RQ_T] -> [RQ_T]+-- > rqt_tuplet_sanity_ [(4/10,t),(1/10,f)] == [(1/2,f)]+rqt_tuplet_sanity_ :: [Rq_Tied] -> [Rq_Tied] rqt_tuplet_sanity_ t =     let last_tied = rqt_tied (last t)         all_tied = all rqt_tied (dropRight 1 t)@@ -301,82 +273,86 @@        then [(sum (map rqt_rq t),last_tied)]        else t -rqt_tuplet_subdivide_seq_sanity_ :: RQ -> [[RQ_T]] -> [[RQ_T]]+rqt_tuplet_subdivide_seq_sanity_ :: Rq -> [[Rq_Tied]] -> [[Rq_Tied]] rqt_tuplet_subdivide_seq_sanity_ i =     map rqt_tuplet_sanity_ .     rqt_tuplet_subdivide_seq i  -- * Divisions --- | Separate 'RQ' sequence into measures given by 'RQ' length.+-- | Separate 'Rq' sequence into measures given by 'Rq' length. ----- > to_measures_rq [3,3] [2,2,2] == Right [[(2,_f),(1,_t)],[(1,_f),(2,_f)]]--- > to_measures_rq [3,3] [6] == Right [[(3,_t)],[(3,_f)]]--- > to_measures_rq [1,1,1] [3] == Right [[(1,_t)],[(1,_t)],[(1,_f)]]+-- > to_measures_rq [3,3] [2,2,2] == Right [[(2,f),(1,t)],[(1,f),(2,f)]]+-- > to_measures_rq [3,3] [6] == Right [[(3,t)],[(3,f)]]+-- > to_measures_rq [1,1,1] [3] == Right [[(1,t)],[(1,t)],[(1,f)]] -- > to_measures_rq [3,3] [2,2,1] -- > to_measures_rq [3,2] [2,2,2] -- -- > let d = [4/7,33/28,9/20,4/5]--- > in to_measures_rq [3] d == Right [[(4/7,_f),(33/28,_f),(9/20,_f),(4/5,_f)]]-to_measures_rq :: [RQ] -> [RQ] -> Either String [[RQ_T]]+-- > in to_measures_rq [3] d == Right [[(4/7,f),(33/28,f),(9/20,f),(4/5,f)]]+to_measures_rq :: [Rq] -> [Rq] -> Either String [[Rq_Tied]] to_measures_rq m = rqt_separate m . map rq_rqt --- | Variant of 'to_measures_rq' that ensures 'RQ_T' are /cmn/+-- | Variant that is applicable only at sequence that do not require splitting and ties, else error.+to_measures_rq_untied_err :: [Rq] -> [Rq] -> [[Rq]]+to_measures_rq_untied_err m = either (error "to_measures_rq_untied") (map (map rqt_to_rq_err)) . to_measures_rq m++-- | Variant of 'to_measures_rq' that ensures 'Rq_Tied' are /cmn/ -- durations.  This is not a good composition. ----- > to_measures_rq_cmn [6,6] [5,5,2] == Right [[(4,_t),(1,_f),(1,_t)]--- >                                           ,[(4,_f),(2,_f)]]+-- > to_measures_rq_cmn [6,6] [5,5,2] == Right [[(4,t),(1,f),(1,t)]+-- >                                           ,[(4,f),(2,f)]] ----- > let r = [[(4/7,_t),(1/7,_f),(1,_f),(6/7,_f),(3/7,_f)]]+-- > let r = [[(4/7,t),(1/7,f),(1,f),(6/7,f),(3/7,f)]] -- > in to_measures_rq_cmn [3] [5/7,1,6/7,3/7] == Right r ----- > to_measures_rq_cmn [1,1,1] [5/7,1,6/7,3/7] == Right [[(4/7,_t),(1/7,_f),(2/7,_t)]--- >                                                     ,[(4/7,_t),(1/7,_f),(2/7,_t)]--- >                                                     ,[(4/7,_f),(3/7,_f)]]-to_measures_rq_cmn :: [RQ] -> [RQ] -> Either String [[RQ_T]]+-- > to_measures_rq_cmn [1,1,1] [5/7,1,6/7,3/7] == Right [[(4/7,t),(1/7,f),(2/7,t)]+-- >                                                     ,[(4/7,t),(1/7,f),(2/7,t)]+-- >                                                     ,[(4/7,f),(3/7,f)]]+to_measures_rq_cmn :: [Rq] -> [Rq] -> Either String [[Rq_Tied]] to_measures_rq_cmn m = fmap (map rqt_set_to_cmn) . to_measures_rq m  -- | Variant of 'to_measures_rq' with measures given by--- 'Time_Signature' values.  Does not ensure 'RQ_T' are /cmn/+-- 'Time_Signature' values.  Does not ensure 'Rq_Tied' are /cmn/ -- durations. ----- > to_measures_ts [(1,4)] [5/8,3/8] /= Right [[(1/2,_t),(1/8,_f),(3/8,_f)]]--- > to_measures_ts [(1,4)] [5/7,2/7] /= Right [[(4/7,_t),(1/7,_f),(2/7,_f)]]+-- > to_measures_ts [(1,4)] [5/8,3/8] /= Right [[(1/2,t),(1/8,f),(3/8,f)]]+-- > to_measures_ts [(1,4)] [5/7,2/7] /= Right [[(4/7,t),(1/7,f),(2/7,f)]] -- -- > let {m = replicate 18 (1,4) -- >     ;x = [3/4,2,5/4,9/4,1/4,3/2,1/2,7/4,1,5/2,11/4,3/2]}--- > in to_measures_ts m x == Right [[(3/4,_f),(1/4,_t)],[(1/1,_t)]--- >                                ,[(3/4,_f),(1/4,_t)],[(1/1,_f)]--- >                                ,[(1/1,_t)],[(1/1,_t)]--- >                                ,[(1/4,_f),(1/4,_f),(1/2,_t)],[(1/1,_f)]--- >                                ,[(1/2,_f),(1/2,_t)],[(1/1,_t)]--- >                                ,[(1/4,_f),(3/4,_t)],[(1/4,_f),(3/4,_t)]--- >                                ,[(1/1,_t)],[(3/4,_f),(1/4,_t)]--- >                                ,[(1/1,_t)],[(1/1,_t)]--- >                                ,[(1/2,_f),(1/2,_t)],[(1/1,_f)]]+-- > in to_measures_ts m x == Right [[(3/4,f),(1/4,t)],[(1/1,t)]+-- >                                ,[(3/4,f),(1/4,t)],[(1/1,f)]+-- >                                ,[(1/1,t)],[(1/1,t)]+-- >                                ,[(1/4,f),(1/4,f),(1/2,t)],[(1/1,f)]+-- >                                ,[(1/2,f),(1/2,t)],[(1/1,t)]+-- >                                ,[(1/4,f),(3/4,t)],[(1/4,f),(3/4,t)]+-- >                                ,[(1/1,t)],[(3/4,f),(1/4,t)]+-- >                                ,[(1/1,t)],[(1/1,t)]+-- >                                ,[(1/2,f),(1/2,t)],[(1/1,f)]] -- -- > to_measures_ts [(3,4)] [4/7,33/28,9/20,4/5] -- > to_measures_ts (replicate 3 (1,4)) [4/7,33/28,9/20,4/5]-to_measures_ts :: [Time_Signature] -> [RQ] -> Either String [[RQ_T]]+to_measures_ts :: [Time_Signature] -> [Rq] -> Either String [[Rq_Tied]] to_measures_ts m = to_measures_rq (map ts_rq m)  -- | Variant of 'to_measures_ts' that allows for duration field -- operation but requires that measures be well formed.  This is -- useful for re-grouping measures after notation and ascription.-to_measures_ts_by_eq :: (a -> RQ) -> [Time_Signature] -> [a] -> Maybe [[a]]+to_measures_ts_by_eq :: (a -> Rq) -> [Time_Signature] -> [a] -> Maybe [[a]] to_measures_ts_by_eq f m = split_sum_by_eq f (map ts_rq m) --- | Divide measure into pulses of indicated 'RQ' durations.  Measure+-- | Divide measure into pulses of indicated 'Rq' durations.  Measure -- must be of correct length but need not contain only /cmn/ -- durations.  Pulses are further subdivided if required to notate -- tuplets correctly, see 'rqt_tuplet_subdivide_seq'. ----- > let d = [(1/4,_f),(1/4,_f),(2/3,_t),(1/6,_f),(16/15,_f),(1/5,_f)--- >         ,(1/5,_f),(2/5,_t),(1/20,_f),(1/2,_f),(1/4,_t)]+-- > let d = [(1/4,f),(1/4,f),(2/3,t),(1/6,f),(16/15,f),(1/5,f)+-- >         ,(1/5,f),(2/5,t),(1/20,f),(1/2,f),(1/4,t)] -- > in m_divisions_rq [1,1,1,1] d ----- > m_divisions_rq [1,1,1] [(4/7,_f),(33/28,_f),(9/20,_f),(4/5,_f)]-m_divisions_rq :: [RQ] -> [RQ_T] -> Either String [[RQ_T]]+-- > m_divisions_rq [1,1,1] [(4/7,f),(33/28,f),(9/20,f),(4/5,f)]+m_divisions_rq :: [Rq] -> [Rq_Tied] -> Either String [[Rq_Tied]] m_divisions_rq z =     fmap (rqt_tuplet_subdivide_seq_sanity_ (1/16) .           map rqt_set_to_cmn) .@@ -385,59 +361,59 @@ -- | Variant of 'm_divisions_rq' that determines pulse divisions from -- 'Time_Signature'. ----- > let d = [(4/7,_t),(1/7,_f),(2/7,_f)]+-- > let d = [(4/7,t),(1/7,f),(2/7,f)] -- > in m_divisions_ts (1,4) d == Just [d] -- -- > let d = map rq_rqt [1/3,1/6,2/5,1/10]--- > in m_divisions_ts (1,4) d == Just [[(1/3,_f),(1/6,_f)]--- >                                   ,[(2/5,_f),(1/10,_f)]]+-- > in m_divisions_ts (1,4) d == Just [[(1/3,f),(1/6,f)]+-- >                                   ,[(2/5,f),(1/10,f)]] -- -- > let d = map rq_rqt [4/7,33/28,9/20,4/5]--- > in m_divisions_ts (3,4) d == Just [[(4/7,_f),(3/7,_t)]--- >                                   ,[(3/4,_f),(1/4,_t)]--- >                                   ,[(1/5,_f),(4/5,_f)]]-m_divisions_ts :: Time_Signature -> [RQ_T] -> Either String [[RQ_T]]+-- > in m_divisions_ts (3,4) d == Just [[(4/7,f),(3/7,t)]+-- >                                   ,[(3/4,f),(1/4,t)]+-- >                                   ,[(1/5,f),(4/5,f)]]+m_divisions_ts :: Time_Signature -> [Rq_Tied] -> Either String [[Rq_Tied]] m_divisions_ts ts = m_divisions_rq (ts_divisions ts)  {-| Composition of 'to_measures_rq' and 'm_divisions_rq', where measures are initially given as sets of divisions.  > let m = [[1,1,1],[1,1,1]]-> in to_divisions_rq m [2,2,2] == Right [[[(1,_t)],[(1,_f)],[(1,_t)]]->                                      ,[[(1,_f)],[(1,_t)],[(1,_f)]]]+> in to_divisions_rq m [2,2,2] == Right [[[(1,t)],[(1,f)],[(1,t)]]+>                                      ,[[(1,f)],[(1,t)],[(1,f)]]]  > let d = [2/7,1/7,4/7,5/7,8/7,1,1/7]-> in to_divisions_rq [[1,1,1,1]] d == Right [[[(2/7,_f),(1/7,_f),(4/7,_f)]->                                           ,[(4/7,_t),(1/7,_f),(2/7,_t)]->                                           ,[(6/7,_f),(1/7,_t)]->                                           ,[(6/7,_f),(1/7,_f)]]]+> in to_divisions_rq [[1,1,1,1]] d == Right [[[(2/7,f),(1/7,f),(4/7,f)]+>                                           ,[(4/7,t),(1/7,f),(2/7,t)]+>                                           ,[(6/7,f),(1/7,t)]+>                                           ,[(6/7,f),(1/7,f)]]]  > let d = [5/7,1,6/7,3/7]-> in to_divisions_rq [[1,1,1]] d == Right [[[(4/7,_t),(1/7,_f),(2/7,_t)]->                                         ,[(4/7,_t),(1/7,_f),(2/7,_t)]->                                         ,[(4/7,_f),(3/7,_f)]]]+> in to_divisions_rq [[1,1,1]] d == Right [[[(4/7,t),(1/7,f),(2/7,t)]+>                                         ,[(4/7,t),(1/7,f),(2/7,t)]+>                                         ,[(4/7,f),(3/7,f)]]]  > let d = [2/7,1/7,4/7,5/7,1,6/7,3/7]-> in to_divisions_rq [[1,1,1,1]] d == Right [[[(2/7,_f),(1/7,_f),(4/7,_f)]->                                           ,[(4/7,_t),(1/7,_f),(2/7,_t)]->                                           ,[(4/7,_t),(1/7,_f),(2/7,_t)]->                                           ,[(4/7,_f),(3/7,_f)]]]+> in to_divisions_rq [[1,1,1,1]] d == Right [[[(2/7,f),(1/7,f),(4/7,f)]+>                                           ,[(4/7,t),(1/7,f),(2/7,t)]+>                                           ,[(4/7,t),(1/7,f),(2/7,t)]+>                                           ,[(4/7,f),(3/7,f)]]]  > let d = [4/7,33/28,9/20,4/5]-> in to_divisions_rq [[1,1,1]] d == Right [[[(4/7,_f),(3/7,_t)]->                                          ,[(3/4,_f),(1/4,_t)]->                                          ,[(1/5,_f),(4/5,_f)]]]+> in to_divisions_rq [[1,1,1]] d == Right [[[(4/7,f),(3/7,t)]+>                                          ,[(3/4,f),(1/4,t)]+>                                          ,[(1/5,f),(4/5,f)]]]  > let {p = [[1/2,1,1/2],[1/2,1]] >     ;d = map (/6) [1,1,1,1,1,1,4,1,2,1,1,2,1,3]}-> in to_divisions_rq p d == Right [[[(1/6,_f),(1/6,_f),(1/6,_f)]->                                  ,[(1/6,_f),(1/6,_f),(1/6,_f),(1/2,True)]->                                  ,[(1/6,_f),(1/6,_f),(1/6,True)]]->                                 ,[[(1/6,_f),(1/6,_f),(1/6,_f)]->                                  ,[(1/3,_f),(1/6,_f),(1/2,_f)]]]+> in to_divisions_rq p d == Right [[[(1/6,f),(1/6,f),(1/6,f)]+>                                  ,[(1/6,f),(1/6,f),(1/6,f),(1/2,True)]+>                                  ,[(1/6,f),(1/6,f),(1/6,True)]]+>                                 ,[[(1/6,f),(1/6,f),(1/6,f)]+>                                  ,[(1/3,f),(1/6,f),(1/2,f)]]]  -}-to_divisions_rq :: [[RQ]] -> [RQ] -> Either String [[[RQ_T]]]+to_divisions_rq :: [[Rq]] -> [Rq] -> Either String [[[Rq_Tied]]] to_divisions_rq m x =     let m' = map sum m     in case to_measures_rq m' x of@@ -448,39 +424,39 @@ -- 'Time_Signature'. -- -- > let d = [3/5,2/5,1/3,1/6,7/10,17/15,1/2,1/6]--- > in to_divisions_ts [(4,4)] d == Just [[[(3/5,_f),(2/5,_f)]--- >                                       ,[(1/3,_f),(1/6,_f),(1/2,_t)]--- >                                       ,[(1/5,_f),(4/5,_t)]--- >                                       ,[(1/3,_f),(1/2,_f),(1/6,_f)]]]+-- > in to_divisions_ts [(4,4)] d == Just [[[(3/5,f),(2/5,f)]+-- >                                       ,[(1/3,f),(1/6,f),(1/2,t)]+-- >                                       ,[(1/5,f),(4/5,t)]+-- >                                       ,[(1/3,f),(1/2,f),(1/6,f)]]] -- -- > let d = [3/5,2/5,1/3,1/6,7/10,29/30,1/2,1/3]--- > in to_divisions_ts [(4,4)] d == Just [[[(3/5,_f),(2/5,_f)]--- >                                       ,[(1/3,_f),(1/6,_f),(1/2,_t)]--- >                                       ,[(1/5,_f),(4/5,_t)]--- >                                       ,[(1/6,_f),(1/2,_f),(1/3,_f)]]]+-- > in to_divisions_ts [(4,4)] d == Just [[[(3/5,f),(2/5,f)]+-- >                                       ,[(1/3,f),(1/6,f),(1/2,t)]+-- >                                       ,[(1/5,f),(4/5,t)]+-- >                                       ,[(1/6,f),(1/2,f),(1/3,f)]]] -- -- > let d = [3/5,2/5,1/3,1/6,7/10,4/5,1/2,1/2]--- > in to_divisions_ts [(4,4)] d == Just [[[(3/5,_f),(2/5,_f)]--- >                                       ,[(1/3,_f),(1/6,_f),(1/2,_t)]--- >                                       ,[(1/5,_f),(4/5,_f)]--- >                                       ,[(1/2,_f),(1/2,_f)]]]+-- > in to_divisions_ts [(4,4)] d == Just [[[(3/5,f),(2/5,f)]+-- >                                       ,[(1/3,f),(1/6,f),(1/2,t)]+-- >                                       ,[(1/5,f),(4/5,f)]+-- >                                       ,[(1/2,f),(1/2,f)]]] -- -- > let d = [4/7,33/28,9/20,4/5]--- > in to_divisions_ts [(3,4)] d == Just [[[(4/7,_f),(3/7,_t)]--- >                                       ,[(3/4,_f),(1/4,_t)]--- >                                       ,[(1/5,_f),(4/5,_f)]]]-to_divisions_ts :: [Time_Signature] -> [RQ] -> Either String [[[RQ_T]]]+-- > in to_divisions_ts [(3,4)] d == Just [[[(4/7,f),(3/7,t)]+-- >                                       ,[(3/4,f),(1/4,t)]+-- >                                       ,[(1/5,f),(4/5,f)]]]+to_divisions_ts :: [Time_Signature] -> [Rq] -> Either String [[[Rq_Tied]]] to_divisions_ts ts = to_divisions_rq (map ts_divisions ts)  -- * Durations  -- | Pulse tuplet derivation. ----- > p_tuplet_rqt [(2/3,_f),(1/3,_t)] == Just ((3,2),[(1,_f),(1/2,_t)])--- > p_tuplet_rqt (map rq_rqt [1/3,1/6]) == Just ((3,2),[(1/2,_f),(1/4,_f)])--- > p_tuplet_rqt (map rq_rqt [2/5,1/10]) == Just ((5,4),[(1/2,_f),(1/8,_f)])+-- > p_tuplet_rqt [(2/3,f),(1/3,t)] == Just ((3,2),[(1,f),(1/2,t)])+-- > p_tuplet_rqt (map rq_rqt [1/3,1/6]) == Just ((3,2),[(1/2,f),(1/4,f)])+-- > p_tuplet_rqt (map rq_rqt [2/5,1/10]) == Just ((5,4),[(1/2,f),(1/8,f)]) -- > p_tuplet_rqt (map rq_rqt [1/3,1/6,2/5,1/10])-p_tuplet_rqt :: [RQ_T] -> Maybe ((Integer,Integer),[RQ_T])+p_tuplet_rqt :: [Rq_Tied] -> Maybe ((Integer,Integer),[Rq_Tied]) p_tuplet_rqt x =     let f t = (t,map (rqt_un_tuplet t) x)     in fmap f (rq_derive_tuplet (map rqt_rq x))@@ -488,31 +464,31 @@ -- | Notate pulse, ie. derive tuplet if neccesary. The flag indicates -- if the initial value is tied left. ----- > p_notate False [(2/3,_f),(1/3,_t)]--- > p_notate False [(2/5,_f),(1/10,_t)]--- > p_notate False [(1/4,_t),(1/8,_f),(1/8,_f)]+-- > p_notate False [(2/3,f),(1/3,t)]+-- > p_notate False [(2/5,f),(1/10,t)]+-- > p_notate False [(1/4,t),(1/8,f),(1/8,f)] -- > p_notate False (map rq_rqt [1/3,1/6]) -- > p_notate False (map rq_rqt [2/5,1/10]) -- > p_notate False (map rq_rqt [1/3,1/6,2/5,1/10]) == Nothing-p_notate :: Bool -> [RQ_T] -> Either String [Duration_A]+p_notate :: Bool -> [Rq_Tied] -> Either String [Duration_A] p_notate z x =     let f = p_simplify . rqt_to_duration_a z         d = case p_tuplet_rqt x of               Just (t,x') -> da_tuplet t (f x')               Nothing -> f x-    in if rq_can_notate (map rqt_rq x)+    in if rq_can_notate 2 (map rqt_rq x)        then Right d        else Left (show ("p_notate",z,x))  -- | Notate measure. ----- > m_notate True [[(2/3,_f),(1/3,_t)],[(1,_t)],[(1,_f)]]+-- > m_notate True [[(2/3,f),(1/3,t)],[(1,t)],[(1,f)]] -- -- > let f = m_notate False . concat -- -- > fmap f (to_divisions_ts [(4,4)] [3/5,2/5,1/3,1/6,7/10,17/15,1/2,1/6]) -- > fmap f (to_divisions_ts [(4,4)] [3/5,2/5,1/3,1/6,7/10,29/30,1/2,1/3])-m_notate :: Bool -> [[RQ_T]] -> Either String [Duration_A]+m_notate :: Bool -> [[Rq_Tied]] -> Either String [Duration_A] m_notate z m =     let z' = z : map (is_tied_right . last) m     in fmap concat (all_right (zipWith p_notate z' m))@@ -533,7 +509,7 @@ > in fmap mm_notate (to_divisions_rq p d)  -}-mm_notate :: [[[RQ_T]]] -> Either String [[Duration_A]]+mm_notate :: [[[Rq_Tied]]] -> Either String [[Duration_A]] mm_notate d =     let z = False : map (is_tied_right . last . last) d     in all_right (zipWith m_notate z d)@@ -542,13 +518,13 @@  -- | Structure given to 'Simplify_P' to decide simplification.  The -- structure is /(ts,start-rq,(left-rq,right-rq))/.-type Simplify_T = (Time_Signature,RQ,(RQ,RQ))+type Simplify_T = (Time_Signature,Rq,(Rq,Rq))  -- | Predicate function at 'Simplify_T'. type Simplify_P = Simplify_T -> Bool  -- | Variant of 'Simplify_T' allowing multiple rules.-type Simplify_M = ([Time_Signature],[RQ],[(RQ,RQ)])+type Simplify_M = ([Time_Signature],[Rq],[(Rq,Rq)])  -- | Transform 'Simplify_M' to 'Simplify_P'. meta_table_p :: Simplify_M -> Simplify_P@@ -641,7 +617,7 @@                 g i = if dots i <= n_dots && t && e && m && r                       then Just (i,a)                       else Nothing-            in join (fmap g d)+            in g =<< d         z i (j,_) = i + duration_to_rq j     in coalesce_sum z 0 f @@ -667,13 +643,13 @@ -- > p_simplify [(e,[Tie_Right]),(s,[Tie_Left]),(e',[])] == [(e',[]),(e',[])] -- -- > let f = rqt_to_duration_a False--- > in p_simplify (f [(1/8,_t),(1/4,_t),(1/8,_f)]) == f [(1/2,_f)]+-- > in p_simplify (f [(1/8,t),(1/4,t),(1/8,f)]) == f [(1/2,f)] p_simplify :: [Duration_A] -> [Duration_A] p_simplify = m_simplify p_simplify_rule undefined  -- * Notate -{-| Notate RQ duration sequence.  Derive pulse divisions from+{-| Notate Rq duration sequence.  Derive pulse divisions from 'Time_Signature' if not given directly.  Composition of 'to_divisions_ts', 'mm_notate' 'm_simplify'. @@ -684,7 +660,7 @@ >  in T.notate_rqp 4 sr ts (Just ts_p) rq  -}-notate_rqp :: Int -> Simplify_P -> [Time_Signature] -> Maybe [[RQ]] -> [RQ] ->+notate_rqp :: Int -> Simplify_P -> [Time_Signature] -> Maybe [[Rq]] -> [Rq] ->               Either String [[Duration_A]] notate_rqp limit r ts ts_p x = do   let ts_p' = fromMaybe (map ts_divisions ts) ts_p@@ -695,9 +671,8 @@ -- | Variant of 'notate_rqp' without pulse divisions (derive). -- -- > notate 4 (default_rule [((3,2),0,(2,2)),((3,2),0,(4,2))]) [(3,2)] [6]-notate :: Int -> Simplify_P -> [Time_Signature] -> [RQ] ->-          Either String [[Duration_A]]-notate limit r ts x = notate_rqp limit r ts Nothing x+notate :: Int -> Simplify_P -> [Time_Signature] -> [Rq] -> Either String [[Duration_A]]+notate limit r ts = notate_rqp limit r ts Nothing  -- * Ascribe @@ -779,15 +754,15 @@                in r : mm_ascribe mm' x'  -- | 'mm_ascribe of 'notate'.-notate_mm_ascribe :: Show a => Int -> [Simplify_T] -> [Time_Signature] -> Maybe [[RQ]] -> [RQ] -> [a] ->+notate_mm_ascribe :: Show a => Int -> [Simplify_T] -> [Time_Signature] -> Maybe [[Rq]] -> [Rq] -> [a] ->                      Either String [[(Duration_A,a)]] notate_mm_ascribe limit r ts rqp d p =     let n = notate_rqp limit (default_rule r) ts rqp d         f = flip mm_ascribe p-        err str = show ("notate_ascribe",str,ts,d,p)+        err str = show ("notate_mm_ascribe",str,ts,d,p)     in either (Left . err) (Right . f) n -notate_mm_ascribe_err :: Show a => Int -> [Simplify_T] -> [Time_Signature] -> Maybe [[RQ]] -> [RQ] -> [a] ->+notate_mm_ascribe_err :: Show a => Int -> [Simplify_T] -> [Time_Signature] -> Maybe [[Rq]] -> [Rq] -> [a] ->                          [[(Duration_A,a)]] notate_mm_ascribe_err = either error id .::::: notate_mm_ascribe
Music/Theory/Dynamic_Mark.hs view
@@ -4,57 +4,71 @@ import Data.Char {- base -} import Data.List {- base -} import Data.Maybe {- base -}+import Text.Read {- base -} -import qualified Music.Theory.List as T+import qualified Music.Theory.List as T {- hmt -}  -- | Enumeration of dynamic mark symbols.-data Dynamic_Mark_T = Niente-                    | PPPPP | PPPP | PPP | PP | P | MP-                    | MF | F | FF | FFF | FFFF | FFFFF-                    | FP | SF | SFP | SFPP | SFZ | SFFZ-                      deriving (Eq,Ord,Enum,Bounded,Show)+data Dynamic_Mark = Niente+                    | Ppppp | Pppp | Ppp | Pp | P | Mp+                    | Mf | F | Ff | Fff | Ffff | Fffff+                    | Fp | Sf | Sfp | Sfpp | Sfz | Sffz+                      deriving (Eq,Ord,Enum,Bounded,Show,Read) --- | Lookup MIDI velocity for 'Dynamic_Mark_T'.  The range is linear--- in @0-127@.------ > let r = [0,6,17,28,39,50,61,72,83,94,105,116,127]--- > in mapMaybe dynamic_mark_midi [Niente .. FFFFF] == r------ > map dynamic_mark_midi [FP,SF,SFP,SFPP,SFZ,SFFZ] == replicate 6 Nothing-dynamic_mark_midi :: (Num n,Enum n) => Dynamic_Mark_T -> Maybe n+{- | Case insensitive reader for 'Dynamic_Mark'.++> map dynamic_mark_t_parse_ci (words "pP p Mp F")+-}+dynamic_mark_t_parse_ci :: String -> Maybe Dynamic_Mark+dynamic_mark_t_parse_ci =+  let capitalise x = toUpper (head x) : map toLower (tail x)+  in readMaybe . capitalise++{- | Lookup Midi velocity for 'Dynamic_Mark'.  The range is linear in @0-127@.++> let r = [0,6,17,28,39,50,61,72,83,94,105,116,127]+> mapMaybe dynamic_mark_midi [Niente .. Fffff] == r++> mapMaybe dynamic_mark_midi [Pp .. Ff] == [39,50,61,72,83,94]++> map dynamic_mark_midi [Fp,Sf,Sfp,Sfpp,Sfz,Sffz] == replicate 6 Nothing+-}+dynamic_mark_midi :: (Num n,Enum n) => Dynamic_Mark -> Maybe n dynamic_mark_midi m =     let r = zip [0..] (0 : reverse [127, 127-11 .. 0])     in lookup (fromEnum m) r  -- | Error variant.-dynamic_mark_midi_err :: Integral n => Dynamic_Mark_T -> n+dynamic_mark_midi_err :: Integral n => Dynamic_Mark -> n dynamic_mark_midi_err = fromMaybe (error "dynamic_mark_midi") . dynamic_mark_midi --- | Map midi velocity (0-127) to dynamic mark.------ > histogram (mapMaybe midi_dynamic_mark [0 .. 127])-midi_dynamic_mark :: (Ord n,Num n,Enum n) => n -> Maybe Dynamic_Mark_T+{- | Map midi velocity (0-127) to dynamic mark.++> histogram (mapMaybe midi_dynamic_mark [0 .. 127])+-}+midi_dynamic_mark :: (Ord n,Num n,Enum n) => n -> Maybe Dynamic_Mark midi_dynamic_mark m =     let r = zip (0 : [12,24 .. 132]) [0..]     in fmap (toEnum . snd) (find ((>= m) . fst) r) --- | Translate /fixed/ 'Dynamic_Mark_T's to /db/ amplitude over given--- /range/.------ > mapMaybe (dynamic_mark_db 120) [Niente,P,F,FFFFF] == [-120,-70,-40,0]--- > mapMaybe (dynamic_mark_db 60) [Niente,P,F,FFFFF] == [-60,-35,-20,0]-dynamic_mark_db :: Fractional n => n -> Dynamic_Mark_T -> Maybe n+{- | Translate /fixed/ 'Dynamic_Mark's to /db/ amplitude over given /range/.++> mapMaybe (dynamic_mark_db 120) [Niente,P,F,Fffff] == [-120,-70,-40,0]+> mapMaybe (dynamic_mark_db 60) [Niente,P,F,Fffff] == [-60,-35,-20,0]+-}+dynamic_mark_db :: Fractional n => n -> Dynamic_Mark -> Maybe n dynamic_mark_db r m =-    let u = [Niente .. FFFFF]+    let u = [Niente .. Fffff]         n = length u - 1         k = r / fromIntegral n         f i = negate r + (fromIntegral i * k)     in fmap f (elemIndex m u) --- | <http://www.csounds.com/manual/html/ampmidid.html>------ > import Sound.SC3.Plot--- > plotTable [map (ampmidid 20) [0 .. 127],map (ampmidid 60) [0 .. 127]]+{- | <http://www.csounds.com/manual/html/ampmidid.html>++> import Sound.Sc3.Plot {- hsc3-plot -}+> plot_p1_ln [map (ampmidid 20) [0 .. 127],map (ampmidid 60) [0 .. 127]]+-} ampmidid :: Floating a => a -> a -> a ampmidid db v =     let r = 10 ** (db / 20)@@ -62,26 +76,29 @@         m = (1 - b) / 127     in (m * v + b) ** 2 --- | JMcC (SC3) equation.------ > plotTable1 (map amp_db [0,0.005 .. 1])+{- | JMcC (Sc3) equation.++> plot_p1_ln [map amp_db [0,0.005 .. 1]]+-} amp_db :: Floating a => a -> a amp_db a = logBase 10 a * 20 --- | JMcC (SC3) equation.------ > plotTable1 (map db_amp [-60,-59 .. 0])+{- | JMcC (Sc3) equation.++> plot_p1_ln [map db_amp [-60,-59 .. 0]]+-} db_amp :: Floating a => a -> a db_amp a = 10 ** (a * 0.05)  -- | Enumeration of hairpin indicators.-data Hairpin_T = Crescendo | Diminuendo | End_Hairpin+data Hairpin = Crescendo | Diminuendo | End_Hairpin                  deriving (Eq,Ord,Enum,Bounded,Show) --- | The 'Hairpin_T' implied by a ordered pair of 'Dynamic_Mark_T's.------ > map (implied_hairpin MF) [MP,F] == [Just Diminuendo,Just Crescendo]-implied_hairpin :: Dynamic_Mark_T -> Dynamic_Mark_T -> Maybe Hairpin_T+{- | The 'Hairpin' implied by a ordered pair of 'Dynamic_Mark's.++> map (implied_hairpin Mf) [Mp,F] == [Just Diminuendo,Just Crescendo]+-}+implied_hairpin :: Dynamic_Mark -> Dynamic_Mark -> Maybe Hairpin implied_hairpin p q =     case compare p q of       LT -> Just Crescendo@@ -89,20 +106,18 @@       GT -> Just Diminuendo  -- | A node in a dynamic sequence.-type Dynamic_Node = (Maybe Dynamic_Mark_T,Maybe Hairpin_T)+type Dynamic_Node = (Maybe Dynamic_Mark,Maybe Hairpin)  -- | The empty 'Dynamic_Node'. empty_dynamic_node :: Dynamic_Node empty_dynamic_node = (Nothing,Nothing) --- | Calculate a 'Dynamic_Node' sequence from a sequence of--- 'Dynamic_Mark_T's.------ > dynamic_sequence [PP,MP,MP,PP] == [(Just PP,Just Crescendo)--- >                                   ,(Just MP,Just End_Hairpin)--- >                                   ,(Nothing,Just Diminuendo)--- >                                   ,(Just PP,Just End_Hairpin)]-dynamic_sequence :: [Dynamic_Mark_T] -> [Dynamic_Node]+{- | Calculate a 'Dynamic_Node' sequence from a sequence of 'Dynamic_Mark's.++> let r = [(Just Pp,Just Crescendo), (Just Mp,Just End_Hairpin) ,(Nothing,Just Diminuendo) ,(Just Pp,Just End_Hairpin)]+> dynamic_sequence [Pp,Mp,Mp,Pp] == r+-}+dynamic_sequence :: [Dynamic_Mark] -> [Dynamic_Node] dynamic_sequence d =     let h = zipWith implied_hairpin d (tail d) ++ [Nothing]         e = Just End_Hairpin@@ -117,11 +132,12 @@                             Just _ -> (j,k) : rec True p'     in rec False (zip (T.indicate_repetitions d) h) --- | Delete redundant (unaltered) dynamic marks.------ > let s = [Just P,Nothing,Just P,Just P,Just F]--- > in delete_redundant_marks s == [Just P,Nothing,Nothing,Nothing,Just F]-delete_redundant_marks :: [Maybe Dynamic_Mark_T] -> [Maybe Dynamic_Mark_T]+{- | Delete redundant (unaltered) dynamic marks.++> let r = [Just P,Nothing,Nothing,Nothing,Just F]+> delete_redundant_marks [Just P,Nothing,Just P,Just P,Just F] == r+-}+delete_redundant_marks :: [Maybe Dynamic_Mark] -> [Maybe Dynamic_Mark] delete_redundant_marks =     let f i j = case (i,j) of                   (Just a,Just b) -> if a == b then (j,Nothing) else (j,j)@@ -129,48 +145,46 @@                   (Nothing,_) -> (j,j)     in snd . mapAccumL f Nothing --- | Variant of 'dynamic_sequence' for sequences of 'Dynamic_Mark_T'--- with holes (ie. rests).  Runs 'delete_redundant_marks'.------ > let r = [Just (Just P,Just Crescendo),Just (Just F,Just End_Hairpin)--- >         ,Nothing,Just (Just P,Nothing)]--- > in dynamic_sequence_sets [Just P,Just F,Nothing,Just P] == r------ > let s = [Just P,Nothing,Just P]--- > in dynamic_sequence_sets s = [Just (Just P,Nothing),Nothing,Nothing]-dynamic_sequence_sets :: [Maybe Dynamic_Mark_T] -> [Maybe Dynamic_Node]+{- | Variant of 'dynamic_sequence' for sequences of 'Dynamic_Mark' with holes (ie. rests).+Runs 'delete_redundant_marks'.++> let r = [Just (Just P,Just Crescendo),Just (Just F,Just End_Hairpin),Nothing,Just (Just P,Nothing)]+> dynamic_sequence_sets [Just P,Just F,Nothing,Just P] == r++> dynamic_sequence_sets [Just P,Nothing,Just P] == [Just (Just P,Nothing),Nothing,Nothing]+-}+dynamic_sequence_sets :: [Maybe Dynamic_Mark] -> [Maybe Dynamic_Node] dynamic_sequence_sets =     let f l = case l of                 Nothing:_ -> map (const Nothing) l                 _ -> map Just (dynamic_sequence (catMaybes l))     in concatMap f . T.group_just . delete_redundant_marks --- | Apply 'Hairpin_T' and 'Dynamic_Mark_T' functions in that order as--- required by 'Dynamic_Node'.------ > let f _ x = show x--- > in apply_dynamic_node f f (Nothing,Just Crescendo) undefined-apply_dynamic_node :: (a -> Dynamic_Mark_T -> a) -> (a -> Hairpin_T -> a)-                   -> Dynamic_Node -> a -> a+{- | Apply 'Hairpin' and 'Dynamic_Mark' functions in that order as required by 'Dynamic_Node'.++> let f _ x = show x+> apply_dynamic_node f f (Nothing,Just Crescendo) undefined+-}+apply_dynamic_node :: (a -> Dynamic_Mark -> a) -> (a -> Hairpin -> a) -> Dynamic_Node -> a -> a apply_dynamic_node f g (i,j) m =     let n = maybe m (g m) j     in maybe n (f n) i --- * ASCII+-- * Ascii --- | ASCII pretty printer for 'Dynamic_Mark_T'.-dynamic_mark_ascii :: Dynamic_Mark_T -> String+-- | Ascii pretty printer for 'Dynamic_Mark'.+dynamic_mark_ascii :: Dynamic_Mark -> String dynamic_mark_ascii = map toLower . show --- | ASCII pretty printer for 'Hairpin_T'.-hairpin_ascii :: Hairpin_T -> String+-- | Ascii pretty printer for 'Hairpin'.+hairpin_ascii :: Hairpin -> String hairpin_ascii hp =     case hp of       Crescendo -> "<"       Diminuendo -> ">"       End_Hairpin -> "" --- | ASCII pretty printer for 'Dynamic_Node'.+-- | Ascii pretty printer for 'Dynamic_Node'. dynamic_node_ascii :: Dynamic_Node -> String dynamic_node_ascii (mk,hp) =     let mk' = maybe "" dynamic_mark_ascii mk@@ -181,9 +195,9 @@          (_,[]) -> mk'          _ -> mk' ++ " " ++ hp' --- | ASCII pretty printer for 'Dynamic_Node' sequence.+-- | Ascii pretty printer for 'Dynamic_Node' sequence. dynamic_sequence_ascii :: [Dynamic_Node] -> String dynamic_sequence_ascii =-    intercalate " " .+    unwords .     filter (not . null) .     map dynamic_node_ascii
− Music/Theory/Either.hs 
@@ -1,16 +0,0 @@--- | Either-module Music.Theory.Either where---- | Maybe 'Left' of 'Either'.-fromLeft :: Either a b -> Maybe a-fromLeft e =-    case e of-      Left x -> Just x-      _ -> Nothing---- | Maybe 'Right' of 'Either'.-fromRight :: Either a b -> Maybe b-fromRight e =-    case e of-      Right x -> Just x-      _ -> Nothing
− Music/Theory/Enum.hs 
@@ -1,38 +0,0 @@--- | Enumeration functions.-module Music.Theory.Enum where---- | Generic variant of 'fromEnum' (p.263).-genericFromEnum :: (Integral i,Enum e) => e -> i-genericFromEnum = fromIntegral . fromEnum---- | Generic variant of 'toEnum' (p.263).-genericToEnum :: (Integral i,Enum e) => i -> e-genericToEnum = toEnum . fromIntegral---- | Variant of 'enumFromTo' that, if /p/ is after /q/, cycles from--- 'maxBound' to 'minBound'.------ > import Data.Word--- > enum_from_to_cyclic (254 :: Word8) 1 == [254,255,0,1]-enum_from_to_cyclic :: (Bounded a, Enum a) => a -> a -> [a]-enum_from_to_cyclic p q =-    if fromEnum p > fromEnum q-    then [p .. maxBound] ++ [minBound .. q]-    else [p .. q]---- | Variant of 'enumFromTo' that, if /p/ is after /q/, enumerates--- from /q/ to /p/.------ > enum_from_to_reverse 5 1 == [5,4,3,2,1]--- > enum_from_to_reverse 1 5 == enumFromTo 1 5-enum_from_to_reverse :: Enum a => a -> a -> [a]-enum_from_to_reverse p q =-    if fromEnum p > fromEnum q-    then reverse [q .. p]-    else [p .. q]---- | All elements in sequence.------ > (enum_univ :: [Data.Word.Word8]) == [0 .. 255]-enum_univ :: (Bounded t,Enum t) => [t]-enum_univ = [minBound .. maxBound]
− Music/Theory/Function.hs 
@@ -1,59 +0,0 @@--- | "Data.Function" related functions.-module Music.Theory.Function where---- | 'const' of 'const'.------ > const2 5 undefined undefined == 5--- > const (const 5) undefined undefined == 5-const2 :: a -> b -> c -> a-const2 x _ _ = x---- * Predicate composition.---- | '&&' of predicates.-predicate_and :: (t -> Bool) -> (t -> Bool) -> t -> Bool-predicate_and f g x = f x && g x---- | 'all' of predicates.------ > let r = [False,False,True,False,True,False]--- > in map (predicate_all [(> 0),(< 5),even]) [0..5] == r-predicate_all :: [t -> Bool] -> t -> Bool-predicate_all p x = all id (map ($ x) p)---- | '||' of predicates.-predicate_or :: (t -> Bool) -> (t -> Bool) -> t -> Bool-predicate_or f g x = f x || g x---- | 'any' of predicates, ie. logical /or/ of list of predicates.------ > let r = [True,False,True,False,True,True]--- > in map (predicate_any [(== 0),(== 5),even]) [0..5] == r-predicate_any :: [t -> Bool] -> t -> Bool-predicate_any p x = any id (map ($ x) p)---- * Function composition.---- . is infixr 9, this allows f . g .: h-infixr 8 .:, .::, .:::, .::::, .:::::---- | 'fmap' '.' 'fmap', ie. @(t -> c) -> (a -> b -> t) -> a -> b -> c@.-(.:) :: (Functor f, Functor g) => (a -> b) -> f (g a) -> f (g b)-(.:) = fmap . fmap---- | 'fmap' '.' '.:', ie. @(t -> d) -> (a -> b -> c -> t) -> a -> b -> c -> d@.-(.::) :: (Functor f, Functor g, Functor h) => (a -> b) -> f (g (h a)) -> f (g (h b))-(.::) = fmap . (.:)---- | 'fmap' '.' '.::'.-(.:::) :: (Functor f, Functor g, Functor h,Functor i) => (a -> b) -> f (g (h (i a))) -> f (g (h (i b)))-(.:::) = fmap . (.::)---- | 'fmap' '.' '.:::'.-(.::::) :: (Functor f, Functor g, Functor h,Functor i,Functor j) => (a -> b) -> f (g (h (i (j a)))) -> f (g (h (i (j b))))-(.::::) = fmap . (.:::)---- | 'fmap' '.' '.::::'.-(.:::::) :: (Functor f, Functor g, Functor h,Functor i,Functor j,Functor k) => (a -> b) -> f (g (h (i (j (k a))))) -> f (g (h (i (j (k b)))))-(.:::::) = fmap . (.::::)-
Music/Theory/Gamelan.hs view
@@ -1,3 +1,4 @@+-- | Gamelan instruments and pitch structures. module Music.Theory.Gamelan where  import Data.Char {- base -}@@ -7,11 +8,12 @@ import Data.Ratio {- base -} import Text.Printf {- base -} +import qualified Music.Theory.Enum as T {- hmt-base -}+ import qualified Music.Theory.Clef as T {- hmt -}-import qualified Music.Theory.Enum as T {- hmt -} import qualified Music.Theory.Pitch as T {- hmt -} import qualified Music.Theory.Tuning as T {- hmt -}-import qualified Music.Theory.Tuning.ET as T {- hmt-diagrams -}+import qualified Music.Theory.Tuning.Et as T {- hmt-diagrams -}  -- | 'fromJust' with error message. fromJust_err :: String -> Maybe a -> a@@ -26,6 +28,7 @@ -- | Enumeration of gamelan instrument families. data Instrument_Family     = Bonang+    | Gambang     | Gender     | Gong     | Saron@@ -39,6 +42,7 @@ data Instrument_Name     = Bonang_Barung -- ^ Bonang Barung (horizontal gong, middle)     | Bonang_Panerus -- ^ Bonang Panerus (horizontal gong, high)+    | Gambang_Kayu -- ^ Gambang Kayu (wooden key&resonator)     | Gender_Barung -- ^ Gender Barung (key&resonator, middle)     | Gender_Panerus -- ^ Gender Panembung (key&resonator, high)     | Gender_Panembung -- ^ Gender Panembung, Slenthem (key&resonator, low)@@ -47,29 +51,30 @@     | Kempul -- ^ Kempul (hanging gong, middle)     | Kempyang -- ^ Kempyang (horizontal gong, high)     | Kenong -- ^ Kenong (horizontal gong, low)-    | Ketuk -- ^ Ketuk (horizontal gong, middle)+    | Ketuk -- ^ Ketuk, Kethuk (horizontal gong, middle)     | Saron_Barung -- ^ Saron Barung, Saron (key, middle)     | Saron_Demung -- ^ Saron Demung, Demung (key, low)     | Saron_Panerus -- ^ Saron Panerus, Peking (key, high)       deriving (Enum,Bounded,Eq,Ord,Show,Read) -instrument_family :: Instrument_Name -> Maybe Instrument_Family+instrument_family :: Instrument_Name -> Instrument_Family instrument_family nm =     case nm of-      Bonang_Barung -> Just Bonang-      Bonang_Panerus -> Just Bonang-      Gender_Barung -> Just Gender-      Gender_Panerus -> Just Gender-      Gender_Panembung -> Just Gender-      Gong_Ageng -> Just Gong-      Gong_Suwukan -> Just Gong-      Kempul -> Just Gong-      Kempyang -> Nothing-      Kenong -> Nothing-      Ketuk -> Nothing-      Saron_Barung -> Just Saron-      Saron_Demung -> Just Saron-      Saron_Panerus -> Just Saron+      Bonang_Barung -> Bonang+      Bonang_Panerus -> Bonang+      Gambang_Kayu -> Gambang+      Gender_Barung -> Gender+      Gender_Panerus -> Gender+      Gender_Panembung -> Gender+      Gong_Ageng -> Gong+      Gong_Suwukan -> Gong+      Kempul -> Gong+      Kempyang -> Gong+      Kenong -> Gong+      Ketuk -> Gong+      Saron_Barung -> Saron+      Saron_Demung -> Saron+      Saron_Panerus -> Saron  instrument_name_pp :: Instrument_Name -> String instrument_name_pp =@@ -82,6 +87,7 @@     case nm of       Bonang_Barung -> T.Clef T.Treble 0       Bonang_Panerus -> T.Clef T.Treble 1+      Gambang_Kayu -> T.Clef T.Treble 0       Gender_Barung -> T.Clef T.Treble 0       Gender_Panerus -> T.Clef T.Treble 1       Gender_Panembung -> T.Clef T.Bass 0@@ -101,15 +107,26 @@ -- | Enumeration of Gamelan scales. data Scale = Pelog | Slendro deriving (Enum,Eq,Ord,Show,Read) +-- | Octaves are zero-indexed and may be negative. type Octave = Integer++-- | Degrees are one-indexed. type Degree = Integer++-- | Frequency in hertz. type Frequency = Double++-- | A text annotation. type Annotation = String +-- | 'Octave' and 'Degree'. data Pitch = Pitch {pitch_octave :: Octave                    ,pitch_degree :: Degree}              deriving (Eq,Ord,Show) +-- | Octaves are written as repeated @-@ or @+@, degrees are printed ordinarily.+--+-- > map pitch_pp_ascii (zipWith Pitch [-2 .. 2] [1 .. 5]) == ["--1","-2","3","+4","++5"] pitch_pp_ascii :: Pitch -> String pitch_pp_ascii (Pitch o d) =     let d' = intToDigit (fromIntegral d)@@ -121,97 +138,121 @@ pitch_pp_duple :: Pitch -> String pitch_pp_duple (Pitch o d) = printf "(%d,%d)" o d +-- | 'Scale' and 'Pitch'. data Note = Note {note_scale :: Scale                  ,note_pitch :: Pitch}-             deriving (Eq,Ord,Show)+             deriving (Eq,Show) +-- | 'pitch_degree' of 'note_pitch'. note_degree :: Note -> Degree note_degree = pitch_degree . note_pitch -data Tone = Tone {tone_instrument_name :: Instrument_Name-                 ,tone_note :: Maybe Note-                 ,tone_frequency :: Maybe Frequency-                 ,tone_annotation :: Maybe Annotation}-             deriving (Eq,Show)+-- | It is an error to compare notes from different scales.+note_compare :: Note -> Note -> Ordering+note_compare (Note s1 p1) (Note s2 p2) =+  if s1 /= s2+  then error "note_compare?"+  else compare p1 p2 -tone_frequency_err :: Tone -> Frequency+-- | Orderable if scales are equal.+instance Ord Note where compare = note_compare++-- | Ascending sequence of 'Note' for 'Scale' from /p1/ to /p2/ inclusive.+note_range_elem :: Scale -> Pitch -> Pitch -> [Note]+note_range_elem scl p1@(Pitch o1 _d1) p2@(Pitch o2 _d2) =+  let univ = [Note scl (Pitch o d) | o <- [o1 .. o2], d <- scale_degrees scl]+  in filter (\n -> note_pitch n >= p1 && note_pitch n <= p2) univ++-- | Ascending sequence of 'Note' from /n1/ to /n2/ inclusive.+--+-- > note_gamut_elem (Note Slendro (Pitch 0 5)) (Note Slendro (Pitch 1 2))+note_gamut_elem :: Note -> Note -> [Note]+note_gamut_elem (Note s1 p1) (Note s2 p2) =+  if s1 /= s2+  then error "note_gamut_elem?"+  else note_range_elem s1 p1 p2++data Tone t = Tone {tone_instrument_name :: Instrument_Name+                   ,tone_note :: Maybe Note+                   ,tone_frequency :: Maybe Frequency+                   ,tone_annotation :: Maybe t}+              deriving (Eq,Show)++tone_frequency_err :: Tone t -> Frequency tone_frequency_err = fromJust_err "tone_frequency" . tone_frequency  -- | Orderable if frequency is given.-instance Ord Tone where compare = tone_compare_frequency+instance Eq t => Ord (Tone t) where compare = tone_compare_frequency  -- | Constructor for 'Tone' without /frequency/ or /annotation/.-plain_tone :: Instrument_Name -> Scale -> Octave -> Degree -> Tone+plain_tone :: Instrument_Name -> Scale -> Octave -> Degree -> Tone t plain_tone nm sc o d = Tone nm (Just (Note sc (Pitch o d))) Nothing Nothing  -- | Tones are considered /equivalent/ if they have the same -- 'Instrument_Name' and 'Note'.-tone_equivalent :: Tone -> Tone -> Bool+tone_equivalent :: Tone t -> Tone t -> Bool tone_equivalent p q =     let Tone nm nt _ _ = p         Tone nm' nt' _ _ = q     in nm == nm' && nt == nt' -tone_24et_pitch :: Tone -> Maybe T.Pitch+tone_24et_pitch :: Tone t -> Maybe T.Pitch tone_24et_pitch =-    let f i = let (_,pt,_,_,_) = T.nearest_24et_tone i in pt+    let f i = let (_,pt,_,_,_) = T.nearest_24et_tone_k0 (69,440) i in pt     in fmap f . tone_frequency -tone_24et_pitch' :: Tone -> T.Pitch+tone_24et_pitch' :: Tone t -> T.Pitch tone_24et_pitch' = fromJust_err "tone_24et_pitch" . tone_24et_pitch -tone_24et_pitch_detune :: Tone -> Maybe T.Pitch_Detune-tone_24et_pitch_detune = fmap T.nearest_pitch_detune_24et . tone_frequency+tone_24et_pitch_detune :: Tone t -> Maybe T.Pitch_Detune+tone_24et_pitch_detune = fmap (T.nearest_pitch_detune_24et_k0 (69,440)) . tone_frequency -tone_24et_pitch_detune' :: Tone -> T.Pitch_Detune+tone_24et_pitch_detune' :: Tone t -> T.Pitch_Detune tone_24et_pitch_detune' = fromJust_err "tone_24et_pitch_detune" . tone_24et_pitch_detune -tone_fmidi :: Tone -> Double+tone_fmidi :: Tone t -> Double tone_fmidi = T.cps_to_fmidi . tone_frequency_err  -- | Fractional (rational) 24-et midi note number of 'Tone'.-tone_24et_fmidi :: Tone -> Rational+tone_24et_fmidi :: Tone t -> Rational tone_24et_fmidi = near_rat . T.pitch_to_fmidi . tone_24et_pitch' -tone_12et_pitch :: Tone -> Maybe T.Pitch+tone_12et_pitch :: Tone t -> Maybe T.Pitch tone_12et_pitch =-    let f i = let (_,pt,_,_,_) = T.nearest_12et_tone i in pt+    let f i = let (_,pt,_,_,_) = T.nearest_12et_tone_k0 (69,440) i in pt     in fmap f . tone_frequency -tone_12et_pitch' :: Tone -> T.Pitch+tone_12et_pitch' :: Tone t -> T.Pitch tone_12et_pitch' = fromJust_err "tone_12et_pitch" . tone_12et_pitch -tone_12et_pitch_detune :: Tone -> Maybe T.Pitch_Detune-tone_12et_pitch_detune = fmap T.nearest_pitch_detune_12et . tone_frequency+tone_12et_pitch_detune :: Tone t -> Maybe T.Pitch_Detune+tone_12et_pitch_detune = fmap (T.nearest_pitch_detune_12et_k0 (69,440)) . tone_frequency -tone_12et_pitch_detune' :: Tone -> T.Pitch_Detune+tone_12et_pitch_detune' :: Tone t -> T.Pitch_Detune tone_12et_pitch_detune' = fromJust_err "tone_12et_pitch_detune" . tone_12et_pitch_detune  -- | Fractional (rational) 24-et midi note number of 'Tone'.-tone_12et_fmidi :: Tone -> Rational+tone_12et_fmidi :: Tone t -> Rational tone_12et_fmidi = near_rat . T.pitch_to_fmidi . tone_12et_pitch' -tone_family :: Tone -> Maybe Instrument_Family+tone_family :: Tone t -> Instrument_Family tone_family = instrument_family . tone_instrument_name -tone_family_err :: Tone -> Instrument_Family-tone_family_err = fromJust_err "tone_family" . tone_family--tone_in_family :: Instrument_Family -> Tone -> Bool-tone_in_family c t = tone_family t == Just c+tone_in_family :: Instrument_Family -> Tone t -> Bool+tone_in_family c t = tone_family t == c -select_tones :: Instrument_Family -> [Tone] -> [Maybe Tone]+select_tones :: Instrument_Family -> [Tone t] -> [Maybe (Tone t)] select_tones c =-    let f t = if tone_family t == Just c then Just t else Nothing+    let f t = if tone_family t == c then Just t else Nothing     in map f  -- | Specify subset as list of families and scales. type Tone_Subset = ([Instrument_Family],[Scale])  -- | Extract subset of 'Tone_Set'.-tone_subset :: Tone_Subset -> Tone_Set -> Tone_Set+tone_subset :: Tone_Subset -> Tone_Set t -> Tone_Set t tone_subset (fm,sc) =-    let f t = fromJust_err "tone_subset" (tone_family t) `elem` fm &&+    let f t = tone_family t `elem` fm &&               fromJust_err "tone_subset" (tone_scale t) `elem` sc     in filter f @@ -221,43 +262,43 @@                              ,instrument_frequencies :: Maybe [Frequency]}                   deriving (Eq,Show) -type Tone_Set = [Tone]-type Tone_Group = [Tone_Set]+type Tone_Set t = [Tone t]+type Tone_Group t = [Tone_Set t] type Gamelan = [Instrument] -tone_scale :: Tone -> Maybe Scale+tone_scale :: Tone t -> Maybe Scale tone_scale = fmap note_scale . tone_note -tone_pitch :: Tone -> Maybe Pitch+tone_pitch :: Tone t -> Maybe Pitch tone_pitch = fmap note_pitch . tone_note -tone_degree :: Tone -> Maybe Degree+tone_degree :: Tone t -> Maybe Degree tone_degree = fmap pitch_degree . tone_pitch -tone_degree' :: Tone -> Degree+tone_degree' :: Tone t -> Degree tone_degree' = fromJust_err "tone_degree" . tone_degree -tone_octave :: Tone -> Maybe Octave+tone_octave :: Tone t -> Maybe Octave tone_octave = fmap pitch_octave . tone_pitch -tone_class :: Tone -> (Instrument_Name,Maybe Scale)+tone_class :: Tone t -> (Instrument_Name,Maybe Scale) tone_class t = (tone_instrument_name t,tone_scale t)  instrument_class :: Instrument -> (Instrument_Name,Maybe Scale) instrument_class i = (instrument_name i,instrument_scale i) -tone_class_p :: (Instrument_Name, Scale) -> Tone -> Bool+tone_class_p :: (Instrument_Name, Scale) -> Tone t -> Bool tone_class_p (nm,sc) t =     tone_instrument_name t == nm &&     tone_scale t == Just sc -tone_family_class_p :: (Instrument_Family,Scale) -> Tone -> Bool+tone_family_class_p :: (Instrument_Family,Scale) -> Tone t -> Bool tone_family_class_p (fm,sc) t =-    instrument_family (tone_instrument_name t) == Just fm &&+    instrument_family (tone_instrument_name t) == fm &&     tone_scale t == Just sc  -- | Given a 'Tone_Set', find those 'Tone's that are within 'T.Cents' of 'Frequency'.-tone_set_near_frequency :: Tone_Set -> T.Cents -> Frequency -> Tone_Set+tone_set_near_frequency :: Tone_Set t -> T.Cents -> Frequency -> Tone_Set t tone_set_near_frequency t k n =     let near i = abs (T.cps_difference_cents i n) <= k         near_t i = maybe False near (tone_frequency i)@@ -265,8 +306,8 @@  -- | Compare 'Tone's by frequency.  'Tone's without frequency compare -- as if at frequency @0@.-tone_compare_frequency :: Tone -> Tone -> Ordering-tone_compare_frequency = compare `on` (maybe 0 id . tone_frequency)+tone_compare_frequency :: Tone t -> Tone t -> Ordering+tone_compare_frequency = compare `on` (fromMaybe 0 . tone_frequency)  -- | If all /f/ of /a/ are 'Just' /b/, then 'Just' /[b]/, else -- 'Nothing'.@@ -275,7 +316,7 @@     let x' = map f x     in if any isNothing x' then Nothing else Just (catMaybes x') -instrument :: Tone_Set -> Instrument+instrument :: Tone_Set t -> Instrument instrument c =     let sf = fmap note_scale . tone_note         pf = fmap note_pitch . tone_note@@ -289,7 +330,7 @@          t:_ -> Instrument (tone_instrument_name t) (sf t) p f          [] -> undefined -instruments :: Tone_Set -> [Instrument]+instruments :: Tone_Set t -> [Instrument] instruments c =     let c' = sortBy (compare `on` tone_instrument_name) c         c'' = groupBy ((==) `on` tone_class) c'@@ -300,26 +341,32 @@     let f p = (head p,last p)     in fmap f . instrument_pitches +-- | Pelog has seven degrees, numbered one to seven.+--   Slendro has five degrees, numbered one to six excluding four.+--+-- > map scale_degrees [Pelog,Slendro] == [[1,2,3,4,5,6,7],[1,2,3,5,6]] scale_degrees :: Scale -> [Degree] scale_degrees s =     case s of       Pelog -> [1..7]       Slendro -> [1,2,3,5,6] +-- | Zero based index of scale degree, or Nothing.+-- -- > degree_index Slendro 4 == Nothing -- > degree_index Pelog 4 == Just 3 degree_index :: Scale -> Degree -> Maybe Int-degree_index s d = findIndex (== d) (scale_degrees s)+degree_index s d = elemIndex d (scale_degrees s)  -- * Tone set -tone_set_gamut :: Tone_Set -> Maybe (Pitch,Pitch)+tone_set_gamut :: Tone_Set t -> Maybe (Pitch,Pitch) tone_set_gamut g =     case mapMaybe (fmap note_pitch . tone_note) g of       [] -> Nothing       p -> Just (minimum p,maximum p) -tone_set_instrument :: Tone_Set -> (Instrument_Name,Maybe Scale) -> Tone_Set+tone_set_instrument :: Tone_Set t -> (Instrument_Name,Maybe Scale) -> Tone_Set t tone_set_instrument db (i,s) =     let f t = tone_class t == (i,s)     in filter f db
Music/Theory/Graph/Deacon_1934.hs view
@@ -6,25 +6,27 @@ -- Ireland, 64:129—175, 1934. module Music.Theory.Graph.Deacon_1934 where +import Data.Bifunctor {- base -} import Data.List {- base -} -import qualified Music.Theory.Array.Cell_Ref as T {- hmt -}+import qualified Music.Theory.Array.Cell_Ref as T {- hmt-base -}+import qualified Music.Theory.List as T {- hmt-base -}+import qualified Music.Theory.Tuple as T {- hmt-base -}+ import qualified Music.Theory.Array.Direction as T {- hmt -} import qualified Music.Theory.Graph.Dot as T {- hmt -}-import qualified Music.Theory.Graph.FGL as T {- hmt -}-import qualified Music.Theory.List as T {- hmt -}-import qualified Music.Theory.Tuple as T {- hmt -}+import qualified Music.Theory.Graph.Fgl as T {- hmt -} -gen_graph :: Ord v => [T.DOT_ATTR] -> T.GR_PP v e -> [T.EDGE_L v e] -> [String]-gen_graph opt pp es = T.g_to_udot opt pp (T.g_from_edges_l es)+gen_graph :: Ord v => [T.Dot_Attr] -> T.Graph_Pp v e -> [T.Edge_Lbl v e] -> [String]+gen_graph opt pp es = T.fgl_to_udot opt pp (T.g_from_edges_l es) -gen_graph_ul :: Ord v => [T.DOT_ATTR] -> (v -> String) -> [T.EDGE v] -> [String]-gen_graph_ul opt pp es = T.g_to_udot opt (T.gr_pp_lift_node_f pp) (T.g_from_edges es)+gen_graph_ul :: Ord v => [T.Dot_Attr] -> (v -> String) -> [T.Edge v] -> [String]+gen_graph_ul opt pp es = T.fgl_to_udot opt (T.gr_pp_label_v pp) (T.g_from_edges es) -gen_digraph :: Ord v => [T.DOT_ATTR] -> T.GR_PP v e -> [T.EDGE_L v e] -> [String]-gen_digraph opt pp es = T.g_to_dot T.G_DIGRAPH opt pp Nothing (T.g_from_edges_l es)+gen_digraph :: Ord v => [T.Dot_Attr] -> T.Graph_Pp v e -> [T.Edge_Lbl v e] -> [String]+gen_digraph opt pp es = T.fgl_to_dot T.Graph_Digraph opt pp (T.g_from_edges_l es) -type G = (T.GRAPH String,[T.DOT_ATTR],FilePath)+type G = ([T.Edge String],[T.Dot_Attr],FilePath)  -- * E g1 :: G@@ -66,7 +68,7 @@ g9 :: G g9 =     let d9' = ("E6",words "U R D LL (03/D6) U R R U L D D LL (11/C6) U R R U U R D L L D D LL (22/B6) U R R U U R R U L D D L L D D LL (38/A6) U R R U U R R U U R D L L D D L L D D LUU (56/A4) R R U U R R U L D D L L D D L UU (71/A3) R R U U R D L L D D L UU (83/A2) R R U L D D L UU (91/A1) R D L")-        d9 = (fst d9',filter T.is_direction (snd d9'))+        d9 = second (filter T.is_direction) d9'         c9 = T.dir_seq_to_cell_seq d9         o9 = [("node:shape","circle"),("edge:len","1.5"),("edge:fontsize","7")]     in (T.adj2 1 c9,o9,"F")@@ -74,7 +76,7 @@ g10 :: G g10 =     let d10' = ("B7",words "U R LL (03/A6) R R U L D D LUU (10/A5) R R U L D D L UU (18/A4) R R U L D D L UU (26/A3) R R U L D D L UU (34/A2) R R U L D D L UU (41/A1) R D L")-        d10 = (fst d10',filter T.is_direction (snd d10'))+        d10 = second (filter T.is_direction) d10'         c10 = T.dir_seq_to_cell_seq d10         e10 = T.adj2 1 c10         o10 = [("node:shape","circle"),("edge:len","1.5"),("edge:fontsize","7")]@@ -83,7 +85,7 @@ g11 :: G g11 =     let d11' = ("C3",words "DR DDL UUR U L (05/C3) DL DDR UUL U R (10/C3) D D U UL UUR DDL (16/B3) DL R U (18/B3) L DR R (21/C4) UR UUL DDR DR L (26/D4) U R DL L U (31/C3) U D (33/C3) R UUR DDDDD UUL L . (40/C4) L DDL UUUUU DDR R (44/C3)")-        d11 = (fst d11',filter T.is_direction (snd d11'))+        d11 = second (filter T.is_direction) d11'         c11 = T.dir_seq_to_cell_seq d11         e11 = T.adj2 1 c11         o11 = [("node:shape","circle"),("edge:len","1.5"),("edge:fontsize","7")]@@ -92,7 +94,7 @@ g12 :: G g12 =     let d12' = ("C2",words "DR UR (02/E2) L DL UL L (06/A2) DR UR UR DR (10/E2) L UL DL L (14/A2) UR DR (16/C2)")-        d12 = (fst d12',filter T.is_direction (snd d12'))+        d12 = second (filter T.is_direction) d12'         c12 = T.dir_seq_to_cell_seq d12         e12 = T.adj2 1 c12         o12 = [("node:shape","circle"),("edge:len","1.5"),("edge:fontsize","7")]@@ -101,7 +103,7 @@ g13 :: G g13 =     let d13' = ("B3",words "U D D U R DDL UUL R (07/C3) R UU DDL L UU DDR (11/C3)")-        d13 = (fst d13',filter T.is_direction (snd d13'))+        d13 = second (filter T.is_direction) d13'         c13 = T.dir_seq_to_cell_seq d13         e13 = T.adj2 1 c13         o13 = [("node:shape","circle"),("edge:len","1.5"),("edge:fontsize","7")]@@ -118,10 +120,10 @@   let mk_nm ty = "/home/rohan/sw/hmt/data/dot/deacon/" ++ nm ++ "_" ++ ty ++ ".dot"       wr_f ty g = writeFile (mk_nm ty) (unlines g)   wr_f "G" (gen_graph_ul o id e)-  wr_f "GL" (gen_graph o T.gr_pp_id_show (T.e_label_seq e))-  wr_f "GC" (gen_graph o T.gr_pp_id_br_csl (T.e_collate_normalised_l (T.e_label_seq e)))+  wr_f "GL" (gen_graph o (T.gr_pp_label id show) (T.e_label_seq e))+  wr_f "GC" (gen_graph o (T.gr_pp_label id T.br_csl_pp) (T.e_collate_normalised_l (T.e_label_seq e)))   wr_f "GF" (gen_graph_ul o id (nub (map T.t2_sort e)))-  wr_f "GD" (gen_digraph o T.gr_pp_id_br_csl (T.e_collate_normalised_l (T.e_label_seq e)))+  wr_f "GD" (gen_digraph o (T.gr_pp_label id T.br_csl_pp) (T.e_collate_normalised_l (T.e_label_seq e))) {-   let o' = ("graph:layout","fdp") : o   wr_f "GC_" (gen_graph o' T.gr_pp_id_br_csl (T.e_collate_normalised_l (T.e_label_seq e)))
Music/Theory/Graph/Dot.hs view
@@ -1,131 +1,213 @@ -- | Graph (dot) functions. module Music.Theory.Graph.Dot where +import Control.Monad {- base -} import Data.Char {- base -} import Data.List {- base -}+import System.FilePath {- filepath -}+import System.Process {- process -}  import qualified Data.Graph.Inductive.Graph as G {- fgl -}-import qualified Data.Graph.Inductive.PatriciaTree as G {- fgl -} -import qualified Music.Theory.List as T {- hmt -}+import qualified Music.Theory.Graph.Type as T {- hmt-base -}+import qualified Music.Theory.List as List {- hmt-base -}+import qualified Music.Theory.Show as Show {- hmt-base -} --- * UTIL+import qualified Music.Theory.Graph.Fgl as T {- hmt -} --- | Separate at element.+-- * Util++-- | Classify /s/ using a first element predicate, a remainder predicate and a unit predicate.+s_classify :: (t -> Bool) -> (t -> Bool) -> ([t] -> Bool) -> [t] -> Bool+s_classify p q r s =+  case s of+    c0:s' -> p c0 && all q s' && r s+    [] -> False++-- | Symbol rule. ----- > sep1 ':' "graph:layout"-sep1 :: Eq t => t -> [t] -> ([t],[t])-sep1 e l =-    case break (== e) l of-      (p,_:q) -> (p,q)-      _ -> error "sep1"+-- > map is_symbol ["sym","Sym2","3sym","1",""] == [True,True,False,False,False]+is_symbol :: String -> Bool+is_symbol = s_classify isAlpha isAlphaNum (const True) --- | Quote /s/ if it includes white space.+-- | Number rule. ----- > map maybe_quote ["abc","a b c"] == ["abc","\"a b c\""]+-- > map is_number ["123","123.45",".25","1.","1.2.3",""] == [True,True,False,True,False,False]+is_number :: String -> Bool+is_number = s_classify isDigit (\c -> isDigit c || c == '.') ((< 2) . length . filter ('.' ==))++-- | Quote /s/ if 'is_symbol' or 'is_number'.+--+-- > map maybe_quote ["abc","a b c","12","12.3"] == ["abc","\"a b c\"","12","12.3"] maybe_quote :: String -> String-maybe_quote s = if any isSpace s then concat ["\"",s,"\""] else s+maybe_quote s = if is_symbol s || is_number s then s else concat ["\"",s,"\""] --- | Left biased union of association lists /p/ and /q/.+-- * Attr/Key++type Dot_Key = String+type Dot_Value = String+type Dot_Attr = (Dot_Key,Dot_Value)++-- | Format 'Dot_Attr'.+dot_attr_pp :: Dot_Attr -> String+dot_attr_pp (lhs,rhs) = concat [lhs,"=",maybe_quote rhs]++-- | Format sequence of Dot_Attr. ----- > assoc_union [(5,"a"),(3,"b")] [(5,"A"),(7,"C")] == [(5,"a"),(3,"b"),(7,"C")]-assoc_union :: Eq k => [(k,v)] -> [(k,v)] -> [(k,v)]-assoc_union p q =-    let p_k = map fst p-        q' = filter ((`notElem` p_k) . fst) q-    in p ++ q'+-- > dot_attr_seq_pp [("layout","neato"),("epsilon","0.0001")]+dot_attr_seq_pp :: [Dot_Attr] -> String+dot_attr_seq_pp opt =+  if null opt+  then ""+  else concat ["[",intercalate "," (map dot_attr_pp opt),"]"] --- * ATTR+-- | Merge attributes, left-biased.+dot_attr_ext :: [Dot_Attr] -> [Dot_Attr] -> [Dot_Attr]+dot_attr_ext = List.assoc_merge --- | area:opt (area = graph|node|edge)-type DOT_KEY = String-type DOT_OPT = String-type DOT_VALUE = String-type DOT_ATTR = (DOT_OPT,DOT_VALUE)-type DOT_ATTR_SET = (String,[DOT_ATTR])+-- | graph|node|edge+type Dot_Type = String --- > dot_key_sep "graph:layout"-dot_key_sep :: String -> (String,String)-dot_key_sep = sep1 ':'+-- | (type,[attr])+type Dot_Attr_Set = (Dot_Type,[Dot_Attr]) -dot_attr_pp :: DOT_ATTR -> String-dot_attr_pp (lhs,rhs) = concat [lhs,"=",maybe_quote rhs]+-- | Format Dot_Attr_Set.+--+-- > a = ("graph",[("layout","neato"),("epsilon","0.0001")])+-- > dot_attr_set_pp a == "graph [layout=neato,epsilon=0.0001]"+dot_attr_set_pp :: Dot_Attr_Set -> String+dot_attr_set_pp (ty,opt) = concat [ty," ",dot_attr_seq_pp opt] -dot_attr_set_pp :: DOT_ATTR_SET -> String-dot_attr_set_pp (ty,opt) = concat [ty," [",intercalate "," (map dot_attr_pp opt),"];"]+-- | type:attr (type = graph|node|edge)+type Dot_Meta_Key = String -dot_attr_collate :: [DOT_ATTR] -> [DOT_ATTR_SET]+type Dot_Meta_Attr = (Dot_Meta_Key,Dot_Value)++-- | Keys are given as "type:attr".+--+-- > dot_key_sep "graph:layout" == ("graph","layout")+dot_key_sep :: Dot_Meta_Key -> (Dot_Type,Dot_Key)+dot_key_sep = List.split_on_1_err ":"++-- | Collate Dot_Key attribute set to Dot_Attr_Set.+dot_attr_collate :: [Dot_Meta_Attr] -> [Dot_Attr_Set] dot_attr_collate opt =     let f (k,v) = let (ty,nm) = dot_key_sep k in (ty,(nm,v))         c = map f opt-    in T.collate c+    in List.collate c -dot_attr_ext :: [DOT_ATTR] -> [DOT_ATTR] -> [DOT_ATTR]-dot_attr_ext = assoc_union+-- | Default values for default meta-keys.+--+-- > k = dot_attr_def ("neato","century schoolbook",10,"plaintext")+-- > map dot_attr_set_pp (dot_attr_collate k)+dot_attr_def :: (String,String,Double,String) -> [Dot_Meta_Attr]+dot_attr_def (ly,fn,fs,sh) =+    [("graph:layout",ly)+    ,("node:fontname",fn)+    ,("node:fontsize",show fs)+    ,("node:shape",sh)] --- > map dot_attr_set_pp (dot_attr_collate dot_attr_def)-dot_attr_def :: [DOT_ATTR]-dot_attr_def =-    [("graph:layout","neato")-    ,("graph:epsilon","0.000001")-    ,("node:shape","plaintext")-    ,("node:fontsize","10")-    ,("node:fontname","century schoolbook")]+-- * Graph --- * GRAPH+-- | Graph pretty-printer, (v -> [attr],e -> [attr])+type Graph_Pp v e = ((Int,v) -> [Dot_Attr],((Int,Int),e) -> [Dot_Attr]) --- | Graph pretty-printer, (node->shape,node->label,edge->label)-type GR_PP v e = (v -> Maybe String,v -> Maybe String,e -> Maybe String)+-- | Make Graph_Pp value given label functions for vertices and edges.+gr_pp_label_m :: Maybe (v -> Dot_Value) -> Maybe (e -> Dot_Value) -> Graph_Pp v e+gr_pp_label_m f_v f_e =+  let lift m (_,x) = case m of+                       Nothing -> []+                       Just f -> [("label",f x)]+  in (lift f_v,lift f_e) -gr_pp_lift_node_f :: (v -> String) -> GR_PP v e-gr_pp_lift_node_f f = (const Nothing, Just . f, const Nothing)+-- | Label V & E.+gr_pp_label :: (v -> Dot_Value) -> (e -> Dot_Value) -> Graph_Pp v e+gr_pp_label f_v f_e = gr_pp_label_m (Just f_v) (Just f_e) -gr_pp_id_show :: Show e => GR_PP String e-gr_pp_id_show = (const Nothing,Just . id,Just . show)+-- | Label V only.+gr_pp_label_v :: (v -> Dot_Value) -> Graph_Pp v e+gr_pp_label_v f = gr_pp_label_m (Just f) Nothing  -- | br = brace, csl = comma separated list br_csl_pp :: Show t => [t] -> String br_csl_pp l =     case l of       [e] -> show e-      _ -> T.bracket ('{','}') (intercalate "," (map show l))--gr_pp_id_br_csl :: Show e => GR_PP String [e]-gr_pp_id_br_csl = (const Nothing,Just . id,Just . br_csl_pp)+      _ -> List.bracket ('{','}') (intercalate "," (map show l))  -- | Graph type, directed or un-directed.-data G_TYPE = G_DIGRAPH | G_UGRAPH+data Graph_Type = Graph_Digraph | Graph_Ugraph -g_type_to_string :: G_TYPE -> String+g_type_to_string :: Graph_Type -> String g_type_to_string ty =     case ty of-      G_DIGRAPH -> "digraph"-      G_UGRAPH -> "graph"+      Graph_Digraph -> "digraph"+      Graph_Ugraph -> "graph" -g_type_to_edge_symbol :: G_TYPE -> String+g_type_to_edge_symbol :: Graph_Type -> String g_type_to_edge_symbol ty =     case ty of-      G_DIGRAPH -> " -> "-      G_UGRAPH -> " -- "+      Graph_Digraph -> " -> "+      Graph_Ugraph -> " -- " +-- | Generate node position attribute given (x,y) coordinate.+node_pos_attr :: (Show n, Real n) => (n,n) -> Dot_Attr+node_pos_attr (x,y) = let pp = Show.real_pp_trunc 2 in ("pos",concat [pp x,",",pp y])++-- | Edge POS attributes are sets of cubic bezier control points.+edge_pos_attr :: Real t => [(t,t)] -> Dot_Attr+edge_pos_attr pt =+  let r_pp = Show.real_pp_trunc 2+      pt_pp (x,y) = concat [r_pp x,",",r_pp y]+  in ("pos",unwords (map pt_pp pt))++-- | Variant that accepts single cubic bezier data set.+edge_pos_attr_1 :: Real t => ((t,t),(t,t),(t,t),(t,t)) -> Dot_Attr+edge_pos_attr_1 (p1,p2,p3,p4) = edge_pos_attr [p1,p2,p3,p4]++{- -- | Vertex position function. type POS_FN v = (v -> (Int,Int)) -g_to_dot :: G_TYPE -> [DOT_ATTR] -> GR_PP v e -> Maybe (POS_FN v) -> G.Gr v e -> [String]-g_to_dot g_typ opt (n_sh,n_pp,e_pp) pos_f gr =-    let p_f (c,r) = concat [",pos=\"",show (c * 100),",",show (r * 100),"\""]-        l_f p x = concat [" [label=\"",x,"\"",p,"]"]-        n_f (k,n) = let p = maybe "" (\f -> p_f (f n)) pos_f-                        p' = maybe p (\z -> p ++ ",shape=\"" ++ z ++ "\"") (n_sh n)-                        a = maybe "" (l_f p') (n_pp n)-                    in concat [show k,a,";"]-        e_f (lhs,rhs,e) = let l = maybe "" (l_f "") (e_pp e)-                          in concat [show lhs,g_type_to_edge_symbol g_typ,show rhs,l,";"]+g_lift_pos_fn :: (v -> (Int,Int)) -> v -> [Dot_Attr]+g_lift_pos_fn f v = let (c,r) = f v in [node_pos_attr (c * 100,r * 100)]+-}++lbl_to_dot :: Graph_Type -> [Dot_Meta_Attr] -> Graph_Pp v e -> T.Lbl v e -> [String]+lbl_to_dot g_typ opt (v_attr,e_attr) (v,e) =+    let ws s = if null s then "" else " " ++ s+        v_f (k,lbl) = concat [show k,ws (dot_attr_seq_pp (v_attr (k,lbl))),";"]+        e_f ((lhs,rhs),lbl) = concat [show lhs,g_type_to_edge_symbol g_typ,show rhs+                                     ,ws (dot_attr_seq_pp (e_attr ((lhs,rhs),lbl))),";"]     in concat [[g_type_to_string g_typ," g {"]-              ,map dot_attr_set_pp (dot_attr_collate (assoc_union opt dot_attr_def))-              ,map n_f (G.labNodes gr)-              ,map e_f (G.labEdges gr)+              ,map dot_attr_set_pp (dot_attr_collate opt)+              ,map v_f v+              ,map e_f e               ,["}"]] -g_to_udot :: [DOT_ATTR] -> GR_PP v e -> G.Gr v e -> [String]-g_to_udot o pp = g_to_dot G_UGRAPH o pp Nothing+lbl_to_udot :: [Dot_Meta_Attr] -> Graph_Pp v e -> T.Lbl v e -> [String]+lbl_to_udot = lbl_to_dot Graph_Ugraph++-- | 'writeFile' of 'lbl_to_udot'+lbl_to_udot_wr :: FilePath -> [Dot_Meta_Attr] -> Graph_Pp v e -> T.Lbl v e -> IO ()+lbl_to_udot_wr fn o pp  = writeFile fn . unlines . lbl_to_udot o pp++fgl_to_dot :: G.Graph gr => Graph_Type -> [Dot_Meta_Attr] -> Graph_Pp v e -> gr v e -> [String]+fgl_to_dot typ opt pp gr = lbl_to_dot typ opt pp (T.fgl_to_lbl gr)++fgl_to_udot :: G.Graph gr => [Dot_Meta_Attr] -> Graph_Pp v e -> gr v e -> [String]+fgl_to_udot opt pp gr = lbl_to_udot opt pp (T.fgl_to_lbl gr)++-- * Dot-Process++{- | Run /dot/ to generate a file type based on the output file extension (ie. .svg, .png, .jpeg, .gif)+     /-n/ must be given to not run the layout algorithm and to use position data in the /dot/ file.+-}+dot_to_ext :: [String] -> FilePath -> FilePath -> IO ()+dot_to_ext opt dot_fn ext_fn =+  let arg = opt ++ ["-T",tail (takeExtension ext_fn),"-o",ext_fn,dot_fn]+  in void (rawSystem "dot" arg)++-- | 'dot_to_ext' generating .svg filename by replacing .dot extension with .svg+dot_to_svg :: [String] -> FilePath -> IO ()+dot_to_svg opt dot_fn = dot_to_ext opt dot_fn (replaceExtension dot_fn "svg")
− Music/Theory/Graph/FGL.hs 
@@ -1,141 +0,0 @@--- | Graph (fgl) functions.-module Music.Theory.Graph.FGL where--import Data.List {- base -}-import Data.Maybe {- base -}--import qualified Data.Map as M {- containers -}--import qualified Data.Graph.Inductive.Graph as G {- fgl -}-import qualified Data.Graph.Inductive.Query as G {- fgl -}-import qualified Data.Graph.Inductive.PatriciaTree as G {- fgl -}--import qualified Control.Monad.Logic as L {- logict -}--import qualified Music.Theory.List as T {- hmt -}---- | Synonym for 'G.noNodes'.-g_degree :: G.Gr v e -> Int-g_degree = G.noNodes---- | 'G.subgraph' of each of 'G.components'.-g_partition :: G.Gr v e -> [G.Gr v e]-g_partition gr = map (\n -> G.subgraph n gr) (G.components gr)---- | Find first 'G.Node' with given label.-g_node_lookup :: (Eq v,G.Graph gr) => gr v e -> v -> Maybe G.Node-g_node_lookup gr l = fmap fst (find ((== l) . snd) (G.labNodes gr))---- | Erroring variant.-g_node_lookup_err :: (Eq v,G.Graph gr) => gr v e -> v -> G.Node-g_node_lookup_err gr = fromMaybe (error "g_node_lookup") . g_node_lookup gr---- | Set of nodes with given labels, plus all neighbours of these nodes.--- (impl = implications)-ug_node_set_impl :: (Eq v,G.DynGraph gr) => gr v e -> [v] -> [G.Node]-ug_node_set_impl gr nl =-    let n = map (g_node_lookup_err gr) nl-    in nub (sort (n ++ concatMap (G.neighbors gr) n))---- * Hamiltonian--type G_NODE_SEL_F v e = G.Gr v e -> G.Node -> [G.Node]---- | 'L.msum' '.' 'map' 'return'.-ml_from_list :: L.MonadLogic m => [t] -> m t-ml_from_list = L.msum . map return---- | Use /sel_f/ of 'G.pre' for directed graphs and 'G.neighbors' for undirected.-g_hamiltonian_path_ml :: L.MonadLogic m => G_NODE_SEL_F v e -> G.Gr v e -> G.Node -> m [G.Node]-g_hamiltonian_path_ml sel_f gr =-    let n_deg = g_degree gr-        recur r c =-            if length r == n_deg - 1-            then return (c:r)-            else do i <- ml_from_list (sel_f gr c)-                    L.guard (i `notElem` r)-                    recur (c:r) i-    in recur []---- > map (L.observeAll . ug_hamiltonian_path_ml_0) (g_partition gr)-ug_hamiltonian_path_ml_0 :: L.MonadLogic m => G.Gr v e -> m [G.Node]-ug_hamiltonian_path_ml_0 gr = g_hamiltonian_path_ml G.neighbors gr (G.nodes gr !! 0)---- * G (from edges)---- | Edge, no label.-type EDGE v = (v,v)---- | Graph as set of edges.-type GRAPH v = [EDGE v]---- | Edge, with label.-type EDGE_L v l = (EDGE v,l)---- | Graph as set of labeled edges.-type GRAPH_L v l = [EDGE_L v l]---- | Generate a graph given a set of labelled edges.-g_from_edges_l :: (Eq v,Ord v) => GRAPH_L v e -> G.Gr v e-g_from_edges_l e =-    let n = nub (concatMap (\((lhs,rhs),_) -> [lhs,rhs]) e)-        n_deg = length n-        n_id = [0 .. n_deg - 1]-        m = M.fromList (zip n n_id)-        m_get k = M.findWithDefault (error "g_from_edges: m_get") k m-        e' = map (\((lhs,rhs),label) -> (m_get lhs,m_get rhs,label)) e-    in G.mkGraph (zip n_id n) e'---- | Variant that supplies '()' as the (constant) edge label.------ > let g = G.mkGraph [(0,'a'),(1,'b'),(2,'c')] [(0,1,()),(1,2,())]--- > in g_from_edges_ul [('a','b'),('b','c')] == g-g_from_edges :: Ord v => GRAPH v -> G.Gr v ()-g_from_edges = let f e = (e,()) in g_from_edges_l . map f---- * Edges---- | Label sequence of edges starting at one.-e_label_seq :: [EDGE v] -> [EDGE_L v Int]-e_label_seq = map (\(k,e) -> (e,k)) . zip [1..]---- | Normalised undirected labeled edge (ie. order nodes).-e_normalise_l :: Ord v => EDGE_L v l -> EDGE_L v l-e_normalise_l ((p,q),r) = ((min p q,max p q),r)---- | Collate labels for edges that are otherwise equal.-e_collate_l :: Ord v => [EDGE_L v l] -> [EDGE_L v [l]]-e_collate_l = T.collate---- | 'e_collate_l' of 'e_normalise_l'.-e_collate_normalised_l :: Ord v => [EDGE_L v l] -> [EDGE_L v [l]]-e_collate_normalised_l = e_collate_l . map e_normalise_l---- | Apply predicate to universe of possible edges.-e_univ_select_edges :: (t -> t -> Bool) -> [t] -> [EDGE t]-e_univ_select_edges f l = [(p,q) | p <- l, q <- l, f p q]---- | Consider only edges (p,q) where p < q.-e_univ_select_u_edges :: Ord t => (t -> t -> Bool) -> [t] -> [EDGE t]-e_univ_select_u_edges f = let g p q = p < q && f p q in e_univ_select_edges g---- | Sequence of connected vertices to edges.------ > e_path_to_edges "abcd" == [('a','b'),('b','c'),('c','d')]-e_path_to_edges :: [t] -> [EDGE t]-e_path_to_edges = T.adj2 1---- | Undirected edge equality.-e_undirected_eq :: Eq t => EDGE t -> EDGE t -> Bool-e_undirected_eq (a,b) (c,d) = (a == c && b == d) || (a == d && b == c)--elem_by :: (p -> q -> Bool) -> p -> [q] -> Bool-elem_by f = any . f---- | Is the sequence of vertices a path at the graph, ie. are all--- adjacencies in the sequence edges.-e_is_path :: Eq t => GRAPH t -> [t] -> Bool-e_is_path e sq =-    case sq of-      p:q:sq' -> elem_by e_undirected_eq (p,q) e && e_is_path e (q:sq')-      _ -> True
+ Music/Theory/Graph/Fgl.hs view
@@ -0,0 +1,175 @@+-- | Graph (fgl) functions.+module Music.Theory.Graph.Fgl where++import Control.Monad {- base -}+import Data.List {- base -}+import Data.Maybe {- base -}++import qualified Data.Map as M {- containers -}++import qualified Data.Graph.Inductive.Graph as G {- fgl -}+import qualified Data.Graph.Inductive.Query as G {- fgl -}+import qualified Data.Graph.Inductive.PatriciaTree as G {- fgl -}++import qualified Control.Monad.Logic as L {- logict -}++import qualified Music.Theory.Graph.Type as T {- hmt -}+import qualified Music.Theory.List as T {- hmt -}++-- | 'T.Lbl' to FGL graph+lbl_to_fgl :: G.Graph gr => T.Lbl v e -> gr v e+lbl_to_fgl (v,e) = let f ((i,j),k) = (i,j,k) in G.mkGraph v (map f e)++-- | Type-specialised.+lbl_to_fgl_gr :: T.Lbl v e -> G.Gr v e+lbl_to_fgl_gr = lbl_to_fgl++-- | FGL graph to 'T.Lbl'+fgl_to_lbl :: G.Graph gr => gr v e -> T.Lbl v e+fgl_to_lbl gr = (G.labNodes gr,map (\(i,j,k) -> ((i,j),k)) (G.labEdges gr))++-- | Synonym for 'G.noNodes'.+g_degree :: G.Gr v e -> Int+g_degree = G.noNodes++-- | 'G.subgraph' of each of 'G.components'.+g_partition :: G.Gr v e -> [G.Gr v e]+g_partition gr = map (`G.subgraph` gr) (G.components gr)++-- | Find first 'G.Node' with given label.+g_node_lookup :: (Eq v,G.Graph gr) => gr v e -> v -> Maybe G.Node+g_node_lookup gr l = fmap fst (find ((== l) . snd) (G.labNodes gr))++-- | Erroring variant.+g_node_lookup_err :: (Eq v,G.Graph gr) => gr v e -> v -> G.Node+g_node_lookup_err gr = fromMaybe (error "g_node_lookup") . g_node_lookup gr++-- | Set of nodes with given labels, plus all neighbours of these nodes.+-- (impl = implications)+ug_node_set_impl :: (Eq v,G.DynGraph gr) => gr v e -> [v] -> [G.Node]+ug_node_set_impl gr nl =+    let n = map (g_node_lookup_err gr) nl+    in nub (sort (n ++ concatMap (G.neighbors gr) n))++-- * Hamiltonian++-- | Node select function, ie. given a graph /g/ and a node /n/ select a set of related nodes from /g/+type G_Node_Sel_f v e = G.Gr v e -> G.Node -> [G.Node]++-- | 'msum' '.' 'map' 'return'.+ml_from_list :: MonadPlus m => [t] -> m t+ml_from_list = msum . map return++-- | Use /sel_f/ of 'G.pre' for directed graphs and 'G.neighbors' for undirected.+g_hamiltonian_path_ml :: (MonadPlus m, L.MonadLogic m) => G_Node_Sel_f v e -> G.Gr v e -> G.Node -> m [G.Node]+g_hamiltonian_path_ml sel_f gr =+    let n_deg = g_degree gr+        recur r c =+            if length r == n_deg - 1+            then return (c:r)+            else do i <- ml_from_list (sel_f gr c)+                    guard (i `notElem` r)+                    recur (c:r) i+    in recur []++-- | 'g_hamiltonian_path_ml' of 'G.neighbors' starting at first node.+--+-- > map (L.observeAll . ug_hamiltonian_path_ml_0) (g_partition gr)+ug_hamiltonian_path_ml_0 :: (MonadPlus m, L.MonadLogic m) => G.Gr v e -> m [G.Node]+ug_hamiltonian_path_ml_0 gr = g_hamiltonian_path_ml G.neighbors gr (G.nodes gr !! 0)++-- * G (from edges)++-- | Edge, no label.+type Edge v = (v,v)++-- | Edge, with label.+type Edge_Lbl v l = (Edge v,l)++-- | Generate a graph given a set of labelled edges.+g_from_edges_l :: (Eq v,Ord v) => [Edge_Lbl v e] -> G.Gr v e+g_from_edges_l e =+    let n = nub (concatMap (\((lhs,rhs),_) -> [lhs,rhs]) e)+        n_deg = length n+        n_id = [0 .. n_deg - 1]+        m = M.fromList (zip n n_id)+        m_get k = M.findWithDefault (error "g_from_edges: m_get") k m+        e' = map (\((lhs,rhs),label) -> (m_get lhs,m_get rhs,label)) e+    in G.mkGraph (zip n_id n) e'++-- | Variant that supplies '()' as the (constant) edge label.+--+-- > let g = G.mkGraph [(0,'a'),(1,'b'),(2,'c')] [(0,1,()),(1,2,())]+-- > in g_from_edges_ul [('a','b'),('b','c')] == g+g_from_edges :: Ord v => [Edge v] -> G.Gr v ()+g_from_edges = let f e = (e,()) in g_from_edges_l . map f++-- * Edges++-- | Label sequence of edges starting at one.+e_label_seq :: [Edge v] -> [Edge_Lbl v Int]+e_label_seq = zipWith (\k e -> (e,k)) [1..]++-- | Normalised undirected labeled edge (ie. order nodes).+e_normalise_l :: Ord v => Edge_Lbl v l -> Edge_Lbl v l+e_normalise_l ((p,q),r) = ((min p q,max p q),r)++-- | Collate labels for edges that are otherwise equal.+e_collate_l :: Ord v => [Edge_Lbl v l] -> [Edge_Lbl v [l]]+e_collate_l = T.collate++-- | 'e_collate_l' of 'e_normalise_l'.+e_collate_normalised_l :: Ord v => [Edge_Lbl v l] -> [Edge_Lbl v [l]]+e_collate_normalised_l = e_collate_l . map e_normalise_l++-- | Apply predicate to universe of possible edges.+e_univ_select_edges :: (t -> t -> Bool) -> [t] -> [Edge t]+e_univ_select_edges f l = [(p,q) | p <- l, q <- l, f p q]++-- | Consider only edges (p,q) where p < q.+e_univ_select_u_edges :: Ord t => (t -> t -> Bool) -> [t] -> [Edge t]+e_univ_select_u_edges f = let g p q = p < q && f p q in e_univ_select_edges g++-- | Sequence of connected vertices to edges.+--+-- > e_path_to_edges "abcd" == [('a','b'),('b','c'),('c','d')]+e_path_to_edges :: [t] -> [Edge t]+e_path_to_edges = T.adj2 1++-- | Undirected edge equality.+e_undirected_eq :: Eq t => Edge t -> Edge t -> Bool+e_undirected_eq (a,b) (c,d) = (a == c && b == d) || (a == d && b == c)++-- | /any/ of /f/.+elem_by :: (p -> q -> Bool) -> p -> [q] -> Bool+elem_by f = any . f++-- | Is the sequence of vertices a path at the graph, ie. are all+-- adjacencies in the sequence edges.+e_is_path :: Eq t => [Edge t] -> [t] -> Bool+e_is_path e sq =+    case sq of+      p:q:sq' -> elem_by e_undirected_eq (p,q) e && e_is_path e (q:sq')+      _ -> True++-- * Analysis++-- | <https://github.com/ivan-m/Graphalyze/blob/master/Data/Graph/Analysis/Algorithms/Common.hs>+--   Graphalyze has pandoc as a dependency...+pathTree             :: (G.DynGraph g) => G.Decomp g a b -> [[G.Node]]+pathTree (Nothing,_) = []+pathTree (Just ct,g)+    | G.isEmpty g = []+    | null sucs = [[n]]+    | otherwise = (:) [n] . map (n:) . concatMap (subPathTree g') $ sucs+    where+      n = G.node' ct+      sucs = G.suc' ct+      ct' = makeLeaf ct+      g' = ct' G.& g+      subPathTree gr n' = pathTree $ G.match n' gr++-- | Remove all outgoing edges+makeLeaf           :: G.Context a b -> G.Context a b+makeLeaf (p,n,a,_) = (p', n, a, [])+    where p' = filter (\(_,n') -> n' /= n) p
Music/Theory/Graph/Johnson_2014.hs view
@@ -2,26 +2,34 @@ module Music.Theory.Graph.Johnson_2014 where  import Control.Monad {- base -}+import Data.Int {- base -} import Data.List {- base -}-import qualified Data.Map as M {- containers -} import Data.Maybe {- base -} -import qualified Music.Theory.Combinations as T {- hmt -}+import qualified Control.Monad.Logic as L {- logict -}+import qualified Data.Map as M {- containers -}+import qualified Data.Graph.Inductive as G {- fgl -}+--import qualified Data.Graph.Inductive.PatriciaTree as G {- fgl -}++import qualified Music.Theory.Combinations as T {- hmt-base -}+import qualified Music.Theory.List as T {- hmt-base -}+import qualified Music.Theory.Tuple as T {- hmt-base -}+ import qualified Music.Theory.Graph.Dot as T {- hmt -}-import qualified Music.Theory.Graph.FGL as T {- hmt -}+import qualified Music.Theory.Graph.Fgl as T {- hmt -} import qualified Music.Theory.Key as T {- hmt -}-import qualified Music.Theory.List as T {- hmt -} import qualified Music.Theory.Pitch.Note as T {- hmt -}+import qualified Music.Theory.Set.List as T {- hmt -} import qualified Music.Theory.Tuning as T {- hmt -}-import qualified Music.Theory.Tuning.Euler as T {- hmt -}-import qualified Music.Theory.Z.SRO as T {- hmt -}+import qualified Music.Theory.Tuning.Graph.Euler as T {- hmt -}+import qualified Music.Theory.Z as T {- hmt -}+import qualified Music.Theory.Z.Forte_1973 as T {- hmt -}+import qualified Music.Theory.Z.Tto as T {- hmt -}+import qualified Music.Theory.Z.Sro as T {- hmt -}  -- * Common -type Z12 = Int--mod12 :: Integral a => a -> a-mod12 n = n `mod` 12+type Z12 = Int8  dif :: Num a => (a, a) -> a dif = uncurry (-)@@ -67,7 +75,7 @@ -- > min_vl [6,11,13] [6,10,14] == 2 min_vl :: (Num a,Ord a) => [a] -> [a] -> a min_vl p q =-    let f x = sum (map absdif (zip p x))+    let f x = sum (zipWith (curry absdif) p x)     in minimum (map f (permutations q))  min_vl_of :: (Num a, Ord a) => a -> [a] -> [a] -> Bool@@ -82,6 +90,12 @@ set_pp :: Show t => [t] -> String set_pp = intercalate "," . map show +tto_rel_to :: Integral t => T.Z t -> [t] -> [t] -> [T.Tto t]+tto_rel_to z p q = T.z_tto_rel 5 z (T.set p) (T.set q)++set_pp_tto_rel :: (Integral t, Show t) => T.Z t -> [t] -> [t] -> String+set_pp_tto_rel z p = intercalate "," . map T.tto_pp . tto_rel_to z p+ -- * Map  m_get :: Ord k => M.Map k v -> k -> v@@ -91,20 +105,78 @@ m_doi_of :: M.Map Int [Z12] -> Int -> Int -> Int -> Bool m_doi_of m n p q = doi_of n (m_get m p) (m_get m q) +-- * Edge++-- | Add /k/ as prefix to both left and right hand sides of edge.+e_add_id :: k -> [(t,u)] -> [((k,t),(k,u))]+e_add_id k = map (\(lhs,rhs) -> ((k,lhs),(k,rhs)))++gen_edges :: (t -> t -> Bool) -> [t] -> [(t,t)]+gen_edges f l = [(p,q) | p <- l, q <- l, f p q]++gen_u_edges :: Ord a => (a -> a -> Bool) -> [a] -> [(a, a)]+gen_u_edges = T.e_univ_select_u_edges+ -- * Graph -gen_graph_ul :: Ord v => [T.DOT_ATTR] -> (v -> String) -> [T.EDGE v] -> [String]-gen_graph_ul opt pp es = T.g_to_udot opt (T.gr_pp_lift_node_f pp) (T.g_from_edges es)+oh_def_opt :: [T.Dot_Meta_Attr]+oh_def_opt =+  [("graph:layout","neato")+  ,("graph:epsilon","0.000001")+  ,("node:shape","plaintext")+  ,("node:fontsize","10")+  ,("node:fontname","century schoolbook")] -gen_graph_ul_ty :: Ord v => String -> (v -> String) -> [T.EDGE v] -> [String]+gen_graph :: Ord v => [T.Dot_Meta_Attr] -> T.Graph_Pp v e -> [T.Edge_Lbl v e] -> [String]+gen_graph opt pp es = T.fgl_to_udot (oh_def_opt ++ opt) pp (T.g_from_edges_l es)++gen_graph_ul :: Ord v => [T.Dot_Meta_Attr] -> (v -> String) -> [T.Edge v] -> [String]+gen_graph_ul opt pp es = T.fgl_to_udot (oh_def_opt ++ opt) (T.gr_pp_label_v pp) (T.g_from_edges es)++gen_graph_ul_ty :: Ord v => String -> (v -> String) -> [T.Edge v] -> [String] gen_graph_ul_ty ty = gen_graph_ul [("graph:layout",ty)] -gen_flt_graph :: (Ord t, Show t) => [T.DOT_ATTR] -> ([t] -> [t] -> Bool) -> [[t]] -> [String]-gen_flt_graph o f p = gen_graph_ul o set_pp (T.e_univ_select_u_edges f p)+gen_flt_graph_pp :: Ord t => [T.Dot_Meta_Attr] -> ([t] -> String) -> ([t] -> [t] -> Bool) -> [[t]] -> [String]+gen_flt_graph_pp opt pp f p = gen_graph_ul opt pp (gen_u_edges f p) +gen_flt_graph :: (Ord t, Show t) => [T.Dot_Meta_Attr] -> ([t] -> [t] -> Bool) -> [[t]] -> [String]+gen_flt_graph opt = gen_flt_graph_pp opt set_pp+ -- * P.12 --- | <http://localhost/rd/?t=j&e=2016-04-04.md>+-- > circ_5 12 0 == [0,7,2,9,4,11,6,1,8,3,10,5]+circ_5 :: Integral a => Int -> a -> [a]+circ_5 l n = take l (iterate (T.z_mod T.z12 . (+ 7)) (T.z_mod T.z12 n))++all_pairs :: [t] -> [u] -> [(t,u)]+all_pairs x y = [(p,q) | p <- x, q <- y]++adj :: [t] -> [(t,t)]+adj = T.adj2 1++adj_cyc :: [t] -> [(t,t)]+adj_cyc = T.adj2_cyclic 1++p12_c5_eset :: [(Int,Int)]+p12_c5_eset =+    let l1 = circ_5 4 9 -- [9,4,11,6]+        l2 = circ_5 5 10 -- [10,5,0,7,2]+        l3 = circ_5 3 1 -- [1,8,3]+        align p q = filter ((== 4) . T.z_mod T.z12 . dif) (all_pairs p q)+    in concatMap adj [l1,l2,l3] ++ align l1 l2 ++ align l2 l3++e_add_label :: (T.Edge v -> l) -> [T.Edge v] -> [T.Edge_Lbl v l]+e_add_label f = let g (p,q) = ((p,q),f (p,q)) in map g++p12_c5_gr :: [String]+p12_c5_gr =+    let o = [("graph:start","187623")+            ,("node:fontsize","10")+            ,("edge:fontsize","9")]+        e_l = e_add_label (i_to_ic . absdif) p12_c5_eset+    in gen_graph o (\(_,v) -> [("label",T.pc_pp v)],\(_,e) -> [("label",show e)]) e_l++-- > T.euler_plane_r p12_euler_plane == [1/1,16/15,9/8,6/5,5/4,4/3,45/32,3/2,8/5,5/3,16/9,15/8] p12_euler_plane :: T.Euler_Plane Rational p12_euler_plane =     let f = T.fold_ratio_to_octave_err@@ -119,36 +191,90 @@  -- * P.14 +p14_eset :: ([(Int, Int)], [(Int, Int)], [(Int, Int)])+p14_eset =+  let univ = [0 .. 11]+      trs n = map (T.z_mod T.z12 . (+ n))+      e_par = zip univ univ+      e_rel = zip univ (trs 9 univ)+      e_med = zip univ (trs 4 univ)+  in (e_par,e_rel,e_med)++p14_mk_e :: [(Int, Int)] -> [(T.Key,T.Key)]+p14_mk_e =+  let pc_to_key m pc = let (n,a) = fromMaybe (error "p14_mk_e?") (T.pc_to_note_alteration_ks pc) in (n,a,m)+      e_lift (lhs,rhs) = (pc_to_key T.Major_Mode lhs,pc_to_key T.Minor_Mode rhs)+  in map e_lift++p14_edges_u :: [(T.Key,T.Key)]+p14_edges_u =+  let (e_par,e_rel,e_med) = p14_eset+  in p14_mk_e (concat [e_par,e_rel,e_med])+ p14_edges :: [(T.Key,T.Key)] p14_edges =-    let univ = [0::Int .. 11]-        trs n = map (mod12 . (+ n))-        e_par = zip univ univ-        e_rel = zip univ (trs 9 univ)-        e_med = zip univ (trs 4 univ)-        del_par = [10]-        del_rel = [5,6]-        del_med = [2,5,8,11]-        rem_set r = filter (\(lhs,_) -> lhs `notElem` r)-        pc_to_key m pc = let Just (n,a) = T.pc_to_note_alteration_ks pc in (n,a,m)-        e_lift (lhs,rhs) = (pc_to_key T.Major_Mode lhs,pc_to_key T.Minor_Mode rhs)-        e_mod = concat [rem_set del_par e_par,rem_set del_rel e_rel,rem_set del_med e_med]-    in map e_lift e_mod+  let (e_par,e_rel,e_med) = p14_eset+      del_par = [10]+      del_rel = [5,6]+      del_med = [2,5,8,11]+      rem_set r = filter (\(lhs,_) -> lhs `notElem` r)+      e_mod = concat [rem_set del_par e_par,rem_set del_rel e_rel,rem_set del_med e_med]+  in p14_mk_e e_mod +p14_mk_gr :: [T.Dot_Meta_Attr] -> [T.Edge T.Key] -> [String]+p14_mk_gr opt e =+    let opt' = ("graph:start","168732") : opt+        pp = T.gr_pp_label_v T.key_lc_uc_pp+        gr = T.g_from_edges e+    in T.fgl_to_udot opt' pp gr++p14_gr_u :: [String]+p14_gr_u =+  p14_mk_gr+  [("edge:len","1.5")+  ,("edge:fontsize","6")+  ,("node:shape","box")+  ,("node:fontsize","10")+  ,("node:fontname","century schoolbook")]+  p14_edges_u+ p14_gr :: [String]-p14_gr =-    let opt = [("graph:start","168732")]-        pp = T.gr_pp_lift_node_f T.key_lc_uc_pp-        gr = T.g_from_edges p14_edges-    in T.g_to_udot opt pp gr+p14_gr = p14_mk_gr [] p14_edges +p14_gen_tonnetz_n :: Int -> [Int] -> [Int] -> [Int]+p14_gen_tonnetz_n n k x =+  let gen_neighbours_n l z = map (+ z) l ++ map (z -) l+  in if n == 0+     then x+     else let r = nub (x ++ concatMap (gen_neighbours_n k) x)+          in p14_gen_tonnetz_n (n - 1) k r++p14_gen_tonnetz_e :: Int -> [Int] -> [Int] -> [((Int, Int), Int)]+p14_gen_tonnetz_e n k =+    let gen_e x y = ((min x y,max x y),abs (x - y))+        gen_e_n d_set x y = if abs (x - y) `elem` d_set then Just (gen_e x y) else Nothing+        f [p,q] = gen_e_n k p q+        f _ = error "p14_gen_tonnetz_e"+    in mapMaybe f . T.combinations 2 . p14_gen_tonnetz_n n k++-- Neo-Riemannian Tonnettz+p14_nrt_gr :: [String]+p14_nrt_gr =+  let e = p14_gen_tonnetz_e 3 [7,9,16] [48]+      o = [("node:shape","circle")+          ,("node:fontsize","10")+          ,("node:fontname","century schoolbook")+          ,("edge:len","1")]+      pp = (\(_,v) -> [("label",T.pc_pp (T.z_mod T.z12 v))],const [])+  in gen_graph o pp e+ -- * P.31  p31_f_4_22 :: [Z12] p31_f_4_22 = [0,2,4,7]  p31_e_set :: [([Z12],[Z12])]-p31_e_set = T.e_univ_select_u_edges (doi_of 3) (map sort (T.z_sro_ti_related mod12 p31_f_4_22))+p31_e_set = T.e_univ_select_u_edges (doi_of 3) (map sort (T.z_sro_ti_related T.z12 p31_f_4_22))  p31_gr :: [String] p31_gr = gen_graph_ul [] set_pp p31_e_set@@ -158,15 +284,32 @@ p114_f_3_7 :: [Z12] p114_f_3_7 = [0,2,5] +p114_mk_o :: Show t => t -> [T.Dot_Meta_Attr]+p114_mk_o el =+  [("node:shape","box")+  ,("edge:len",show el)+  ,("edge:fontsize","10")]+ p114_mk_gr :: Double -> ([Z12] -> [Z12] -> Bool) -> [String] p114_mk_gr el flt =-    let o = [("node:shape","box")-            ,("edge:len",show el)]-    in gen_flt_graph o flt (map sort (T.z_sro_ti_related mod12 p114_f_3_7))+  let n = map sort (T.z_sro_ti_related T.z12 p114_f_3_7)+  in gen_flt_graph (p114_mk_o el) flt n +p114_f37_sc_pp :: [Z12] -> String+p114_f37_sc_pp = set_pp_tto_rel T.z12 [0,2,5]++p114_g0 :: [String]+p114_g0 =+  let mk_e flt = gen_u_edges flt (map sort (T.z_sro_ti_related T.z12 p114_f_3_7))+  in gen_graph_ul (p114_mk_o (2.5::Double)) p114_f37_sc_pp (mk_e (doi_of 2))++p114_g1 :: [String]+p114_g1 = p114_mk_gr 2.5 (doi_of 2)+ p114_gr_set :: [(String,[String])] p114_gr_set =-  [("p114.1.dot",p114_mk_gr 2.5 (doi_of 2))+  [("p114.0.dot",p114_g0)+  ,("p114.1.dot",p114_g1)   ,("p114.2.dot"    ,let o = [("edge:len","1.25")]     in gen_flt_graph o (loc_dif_of 1) (T.combinations 3 [1::Int .. 6]))@@ -184,7 +327,7 @@ p125_gr :: [String] p125_gr =     let t :: [[Int]]-        t = [[p,q,r] | p <- [0 .. 11], q <- [0 .. 11], r <- [0 ..11], q > p, r > q]+        t = [[p,q,r] | p <- [0 .. 11], q <- [0 .. 11], q > p, r <- [0 ..11], r > q]         c = T.collate (zip (map sum t) t)         with_h n = lookup n c         ch = fromJust (liftM2 (++) (with_h 15) (with_h 16))@@ -195,7 +338,7 @@ p131_gr :: [String] p131_gr =     let c = let u = [6::Int .. 14]-            in [[p,q,r] | p <- u, q <- u, r <- u, q > p, r > q, p + q + r == 30]+            in [[p,q,r] | p <- u, q <- u, q > p, r <- u, r > q, p + q + r == 30]     in gen_graph_ul [] set_pp (T.e_univ_select_u_edges (min_vl_of 2) c)  -- * P.148@@ -223,35 +366,103 @@  -- * P.162 +-- > length p162_ch == 30+p162_ch :: [[Int]]+p162_ch =+  let n = [0::Int,1,2,3,4,5,6,7,8]+      c = T.combinations 4 n+  in filter ((== 1) . (`mod` 4) . sum) c++-- > length p162_e == 47+p162_e :: [T.Edge [Int]]+p162_e = T.e_univ_select_u_edges (doi_of 3) p162_ch+ p162_gr :: [String] p162_gr =-    let n = [0::Int,1,2,3,4,5,6,7,8]-        c = T.combinations 4 n-        ch = filter ((== 1) . (`mod` 4) . sum) c-        opt = [("graph:layout","neato")+    let opt = [("graph:layout","neato")               ,("edge:len","1.75")]-    in gen_graph_ul opt set_pp (T.e_univ_select_u_edges (doi_of 3) ch)+    in gen_graph_ul opt set_pp p162_e  -- * P.172 +-- > M.size p172_nd_map == 24 p172_nd_map :: M.Map Int [Z12] p172_nd_map =-    let nd_exp = map sort (T.z_sro_ti_related mod12 [0,1,3,7])+    let nd_exp = map sort (T.z_sro_ti_related T.z12 [0,1,3,7])     in M.fromList (zip [0..] nd_exp) +p172_nd_e_set :: [(Int,Int)]+p172_nd_e_set = T.e_univ_select_u_edges (m_doi_of p172_nd_map 0) [0..23]++p172_nd_e_set_alt :: [T.Edge Int]+p172_nd_e_set_alt = concatMap (T.e_path_to_edges . T.close 1) p172_cyc0++p172_gr :: G.Gr () ()+p172_gr = G.mkUGraph [0..23] p172_nd_e_set+ p172_set_pp :: Int -> String p172_set_pp = set_pp . m_get p172_nd_map +-- > let (c0,c1) = p172_all_cyc p172_gr+-- > (length c0,length c1) == (48,48)+p172_all_cyc :: ([[Int]], [[Int]])+p172_all_cyc =+    let (a, b) = T.firstSecond (T.g_partition p172_gr)+    in (L.observeAll (T.ug_hamiltonian_path_ml_0 a)+       ,L.observeAll (T.ug_hamiltonian_path_ml_0 b))++p172_cyc0 :: [[Int]]+p172_cyc0 = map (!! 0) [fst p172_all_cyc,snd p172_all_cyc]++p172_g1 :: [String]+p172_g1 = gen_graph_ul [("edge:len","2.0")] p172_set_pp p172_nd_e_set++p172_g2 :: [String]+p172_g2 = gen_graph_ul [] p172_set_pp p172_nd_e_set_alt++p172_g3 :: [String]+p172_g3 =+  let m_set_pp_tto_rel = set_pp_tto_rel T.z12 [0,1,3,7] . m_get p172_nd_map+  in gen_graph_ul [("node:shape","box"),("edge:len","2.0")] m_set_pp_tto_rel p172_nd_e_set++-- | 'T.Tto' T/n/.+tto_tn :: Integral t => t -> T.Tto t+tto_tn n = T.Tto (T.z_mod T.z12 n) 1 False++-- | 'Z.Tto' T/n/I.+tto_tni :: Integral t => t -> T.Tto t+tto_tni n = T.Tto (T.z_mod T.z12 n) 1 True++gen_tto_alt_seq :: Integral t => (t -> T.Tto t,t -> T.Tto t) -> Int -> t -> t -> t -> [T.Tto t]+gen_tto_alt_seq (f,g) k n m x =+    let t = map f (take k [x,x + n ..])+        i = map g (take k [x + m,x + m + n ..])+    in T.interleave t i++-- | /k/ is length of the T & I sequences, /n/ is the T & I sequence+-- interval, /m/ is the interval between the T & I sequence.+--+-- > r = ["T0 T5I T3 T8I T6 T11I T9 T2I","T1 T6I T4 T9I T7 T0I T10 T3I"]+-- > map (unwords . map T.tto_pp . gen_tni_seq 4 3 5) [0,1] == r+gen_tni_seq :: Integral t => Int -> t -> t -> t -> [T.Tto t]+gen_tni_seq = gen_tto_alt_seq (tto_tn,tto_tni)++-- > putStrLn $ unlines $ map (unwords . map Z.tto_pp) c4+p172_c4 :: [[T.Tto Int]]+p172_c4 = map (gen_tni_seq 3 4 9) [0 .. 3] ++ map (gen_tni_seq 2 6 11) [0 .. 5]++tto_seq_edges :: (Show t,Num t,Eq t) => [[T.Tto t]] -> [(String, String)]+tto_seq_edges = nub . sort . concatMap (map T.t2_sort . adj_cyc . map T.tto_pp)++p172_g4 :: [String]+p172_g4 = gen_graph_ul [("edge:len","2.0")] id (tto_seq_edges p172_c4)+ p172_gr_set :: [(String,[String])] p172_gr_set =-    [("p172.0.dot"-     ,let nd_e_set = T.e_univ_select_u_edges (m_doi_of p172_nd_map 0) [0..23]-      in gen_graph_ul_ty "circo" p172_set_pp nd_e_set)-    ,("p172.1.dot"-     ,let nd_e_set = concatMap T.e_path_to_edges-                     [[22,11,20,9,18,7,16,5,14,3,12,1,22]-                     ,[23,2,13,8,19,10,21,4,15,6,17,0,23]]-      in gen_graph_ul_ty "circo" p172_set_pp nd_e_set)]+    [("p172.0.dot",p172_g1)+    ,("p172.1.dot",p172_g2)+    ,("p172.2.dot",p172_g3)+    ,("p172.3.dot",p172_g4)]  -- * P.177 @@ -265,21 +476,149 @@  p177_gr_set :: [(String,[String])] p177_gr_set =-    let p_set = concatMap (T.z_sro_ti_related mod12) [[0::Int,1,4,6],[0,1,3,7]]+    let p_set = concatMap (T.z_sro_ti_related T.z12) [[0::Int,1,4,6],[0,1,3,7]]     in [("p177.0.dot",gen_graph_ul [] set_pp (map (partition_ic 4) p_set))        ,("p177.1.dot",gen_graph_ul_ty "circo" set_pp (map (partition_ic 6) p_set))        ,("p177.2.dot"-        ,let gr_pp = T.gr_pp_lift_node_f set_pp+        ,let gr_pp = T.gr_pp_label_v set_pp              gr = T.g_from_edges (map (partition_ic 6) p_set)-         in T.g_to_udot [("edge:len","1.5")] gr_pp gr)]+         in T.fgl_to_udot [("edge:len","1.5")] gr_pp gr)] +-- * P.178++type SC = [Int]+type PCSET = [Int]++ait :: [SC]+ait = map T.sc ["4-Z15","4-Z29"]++-- | List of pcsets /s/ where /prime(p+s)=r/ and /prime(q+s)=r/.+-- /#p/ and /#q/ must be equal, and less than /#r/.+--+-- > mk_bridge (T.sc "4-Z15") [0,6] [1,7] == [[2,5],[8,11]]+-- > mk_bridge (T.sc "4-Z29") [0,6] [1,7] == [[2,11],[5,8]]+mk_bridge :: SC -> PCSET -> PCSET -> [PCSET]+mk_bridge r p q =+    let n = length r - length p+        c = T.combinations n [0..11]+        f s = T.z_forte_prime T.z12 (p ++ s) == r && T.z_forte_prime T.z12 (q ++ s) == r+    in filter f c++-- | 'concatMap' of 'mk_bridge'.+--+-- > mk_bridge_set ait [0,6] [1,7] == [[2,5],[8,11],[2,11],[5,8]]+mk_bridge_set :: [SC] -> PCSET -> PCSET -> [PCSET]+mk_bridge_set r_set p q = concatMap (\r -> mk_bridge r p q) r_set++mk_bridge_set_seq :: [SC] -> [PCSET] -> [[PCSET]]+mk_bridge_set_seq r_set k_seq =+    case k_seq of+      p:q:k_seq' -> mk_bridge_set r_set p q : mk_bridge_set_seq r_set (q : k_seq')+      _ -> []++-- > zip [0..] (mk_bridge_set_seq ait p178_i6_seq)+p178_i6_seq :: [PCSET]+p178_i6_seq = map (sort . (\n -> T.z_pcset T.z12 [n,n+6])) [0..6]++p178_ch :: [(PCSET,[PCSET],PCSET)]+p178_ch = zip3 p178_i6_seq (mk_bridge_set_seq ait p178_i6_seq) (tail p178_i6_seq)++type ID = Char++-- | Add 'ID' to vertices, the @2,11@ the is between @0,6@ and @1,7@+-- is /not/ the same @2,11@ that is between @3,9@ and @4,10@.+p178_e :: [((ID,PCSET),(ID,PCSET))]+p178_e =+    let f k (p,c,q) = map (\x -> (('.',p),(k,x))) c ++ map (\x -> ((k,x),('.',q))) c+    in concat (zipWith f ['a'..] p178_ch)++p178_gr_1 :: [String]+p178_gr_1 =+    let opt = [("node:shape","rectangle")+              ,("node:start","1362874")+              ,("edge:len","2")]+    in gen_graph_ul opt (set_pp . snd) p178_e++p178_gr_2 :: [String]+p178_gr_2 =+    let opt = [("node:shape","point")]+    in gen_graph_ul opt (const "") p178_e++-- * P.196++p196_gr :: [String]+p196_gr = gen_flt_graph [("edge:len","1.25")] (loc_dif_of 1) (T.combinations 3 [1::Int .. 6])++-- * P.201++type SET = [Int]+type E = (SET,SET)++bd_9_3_2_12 :: [SET]+bd_9_3_2_12 =+    [[0,1,2],[0,1,2],[0,3,4],[0,3,4],[0,5,6],[0,5,7],[0,6,8],[0,7,8]+    ,[1,3,5],[1,3,8],[1,4,5],[1,4,8],[1,6,7],[1,6,7]+    ,[2,3,6],[2,3,7],[2,4,6],[2,4,7],[2,5,8],[2,5,8]+    ,[3,5,6],[3,7,8]+    ,[4,5,7],[4,6,8]]++p201_mk_e :: [Int] -> [E]+p201_mk_e =+    let f n s = if n `elem` s then Just ([n],sort (n `delete` s)) else Nothing+        g n = mapMaybe (f n) bd_9_3_2_12+    in concatMap g++p201_e :: [[E]]+p201_e = map p201_mk_e [[0,3,4],[1,6,7],[2,5,8]]++p201_o :: [T.Dot_Meta_Attr]+p201_o =+  [("graph:splines","false")+  ,("node:shape","box")+  ,("edge:len","1.75")]++-- > length p201_gr_set+p201_gr_set :: [[String]]+p201_gr_set = map (gen_graph_ul p201_o set_pp) p201_e++p201_gr_join :: [String]+p201_gr_join =+    let e = zipWith e_add_id [0::Int ..] p201_e+    in gen_graph_ul p201_o (set_pp . snd) (concat e)++-- * P.205++bd_9_3_2_34 :: [SET]+bd_9_3_2_34 =+    [[0,1,2],[0,1,3],[0,2,4],[0,3,4]+    ,[0,5,6],[0,5,7],[0,6,8],[0,7,8]+    ,[1,2,5],[1,3,6],[1,4,5],[1,4,8]+    ,[1,6,7],[1,7,8],[2,3,6],[2,3,7]+    ,[2,4,7],[2,5,8],[2,6,8],[3,4,8]+    ,[3,5,7],[3,5,8],[4,5,6],[4,6,7]]++p205_mk_e :: [Int] -> [E]+p205_mk_e =+    let f n s = if n `elem` s then Just ([n],sort (n `delete` s)) else Nothing+        g n = mapMaybe (f n) bd_9_3_2_34+    in concatMap g++p205_gr :: [String]+p205_gr =+    let o = [("graph:splines","false"),("node:shape","box"),("edge:len","2.25")]+    in gen_graph_ul o set_pp (p205_mk_e [0..8])+ -- * IO -wr_graphs :: IO ()-wr_graphs = do-  let f (nm,gr) = writeFile ("/home/rohan/sw/hmt/data/dot/tj_oh_" ++ nm) (unlines gr)-  f ("p012.dot",p12_euler_plane_gr)-  f ("p014.dot",p14_gr)+-- > wr_graphs "/home/rohan/sw/hmt/data/dot/tj/oh/"+wr_graphs :: FilePath -> IO ()+wr_graphs dir = do+  let f (nm,gr) = writeFile (dir ++ "tj_oh_" ++ nm) (unlines gr)+  f ("p012.1.dot",p12_c5_gr)+  f ("p012.2.dot",p12_euler_plane_gr)+  f ("p014.1.dot",p14_gr_u)+  f ("p014.2.dot",p14_gr)+  f ("p014.3.dot",p14_nrt_gr)   f ("p031.dot",p31_gr)   mapM_ f p114_gr_set   f ("p125.dot",p125_gr)@@ -288,3 +627,9 @@   f ("p162.dot",p162_gr)   mapM_ f p172_gr_set   mapM_ f p177_gr_set+  f ("p178.1.dot",p178_gr_1)+  f ("p178.2.dot",p178_gr_2)+  f ("p196.dot",p196_gr)+  mapM_ f (zip ["p201.1.dot","p201.2.dot","p201.3.dot"] p201_gr_set)+  f ("p201.4.dot",p201_gr_join)+  f ("p205.dot",p205_gr)
− Music/Theory/IO.hs 
@@ -1,34 +0,0 @@--- | "System.IO" related functions.-module Music.Theory.IO where--import qualified Data.ByteString as B {- bytestring -}-import qualified Data.Text as T {- text -}-import qualified Data.Text.Encoding as T {- text -}-import qualified Data.Text.IO as T {- text -}-import qualified System.Directory as D {- directory -}---- | 'T.decodeUtf8' of 'B.readFile'.-read_file_utf8_text :: FilePath -> IO T.Text-read_file_utf8_text = fmap T.decodeUtf8 . B.readFile---- | Read (strictly) a UTF-8 encoded text file, implemented via "Data.Text".-read_file_utf8 :: FilePath -> IO String-read_file_utf8 = fmap T.unpack . read_file_utf8_text---- | 'read_file_utf8', or a default value if the file doesn't exist.-read_file_utf8_or :: String -> FilePath -> IO String-read_file_utf8_or def f = do-  x <- D.doesFileExist f-  if x then read_file_utf8 f else return def---- | Write UTF8 string as file, via "Data.Text".-write_file_utf8 :: FilePath -> String -> IO ()-write_file_utf8 fn = B.writeFile fn . T.encodeUtf8 . T.pack---- | 'readFile' variant using 'Text' for @ISO 8859-1@ (Latin 1) encoding.-read_file_iso_8859_1 :: FilePath -> IO String-read_file_iso_8859_1 = fmap (T.unpack . T.decodeLatin1) . B.readFile---- | 'readFile' variant using 'Text' for local encoding.-read_file_locale :: FilePath -> IO String-read_file_locale = fmap T.unpack . T.readFile
Music/Theory/Instrument/Choir.hs view
@@ -1,9 +1,9 @@ module Music.Theory.Instrument.Choir where  import Data.List.Split {- split -}-import Data.Maybe {- base -}  import qualified Music.Theory.Clef as T {- hmt -}+import qualified Music.Theory.List as T {- hmt -} import qualified Music.Theory.Pitch as T {- hmt -} import qualified Music.Theory.Pitch.Name as T {- hmt -} @@ -43,13 +43,9 @@     ,(Alto,(T.g3,T.c5))     ,(Soprano,(T.c4,T.f5))] --- | Erroring variant.-lookup_err :: Eq a => a -> [(a,b)] -> b-lookup_err e = fromMaybe (error "lookup_err") . lookup e- -- | Lookup voice range table. voice_rng :: Voice_Rng_Tbl -> Voice -> (T.Pitch,T.Pitch)-voice_rng tbl v = lookup_err v tbl+voice_rng tbl v = T.lookup_err v tbl  -- | Lookup 'voice_rng_tbl_std'. voice_rng_std :: Voice -> (T.Pitch,T.Pitch)
Music/Theory/Instrument/Names.hs view
@@ -2,7 +2,7 @@  import Data.List.Split {- split -} --- (family,abbreviations,names,transpositions)+-- | (family,abbreviations,names,transpositions) instrument_db' :: [(String,String,String,String)] instrument_db' =     [("br","b.tbn","bass trombone","")@@ -106,7 +106,7 @@     ,("ww","oca","ocarina","")     ] --- (family,[abbreviations],[names],[transpositions])+-- | (family,[abbreviations],[names],[transpositions]) instrument_db :: [(String,[String],[String],[String])] instrument_db =     let sep = splitOn ";"
Music/Theory/Interval.hs view
@@ -4,17 +4,17 @@ import Data.List {- base -} import Data.Maybe {- base -} -import qualified Music.Theory.Ord as T-import qualified Music.Theory.Pitch as T-import qualified Music.Theory.Pitch.Note as T+import qualified Music.Theory.Ord as T {- hmt -}+import qualified Music.Theory.Pitch as T {- hmt -}+import qualified Music.Theory.Pitch.Note as T {- hmt -}  -- | Interval type or degree.-data Interval_T = Unison | Second | Third | Fourth+data Interval_Type = Unison | Second | Third | Fourth                 | Fifth | Sixth | Seventh                   deriving (Eq,Enum,Bounded,Ord,Show)  -- | Interval quality.-data Interval_Q = Diminished | Minor+data Interval_Quality = Diminished | Minor                 | Perfect                 | Major | Augmented                   deriving (Eq,Enum,Bounded,Ord,Show)@@ -22,23 +22,23 @@ -- | Common music notation interval.  An 'Ordering' of 'LT' indicates -- an ascending interval, 'GT' a descending interval, and 'EQ' a -- unison.-data Interval = Interval {interval_type :: Interval_T-                         ,interval_quality :: Interval_Q+data Interval = Interval {interval_type :: Interval_Type+                         ,interval_quality :: Interval_Quality                          ,interval_direction :: Ordering                          ,interval_octave :: T.Octave}                 deriving (Eq,Show) --- | Interval type between 'Note_T' values.+-- | Interval type between 'Note' values. -- -- > map (interval_ty C) [E,B] == [Third,Seventh]-interval_ty :: T.Note_T -> T.Note_T -> Interval_T+interval_ty :: T.Note -> T.Note -> Interval_Type interval_ty n1 n2 = toEnum ((fromEnum n2 - fromEnum n1) `mod` 7) --- | Table of interval qualities.  For each 'Interval_T' gives--- directed semitone interval counts for each allowable 'Interval_Q'.+-- | Table of interval qualities.  For each 'Interval_Type' gives+-- directed semitone interval counts for each allowable 'Interval_Quality'. -- For lookup function see 'interval_q', for reverse lookup see -- 'interval_q_reverse'.-interval_q_tbl :: Integral n => [(Interval_T, [(n,Interval_Q)])]+interval_q_tbl :: Integral n => [(Interval_Type, [(n,Interval_Quality)])] interval_q_tbl =     [(Unison,[(11,Diminished)              ,(0,Perfect)@@ -66,20 +66,20 @@               ,(11,Major)               ,(12,Augmented)])] --- | Lookup 'Interval_Q' for given 'Interval_T' and semitone count.+-- | Lookup 'Interval_Quality' for given 'Interval_Type' and semitone count. -- -- > interval_q Unison 11 == Just Diminished -- > interval_q Third 5 == Just Augmented -- > interval_q Fourth 5 == Just Perfect -- > interval_q Unison 3 == Nothing-interval_q :: Interval_T -> Int -> Maybe Interval_Q+interval_q :: Interval_Type -> Int -> Maybe Interval_Quality interval_q i n = lookup i interval_q_tbl >>= lookup n --- | Lookup semitone difference of 'Interval_T' with 'Interval_Q'.+-- | Lookup semitone difference of 'Interval_Type' with 'Interval_Quality'. -- -- > interval_q_reverse Third Minor == Just 3 -- > interval_q_reverse Unison Diminished == Just 11-interval_q_reverse :: Interval_T -> Interval_Q -> Maybe Int+interval_q_reverse :: Interval_Type -> Interval_Quality -> Maybe Int interval_q_reverse ty qu =     case lookup ty interval_q_tbl of       Nothing -> Nothing@@ -98,8 +98,8 @@  -- | Determine 'Interval' between two 'Pitch'es. ----- > interval (Pitch C Sharp 4) (Pitch D Flat 4) == Interval Second Diminished EQ 0--- > interval (Pitch C Sharp 4) (Pitch E Sharp 5) == Interval Third Major LT 1+-- > interval (T.Pitch T.C T.Sharp 4) (T.Pitch T.D T.Flat 4) == Interval Second Diminished EQ 0+-- > interval (T.Pitch T.C T.Sharp 4) (T.Pitch T.E T.Sharp 5) == Interval Third Major LT 1 interval :: T.Pitch -> T.Pitch -> Interval interval p1 p2 =     let c = compare p1 p2@@ -109,7 +109,7 @@         p2' = T.pitch_to_pc p2         st = (p2' - p1') `mod` 12         ty = interval_ty n1 n2-        (Just qu) = interval_q ty (fromIntegral st)+        qu = fromMaybe (error "interval?") (interval_q ty (fromIntegral st))         o_a = if n1 > n2 then -1 else 0     in case c of          GT -> (interval p2 p1) { interval_direction = GT }@@ -121,14 +121,14 @@ invert_interval :: Interval -> Interval invert_interval (Interval t qu d o) = Interval t qu (T.ord_invert d) o --- | The signed difference in semitones between two 'Interval_Q'--- values when applied to the same 'Interval_T'.  Can this be written--- correctly without knowing the Interval_T?+-- | The signed difference in semitones between two 'Interval_Quality'+-- values when applied to the same 'Interval_Type'.  Can this be written+-- correctly without knowing the Interval_Type? -- -- > quality_difference_m Minor Augmented == Just 2 -- > quality_difference_m Augmented Diminished == Just (-3) -- > quality_difference_m Major Perfect == Nothing-quality_difference_m :: Interval_Q -> Interval_Q -> Maybe Int+quality_difference_m :: Interval_Quality -> Interval_Quality -> Maybe Int quality_difference_m a b =     let rule (x,y) =             if x == y@@ -152,7 +152,7 @@                       Nothing -> Nothing  -- | Erroring variant of 'quality_difference_m'.-quality_difference :: Interval_Q -> Interval_Q -> Int+quality_difference :: Interval_Quality -> Interval_Quality -> Int quality_difference a b =     let err = error ("quality_difference: " ++ show (a,b))     in fromMaybe err (quality_difference_m a b)@@ -203,7 +203,7 @@ -- displacement. -- -- > mapMaybe parse_interval_type (map show [1 .. 15])-parse_interval_type :: String -> Maybe (Interval_T,T.Octave)+parse_interval_type :: String -> Maybe (Interval_Type,T.Octave) parse_interval_type n =     case reads n of       [(n',[])] -> if n' == 0@@ -215,7 +215,7 @@ -- | Parse interval quality notation. -- -- > mapMaybe parse_interval_quality "dmPMA" == [minBound .. maxBound]-parse_interval_quality :: Char -> Maybe Interval_Q+parse_interval_quality :: Char -> Maybe Interval_Quality parse_interval_quality q =     let c = zip "dmPMA" [0..]     in fmap toEnum (lookup q c)@@ -224,11 +224,11 @@ -- 'parse_interval_type'. -- -- > map interval_type_degree [(Third,0),(Second,1),(Unison,2)] == [3,9,15]-interval_type_degree :: (Interval_T,T.Octave) -> Int+interval_type_degree :: (Interval_Type,T.Octave) -> Int interval_type_degree (t,o) = fromEnum t + 1 + (fromIntegral o * 7)  -- | Inverse of 'parse_interval_quality.-interval_quality_pp :: Interval_Q -> Char+interval_quality_pp :: Interval_Quality -> Char interval_quality_pp q = "dmPMA" !! fromEnum q  -- | Parse standard common music interval notation.
Music/Theory/Interval/Barlow_1987.hs view
@@ -4,12 +4,11 @@ module Music.Theory.Interval.Barlow_1987 where  import Data.List {- base -}-import Data.Maybe {- base -} import Data.Ratio {- base -} import Text.Printf {- base -} -import qualified Data.Numbers.Primes as P {- primes -}-+import qualified Music.Theory.Math as T {- hmt -}+import qualified Music.Theory.Math.Prime as T {- hmt -} import qualified Music.Theory.Tuning as T {- hmt -}  -- | Barlow's /indigestibility/ function for prime numbers.@@ -21,118 +20,49 @@         square n = n * n     in 2 * (square (p' - 1) / p') --- | Generate list of factors of /n/ from /x/.------ > factor P.primes 315 == [3,3,5,7]--- > P.primeFactors 315 == [3,3,5,7]-factor :: Integral a => [a] -> a -> [a]-factor x n =-    case x of-      [] -> undefined-      i:x' -> if n < i-              then [] -- ie. prime factors of 1...-              else if i * i > n-                   then [n]-                   else if rem n i == 0-                        then i : factor x (quot n i)-                        else factor x' n---- | 'factor' /n/ from 'primes'.------ > map prime_factors [1,4,231,315] == [[],[2,2],[3,7,11],[3,3,5,7]]--- > map P.primeFactors [1,4,231,315] == [[],[2,2],[3,7,11],[3,3,5,7]]-prime_factors :: Integral a => a -> [a]-prime_factors = factor P.primes---- | Collect number of occurences of each element of a sorted list.------ > multiplicities [1,1,1,2,2,3] == [(1,3),(2,2),(3,1)]-multiplicities :: (Eq a,Integral n) => [a] -> [(a,n)]-multiplicities =-    let f x = case x of-                [] -> undefined-                e:_ -> (e,genericLength x)-    in map f . group---- | 'multiplicities' '.' 'P.primeFactors'.------ > prime_factors_m 315 == [(3,2),(5,1),(7,1)]-prime_factors_m :: Integral a => a -> [(a,a)]-prime_factors_m = multiplicities . P.primeFactors---- | Merging function for 'rational_prime_factors_m'.-merge :: (Ord a,Num b,Eq b) => [(a,b)] -> [(a,b)] -> [(a,b)]-merge p q =-    case (p,q) of-      (_,[]) -> p-      ([],_) -> map (\(i,j) -> (i,-j)) q-      ((a,b):p',(c,d):q') ->-          if a < c-          then (a,b) : merge p' q-          else if a > c-               then (c,-d) : merge p q'-               else if b /= d-                    then (a,b-d) : merge p' q'-                    else merge p' q'---- | Collect the prime factors in a rational number given as a--- numerator/ denominator pair (n,m). Prime factors are listed in--- ascending order with their positive or negative multiplicities,--- depending on whether the prime factor occurs in the numerator or--- the denominator (after cancelling out common factors).------ > rational_prime_factors_m (16,15) == [(2,4),(3,-1),(5,-1)]--- > rational_prime_factors_m (10,9) == [(2,1),(3,-2),(5,1)]--- > rational_prime_factors_m (81,64) == [(2,-6),(3,4)]--- > rational_prime_factors_m (27,16) == [(2,-4),(3,3)]--- > rational_prime_factors_m (12,7) == [(2,2),(3,1),(7,-1)]-rational_prime_factors_m :: Integral b => (b,b) -> [(b,b)]-rational_prime_factors_m (n,m) =-    let n' = prime_factors_m n-        m' = prime_factors_m m-    in merge n' m'---- | Variant of 'rational_prime_factors_m' giving results in a table--- up to the /n/th prime.------ > rational_prime_factors_t 6 (12,7) == [2,1,0,-1,0,0]--- > rational_prime_factors_t 6 (32,9) == [5,-2,0,0,0,0]-rational_prime_factors_t :: Integral b => Int -> (b,b) -> [b]-rational_prime_factors_t n x =-    let r = rational_prime_factors_m x-    in map (\i -> fromMaybe 0 (lookup i r)) (take n P.primes)- -- | Compute the disharmonicity of the interval /(p,q)/ using the -- prime valuation function /pv/. ----- > map (disharmonicity barlow) [(9,10),(8,9)] ~= [12.733333,8.333333]+-- > map (disharmonicity barlow) [(9,10),(8,9)] == ([12 + 11/15,8 + 1/3] :: [Rational]) disharmonicity :: (Integral a,Num b) => (a -> b) -> (a,a) -> b disharmonicity pv (p,q) =-    let n = rational_prime_factors_m (p,q)+    let n = T.rat_prime_factors_m (p,q)     in sum [abs (fromIntegral j) * pv i | (i,j) <- n]  -- | The reciprocal of 'disharmonicity'. ----- > map (harmonicity barlow) [(9,10),(8,9)] ~= [0.078534,0.120000]+-- > map (harmonicity barlow) [(9,10),(8,9),(2,1)] == ([15/191,3/25,1] :: [Rational]) harmonicity :: (Integral a,Fractional b) => (a -> b) -> (a,a) -> b harmonicity pv = recip . disharmonicity pv +harmonicity_m :: (Eq b,Integral a,Fractional b) => (a -> b) -> (a,a) -> Maybe b+harmonicity_m pv = T.recip_m . disharmonicity pv+ -- | Variant of 'harmonicity' with 'Ratio' input.+--+-- > harmonicity_r barlow 1 == 1/0 harmonicity_r :: (Integral a,Fractional b) => (a -> b) -> Ratio a -> b-harmonicity_r pv = harmonicity pv . from_rational---- | 'uncurry' ('%').-to_rational :: Integral a => (a,a) -> Ratio a-to_rational = uncurry (%)+harmonicity_r pv = harmonicity pv . T.rational_nd --- | Make 'numerator' 'denominator' pair of /n/.-from_rational :: Ratio t -> (t, t)-from_rational n = (numerator n,denominator n)+-- | Variant of 'harmonicity_r' with output in (0,100), infinity maps to 100.+harmonicity_r_100 :: (RealFrac b, Integral a) => (a -> b) -> Ratio a -> Int+harmonicity_r_100 pv x =+  case harmonicity_m pv (T.rational_nd x) of+    Nothing -> 100+    Just y -> round (y * 100)  -- | Set of 1. interval size (cents), 2. intervals as product of -- powers of primes, 3. frequency ratio and 4. harmonicity value.-type Table_2_Row = (Double,[Integer],Rational,Double)+type Table_2_Row = (Double,[Int],Rational,Double) +-- | Given ratio /r/ generate 'Table_2_Row'+mk_table_2_row :: Rational -> Table_2_Row+mk_table_2_row r =+  (T.fratio_to_cents r+  ,T.rat_prime_factors_t 6 (T.rational_nd r)+  ,r+  ,harmonicity_r barlow r)+ -- | Table 2 (p.45) -- -- > length (table_2 0.06) == 24@@ -141,43 +71,42 @@ table_2 z =     let g n = n <= 2 && n >= 1         r = nub (sort (filter g [p % q | p <- [1..81],q <- [1..81]]))-        h = map (harmonicity_r barlow) r-        f = (> z) . snd-        k (i,j) = (T.fratio_to_cents i,rational_prime_factors_t 6 (from_rational i),i,j)-    in map k (filter f (zip r h))+        f (_,_,_,h) = h > z+    in filter f (map mk_table_2_row r) --- | Pretty printer for 'Table_2_Row' values.------ > mapM_ (putStrLn . table_2_pp) (table_2 0.06)------ >    0.000 |  0  0  0  0  0  0 |  1:1  | Infinity--- >  111.731 |  4 -1 -1  0  0  0 | 15:16 | 0.076531--- >  182.404 |  1 -2  1  0  0  0 |  9:10 | 0.078534--- >  203.910 | -3  2  0  0  0  0 |  8:9  | 0.120000--- >  231.174 |  3  0  0 -1  0  0 |  7:8  | 0.075269--- >  266.871 | -1 -1  0  1  0  0 |  6:7  | 0.071672--- >  294.135 |  5 -3  0  0  0  0 | 27:32 | 0.076923--- >  315.641 |  1  1 -1  0  0  0 |  5:6  | 0.099338--- >  386.314 | -2  0  1  0  0  0 |  4:5  | 0.119048--- >  407.820 | -6  4  0  0  0  0 | 64:81 | 0.060000--- >  435.084 |  0  2  0 -1  0  0 |  7:9  | 0.064024--- >  498.045 |  2 -1  0  0  0  0 |  3:4  | 0.214286--- >  519.551 | -2  3 -1  0  0  0 | 20:27 | 0.060976--- >  701.955 | -1  1  0  0  0  0 |  2:3  | 0.272727--- >  764.916 |  1 -2  0  1  0  0 |  9:14 | 0.060172--- >  813.686 |  3  0 -1  0  0  0 |  5:8  | 0.106383--- >  884.359 |  0 -1  1  0  0  0 |  3:5  | 0.110294--- >  905.865 | -4  3  0  0  0  0 | 16:27 | 0.083333--- >  933.129 |  2  1  0 -1  0  0 |  7:12 | 0.066879--- >  968.826 | -2  0  0  1  0  0 |  4:7  | 0.081395--- >  996.090 |  4 -2  0  0  0  0 |  9:16 | 0.107143--- > 1017.596 |  0  2 -1  0  0  0 |  5:9  | 0.085227--- > 1088.269 | -3  1  1  0  0  0 |  8:15 | 0.082873--- > 1200.000 |  1  0  0  0  0  0 |  1:2  | 1.000000+{- | Pretty printer for 'Table_2_Row' values.++> mapM_ (putStrLn . table_2_pp) (table_2 0.06)++> >    0.000 |  0  0  0  0  0  0 |  1:1  | Infinity+> >  111.731 |  4 -1 -1  0  0  0 | 15:16 | 0.076531+> >  182.404 |  1 -2  1  0  0  0 |  9:10 | 0.078534+> >  203.910 | -3  2  0  0  0  0 |  8:9  | 0.120000+> >  231.174 |  3  0  0 -1  0  0 |  7:8  | 0.075269+> >  266.871 | -1 -1  0  1  0  0 |  6:7  | 0.071672+> >  294.135 |  5 -3  0  0  0  0 | 27:32 | 0.076923+> >  315.641 |  1  1 -1  0  0  0 |  5:6  | 0.099338+> >  386.314 | -2  0  1  0  0  0 |  4:5  | 0.119048+> >  407.820 | -6  4  0  0  0  0 | 64:81 | 0.060000+> >  435.084 |  0  2  0 -1  0  0 |  7:9  | 0.064024+> >  498.045 |  2 -1  0  0  0  0 |  3:4  | 0.214286+> >  519.551 | -2  3 -1  0  0  0 | 20:27 | 0.060976+> >  701.955 | -1  1  0  0  0  0 |  2:3  | 0.272727+> >  764.916 |  1 -2  0  1  0  0 |  9:14 | 0.060172+> >  813.686 |  3  0 -1  0  0  0 |  5:8  | 0.106383+> >  884.359 |  0 -1  1  0  0  0 |  3:5  | 0.110294+> >  905.865 | -4  3  0  0  0  0 | 16:27 | 0.083333+> >  933.129 |  2  1  0 -1  0  0 |  7:12 | 0.066879+> >  968.826 | -2  0  0  1  0  0 |  4:7  | 0.081395+> >  996.090 |  4 -2  0  0  0  0 |  9:16 | 0.107143+> > 1017.596 |  0  2 -1  0  0  0 |  5:9  | 0.085227+> > 1088.269 | -3  1  1  0  0  0 |  8:15 | 0.082873+> > 1200.000 |  1  0  0  0  0  0 |  1:2  | 1.000000+-} table_2_pp :: Table_2_Row -> String table_2_pp (i,j,k,l) =     let i' = printf "%8.3f" i         j' = unwords (map (printf "%2d") j)-        k' = let (p,q) = from_rational k in printf "%2d:%-2d" q p+        k' = let (p,q) = T.rational_nd k in printf "%2d:%-2d" q p         l' = printf "%1.6f" l     in intercalate " | " [i',j',k',l']
Music/Theory/Key.hs view
@@ -13,35 +13,35 @@ import qualified Music.Theory.Interval as T  -- | Enumeration of common music notation modes.-data Mode_T = Minor_Mode | Major_Mode+data Mode = Minor_Mode | Major_Mode               deriving (Eq,Ord,Show) --- | Pretty printer for 'Mode_T'.-mode_pp :: Mode_T -> String+-- | Pretty printer for 'Mode'.+mode_pp :: Mode -> String mode_pp m =     case m of       Minor_Mode -> "Minor"       Major_Mode -> "Major"  -- | Lower-cased 'mode_pp'.-mode_identifier_pp :: Mode_T -> String+mode_identifier_pp :: Mode -> String mode_identifier_pp = map toLower . mode_pp  -- | There are two modes, given one return the other.-mode_parallel :: Mode_T -> Mode_T+mode_parallel :: Mode -> Mode mode_parallel m = if m == Minor_Mode then Major_Mode else Minor_Mode -mode_pc_seq :: Num t => Mode_T -> [t]+mode_pc_seq :: Num t => Mode -> [t] mode_pc_seq md =     case md of       Major_Mode -> [0,2,4,5,7,9,11]       Minor_Mode -> [0,2,3,5,7,8,10] --- | A common music notation key is a 'Note_T', 'Alteration_T', 'Mode_T' triple.-type Key = (T.Note_T,T.Alteration_T,Mode_T)+-- | A common music notation key is a 'Note', 'Alteration', 'Mode' triple.+type Key = (T.Note,T.Alteration,Mode) --- | 'Mode_T' of 'Key'.-key_mode :: Key -> Mode_T+-- | 'Mode' of 'Key'.+key_mode :: Key -> Mode key_mode (_,_,m) = m  -- | Enumeration of 42 CMN keys.@@ -58,7 +58,7 @@ -- -- > length key_sequence_30 == 30 key_sequence_30 :: [Key]-key_sequence_30 = filter (\k -> maybe False ((< 8) . abs) (key_fifths k)) key_sequence_42+key_sequence_30 = filter (maybe False ((< 8) . abs) . key_fifths) key_sequence_42  -- | Parallel key, ie. 'mode_parallel' of 'Key'. key_parallel :: Key -> Key@@ -67,8 +67,8 @@ -- | Transposition of 'Key'. key_transpose :: Key -> Int -> Key key_transpose (n,a,m) x =-    let Just pc = T.note_alteration_to_pc (n,a)-        Just (n',a') = T.pc_to_note_alteration_ks ((pc + x) `mod` 12)+    let pc = fromMaybe (error "key_transpose?") (T.note_alteration_to_pc (n,a))+        (n',a') = fromMaybe (error "key_transpose?") (T.pc_to_note_alteration_ks ((pc + x) `mod` 12))     in (n',a',m)  -- | Relative key (ie. 'mode_parallel' with the same number of and type of alterations.@@ -98,7 +98,7 @@  -- | Pretty-printer where 'Minor_Mode' is written in lower case (lc) and -- alteration symbol is shown using indicated function.-key_lc_pp :: (T.Alteration_T -> String) -> Key -> String+key_lc_pp :: (T.Alteration -> String) -> Key -> String key_lc_pp a_pp (n,a,m) =     let c = T.note_pp n         c' = if m == Minor_Mode then toLower c else c@@ -121,7 +121,7 @@ key_lc_tonh_pp = key_lc_pp T.alteration_tonh  -- > map key_identifier_pp [(T.C,T.Sharp,Minor_Mode),(T.E,T.Flat,Major_Mode)]-key_identifier_pp :: (Show a, Show a1) => (a, a1, Mode_T) -> [Char]+key_identifier_pp :: (Show a, Show a1) => (a, a1, Mode) -> [Char] key_identifier_pp (n,a,m) = map toLower (intercalate "_" [show n,show a,mode_pp m])  -- > import Data.Maybe@@ -133,17 +133,15 @@  -- | Parse 'Key' from /lc-uc/ string. ----- > import Data.Maybe--- -- > let k = mapMaybe key_lc_uc_parse ["c","E","f♯","ab","G#"]--- > in map key_lc_uc_pp k == ["c♮","E♮","f♯","a♭","G♯"]+-- > map key_lc_uc_pp k == ["c♮","E♮","f♯","a♭","G♯"] key_lc_uc_parse :: String -> Maybe Key key_lc_uc_parse k =     let with_k a (n,_,m) = (n,a,m)         with_a n a = fmap (with_k a) (note_char_to_key n)     in case k of          [c] -> note_char_to_key c-         [n,a] -> join (fmap (with_a n) (T.symbol_to_alteration_iso a))+         [n,a] -> with_a n =<< T.symbol_to_alteration_unicode_plus_iso a          _ -> Nothing  -- | Distance along circle of fifths path of indicated 'Key'.  A@@ -170,7 +168,7 @@ -- | Table mapping 'Key' to 'key_fifths' value. key_fifths_tbl :: [(Key,Int)] key_fifths_tbl =-    let f (k,n) = maybe Nothing (\n' -> Just (k,n')) n+    let f (k,n) = fmap (\n' -> (k,n')) n     in mapMaybe f (zip key_sequence_42 (map key_fifths key_sequence_42))  -- | Lookup 'key_fifths' value in 'key_fifths_tbl'.@@ -179,7 +177,7 @@ -- > let f md = map key_lc_iso_pp . mapMaybe (fifths_to_key md) -- > f Minor_Mode a -- > f Major_Mode a-fifths_to_key :: Mode_T -> Int -> Maybe Key+fifths_to_key :: Mode -> Int -> Maybe Key fifths_to_key md n =     let eq_f = (\((_,_,md'),n') -> md == md' && n == n')     in fmap fst (find eq_f key_fifths_tbl)@@ -188,18 +186,18 @@ -- -- > mapMaybe (implied_key Major_Mode) [[0,2,4],[1,3],[4,10],[3,9],[8,9]] -- > map (implied_key Major_Mode) [[0,1,2],[0,1,3,4]] == [Nothing,Nothing]-implied_key :: Integral i => Mode_T -> [i] -> Maybe Key+implied_key :: Integral i => Mode -> [i] -> Maybe Key implied_key md pc_set =     let a_seq = [0,1,-1,2,-2,3,-3,4,-4,5,-5,6,-6]         key_seq = mapMaybe (fifths_to_key md) a_seq     in find (\k -> pc_set `T.is_subset` key_pc_set k) key_seq  -- | 'key_fifths' of 'implied_key'.-implied_fifths :: Integral i => Mode_T -> [i] -> Maybe Int-implied_fifths md = join . fmap key_fifths . implied_key md+implied_fifths :: Integral i => Mode -> [i] -> Maybe Int+implied_fifths md = key_fifths <=< implied_key md -implied_key_err :: Integral i => Mode_T -> [i] -> Key+implied_key_err :: Integral i => Mode -> [i] -> Key implied_key_err md = fromMaybe (error "implied_key") . implied_key md -implied_fifths_err :: Integral i => Mode_T -> [i] -> Int+implied_fifths_err :: Integral i => Mode -> [i] -> Int implied_fifths_err md = fromMaybe (error "implied_fifths") . key_fifths . implied_key_err md
− Music/Theory/List.hs 
@@ -1,1103 +0,0 @@--- | List functions.-module Music.Theory.List where--import Data.Either {- base -}-import Data.Function {- base -}-import qualified Data.IntMap as Map {- containers -}-import Data.List {- base -}-import Data.Maybe {- base -}-import Data.Tree {- containers -}-import qualified Data.Traversable as T {- base -}--import qualified Data.List.Ordered as O {- data-ordlist -}-import qualified Data.List.Split as S {- split -}-import qualified Data.List.Split.Internals as S {- split -}--import qualified Control.Monad.Logic as L {- logict -}---- | Data.Vector.slice, ie. starting index (zero-indexed) and number of elements.------ > slice 4 5 [1..] == [5,6,7,8,9]-slice :: Int -> Int -> [a] -> [a]-slice i n = take n . drop i---- | Variant of slice with start and end indices (zero-indexed).------ > section 4 8 [1..] == [5,6,7,8,9]-section :: Int -> Int -> [a] -> [a]-section l r = take (r - l + 1) . drop l---- | Bracket sequence with left and right values.------ > bracket ('<','>') "1,2,3" == "<1,2,3>"-bracket :: (a,a) -> [a] -> [a]-bracket (l,r) x = l : x ++ [r]--unbracket' :: [a] -> (Maybe a,[a],Maybe a)-unbracket' x =-    case x of-      [] -> (Nothing,[],Nothing)-      l:x' -> let (m,r) = separate_last' x' in (Just l,m,r)---- | The first & middle & last elements of a list.------ > unbracket "[12]" == Just ('[',"12",']')-unbracket :: [t] -> Maybe (t,[t],t)-unbracket x =-    case unbracket' x of-      (Just l,m,Just r) -> Just (l,m,r)-      _ -> Nothing--unbracket_err :: [t] -> (t,[t],t)-unbracket_err = fromMaybe (error "unbracket") . unbracket---- | Variant where brackets are sequences.------ > bracket_l ("<:",":>") "1,2,3" == "<:1,2,3:>"-bracket_l :: ([a],[a]) -> [a] -> [a]-bracket_l (l,r) s = l ++ s ++ r---- * Split---- | Relative of 'splitOn', but only makes first separation.------ > splitOn "//" "lhs//rhs//rem" == ["lhs","rhs","rem"]--- > separate_at "//" "lhs//rhs//rem" == Just ("lhs","rhs//rem")-separate_at :: Eq a => [a] -> [a] -> Maybe ([a],[a])-separate_at x =-    let n = length x-        f lhs rhs =-            if null rhs-            then Nothing-            else if x == take n rhs-                 then Just (reverse lhs,drop n rhs)-                 else f (head rhs : lhs) (tail rhs)-    in f []---- | 'Splitter' comparing single element.-on_elem :: Eq a => a -> S.Splitter a-on_elem e = S.defaultSplitter { S.delimiter = S.Delimiter [(==) e] }---- | Split before the indicated element.------ > split_before 'x' "axbcxdefx" == ["a","xbc","xdef","x"]--- > split_before 'x' "xa" == ["","xa"]------ > map (flip split_before "abcde") "ae_" == [["","abcde"],["abcd","e"],["abcde"]]--- > map (flip break "abcde" . (==)) "ae_" == [("","abcde"),("abcd","e"),("abcde","")]-split_before :: Eq a => a -> [a] -> [[a]]-split_before = S.split . S.keepDelimsL . on_elem---- * Rotate---- | Generic form of 'rotate_left'.-genericRotate_left :: Integral i => i -> [a] -> [a]-genericRotate_left n =-    let f (p,q) = q ++ p-    in f . genericSplitAt n---- | Left rotation.------ > rotate_left 1 [1..3] == [2,3,1]--- > rotate_left 3 [1..5] == [4,5,1,2,3]-rotate_left :: Int -> [a] -> [a]-rotate_left = genericRotate_left---- | Generic form of 'rotate_right'.-genericRotate_right :: Integral n => n -> [a] -> [a]-genericRotate_right n = reverse . genericRotate_left n . reverse---- | Right rotation.------ > rotate_right 1 [1..3] == [3,1,2]-rotate_right :: Int -> [a] -> [a]-rotate_right = genericRotate_right---- | Rotate left by /n/ 'mod' /#p/ places.------ > rotate 1 [1..3] == [2,3,1]--- > rotate 8 [1..5] == [4,5,1,2,3]-rotate :: (Integral n) => n -> [a] -> [a]-rotate n p =-    let m = n `mod` genericLength p-    in genericRotate_left m p---- | Rotate right by /n/ places.------ > rotate_r 8 [1..5] == [3,4,5,1,2]-rotate_r :: (Integral n) => n -> [a] -> [a]-rotate_r = rotate . negate---- | All rotations.------ > rotations [0,1,3] == [[0,1,3],[1,3,0],[3,0,1]]-rotations :: [a] -> [[a]]-rotations p = map (`rotate_left` p) [0 .. length p - 1]---- | Rotate list so that is starts at indicated element.------ > rotate_starting_from 'c' "abcde" == Just "cdeab"--- > rotate_starting_from '_' "abc" == Nothing-rotate_starting_from :: Eq a => a -> [a] -> Maybe [a]-rotate_starting_from x l =-    case break (== x) l of-      (_,[]) -> Nothing-      (lhs,rhs) -> Just (rhs ++ lhs)---- | Erroring variant.-rotate_starting_from_err :: Eq a => a -> [a] -> [a]-rotate_starting_from_err x =-    fromMaybe (error "rotate_starting_from: non-element") .-    rotate_starting_from x---- | Sequence of /n/ adjacent elements, moving forward by /k/ places.--- The last element may have fewer than /n/ places, but will reach the--- end of the input sequence.------ > adj 3 2 "adjacent" == ["adj","jac","cen","nt"]-adj :: Int -> Int -> [a] -> [[a]]-adj n k l =-    case take n l of-      [] -> []-      r -> r : adj n k (drop k l)---- | Variant of 'adj' where the last element has /n/ places but may--- not reach the end of the input sequence.------ > adj' 3 2 "adjacent" == ["adj","jac","cen"]-adj' :: Int -> Int -> [a] -> [[a]]-adj' n k l =-    let r = take n l-    in if length r == n then r : adj' n k (drop k l) else []---- | Generic form of 'adj2'.-genericAdj2 :: (Integral n) => n -> [t] -> [(t,t)]-genericAdj2 n l =-    case l of-      p:q:_ -> (p,q) : genericAdj2 n (genericDrop n l)-      _ -> []---- | Adjacent elements of list, at indicated distance, as pairs.------ > adj2 1 [1..5] == [(1,2),(2,3),(3,4),(4,5)]--- > let l = [1..5] in zip l (tail l) == adj2 1 l--- > adj2 2 [1..4] == [(1,2),(3,4)]--- > adj2 3 [1..5] == [(1,2),(4,5)]-adj2 :: Int -> [t] -> [(t,t)]-adj2 = genericAdj2---- | Append first element to end of list.------ > close [1..3] == [1,2,3,1]-close :: [a] -> [a]-close x =-    case x of-      [] -> []-      e:_ -> x ++ [e]---- | 'adj2' '.' 'close'.------ > adj2_cyclic 1 [1..3] == [(1,2),(2,3),(3,1)]-adj2_cyclic :: Int -> [t] -> [(t,t)]-adj2_cyclic n = adj2 n . close---- | Interleave elements of /p/ and /q/.------ > interleave [1..3] [4..6] == [1,4,2,5,3,6]--- > interleave ".+-" "abc" == ".a+b-c"--- > interleave [1..3] [] == []-interleave :: [a] -> [a] -> [a]-interleave p q =-    let u (i,j) = [i,j]-    in concatMap u (zip p q)---- | Interleave list of lists.  Allows lists to be of non-equal lenghts.------ > interleave_set ["abcd","efgh","ijkl"] == "aeibfjcgkdhl"--- > interleave_set ["abc","defg","hijkl"] == "adhbeicfjgkl"-interleave_set :: [[a]] -> [a]-interleave_set = concat . transpose--{--import Safe {- safe -}--interleave_set l =-    case mapMaybe headMay l of-      [] -> []-      r -> r ++ interleave_set (mapMaybe tailMay l)--}---- | De-interleave /n/ lists.------ > deinterleave 2 ".a+b-c" == [".+-","abc"]--- > deinterleave 3 "aeibfjcgkdhl" == ["abcd","efgh","ijkl"]-deinterleave :: Int -> [a] -> [[a]]-deinterleave n = transpose . S.chunksOf n---- | Special case for two-part deinterleaving.------ > deinterleave2 ".a+b-c" == (".+-","abc")-deinterleave2 :: [t] -> ([t], [t])-deinterleave2 =-    let f l =-            case l of-              p:q:l' -> (p,q) : f l'-              _ -> []-    in unzip . f--{--deinterleave2 =-    let f p q l =-            case l of-              [] -> (reverse p,reverse q)-              [a] -> (reverse (a:p),reverse q)-              a:b:l' -> rec (a:p) (b:q) l'-    in f [] []--}---- | Variant that continues with the longer input.------ > interleave_continue ".+-" "abc" == ".a+b-c"--- > interleave_continue [1..3] [] == [1..3]--- > interleave_continue [] [1..3] == [1..3]-interleave_continue :: [a] -> [a] -> [a]-interleave_continue p q =-    case (p,q) of-      ([],_) -> q-      (_,[]) -> p-      (i:p',j:q') -> i : j : interleave_continue p' q'---- | 'interleave' of 'rotate_left' by /i/ and /j/.------ > interleave_rotations 9 3 [1..13] == [10,4,11,5,12,6,13,7,1,8,2,9,3,10,4,11,5,12,6,13,7,1,8,2,9,3]-interleave_rotations :: Int -> Int -> [b] -> [b]-interleave_rotations i j s = interleave (rotate_left i s) (rotate_left j s)--generic_histogram :: (Ord a,Integral i) => [a] -> [(a,i)]-generic_histogram x =-    let g = group (sort x)-    in zip (map head g) (map genericLength g)--histogram_by :: Ord a => (a -> a -> Bool) -> [a] -> [(a,Int)]-histogram_by f x =-    let g = groupBy f (sort x)-    in zip (map head g) (map length g)---- | Count occurences of elements in list.------ > map histogram ["","hohoh"] == [[],[('h',3),('o',2)]]-histogram :: Ord a => [a] -> [(a,Int)]-histogram = histogram_by (==)--duplicates_by :: Ord a => (a -> a -> Bool) -> [a] -> [a]-duplicates_by f = map fst . filter (\(_,n) -> n > 1) . histogram_by f---- | Elements that appear more than once in the input.------ > map duplicates ["duplicates","redundant"] == ["","dn"]-duplicates :: Ord a => [a] -> [a]-duplicates = duplicates_by (==)---- | List segments of length /i/ at distance /j/.------ > segments 2 1 [1..5] == [[1,2],[2,3],[3,4],[4,5]]--- > segments 2 2 [1..5] == [[1,2],[3,4]]-segments :: Int -> Int -> [a] -> [[a]]-segments i j p =-    let q = take i p-        p' = drop j p-    in if length q /= i then [] else q : segments i j p'---- | 'foldl1' 'intersect'.------ > intersect_l [[1,2],[1,2,3],[1,2,3,4]] == [1,2]-intersect_l :: Eq a => [[a]] -> [a]-intersect_l = foldl1 intersect---- | 'foldl1' 'union'.------ > sort (union_l [[1,3],[2,3],[3]]) == [1,2,3]-union_l :: Eq a => [[a]] -> [a]-union_l = foldl1 union---- | Intersection of adjacent elements of list at distance /n/.------ > adj_intersect 1 [[1,2],[1,2,3],[1,2,3,4]] == [[1,2],[1,2,3]]-adj_intersect :: Eq a => Int -> [[a]] -> [[a]]-adj_intersect n = map intersect_l . segments 2 n---- | List of cycles at distance /n/.------ > cycles 2 [1..6] == [[1,3,5],[2,4,6]]--- > cycles 3 [1..9] == [[1,4,7],[2,5,8],[3,6,9]]--- > cycles 4 [1..8] == [[1,5],[2,6],[3,7],[4,8]]-cycles :: Int -> [a] -> [[a]]-cycles n = transpose . S.chunksOf n---- | Variant of 'filter' that has a predicate to halt processing,--- ie. 'filter' of 'takeWhile'.------ > filter_halt (even . fst) ((< 5) . snd) (zip [1..] [0..])-filter_halt :: (a -> Bool) -> (a -> Bool) -> [a] -> [a]-filter_halt sel end = filter sel . takeWhile end---- | Replace all /p/ with /q/ in /s/.------ > replace "_x_" "-X-" "an _x_ string" == "an -X- string"--- > replace "ab" "cd" "ab ab cd ab" == "cd cd cd cd"-replace :: Eq a => [a] -> [a] -> [a] -> [a]-replace p q s =-    let n = length p-    in case s of-         [] -> []-         c:s' -> if p `isPrefixOf` s-                 then q ++ replace p q (drop n s)-                 else c : replace p q s'---- | Replace the /i/th value at /ns/ with /x/.------ > replace_at "test" 2 'n' == "tent"-replace_at :: Integral i => [a] -> i -> a -> [a]-replace_at ns i x =-    let f j y = if i == j then x else y-    in zipWith f [0..] ns---- * Association lists---- | Equivalent to 'groupBy' '==' 'on' /f/.------ > let r = [[(1,'a'),(1,'b')],[(2,'c')],[(3,'d'),(3,'e')],[(4,'f')]]--- > in group_on fst (zip [1,1,2,3,3,4] "abcdef") == r-group_on :: Eq x => (a -> x) -> [a] -> [[a]]-group_on f = map (map snd) . groupBy ((==) `on` fst) . map (\x -> (f x,x))---- | Given accesors for /key/ and /value/ collate adjacent values.-collate_on_adjacent :: (Eq k,Ord k) => (a -> k) -> (a -> v) -> [a] -> [(k,[v])]-collate_on_adjacent f g =-    let h l = case l of-                [] -> error "collate_on_adjacent"-                l0:_ -> (f l0,map g l)-    in map h . group_on f---- | 'collate_on_adjacent' of 'fst' and 'snd'.------ > collate_adjacent (zip "TDD" "xyz") == [('T',"x"),('D',"yz")]-collate_adjacent :: Ord a => [(a,b)] -> [(a,[b])]-collate_adjacent = collate_on_adjacent fst snd---- | 'sortOn' prior to 'collate_on_adjacent'.------ > let r = [('A',"a"),('B',"bd"),('C',"ce"),('D',"f")]--- > in collate_on fst snd (zip "ABCBCD" "abcdef") == r-collate_on :: Ord k => (a -> k) -> (a -> v) -> [a] -> [(k,[v])]-collate_on f g = collate_on_adjacent f g . sortOn f---- | 'collate_on' of 'fst' and 'snd'.------ > collate (zip "TDD" "xyz") == [('D',"yz"),('T',"x")]--- > collate (zip [1,2,1] "abc") == [(1,"ac"),(2,"b")]-collate :: Ord a => [(a,b)] -> [(a,[b])]-collate = collate_on fst snd---- | Reverse of 'collate', inverse if order is not considered.------ > uncollate [(1,"ac"),(2,"b")] == zip [1,1,2] "acb"-uncollate :: [(k,[v])] -> [(k,v)]-uncollate = concatMap (\(k,v) -> zip (repeat k) v)---- | Make /assoc/ list with given /key/.------ > with_key 'a' [1..3] == [('a',1),('a',2),('a',3)]-with_key :: k -> [v] -> [(k,v)]-with_key h = zip (repeat h)---- | Intervals to values, zero is /n/.------ > dx_d 5 [1,2,3] == [5,6,8,11]-dx_d :: (Num a) => a -> [a] -> [a]-dx_d = scanl (+)---- | Variant that takes initial value and separates final value.  This--- is an appropriate function for 'mapAccumL'.------ > dx_d' 5 [1,2,3] == (11,[5,6,8])--- > dx_d' 0 [1,1,1] == (3,[0,1,2])-dx_d' :: Num t => t -> [t] -> (t,[t])-dx_d' n l =-    case reverse (scanl (+) n l) of-      e:r -> (e,reverse r)-      _ -> error "dx_d'"---- | Apply flip of /f/ between elements of /l/.------ > d_dx_by (,) "abcd" == [('b','a'),('c','b'),('d','c')]-d_dx_by :: (t -> t -> u) -> [t] -> [u]-d_dx_by f l = if null l then [] else zipWith f (tail l) l---- | Integrate, 'd_dx_by' '-', ie. pitch class segment to interval sequence.------ > d_dx [5,6,8,11] == [1,2,3]--- > d_dx [] == []-d_dx :: (Num a) => [a] -> [a]-d_dx = d_dx_by (-)---- | Elements of /p/ not in /q/.------ > [1,2,3] `difference` [1,2] == [3]-difference :: (Eq a) => [a] -> [a] -> [a]-difference p q =-    let f e = e `notElem` q-    in filter f p---- | Is /p/ a subset of /q/, ie. is 'intersect' of /p/ and /q/ '==' /p/.------ > is_subset [1,2] [1,2,3] == True-is_subset :: Eq a => [a] -> [a] -> Bool-is_subset p q = p `intersect` q == p---- | Is /p/ a superset of /q/, ie. 'flip' 'is_subset'.------ > is_superset [1,2,3] [1,2] == True-is_superset :: Eq a => [a] -> [a] -> Bool-is_superset = flip is_subset---- | Is /p/ a subsequence of /q/, ie. synonym for 'isInfixOf'.------ > subsequence [1,2] [1,2,3] == True-subsequence :: (Eq a) => [a] -> [a] -> Bool-subsequence = isInfixOf---- | Variant of 'elemIndices' that requires /e/ to be unique in /p/.------ > elem_index_unique 'a' "abcda" == undefined-elem_index_unique :: (Eq a) => a -> [a] -> Int-elem_index_unique e p =-    case elemIndices e p of-      [i] -> i-      _ -> error "elem_index_unique"---- | Lookup that errors and prints message.-lookup_err_msg :: (Eq k,Show k) => String -> k -> [(k,v)] -> v-lookup_err_msg err k = fromMaybe (error (err ++ ": " ++ show k)) . lookup k---- | Error variant.-lookup_err :: Eq k => k -> [(k,v)] -> v-lookup_err n = fromMaybe (error "lookup") . lookup n---- | 'lookup' variant with default value.-lookup_def :: Eq k => k -> v -> [(k,v)] -> v-lookup_def k d = fromMaybe d . lookup k---- | Reverse lookup.------ > reverse_lookup 'c' [] == Nothing--- > reverse_lookup 'c' (zip [0..4] ['a'..]) == Just 2-reverse_lookup :: Eq b => b -> [(a,b)] -> Maybe a-reverse_lookup k = fmap fst . find ((== k) . snd)--{--reverse_lookup :: Eq b => b -> [(a,b)] -> Maybe a-reverse_lookup key ls =-    case ls of-      [] -> Nothing-      (x,y):ls' -> if key == y then Just x else reverse_lookup key ls'--}----- | Basis of 'find_bounds_scl', indicates if /x/ is to the left or--- right of the list, and it to the right whether equal or not.--- 'Right' values will be correct if the list is not ascending,--- however 'Left' values only make sense for ascending ranges.------ > map (find_bounds' compare [(0,1),(1,2)]) [-1,0,1,2,3]-find_bounds' :: (t -> s -> Ordering) -> [(t,t)] -> s -> Either ((t,t),Ordering) (t,t)-find_bounds' f l x =-    let g (p,q) = f p x /= GT && f q x == GT-    in case l of-         [] -> error "find_bounds': nil"-         [(p,q)] -> if g (p,q) then Right (p,q) else Left ((p,q),f q x)-         (p,q):l' -> if f p x == GT-                     then Left ((p,q),GT)-                     else if g (p,q) then Right (p,q) else find_bounds' f l' x--decide_nearest' :: Ord o => (p -> o) -> (p,p) -> p-decide_nearest' f (p,q) = if f p < f q then p else q---- | Decide if value is nearer the left or right value of a range.-decide_nearest :: (Num o,Ord o) => o -> (o, o) -> o-decide_nearest x = decide_nearest' (abs . (x -))---- | Find the number that is nearest the requested value in an--- ascending list of numbers.------ > map (find_nearest_err [0,3.5,4,7]) [-1,1,3,5,7,9] == [0,0,3.5,4,7,7]-find_nearest_err :: (Num n,Ord n) => [n] -> n -> n-find_nearest_err l x =-    case find_bounds' compare (adj2 1 l) x of-      Left ((p,_),GT) -> p-      Left ((_,q),_) -> q-      Right (p,q) -> decide_nearest x (p,q)--find_nearest :: (Num n,Ord n) => [n] -> n -> Maybe n-find_nearest l x = if null l then Nothing else Just (find_nearest_err l x)---- | Basis of 'find_bounds'.  There is an option to consider the last--- element specially, and if equal to the last span is given.-find_bounds_scl :: Bool -> (t -> s -> Ordering) -> [(t,t)] -> s -> Maybe (t,t)-find_bounds_scl scl f l x =-    case find_bounds' f l x of-         Right r -> Just r-         Left (r,EQ) -> if scl then Just r else Nothing-         _ -> Nothing---- | Find adjacent elements of list that bound element under given--- comparator.------ > let {f = find_bounds True compare [1..5]--- >     ;r = [Nothing,Just (1,2),Just (3,4),Just (4,5)]}--- > in map f [0,1,3.5,5] == r-find_bounds :: Bool -> (t -> s -> Ordering) -> [t] -> s -> Maybe (t,t)-find_bounds scl f l = find_bounds_scl scl f (adj2 1 l)---- | Special case of 'dropRight'.------ > map drop_last ["","?","remove"] == ["","","remov"]-drop_last :: [t] -> [t]-drop_last l =-    case l of-      [] -> []-      [_] -> []-      e:l' -> e : drop_last l'---- | Variant of 'drop' from right of list.------ > dropRight 1 [1..9] == [1..8]-dropRight :: Int -> [a] -> [a]-dropRight n = reverse . drop n . reverse---- | Variant of 'dropWhile' from right of list.------ > dropWhileRight Data.Char.isDigit "A440" == "A"-dropWhileRight :: (a -> Bool) -> [a] -> [a]-dropWhileRight p = reverse . dropWhile p . reverse---- | 'take' from right.------ > take_right 3 "taking" == "ing"-take_right :: Int -> [a] -> [a]-take_right n = reverse . take n . reverse---- | 'takeWhile' from right.------ > take_while_right Data.Char.isDigit "A440" == "440"-take_while_right :: (a -> Bool) -> [a] -> [a]-take_while_right p = reverse . takeWhile p . reverse---- | Apply /f/ at first element, and /g/ at all other elements.------ > at_head negate id [1..5] == [-1,2,3,4,5]-at_head :: (a -> b) -> (a -> b) -> [a] -> [b]-at_head f g x =-    case x of-      [] -> []-      e:x' -> f e : map g x'---- | Apply /f/ at all but last element, and /g/ at last element.------ > at_last (* 2) negate [1..4] == [2,4,6,-4]-at_last :: (a -> b) -> (a -> b) -> [a] -> [b]-at_last f g x =-    case x of-      [] -> []-      [i] -> [g i]-      i:x' -> f i : at_last f g x'---- | Separate list into an initial list and perhaps the last element tuple.------ > separate_last' [] == ([],Nothing)-separate_last' :: [a] -> ([a],Maybe a)-separate_last' x =-    case reverse x of-      [] -> ([],Nothing)-      e:x' -> (reverse x',Just e)---- | Error on null input.------ > separate_last [1..5] == ([1..4],5)-separate_last :: [a] -> ([a],a)-separate_last = fmap (fromMaybe (error "separate_last")) . separate_last'---- | Replace directly repeated elements with 'Nothing'.------ > indicate_repetitions "abba" == [Just 'a',Just 'b',Nothing,Just 'a']-indicate_repetitions :: Eq a => [a] -> [Maybe a]-indicate_repetitions =-    let f l = case l of-                [] -> []-                e:l' -> Just e : map (const Nothing) l'-    in concatMap f . group---- | 'zipWith' of list and it's own tail.------ > zip_with_adj (,) "abcde" == [('a','b'),('b','c'),('c','d'),('d','e')]-zip_with_adj :: (a -> a -> b) -> [a] -> [b]-zip_with_adj f xs = zipWith f xs (tail xs)---- | Type-specialised 'zip_with_adj'.-compare_adjacent_by :: (a -> a -> Ordering) -> [a] -> [Ordering]-compare_adjacent_by = zip_with_adj---- | 'compare_adjacent_by' of 'compare'.------ > compare_adjacent [0,1,3,2] == [LT,LT,GT]-compare_adjacent :: Ord a => [a] -> [Ordering]-compare_adjacent = compare_adjacent_by compare---- | 'Data.List.groupBy' does not make adjacent comparisons, it--- compares each new element to the start of the group.  This function--- is the adjacent variant.------ > groupBy (<) [1,2,3,2,4,1,5,9] == [[1,2,3,2,4],[1,5,9]]--- > adjacent_groupBy (<) [1,2,3,2,4,1,5,9] == [[1,2,3],[2,4],[1,5,9]]-adjacent_groupBy :: (a -> a -> Bool) -> [a] -> [[a]]-adjacent_groupBy f p =-    case p of-      [] -> []-      [x] -> [[x]]-      x:y:p' -> let r = adjacent_groupBy f (y:p')-                    r0:r' = r-                in if f x y-                   then (x:r0) : r'-                   else [x] : r---- | Reduce sequences of consecutive values to ranges.------ > group_ranges [-1,0,3,4,5,8,9,12] == [(-1,0),(3,5),(8,9),(12,12)]--- > group_ranges [3,2,3,4,3] == [(3,3),(2,4),(3,3)]-group_ranges :: (Num t, Eq t) => [t] -> [(t,t)]-group_ranges =-    let f l = (head l,last l)-    in map f . adjacent_groupBy (\p q -> p + 1 == q)---- | 'groupBy' on /structure/ of 'Maybe', ie. all 'Just' compare equal.------ > let r = [[Just 1],[Nothing,Nothing],[Just 4,Just 5]]--- > in group_just [Just 1,Nothing,Nothing,Just 4,Just 5] == r-group_just :: [Maybe a] -> [[Maybe a]]-group_just = group_on isJust---- | Predicate to determine if all elements of the list are '=='.------ > all_equal "aaa" == True-all_equal :: Eq a => [a] -> Bool-all_equal l =-    case l of-      [] -> True-      [_] -> True-      x:xs -> all id (map (== x) xs)---- | Variant using 'nub'.-all_eq :: Eq n => [n] -> Bool-all_eq = (== 1) . length . nub---- | 'group_on' of 'sortOn'.------ > let r = [[('1','a'),('1','c')],[('2','d')],[('3','b'),('3','e')]]--- > in sort_group_on fst (zip "13123" "abcde") == r-sort_group_on :: Ord b => (a -> b) -> [a] -> [[a]]-sort_group_on f = group_on f . sortOn f---- | Maybe cons element onto list.------ > Nothing `mcons` "something" == "something"--- > Just 's' `mcons` "omething" == "something"-mcons :: Maybe a -> [a] -> [a]-mcons e l = maybe l (:l) e---- * Ordering---- | Comparison function type.-type Compare_F a = a -> a -> Ordering---- | If /f/ compares 'EQ', defer to /g/.-two_stage_compare :: Compare_F a -> Compare_F a -> Compare_F a-two_stage_compare f g p q =-    case f p q of-      EQ -> g p q-      r -> r---- | Sequence of comparison functions, continue comparing until not EQ.------ > compare (1,0) (0,1) == GT--- > n_stage_compare [compare `on` snd,compare `on` fst] (1,0) (0,1) == LT-n_stage_compare :: [Compare_F a] -> Compare_F a-n_stage_compare l p q =-    case l of-      [] -> EQ-      f:l' -> case f p q of-                EQ -> n_stage_compare l' p q-                r -> r---- | Sort sequence /a/ based on ordering of sequence /b/.------ > sort_to "abc" [1,3,2] == "acb"--- > sort_to "adbce" [1,4,2,3,5] == "abcde"-sort_to :: Ord i => [e] -> [i] -> [e]-sort_to e = map fst . sortOn snd . zip e---- | 'flip' of 'sort_to'.------ > sort_on [1,4,2,3,5] "adbce" == "abcde"-sort_on :: Ord i => [i] -> [e] -> [e]-sort_on = flip sort_to---- | 'sortBy' of 'two_stage_compare'.-sort_by_two_stage :: (Ord b,Ord c) => (a -> b) -> (a -> c) -> [a] -> [a]-sort_by_two_stage f g = sortBy (two_stage_compare (compare `on` f) (compare `on` g))---- | 'sortBy' of 'n_stage_compare'.-sort_by_n_stage :: Ord b => [a -> b] -> [a] -> [a]-sort_by_n_stage f = sortBy (n_stage_compare (map (compare `on`) f))---- | Given a comparison function, merge two ascending lists.------ > mergeBy compare [1,3,5] [2,4] == [1..5]-merge_by :: Compare_F a -> [a] -> [a] -> [a]-merge_by = O.mergeBy---- | 'merge_by' 'compare' 'on'.-merge_on :: Ord x => (a -> x) -> [a] -> [a] -> [a]-merge_on f = merge_by (compare `on` f)---- | 'O.mergeBy' of 'two_stage_compare'.-merge_by_two_stage :: Ord b => (a -> b) -> Compare_F c -> (a -> c) -> [a] -> [a] -> [a]-merge_by_two_stage f cmp g = O.mergeBy (two_stage_compare (compare `on` f) (cmp `on` g))---- | 'mergeBy' 'compare'.-merge :: Ord a => [a] -> [a] -> [a]-merge = O.merge---- | Merge list of sorted lists given comparison function.  Note that--- this is not equal to 'O.mergeAll'.-merge_set_by :: (a -> a -> Ordering) -> [[a]] -> [a]-merge_set_by f = foldr (merge_by f) []---- | 'merge_set_by' of 'compare'.------ > merge_set [[1,3,5,7,9],[2,4,6,8],[10]] == [1..10]-merge_set :: Ord a => [[a]] -> [a]-merge_set = merge_set_by compare--{-| 'merge_by' variant that joins (resolves) equal elements.--> let {left p _ = p->     ;right _ q = q->     ;cmp = compare `on` fst->     ;p = zip [1,3,5] "abc"->     ;q = zip [1,2,3] "ABC"->     ;left_r = [(1,'a'),(2,'B'),(3,'b'),(5,'c')]->     ;right_r = [(1,'A'),(2,'B'),(3,'C'),(5,'c')]}-> in merge_by_resolve left cmp p q == left_r &&->    merge_by_resolve right cmp p q == right_r---}-merge_by_resolve :: (a -> a -> a) -> Compare_F a -> [a] -> [a] -> [a]-merge_by_resolve jn cmp =-    let recur p q =-            case (p,q) of-              ([],_) -> q-              (_,[]) -> p-              (l:p',r:q') -> case cmp l r of-                               LT -> l : recur p' q-                               EQ -> jn l r : recur p' q'-                               GT -> r : recur p q'-    in recur---- | First non-ascending pair of elements.-find_non_ascending :: (a -> a -> Ordering) -> [a] -> Maybe (a,a)-find_non_ascending cmp xs =-    case xs of-      p:q:xs' -> if cmp p q == GT then Just (p,q) else find_non_ascending cmp (q:xs')-      _ -> Nothing---- | 'isNothing' of 'find_non_ascending'.-is_ascending_by :: (a -> a -> Ordering) -> [a] -> Bool-is_ascending_by cmp = isNothing . find_non_ascending cmp---- | 'is_ascending_by' 'compare'.-is_ascending :: Ord a => [a] -> Bool-is_ascending = is_ascending_by compare---- | Variant of `elem` that operates on a sorted list, halting.---   This is 'O.member'.------ > 16 `elem_ordered` [1,3 ..] == False--- > 16 `elem` [1,3 ..] == undefined-elem_ordered :: Ord t => t -> [t] -> Bool-elem_ordered = O.member---- | Variant of `elemIndex` that operates on a sorted list, halting.------ > 16 `elemIndex_ordered` [1,3 ..] == Nothing--- > 16 `elemIndex_ordered` [0,1,4,9,16,25,36,49,64,81,100] == Just 4-elemIndex_ordered :: Ord t => t -> [t] -> Maybe Int-elemIndex_ordered e =-    let recur k l =-            case l of-              [] -> Nothing-              x:l' -> if e == x-                      then Just k-                      else if x > e-                           then Nothing-                           else recur (k + 1) l'-    in recur 0---- | Keep right variant of 'zipWith', where unused rhs values are returned.------ > zip_with_kr (,) [1..3] ['a'..'e'] == ([(1,'a'),(2,'b'),(3,'c')],"de")-zip_with_kr :: (a -> b -> c) -> [a] -> [b] -> ([c],[b])-zip_with_kr f =-    let go r p q =-            case (p,q) of-              (i:p',j:q') -> go (f i j : r) p' q'-              _ -> (reverse r,q)-    in go []---- | A 'zipWith' variant that always consumes an element from the left--- hand side (lhs), but only consumes an element from the right hand--- side (rhs) if the zip function is 'Right' and not if 'Left'.--- There's also a secondary function to continue if the rhs ends--- before the lhs.-zip_with_perhaps_rhs :: (a -> b -> Either c c) -> (a -> c) -> [a] -> [b] -> [c]-zip_with_perhaps_rhs f g lhs rhs =-    case (lhs,rhs) of-      ([],_) -> []-      (_,[]) -> map g lhs-      (p:lhs',q:rhs') -> case f p q of-                           Left r -> r : zip_with_perhaps_rhs f g lhs' rhs-                           Right r -> r : zip_with_perhaps_rhs f g lhs' rhs'---- | Fill gaps in a sorted association list, range is inclusive at both ends.------ > let r = [(1,'a'),(2,'x'),(3,'x'),(4,'x'),(5,'b'),(6,'x'),(7,'c'),(8,'x'),(9,'x')]--- > in fill_gaps_ascending' 'x' (1,9) (zip [1,5,7] "abc") == r-fill_gaps_ascending :: (Enum n, Ord n) => t -> (n,n) -> [(n,t)] -> [(n,t)]-fill_gaps_ascending def_e (l,r) =-    let f i (j,e) = if j > i then Left (i,def_e) else Right (j,e)-        g i = (i,def_e)-    in zip_with_perhaps_rhs f g [l .. r]---- | Direct definition.-fill_gaps_ascending' :: (Num n,Enum n, Ord n) => t -> (n,n) -> [(n,t)] -> [(n,t)]-fill_gaps_ascending' def (l,r) =-    let recur n x =-            if n > r-            then []-            else case x of-                   [] -> zip [n .. r] (repeat def)-                   (m,e):x' -> if n < m-                               then (n,def) : recur (n + 1) x-                               else (m,e) : recur (n + 1) x'-    in recur l---- | 'minimum' and 'maximum' in one pass.------ > minmax "minimumandmaximum" == ('a','x')-minmax :: Ord t => [t] -> (t,t)-minmax inp =-    case inp of-      [] -> error "minmax: null"-      x:xs -> let mm p (l,r) = (min p l,max p r) in foldr mm (x,x) xs---- * Bimap---- | Apply /f/ to both elements of a two-tuple, ie. 'bimap' /f/ /f/.-bimap1 :: (t -> u) -> (t,t) -> (u,u)-bimap1 f (p,q) = (f p,f q)---- | Append /k/ to the right of /l/ until result has /n/ places.------ > map (pad_right '0' 2 . return) ['0' .. '9']--- > pad_right '0' 12 "1101" == "110100000000"--- > map (pad_right ' '3) ["S","E-L"] == ["S  ","E-L"]-pad_right :: a -> Int -> [a] -> [a]-pad_right k n l = take n (l ++ repeat k)---- | Append /k/ to the left of /l/ until result has /n/ places.------ > map (pad_left '0' 2 . return) ['0' .. '9']-pad_left :: a -> Int -> [a] -> [a]-pad_left k n l = replicate (n - length l) k ++ l---- * Embedding---- | Locate first (leftmost) embedding of /q/ in /p/.--- Return partial indices for failure at 'Left'.------ > embedding ("embedding","ming") == Right [1,6,7,8]--- > embedding ("embedding","mind") == Left [1,6,7]-embedding :: Eq t => ([t],[t]) -> Either [Int] [Int]-embedding =-    let recur n r (p,q) =-            case (p,q) of-              (_,[]) -> Right (reverse r)-              ([],_) -> Left (reverse r)-              (x:p',y:q') ->-                  let n' = n + 1-                      r' = if x == y then n : r else r-                  in recur n' r' (p',if x == y then q' else q)-    in recur 0 []--embedding_err :: Eq t => ([t],[t]) -> [Int]-embedding_err = either (error "embedding_err") id . embedding---- | Does /q/ occur in sequence, though not necessarily adjacently, in /p/.------ > is_embedding [1 .. 9] [1,3,7] == True--- > is_embedding "embedding" "ming" == True--- > is_embedding "embedding" "mind" == False-is_embedding :: Eq t => [t] -> [t] -> Bool-is_embedding p q = isRight (embedding (p,q))--all_embeddings_m :: (Eq t,L.MonadLogic m) => [t] -> [t] -> m [Int]-all_embeddings_m p q =-    let q_n = length q-        recur p' q' n k = -- n = length k-            if n == q_n-            then return (reverse k)-            else do (m,c) <- L.msum (map return p')-                    let k0:_ = k-                        c':_ = q'-                    L.guard (c == c' && (null k || m > k0))-                    let _:p'' = p'-                        _:q'' = q'-                    recur p'' q'' (n + 1) (m : k)-    in recur (zip [0..] p) q 0 []---- | Enumerate indices for all embeddings of /q/ in /p/.------ > all_embeddings "all_embeddings" "leg" == [[1,4,12],[1,7,12],[2,4,12],[2,7,12]]-all_embeddings :: Eq t => [t] -> [t] -> [[Int]]-all_embeddings p = L.observeAll . all_embeddings_m p---- * Un-list---- | Unpack one element list.-unlist1 :: [t] -> Maybe t-unlist1 l =-    case l of-      [e] -> Just e-      _ -> Nothing---- | Erroring variant.-unlist1_err :: [t] -> t-unlist1_err = fromMaybe (error "unlist1") . unlist1---- * Traversable---- | Replace elements at 'Traversable' with result of joining with elements from list.------ > let t = Node 0 [Node 1 [Node 2 [],Node 3 []],Node 4 []]--- > putStrLn $ drawTree (fmap show t)--- > let u = (adopt_shape (\_ x -> x) "abcde" t)--- > putStrLn $ drawTree (fmap return u)-adopt_shape :: T.Traversable t => (a -> b -> c) -> [b] -> t a -> t c-adopt_shape jn l =-    let f (i:j) k = (j,jn k i)-        f [] _ = error "adopt_shape: rhs ends"-    in snd . T.mapAccumL f l---- | Variant of 'adopt_shape' that considers only 'Just' elements at 'Traversable'.------ > let {s = "a(b(cd)ef)ghi"--- >     ;t = group_tree (begin_end_cmp_eq '(' ')') s}--- > in adopt_shape_m (,) [1..13] t-adopt_shape_m :: T.Traversable t => (a -> b-> c) -> [b] -> t (Maybe a) -> t (Maybe c)-adopt_shape_m jn l =-    let f (i:j) k = case k of-                      Nothing -> (i:j,Nothing)-                      Just k' -> (j,Just (jn k' i))-        f [] _ = error "adopt_shape_m: rhs ends"-    in snd . T.mapAccumL f l---- * Tree--{- | Given an 'Ordering' predicate where 'LT' opens a group, 'GT'-closes a group, and 'EQ' continues current group, construct tree-from list.--> let {l = "a {b {c d} e f} g h i"->     ;t = group_tree ((==) '{',(==) '}') l}-> in catMaybes (flatten t) == l--> let {d = putStrLn . drawTree . fmap show}-> in d (group_tree ((==) '(',(==) ')') "a(b(cd)ef)ghi")---}-group_tree :: (a -> Bool,a -> Bool) -> [a] -> Tree (Maybe a)-group_tree (open_f,close_f) =-    let unit e = Node (Just e) []-        nil = Node Nothing []-        insert_e (Node t l) e = Node t (e:l)-        reverse_n (Node t l) = Node t (reverse l)-        do_push (r,z) e =-            case z of-              h:z' -> (r,insert_e h (unit e) : z')-              [] -> (unit e : r,[])-        do_open (r,z) = (r,nil:z)-        do_close (r,z) =-            case z of-              h0:h1:z' -> (r,insert_e h1 (reverse_n h0) : z')-              h:z' -> (reverse_n h : r,z')-              [] -> (r,z)-        go st x =-            case x of-              [] -> Node Nothing (reverse (fst st))-              e:x' -> if open_f e-                      then go (do_push (do_open st) e) x'-                      else if close_f e-                           then go (do_close (do_push st e)) x'-                           else go (do_push st e) x'-    in go ([],[])---- * Indexing---- | Remove element at index.------ > remove_ix 5 "remove" == "remov"--- > remove_ix 5 "short" == undefined-remove_ix :: Int -> [a] -> [a]-remove_ix k l = let (p,q) = splitAt k l in p ++ tail q--operate_ixs :: Bool -> [Int] -> [a] -> [a]-operate_ixs mode k =-    let sel = if mode then notElem else elem-        f (n,e) = if n `sel` k then Nothing else Just e-    in mapMaybe f . zip [0..]---- > select_ixs [1,3] "select" == "ee"-select_ixs :: [Int] -> [a] -> [a]-select_ixs = operate_ixs True---- > remove_ixs [1,3,5] "remove" == "rmv"-remove_ixs :: [Int] -> [a] -> [a]-remove_ixs = operate_ixs False---- | Replace element at /i/ in /p/ by application of /f/.------ > replace_ix negate 1 [1..3] == [1,-2,3]-replace_ix :: (a -> a) -> Int -> [a] -> [a]-replace_ix f i p =-    let (q,r:s) = splitAt i p-    in q ++ (f r : s)---- | Cyclic indexing function.------ > map (at_cyclic "cycle") [0..9] == "cyclecycle"-at_cyclic :: [a] -> Int -> a-at_cyclic l n =-    let m = Map.fromList (zip [0..] l)-        k = Map.size m-        n' = n `mod` k-    in fromMaybe (error "cyc_at") (Map.lookup n' m)-
+ Music/Theory/List/Logic.hs view
@@ -0,0 +1,29 @@+-- | List/Logic functions.+module Music.Theory.List.Logic where++import Control.Monad {- base -}++import qualified Control.Monad.Logic as L {- logict -}++-- | 'L.MonadLogic' value to enumerate indices for all embeddings of /q/ in /p/.+all_embeddings_m :: (Eq t, MonadPlus m, L.MonadLogic m) => [t] -> [t] -> m [Int]+all_embeddings_m p q =+    let q_n = length q+        recur p' q' n k = -- n = length k+            if n == q_n+            then return (reverse k)+            else do (m,c) <- msum (map return p')+                    let k0 = head k+                        c' = head q'+                    guard (c == c' && (null k || m > k0))+                    let p'' = tail p'+                        q'' = tail q'+                    recur p'' q'' (n + 1) (m : k)+    in recur (zip [0..] p) q 0 []++-- | 'L.observeAll' of 'all_embeddings_m'+--+-- > all_embeddings "all_embeddings" "leg" == [[1,4,12],[1,7,12],[2,4,12],[2,7,12]]+all_embeddings :: Eq t => [t] -> [t] -> [[Int]]+all_embeddings p = L.observeAll . all_embeddings_m p+
− Music/Theory/Map.hs 
@@ -1,17 +0,0 @@--- | Map functions.-module Music.Theory.Map where--import qualified Data.Map as M {- containers -}-import Data.Maybe {- base -}---- | Erroring 'M.lookup'.-map_lookup_err :: Ord k => k -> M.Map k c -> c-map_lookup_err k = fromMaybe (error "M.lookup") . M.lookup k---- | 'flip' of 'M.lookup'.-map_ix :: Ord k => M.Map k c -> k -> Maybe c-map_ix = flip M.lookup---- | 'flip' of 'map_lookup_err'.-map_ix_err :: Ord k => M.Map k c -> k -> c-map_ix_err = flip map_lookup_err
− Music/Theory/Math.hs 
@@ -1,207 +0,0 @@--- | Math functions.-module Music.Theory.Math where--import Data.Maybe {- base -}-import Data.Ratio {- base -}-import Numeric {- base -}--import qualified Music.Theory.Math.Convert as T---- | Real (alias for 'Double').-type R = Double---- | <http://reference.wolfram.com/mathematica/ref/FractionalPart.html>------ > integral_and_fractional_parts 1.5 == (1,0.5)-integral_and_fractional_parts :: (Integral i, RealFrac t) => t -> (i,t)-integral_and_fractional_parts n =-    if n >= 0-    then let n' = floor n in (n',n - fromIntegral n')-    else let n' = ceiling n in (n',n - fromIntegral n')---- | Type specialised.-integer_and_fractional_parts :: RealFrac t => t -> (Integer,t)-integer_and_fractional_parts = integral_and_fractional_parts---- | <http://reference.wolfram.com/mathematica/ref/FractionalPart.html>------ > import Sound.SC3.Plot {- hsc3-plot -}--- > plotTable1 (map fractional_part [-2.0,-1.99 .. 2.0])-fractional_part :: RealFrac a => a -> a-fractional_part = snd . integer_and_fractional_parts---- | 'floor' of 'T.real_to_double'.-real_floor :: (Real r,Integral i)  => r -> i-real_floor = floor . T.real_to_double---- | Type specialised 'real_floor'.-real_floor_int :: Real r => r -> Int-real_floor_int = real_floor---- | 'round' of 'T.real_to_double'.-real_round :: (Real r,Integral i)  => r -> i-real_round = round . T.real_to_double---- | Type specialised 'real_round'.-real_round_int :: Real r => r -> Int-real_round_int = real_round---- | Is /r/ zero to /k/ decimal places.------ > map (flip zero_to_precision 0.00009) [4,5] == [True,False]--- > zero_to_precision 4 1.00009 == False-zero_to_precision :: Real r => Int -> r -> Bool-zero_to_precision k r = real_floor_int (r * (fromIntegral ((10::Int) ^ k))) == 0---- | Is /r/ whole to /k/ decimal places.------ > map (flip whole_to_precision 1.00009) [4,5] == [True,False]-whole_to_precision :: Real r => Int -> r -> Bool-whole_to_precision k = zero_to_precision k . fractional_part . T.real_to_double---- | <http://reference.wolfram.com/mathematica/ref/SawtoothWave.html>------ > plotTable1 (map sawtooth_wave [-2.0,-1.99 .. 2.0])-sawtooth_wave :: RealFrac a => a -> a-sawtooth_wave n = n - floor_f n---- | Pretty printer for 'Rational' that elides denominators of @1@.------ > map rational_pp [1,3/2,2] == ["1","3/2","2"]-rational_pp :: (Show a,Integral a) => Ratio a -> String-rational_pp r =-    let n = numerator r-        d = denominator r-    in if d == 1-       then show n-       else concat [show n,"/",show d]---- | Pretty print ratio as @:@ separated integers.------ > map ratio_pp [1,3/2,2] == ["1:1","3:2","2:1"]-ratio_pp :: Rational -> String-ratio_pp r =-    let (n,d) = rational_nd r-    in concat [show n,":",show d]---- | Predicate that is true if @n/d@ can be simplified, ie. where--- 'gcd' of @n@ and @d@ is not @1@.------ > let r = [False,True,False]--- > in map rational_simplifies [(2,3),(4,6),(5,7)] == r-rational_simplifies :: Integral a => (a,a) -> Bool-rational_simplifies (n,d) = gcd n d /= 1---- | 'numerator' and 'denominator' of rational.-rational_nd :: Ratio t -> (t,t)-rational_nd r = (numerator r,denominator r)---- | Rational as a whole number, or 'Nothing'.-rational_whole :: Integral a => Ratio a -> Maybe a-rational_whole r = if denominator r == 1 then Just (numerator r) else Nothing---- | Erroring variant.-rational_whole_err :: Integral a => Ratio a -> a-rational_whole_err = fromMaybe (error "rational_whole") . rational_whole---- | Show rational to /n/ decimal places.------ > let r = approxRational pi 1e-100--- > r == 884279719003555 / 281474976710656--- > show_rational_decimal 12 r == "3.141592653590"-show_rational_decimal :: Int -> Rational -> String-show_rational_decimal n r =-    let d = round (abs r * 10^n)-        s = show (d :: Integer)-        s' = replicate (n - length s + 1) '0' ++ s-        (h, f) = splitAt (length s' - n) s'-    in  (if r < 0 then "-" else "") ++ h ++ "." ++ f---- | Variant of 'showFFloat'.  The 'Show' instance for floats resorts--- to exponential notation very readily.------ > [show 0.01,realfloat_pp 2 0.01] == ["1.0e-2","0.01"]-realfloat_pp :: RealFloat a => Int -> a -> String-realfloat_pp k n = showFFloat (Just k) n ""---- | Show /r/ as float to /k/ places.-real_pp :: Real t => Int -> t -> String-real_pp k t = showFFloat (Just k) (T.real_to_double t) ""---- | Type specialised 'realfloat_pp'.-float_pp :: Int -> Float -> String-float_pp = realfloat_pp---- | Type specialised 'realfloat_pp'.-double_pp :: Int -> Double -> String-double_pp = realfloat_pp---- | Show /only/ positive and negative values, always with sign.------ > map num_diff_str [-2,-1,0,1,2] == ["-2","-1","","+1","+2"]--- > map show [-2,-1,0,1,2] == ["-2","-1","0","1","2"]-num_diff_str :: (Num a, Ord a, Show a) => a -> String-num_diff_str n =-    case compare n 0 of-      LT -> '-' : show (abs n)-      EQ -> ""-      GT -> '+' : show n---- | 'fromInteger' . 'floor'.-floor_f :: (RealFrac a, Num b) => a -> b-floor_f = fromInteger . floor---- | Round /b/ to nearest multiple of /a/.------ > map (round_to 0.25) [0,0.1 .. 1] == [0.0,0.0,0.25,0.25,0.5,0.5,0.5,0.75,0.75,1.0,1.0]--- > map (round_to 25) [0,10 .. 100] == [0,0,25,25,50,50,50,75,75,100,100]-round_to :: RealFrac n => n -> n -> n-round_to a b = if a == 0 then b else floor_f ((b / a) + 0.5) * a---- * One-indexed---- | One-indexed 'mod' function.------ > map (`oi_mod` 5) [1..10] == [1,2,3,4,5,1,2,3,4,5]-oi_mod :: Integral a => a -> a -> a-oi_mod n m = ((n - 1) `mod` m) + 1---- | One-indexed 'divMod' function.------ > map (`oi_divMod` 5) [1,3 .. 9] == [(0,1),(0,3),(0,5),(1,2),(1,4)]-oi_divMod :: Integral t => t -> t -> (t, t)-oi_divMod n m = let (i,j) = (n - 1) `divMod` m in (i,j + 1)---- * I = integral---- | Integral square root function.------ > map i_square_root [0,1,4,9,16,25,36,49,64,81,100] == [0 .. 10]--- > map i_square_root [4 .. 16] == [2,2,2,2,2,3,3,3,3,3,3,3,4]-i_square_root :: Integral t => t -> t-i_square_root n =-    let babylon a =-            let b  = quot (a + quot n a) 2-            in if a > b then babylon b else a-    in case compare n 0 of-         GT -> babylon n-         EQ -> 0-         _ -> error "i_square_root: negative?"---- * Interval---- | (0,1) = {x | 0 < x < 1}-in_open_interval :: Ord a => (a, a) -> a -> Bool-in_open_interval (p,q) n = p < n && n < q---- | [0,1] = {x | 0 ≤ x ≤ 1}-in_closed_interval :: Ord a => (a, a) -> a -> Bool-in_closed_interval (p,q) n = p <= n && n <= q---- | (p,q] (0,1] = {x | 0 < x ≤ 1}-in_left_half_open_interval :: Ord a => (a, a) -> a -> Bool-in_left_half_open_interval (p,q) n = p < n && n <= q---- | [p,q) [0,1) = {x | 0 ≤ x < 1}-in_right_half_open_interval :: Ord a => (a, a) -> a -> Bool-in_right_half_open_interval (p,q) n = p <= n && n < q
− Music/Theory/Math/Convert.hs 
@@ -1,1121 +0,0 @@-{- | Specialised type conversions, see mk/mk-convert.hs--> map int_to_word8 [-1,0,255,256] == [255,0,255,0]-> map int_to_word8_maybe [-1,0,255,256] == [Nothing,Just 0,Just 255,Nothing]--> map integer_to_int64_maybe [-2 ^ 63 - 1,2 ^ 63] == [Nothing,Nothing]-> map integer_to_word64_maybe [2 ^64 - 1,2 ^ 64] == [Just 18446744073709551615,Nothing]--> map int16_to_float [-1,0,1] == [-1,0,1]---}-module Music.Theory.Math.Convert where--import Data.Int {- base -}-import Data.Word {- base -}---- | Type specialised 'realToFrac'-real_to_float :: Real t => t -> Float-real_to_float = realToFrac---- | Type specialised 'realToFrac'-real_to_double :: Real t => t -> Double-real_to_double = realToFrac---- | Type specialised 'realToFrac'-double_to_float :: Double -> Float-double_to_float = realToFrac---- | Type specialised 'realToFrac'-float_to_double :: Float -> Double-float_to_double = realToFrac---- AUTOGEN (see mk/mk-convert.hs)---- | Type specialised 'fromIntegral'-word8_to_word16 :: Word8 -> Word16-word8_to_word16 = fromIntegral---- | Type specialised 'fromIntegral'-word8_to_word32 :: Word8 -> Word32-word8_to_word32 = fromIntegral---- | Type specialised 'fromIntegral'-word8_to_word64 :: Word8 -> Word64-word8_to_word64 = fromIntegral---- | Type specialised 'fromIntegral'-word8_to_int8 :: Word8 -> Int8-word8_to_int8 = fromIntegral---- | Type specialised 'fromIntegral'-word8_to_int16 :: Word8 -> Int16-word8_to_int16 = fromIntegral---- | Type specialised 'fromIntegral'-word8_to_int32 :: Word8 -> Int32-word8_to_int32 = fromIntegral---- | Type specialised 'fromIntegral'-word8_to_int64 :: Word8 -> Int64-word8_to_int64 = fromIntegral---- | Type specialised 'fromIntegral'-word8_to_int :: Word8 -> Int-word8_to_int = fromIntegral---- | Type specialised 'fromIntegral'-word8_to_integer :: Word8 -> Integer-word8_to_integer = fromIntegral---- | Type specialised 'fromIntegral'-word8_to_float :: Word8 -> Float-word8_to_float = fromIntegral---- | Type specialised 'fromIntegral'-word8_to_double :: Word8 -> Double-word8_to_double = fromIntegral---- | Type specialised 'fromIntegral'-word16_to_word8 :: Word16 -> Word8-word16_to_word8 = fromIntegral---- | Type specialised 'fromIntegral'-word16_to_word32 :: Word16 -> Word32-word16_to_word32 = fromIntegral---- | Type specialised 'fromIntegral'-word16_to_word64 :: Word16 -> Word64-word16_to_word64 = fromIntegral---- | Type specialised 'fromIntegral'-word16_to_int8 :: Word16 -> Int8-word16_to_int8 = fromIntegral---- | Type specialised 'fromIntegral'-word16_to_int16 :: Word16 -> Int16-word16_to_int16 = fromIntegral---- | Type specialised 'fromIntegral'-word16_to_int32 :: Word16 -> Int32-word16_to_int32 = fromIntegral---- | Type specialised 'fromIntegral'-word16_to_int64 :: Word16 -> Int64-word16_to_int64 = fromIntegral---- | Type specialised 'fromIntegral'-word16_to_int :: Word16 -> Int-word16_to_int = fromIntegral---- | Type specialised 'fromIntegral'-word16_to_integer :: Word16 -> Integer-word16_to_integer = fromIntegral---- | Type specialised 'fromIntegral'-word16_to_float :: Word16 -> Float-word16_to_float = fromIntegral---- | Type specialised 'fromIntegral'-word16_to_double :: Word16 -> Double-word16_to_double = fromIntegral---- | Type specialised 'fromIntegral'-word32_to_word8 :: Word32 -> Word8-word32_to_word8 = fromIntegral---- | Type specialised 'fromIntegral'-word32_to_word16 :: Word32 -> Word16-word32_to_word16 = fromIntegral---- | Type specialised 'fromIntegral'-word32_to_word64 :: Word32 -> Word64-word32_to_word64 = fromIntegral---- | Type specialised 'fromIntegral'-word32_to_int8 :: Word32 -> Int8-word32_to_int8 = fromIntegral---- | Type specialised 'fromIntegral'-word32_to_int16 :: Word32 -> Int16-word32_to_int16 = fromIntegral---- | Type specialised 'fromIntegral'-word32_to_int32 :: Word32 -> Int32-word32_to_int32 = fromIntegral---- | Type specialised 'fromIntegral'-word32_to_int64 :: Word32 -> Int64-word32_to_int64 = fromIntegral---- | Type specialised 'fromIntegral'-word32_to_int :: Word32 -> Int-word32_to_int = fromIntegral---- | Type specialised 'fromIntegral'-word32_to_integer :: Word32 -> Integer-word32_to_integer = fromIntegral---- | Type specialised 'fromIntegral'-word32_to_float :: Word32 -> Float-word32_to_float = fromIntegral---- | Type specialised 'fromIntegral'-word32_to_double :: Word32 -> Double-word32_to_double = fromIntegral---- | Type specialised 'fromIntegral'-word64_to_word8 :: Word64 -> Word8-word64_to_word8 = fromIntegral---- | Type specialised 'fromIntegral'-word64_to_word16 :: Word64 -> Word16-word64_to_word16 = fromIntegral---- | Type specialised 'fromIntegral'-word64_to_word32 :: Word64 -> Word32-word64_to_word32 = fromIntegral---- | Type specialised 'fromIntegral'-word64_to_int8 :: Word64 -> Int8-word64_to_int8 = fromIntegral---- | Type specialised 'fromIntegral'-word64_to_int16 :: Word64 -> Int16-word64_to_int16 = fromIntegral---- | Type specialised 'fromIntegral'-word64_to_int32 :: Word64 -> Int32-word64_to_int32 = fromIntegral---- | Type specialised 'fromIntegral'-word64_to_int64 :: Word64 -> Int64-word64_to_int64 = fromIntegral---- | Type specialised 'fromIntegral'-word64_to_int :: Word64 -> Int-word64_to_int = fromIntegral---- | Type specialised 'fromIntegral'-word64_to_integer :: Word64 -> Integer-word64_to_integer = fromIntegral---- | Type specialised 'fromIntegral'-word64_to_float :: Word64 -> Float-word64_to_float = fromIntegral---- | Type specialised 'fromIntegral'-word64_to_double :: Word64 -> Double-word64_to_double = fromIntegral---- | Type specialised 'fromIntegral'-int8_to_word8 :: Int8 -> Word8-int8_to_word8 = fromIntegral---- | Type specialised 'fromIntegral'-int8_to_word16 :: Int8 -> Word16-int8_to_word16 = fromIntegral---- | Type specialised 'fromIntegral'-int8_to_word32 :: Int8 -> Word32-int8_to_word32 = fromIntegral---- | Type specialised 'fromIntegral'-int8_to_word64 :: Int8 -> Word64-int8_to_word64 = fromIntegral---- | Type specialised 'fromIntegral'-int8_to_int16 :: Int8 -> Int16-int8_to_int16 = fromIntegral---- | Type specialised 'fromIntegral'-int8_to_int32 :: Int8 -> Int32-int8_to_int32 = fromIntegral---- | Type specialised 'fromIntegral'-int8_to_int64 :: Int8 -> Int64-int8_to_int64 = fromIntegral---- | Type specialised 'fromIntegral'-int8_to_int :: Int8 -> Int-int8_to_int = fromIntegral---- | Type specialised 'fromIntegral'-int8_to_integer :: Int8 -> Integer-int8_to_integer = fromIntegral---- | Type specialised 'fromIntegral'-int8_to_float :: Int8 -> Float-int8_to_float = fromIntegral---- | Type specialised 'fromIntegral'-int8_to_double :: Int8 -> Double-int8_to_double = fromIntegral---- | Type specialised 'fromIntegral'-int16_to_word8 :: Int16 -> Word8-int16_to_word8 = fromIntegral---- | Type specialised 'fromIntegral'-int16_to_word16 :: Int16 -> Word16-int16_to_word16 = fromIntegral---- | Type specialised 'fromIntegral'-int16_to_word32 :: Int16 -> Word32-int16_to_word32 = fromIntegral---- | Type specialised 'fromIntegral'-int16_to_word64 :: Int16 -> Word64-int16_to_word64 = fromIntegral---- | Type specialised 'fromIntegral'-int16_to_int8 :: Int16 -> Int8-int16_to_int8 = fromIntegral---- | Type specialised 'fromIntegral'-int16_to_int32 :: Int16 -> Int32-int16_to_int32 = fromIntegral---- | Type specialised 'fromIntegral'-int16_to_int64 :: Int16 -> Int64-int16_to_int64 = fromIntegral---- | Type specialised 'fromIntegral'-int16_to_int :: Int16 -> Int-int16_to_int = fromIntegral---- | Type specialised 'fromIntegral'-int16_to_integer :: Int16 -> Integer-int16_to_integer = fromIntegral---- | Type specialised 'fromIntegral'-int16_to_float :: Int16 -> Float-int16_to_float = fromIntegral---- | Type specialised 'fromIntegral'-int16_to_double :: Int16 -> Double-int16_to_double = fromIntegral---- | Type specialised 'fromIntegral'-int32_to_word8 :: Int32 -> Word8-int32_to_word8 = fromIntegral---- | Type specialised 'fromIntegral'-int32_to_word16 :: Int32 -> Word16-int32_to_word16 = fromIntegral---- | Type specialised 'fromIntegral'-int32_to_word32 :: Int32 -> Word32-int32_to_word32 = fromIntegral---- | Type specialised 'fromIntegral'-int32_to_word64 :: Int32 -> Word64-int32_to_word64 = fromIntegral---- | Type specialised 'fromIntegral'-int32_to_int8 :: Int32 -> Int8-int32_to_int8 = fromIntegral---- | Type specialised 'fromIntegral'-int32_to_int16 :: Int32 -> Int16-int32_to_int16 = fromIntegral---- | Type specialised 'fromIntegral'-int32_to_int64 :: Int32 -> Int64-int32_to_int64 = fromIntegral---- | Type specialised 'fromIntegral'-int32_to_int :: Int32 -> Int-int32_to_int = fromIntegral---- | Type specialised 'fromIntegral'-int32_to_integer :: Int32 -> Integer-int32_to_integer = fromIntegral---- | Type specialised 'fromIntegral'-int32_to_float :: Int32 -> Float-int32_to_float = fromIntegral---- | Type specialised 'fromIntegral'-int32_to_double :: Int32 -> Double-int32_to_double = fromIntegral---- | Type specialised 'fromIntegral'-int64_to_word8 :: Int64 -> Word8-int64_to_word8 = fromIntegral---- | Type specialised 'fromIntegral'-int64_to_word16 :: Int64 -> Word16-int64_to_word16 = fromIntegral---- | Type specialised 'fromIntegral'-int64_to_word32 :: Int64 -> Word32-int64_to_word32 = fromIntegral---- | Type specialised 'fromIntegral'-int64_to_word64 :: Int64 -> Word64-int64_to_word64 = fromIntegral---- | Type specialised 'fromIntegral'-int64_to_int8 :: Int64 -> Int8-int64_to_int8 = fromIntegral---- | Type specialised 'fromIntegral'-int64_to_int16 :: Int64 -> Int16-int64_to_int16 = fromIntegral---- | Type specialised 'fromIntegral'-int64_to_int32 :: Int64 -> Int32-int64_to_int32 = fromIntegral---- | Type specialised 'fromIntegral'-int64_to_int :: Int64 -> Int-int64_to_int = fromIntegral---- | Type specialised 'fromIntegral'-int64_to_integer :: Int64 -> Integer-int64_to_integer = fromIntegral---- | Type specialised 'fromIntegral'-int64_to_float :: Int64 -> Float-int64_to_float = fromIntegral---- | Type specialised 'fromIntegral'-int64_to_double :: Int64 -> Double-int64_to_double = fromIntegral---- | Type specialised 'fromIntegral'-int_to_word8 :: Int -> Word8-int_to_word8 = fromIntegral---- | Type specialised 'fromIntegral'-int_to_word16 :: Int -> Word16-int_to_word16 = fromIntegral---- | Type specialised 'fromIntegral'-int_to_word32 :: Int -> Word32-int_to_word32 = fromIntegral---- | Type specialised 'fromIntegral'-int_to_word64 :: Int -> Word64-int_to_word64 = fromIntegral---- | Type specialised 'fromIntegral'-int_to_int8 :: Int -> Int8-int_to_int8 = fromIntegral---- | Type specialised 'fromIntegral'-int_to_int16 :: Int -> Int16-int_to_int16 = fromIntegral---- | Type specialised 'fromIntegral'-int_to_int32 :: Int -> Int32-int_to_int32 = fromIntegral---- | Type specialised 'fromIntegral'-int_to_int64 :: Int -> Int64-int_to_int64 = fromIntegral---- | Type specialised 'fromIntegral'-int_to_integer :: Int -> Integer-int_to_integer = fromIntegral---- | Type specialised 'fromIntegral'-int_to_float :: Int -> Float-int_to_float = fromIntegral---- | Type specialised 'fromIntegral'-int_to_double :: Int -> Double-int_to_double = fromIntegral---- | Type specialised 'fromIntegral'-integer_to_word8 :: Integer -> Word8-integer_to_word8 = fromIntegral---- | Type specialised 'fromIntegral'-integer_to_word16 :: Integer -> Word16-integer_to_word16 = fromIntegral---- | Type specialised 'fromIntegral'-integer_to_word32 :: Integer -> Word32-integer_to_word32 = fromIntegral---- | Type specialised 'fromIntegral'-integer_to_word64 :: Integer -> Word64-integer_to_word64 = fromIntegral---- | Type specialised 'fromIntegral'-integer_to_int8 :: Integer -> Int8-integer_to_int8 = fromIntegral---- | Type specialised 'fromIntegral'-integer_to_int16 :: Integer -> Int16-integer_to_int16 = fromIntegral---- | Type specialised 'fromIntegral'-integer_to_int32 :: Integer -> Int32-integer_to_int32 = fromIntegral---- | Type specialised 'fromIntegral'-integer_to_int64 :: Integer -> Int64-integer_to_int64 = fromIntegral---- | Type specialised 'fromIntegral'-integer_to_int :: Integer -> Int-integer_to_int = fromIntegral---- | Type specialised 'fromIntegral'-integer_to_float :: Integer -> Float-integer_to_float = fromIntegral---- | Type specialised 'fromIntegral'-integer_to_double :: Integer -> Double-integer_to_double = fromIntegral---- | Type specialised 'fromIntegral'-word8_to_word16_maybe :: Word8 -> Maybe Word16-word8_to_word16_maybe n =-    if n < fromIntegral (minBound::Word16) ||-       n > fromIntegral (maxBound::Word16)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-word8_to_word32_maybe :: Word8 -> Maybe Word32-word8_to_word32_maybe n =-    if n < fromIntegral (minBound::Word32) ||-       n > fromIntegral (maxBound::Word32)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-word8_to_word64_maybe :: Word8 -> Maybe Word64-word8_to_word64_maybe n =-    if n < fromIntegral (minBound::Word64) ||-       n > fromIntegral (maxBound::Word64)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-word8_to_int8_maybe :: Word8 -> Maybe Int8-word8_to_int8_maybe n =-    if n < fromIntegral (minBound::Int8) ||-       n > fromIntegral (maxBound::Int8)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-word8_to_int16_maybe :: Word8 -> Maybe Int16-word8_to_int16_maybe n =-    if n < fromIntegral (minBound::Int16) ||-       n > fromIntegral (maxBound::Int16)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-word8_to_int32_maybe :: Word8 -> Maybe Int32-word8_to_int32_maybe n =-    if n < fromIntegral (minBound::Int32) ||-       n > fromIntegral (maxBound::Int32)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-word8_to_int64_maybe :: Word8 -> Maybe Int64-word8_to_int64_maybe n =-    if n < fromIntegral (minBound::Int64) ||-       n > fromIntegral (maxBound::Int64)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-word8_to_int_maybe :: Word8 -> Maybe Int-word8_to_int_maybe n =-    if n < fromIntegral (minBound::Int) ||-       n > fromIntegral (maxBound::Int)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-word16_to_word8_maybe :: Word16 -> Maybe Word8-word16_to_word8_maybe n =-    if n < fromIntegral (minBound::Word8) ||-       n > fromIntegral (maxBound::Word8)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-word16_to_word32_maybe :: Word16 -> Maybe Word32-word16_to_word32_maybe n =-    if n < fromIntegral (minBound::Word32) ||-       n > fromIntegral (maxBound::Word32)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-word16_to_word64_maybe :: Word16 -> Maybe Word64-word16_to_word64_maybe n =-    if n < fromIntegral (minBound::Word64) ||-       n > fromIntegral (maxBound::Word64)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-word16_to_int8_maybe :: Word16 -> Maybe Int8-word16_to_int8_maybe n =-    if n < fromIntegral (minBound::Int8) ||-       n > fromIntegral (maxBound::Int8)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-word16_to_int16_maybe :: Word16 -> Maybe Int16-word16_to_int16_maybe n =-    if n < fromIntegral (minBound::Int16) ||-       n > fromIntegral (maxBound::Int16)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-word16_to_int32_maybe :: Word16 -> Maybe Int32-word16_to_int32_maybe n =-    if n < fromIntegral (minBound::Int32) ||-       n > fromIntegral (maxBound::Int32)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-word16_to_int64_maybe :: Word16 -> Maybe Int64-word16_to_int64_maybe n =-    if n < fromIntegral (minBound::Int64) ||-       n > fromIntegral (maxBound::Int64)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-word16_to_int_maybe :: Word16 -> Maybe Int-word16_to_int_maybe n =-    if n < fromIntegral (minBound::Int) ||-       n > fromIntegral (maxBound::Int)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-word32_to_word8_maybe :: Word32 -> Maybe Word8-word32_to_word8_maybe n =-    if n < fromIntegral (minBound::Word8) ||-       n > fromIntegral (maxBound::Word8)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-word32_to_word16_maybe :: Word32 -> Maybe Word16-word32_to_word16_maybe n =-    if n < fromIntegral (minBound::Word16) ||-       n > fromIntegral (maxBound::Word16)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-word32_to_word64_maybe :: Word32 -> Maybe Word64-word32_to_word64_maybe n =-    if n < fromIntegral (minBound::Word64) ||-       n > fromIntegral (maxBound::Word64)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-word32_to_int8_maybe :: Word32 -> Maybe Int8-word32_to_int8_maybe n =-    if n < fromIntegral (minBound::Int8) ||-       n > fromIntegral (maxBound::Int8)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-word32_to_int16_maybe :: Word32 -> Maybe Int16-word32_to_int16_maybe n =-    if n < fromIntegral (minBound::Int16) ||-       n > fromIntegral (maxBound::Int16)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-word32_to_int32_maybe :: Word32 -> Maybe Int32-word32_to_int32_maybe n =-    if n < fromIntegral (minBound::Int32) ||-       n > fromIntegral (maxBound::Int32)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-word32_to_int64_maybe :: Word32 -> Maybe Int64-word32_to_int64_maybe n =-    if n < fromIntegral (minBound::Int64) ||-       n > fromIntegral (maxBound::Int64)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-word32_to_int_maybe :: Word32 -> Maybe Int-word32_to_int_maybe n =-    if n < fromIntegral (minBound::Int) ||-       n > fromIntegral (maxBound::Int)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-word64_to_word8_maybe :: Word64 -> Maybe Word8-word64_to_word8_maybe n =-    if n < fromIntegral (minBound::Word8) ||-       n > fromIntegral (maxBound::Word8)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-word64_to_word16_maybe :: Word64 -> Maybe Word16-word64_to_word16_maybe n =-    if n < fromIntegral (minBound::Word16) ||-       n > fromIntegral (maxBound::Word16)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-word64_to_word32_maybe :: Word64 -> Maybe Word32-word64_to_word32_maybe n =-    if n < fromIntegral (minBound::Word32) ||-       n > fromIntegral (maxBound::Word32)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-word64_to_int8_maybe :: Word64 -> Maybe Int8-word64_to_int8_maybe n =-    if n < fromIntegral (minBound::Int8) ||-       n > fromIntegral (maxBound::Int8)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-word64_to_int16_maybe :: Word64 -> Maybe Int16-word64_to_int16_maybe n =-    if n < fromIntegral (minBound::Int16) ||-       n > fromIntegral (maxBound::Int16)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-word64_to_int32_maybe :: Word64 -> Maybe Int32-word64_to_int32_maybe n =-    if n < fromIntegral (minBound::Int32) ||-       n > fromIntegral (maxBound::Int32)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-word64_to_int64_maybe :: Word64 -> Maybe Int64-word64_to_int64_maybe n =-    if n < fromIntegral (minBound::Int64) ||-       n > fromIntegral (maxBound::Int64)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-word64_to_int_maybe :: Word64 -> Maybe Int-word64_to_int_maybe n =-    if n < fromIntegral (minBound::Int) ||-       n > fromIntegral (maxBound::Int)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-int8_to_word8_maybe :: Int8 -> Maybe Word8-int8_to_word8_maybe n =-    if n < fromIntegral (minBound::Word8) ||-       n > fromIntegral (maxBound::Word8)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-int8_to_word16_maybe :: Int8 -> Maybe Word16-int8_to_word16_maybe n =-    if n < fromIntegral (minBound::Word16) ||-       n > fromIntegral (maxBound::Word16)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-int8_to_word32_maybe :: Int8 -> Maybe Word32-int8_to_word32_maybe n =-    if n < fromIntegral (minBound::Word32) ||-       n > fromIntegral (maxBound::Word32)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-int8_to_word64_maybe :: Int8 -> Maybe Word64-int8_to_word64_maybe n =-    if n < fromIntegral (minBound::Word64) ||-       n > fromIntegral (maxBound::Word64)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-int8_to_int16_maybe :: Int8 -> Maybe Int16-int8_to_int16_maybe n =-    if n < fromIntegral (minBound::Int16) ||-       n > fromIntegral (maxBound::Int16)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-int8_to_int32_maybe :: Int8 -> Maybe Int32-int8_to_int32_maybe n =-    if n < fromIntegral (minBound::Int32) ||-       n > fromIntegral (maxBound::Int32)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-int8_to_int64_maybe :: Int8 -> Maybe Int64-int8_to_int64_maybe n =-    if n < fromIntegral (minBound::Int64) ||-       n > fromIntegral (maxBound::Int64)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-int8_to_int_maybe :: Int8 -> Maybe Int-int8_to_int_maybe n =-    if n < fromIntegral (minBound::Int) ||-       n > fromIntegral (maxBound::Int)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-int16_to_word8_maybe :: Int16 -> Maybe Word8-int16_to_word8_maybe n =-    if n < fromIntegral (minBound::Word8) ||-       n > fromIntegral (maxBound::Word8)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-int16_to_word16_maybe :: Int16 -> Maybe Word16-int16_to_word16_maybe n =-    if n < fromIntegral (minBound::Word16) ||-       n > fromIntegral (maxBound::Word16)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-int16_to_word32_maybe :: Int16 -> Maybe Word32-int16_to_word32_maybe n =-    if n < fromIntegral (minBound::Word32) ||-       n > fromIntegral (maxBound::Word32)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-int16_to_word64_maybe :: Int16 -> Maybe Word64-int16_to_word64_maybe n =-    if n < fromIntegral (minBound::Word64) ||-       n > fromIntegral (maxBound::Word64)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-int16_to_int8_maybe :: Int16 -> Maybe Int8-int16_to_int8_maybe n =-    if n < fromIntegral (minBound::Int8) ||-       n > fromIntegral (maxBound::Int8)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-int16_to_int32_maybe :: Int16 -> Maybe Int32-int16_to_int32_maybe n =-    if n < fromIntegral (minBound::Int32) ||-       n > fromIntegral (maxBound::Int32)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-int16_to_int64_maybe :: Int16 -> Maybe Int64-int16_to_int64_maybe n =-    if n < fromIntegral (minBound::Int64) ||-       n > fromIntegral (maxBound::Int64)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-int16_to_int_maybe :: Int16 -> Maybe Int-int16_to_int_maybe n =-    if n < fromIntegral (minBound::Int) ||-       n > fromIntegral (maxBound::Int)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-int32_to_word8_maybe :: Int32 -> Maybe Word8-int32_to_word8_maybe n =-    if n < fromIntegral (minBound::Word8) ||-       n > fromIntegral (maxBound::Word8)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-int32_to_word16_maybe :: Int32 -> Maybe Word16-int32_to_word16_maybe n =-    if n < fromIntegral (minBound::Word16) ||-       n > fromIntegral (maxBound::Word16)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-int32_to_word32_maybe :: Int32 -> Maybe Word32-int32_to_word32_maybe n =-    if n < fromIntegral (minBound::Word32) ||-       n > fromIntegral (maxBound::Word32)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-int32_to_word64_maybe :: Int32 -> Maybe Word64-int32_to_word64_maybe n =-    if n < fromIntegral (minBound::Word64) ||-       n > fromIntegral (maxBound::Word64)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-int32_to_int8_maybe :: Int32 -> Maybe Int8-int32_to_int8_maybe n =-    if n < fromIntegral (minBound::Int8) ||-       n > fromIntegral (maxBound::Int8)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-int32_to_int16_maybe :: Int32 -> Maybe Int16-int32_to_int16_maybe n =-    if n < fromIntegral (minBound::Int16) ||-       n > fromIntegral (maxBound::Int16)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-int32_to_int64_maybe :: Int32 -> Maybe Int64-int32_to_int64_maybe n =-    if n < fromIntegral (minBound::Int64) ||-       n > fromIntegral (maxBound::Int64)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-int32_to_int_maybe :: Int32 -> Maybe Int-int32_to_int_maybe n =-    if n < fromIntegral (minBound::Int) ||-       n > fromIntegral (maxBound::Int)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-int64_to_word8_maybe :: Int64 -> Maybe Word8-int64_to_word8_maybe n =-    if n < fromIntegral (minBound::Word8) ||-       n > fromIntegral (maxBound::Word8)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-int64_to_word16_maybe :: Int64 -> Maybe Word16-int64_to_word16_maybe n =-    if n < fromIntegral (minBound::Word16) ||-       n > fromIntegral (maxBound::Word16)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-int64_to_word32_maybe :: Int64 -> Maybe Word32-int64_to_word32_maybe n =-    if n < fromIntegral (minBound::Word32) ||-       n > fromIntegral (maxBound::Word32)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-int64_to_word64_maybe :: Int64 -> Maybe Word64-int64_to_word64_maybe n =-    if n < fromIntegral (minBound::Word64) ||-       n > fromIntegral (maxBound::Word64)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-int64_to_int8_maybe :: Int64 -> Maybe Int8-int64_to_int8_maybe n =-    if n < fromIntegral (minBound::Int8) ||-       n > fromIntegral (maxBound::Int8)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-int64_to_int16_maybe :: Int64 -> Maybe Int16-int64_to_int16_maybe n =-    if n < fromIntegral (minBound::Int16) ||-       n > fromIntegral (maxBound::Int16)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-int64_to_int32_maybe :: Int64 -> Maybe Int32-int64_to_int32_maybe n =-    if n < fromIntegral (minBound::Int32) ||-       n > fromIntegral (maxBound::Int32)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-int64_to_int_maybe :: Int64 -> Maybe Int-int64_to_int_maybe n =-    if n < fromIntegral (minBound::Int) ||-       n > fromIntegral (maxBound::Int)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-int_to_word8_maybe :: Int -> Maybe Word8-int_to_word8_maybe n =-    if n < fromIntegral (minBound::Word8) ||-       n > fromIntegral (maxBound::Word8)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-int_to_word16_maybe :: Int -> Maybe Word16-int_to_word16_maybe n =-    if n < fromIntegral (minBound::Word16) ||-       n > fromIntegral (maxBound::Word16)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-int_to_word32_maybe :: Int -> Maybe Word32-int_to_word32_maybe n =-    if n < fromIntegral (minBound::Word32) ||-       n > fromIntegral (maxBound::Word32)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-int_to_word64_maybe :: Int -> Maybe Word64-int_to_word64_maybe n =-    if n < fromIntegral (minBound::Word64) ||-       n > fromIntegral (maxBound::Word64)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-int_to_int8_maybe :: Int -> Maybe Int8-int_to_int8_maybe n =-    if n < fromIntegral (minBound::Int8) ||-       n > fromIntegral (maxBound::Int8)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-int_to_int16_maybe :: Int -> Maybe Int16-int_to_int16_maybe n =-    if n < fromIntegral (minBound::Int16) ||-       n > fromIntegral (maxBound::Int16)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-int_to_int32_maybe :: Int -> Maybe Int32-int_to_int32_maybe n =-    if n < fromIntegral (minBound::Int32) ||-       n > fromIntegral (maxBound::Int32)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-int_to_int64_maybe :: Int -> Maybe Int64-int_to_int64_maybe n =-    if n < fromIntegral (minBound::Int64) ||-       n > fromIntegral (maxBound::Int64)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-integer_to_word8_maybe :: Integer -> Maybe Word8-integer_to_word8_maybe n =-    if n < fromIntegral (minBound::Word8) ||-       n > fromIntegral (maxBound::Word8)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-integer_to_word16_maybe :: Integer -> Maybe Word16-integer_to_word16_maybe n =-    if n < fromIntegral (minBound::Word16) ||-       n > fromIntegral (maxBound::Word16)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-integer_to_word32_maybe :: Integer -> Maybe Word32-integer_to_word32_maybe n =-    if n < fromIntegral (minBound::Word32) ||-       n > fromIntegral (maxBound::Word32)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-integer_to_word64_maybe :: Integer -> Maybe Word64-integer_to_word64_maybe n =-    if n < fromIntegral (minBound::Word64) ||-       n > fromIntegral (maxBound::Word64)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-integer_to_int8_maybe :: Integer -> Maybe Int8-integer_to_int8_maybe n =-    if n < fromIntegral (minBound::Int8) ||-       n > fromIntegral (maxBound::Int8)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-integer_to_int16_maybe :: Integer -> Maybe Int16-integer_to_int16_maybe n =-    if n < fromIntegral (minBound::Int16) ||-       n > fromIntegral (maxBound::Int16)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-integer_to_int32_maybe :: Integer -> Maybe Int32-integer_to_int32_maybe n =-    if n < fromIntegral (minBound::Int32) ||-       n > fromIntegral (maxBound::Int32)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-integer_to_int64_maybe :: Integer -> Maybe Int64-integer_to_int64_maybe n =-    if n < fromIntegral (minBound::Int64) ||-       n > fromIntegral (maxBound::Int64)-    then Nothing-    else Just (fromIntegral n)---- | Type specialised 'fromIntegral'-integer_to_int_maybe :: Integer -> Maybe Int-integer_to_int_maybe n =-    if n < fromIntegral (minBound::Int) ||-       n > fromIntegral (maxBound::Int)-    then Nothing-    else Just (fromIntegral n)
+ Music/Theory/Math/Convert/Fx.hs view
@@ -0,0 +1,1286 @@+-- | Conversion between signed and sized integral types with bounds checking.+--   Types are aliased as Ux and Ix.+--   Includes sizes 4 (MIDI), 7 (ASCII,MIDI), 12 (SND,AKAI), 14 (MIDI) and 24 (SND).+--   Autogenerated: see mk/mk-convert.hs.+module Music.Theory.Math.Convert.Fx where++import Data.Int {- base -}+import Data.Word {- base -}++-- | Alias+type U4 = Word8++-- | Alias+type U7 = Word8++-- | Alias+type U8 = Word8++-- | Alias+type U12 = Word16++-- | Alias+type U14 = Word16++-- | Alias+type U16 = Word16++-- | Alias+type U24 = Word32++-- | Alias+type U32 = Word32++-- | Alias+type U64 = Word64++-- | Alias+type I4 = Int8++-- | Alias+type I7 = Int8++-- | Alias+type I8 = Int8++-- | Alias+type I12 = Int16++-- | Alias+type I14 = Int16++-- | Alias+type I16 = Int16++-- | Alias+type I24 = Int32++-- | Alias+type I32 = Int32++-- | Alias+type I64 = Int64++-- | Type specialised 'fromIntegral'+u4_to_u7 :: U4 -> U7+u4_to_u7 = fromIntegral++-- | Type specialised 'fromIntegral'+u4_to_u8 :: U4 -> U8+u4_to_u8 = fromIntegral++-- | Type specialised 'fromIntegral'+u4_to_u12 :: U4 -> U12+u4_to_u12 = fromIntegral++-- | Type specialised 'fromIntegral'+u4_to_u14 :: U4 -> U14+u4_to_u14 = fromIntegral++-- | Type specialised 'fromIntegral'+u4_to_u16 :: U4 -> U16+u4_to_u16 = fromIntegral++-- | Type specialised 'fromIntegral'+u4_to_u24 :: U4 -> U24+u4_to_u24 = fromIntegral++-- | Type specialised 'fromIntegral'+u4_to_u32 :: U4 -> U32+u4_to_u32 = fromIntegral++-- | Type specialised 'fromIntegral'+u4_to_u64 :: U4 -> U64+u4_to_u64 = fromIntegral++-- | Type specialised 'fromIntegral' with out-of-range error.+u4_to_i4 :: U4 -> I4+u4_to_i4 x = if x < 0 || x > 7 then error "u4_to_i4: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral'+u4_to_i7 :: U4 -> I7+u4_to_i7 = fromIntegral++-- | Type specialised 'fromIntegral'+u4_to_i8 :: U4 -> I8+u4_to_i8 = fromIntegral++-- | Type specialised 'fromIntegral'+u4_to_i12 :: U4 -> I12+u4_to_i12 = fromIntegral++-- | Type specialised 'fromIntegral'+u4_to_i14 :: U4 -> I14+u4_to_i14 = fromIntegral++-- | Type specialised 'fromIntegral'+u4_to_i16 :: U4 -> I16+u4_to_i16 = fromIntegral++-- | Type specialised 'fromIntegral'+u4_to_i24 :: U4 -> I24+u4_to_i24 = fromIntegral++-- | Type specialised 'fromIntegral'+u4_to_i32 :: U4 -> I32+u4_to_i32 = fromIntegral++-- | Type specialised 'fromIntegral'+u4_to_i64 :: U4 -> I64+u4_to_i64 = fromIntegral++-- | Type specialised 'fromIntegral' with out-of-range error.+u7_to_u4 :: U7 -> U4+u7_to_u4 x = if x < 0 || x > 15 then error "u7_to_u4: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral'+u7_to_u8 :: U7 -> U8+u7_to_u8 = fromIntegral++-- | Type specialised 'fromIntegral'+u7_to_u12 :: U7 -> U12+u7_to_u12 = fromIntegral++-- | Type specialised 'fromIntegral'+u7_to_u14 :: U7 -> U14+u7_to_u14 = fromIntegral++-- | Type specialised 'fromIntegral'+u7_to_u16 :: U7 -> U16+u7_to_u16 = fromIntegral++-- | Type specialised 'fromIntegral'+u7_to_u24 :: U7 -> U24+u7_to_u24 = fromIntegral++-- | Type specialised 'fromIntegral'+u7_to_u32 :: U7 -> U32+u7_to_u32 = fromIntegral++-- | Type specialised 'fromIntegral'+u7_to_u64 :: U7 -> U64+u7_to_u64 = fromIntegral++-- | Type specialised 'fromIntegral' with out-of-range error.+u7_to_i4 :: U7 -> I4+u7_to_i4 x = if x < 0 || x > 7 then error "u7_to_i4: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u7_to_i7 :: U7 -> I7+u7_to_i7 x = if x < 0 || x > 63 then error "u7_to_i7: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral'+u7_to_i8 :: U7 -> I8+u7_to_i8 = fromIntegral++-- | Type specialised 'fromIntegral'+u7_to_i12 :: U7 -> I12+u7_to_i12 = fromIntegral++-- | Type specialised 'fromIntegral'+u7_to_i14 :: U7 -> I14+u7_to_i14 = fromIntegral++-- | Type specialised 'fromIntegral'+u7_to_i16 :: U7 -> I16+u7_to_i16 = fromIntegral++-- | Type specialised 'fromIntegral'+u7_to_i24 :: U7 -> I24+u7_to_i24 = fromIntegral++-- | Type specialised 'fromIntegral'+u7_to_i32 :: U7 -> I32+u7_to_i32 = fromIntegral++-- | Type specialised 'fromIntegral'+u7_to_i64 :: U7 -> I64+u7_to_i64 = fromIntegral++-- | Type specialised 'fromIntegral' with out-of-range error.+u8_to_u4 :: U8 -> U4+u8_to_u4 x = if x < 0 || x > 15 then error "u8_to_u4: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u8_to_u7 :: U8 -> U7+u8_to_u7 x = if x < 0 || x > 127 then error "u8_to_u7: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral'+u8_to_u12 :: U8 -> U12+u8_to_u12 = fromIntegral++-- | Type specialised 'fromIntegral'+u8_to_u14 :: U8 -> U14+u8_to_u14 = fromIntegral++-- | Type specialised 'fromIntegral'+u8_to_u16 :: U8 -> U16+u8_to_u16 = fromIntegral++-- | Type specialised 'fromIntegral'+u8_to_u24 :: U8 -> U24+u8_to_u24 = fromIntegral++-- | Type specialised 'fromIntegral'+u8_to_u32 :: U8 -> U32+u8_to_u32 = fromIntegral++-- | Type specialised 'fromIntegral'+u8_to_u64 :: U8 -> U64+u8_to_u64 = fromIntegral++-- | Type specialised 'fromIntegral' with out-of-range error.+u8_to_i4 :: U8 -> I4+u8_to_i4 x = if x < 0 || x > 7 then error "u8_to_i4: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u8_to_i7 :: U8 -> I7+u8_to_i7 x = if x < 0 || x > 63 then error "u8_to_i7: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u8_to_i8 :: U8 -> I8+u8_to_i8 x = if x < 0 || x > 127 then error "u8_to_i8: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral'+u8_to_i12 :: U8 -> I12+u8_to_i12 = fromIntegral++-- | Type specialised 'fromIntegral'+u8_to_i14 :: U8 -> I14+u8_to_i14 = fromIntegral++-- | Type specialised 'fromIntegral'+u8_to_i16 :: U8 -> I16+u8_to_i16 = fromIntegral++-- | Type specialised 'fromIntegral'+u8_to_i24 :: U8 -> I24+u8_to_i24 = fromIntegral++-- | Type specialised 'fromIntegral'+u8_to_i32 :: U8 -> I32+u8_to_i32 = fromIntegral++-- | Type specialised 'fromIntegral'+u8_to_i64 :: U8 -> I64+u8_to_i64 = fromIntegral++-- | Type specialised 'fromIntegral' with out-of-range error.+u12_to_u4 :: U12 -> U4+u12_to_u4 x = if x < 0 || x > 15 then error "u12_to_u4: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u12_to_u7 :: U12 -> U7+u12_to_u7 x = if x < 0 || x > 127 then error "u12_to_u7: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u12_to_u8 :: U12 -> U8+u12_to_u8 x = if x < 0 || x > 255 then error "u12_to_u8: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral'+u12_to_u14 :: U12 -> U14+u12_to_u14 = fromIntegral++-- | Type specialised 'fromIntegral'+u12_to_u16 :: U12 -> U16+u12_to_u16 = fromIntegral++-- | Type specialised 'fromIntegral'+u12_to_u24 :: U12 -> U24+u12_to_u24 = fromIntegral++-- | Type specialised 'fromIntegral'+u12_to_u32 :: U12 -> U32+u12_to_u32 = fromIntegral++-- | Type specialised 'fromIntegral'+u12_to_u64 :: U12 -> U64+u12_to_u64 = fromIntegral++-- | Type specialised 'fromIntegral' with out-of-range error.+u12_to_i4 :: U12 -> I4+u12_to_i4 x = if x < 0 || x > 7 then error "u12_to_i4: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u12_to_i7 :: U12 -> I7+u12_to_i7 x = if x < 0 || x > 63 then error "u12_to_i7: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u12_to_i8 :: U12 -> I8+u12_to_i8 x = if x < 0 || x > 127 then error "u12_to_i8: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u12_to_i12 :: U12 -> I12+u12_to_i12 x = if x < 0 || x > 2047 then error "u12_to_i12: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral'+u12_to_i14 :: U12 -> I14+u12_to_i14 = fromIntegral++-- | Type specialised 'fromIntegral'+u12_to_i16 :: U12 -> I16+u12_to_i16 = fromIntegral++-- | Type specialised 'fromIntegral'+u12_to_i24 :: U12 -> I24+u12_to_i24 = fromIntegral++-- | Type specialised 'fromIntegral'+u12_to_i32 :: U12 -> I32+u12_to_i32 = fromIntegral++-- | Type specialised 'fromIntegral'+u12_to_i64 :: U12 -> I64+u12_to_i64 = fromIntegral++-- | Type specialised 'fromIntegral' with out-of-range error.+u14_to_u4 :: U14 -> U4+u14_to_u4 x = if x < 0 || x > 15 then error "u14_to_u4: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u14_to_u7 :: U14 -> U7+u14_to_u7 x = if x < 0 || x > 127 then error "u14_to_u7: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u14_to_u8 :: U14 -> U8+u14_to_u8 x = if x < 0 || x > 255 then error "u14_to_u8: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u14_to_u12 :: U14 -> U12+u14_to_u12 x = if x < 0 || x > 4095 then error "u14_to_u12: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral'+u14_to_u16 :: U14 -> U16+u14_to_u16 = fromIntegral++-- | Type specialised 'fromIntegral'+u14_to_u24 :: U14 -> U24+u14_to_u24 = fromIntegral++-- | Type specialised 'fromIntegral'+u14_to_u32 :: U14 -> U32+u14_to_u32 = fromIntegral++-- | Type specialised 'fromIntegral'+u14_to_u64 :: U14 -> U64+u14_to_u64 = fromIntegral++-- | Type specialised 'fromIntegral' with out-of-range error.+u14_to_i4 :: U14 -> I4+u14_to_i4 x = if x < 0 || x > 7 then error "u14_to_i4: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u14_to_i7 :: U14 -> I7+u14_to_i7 x = if x < 0 || x > 63 then error "u14_to_i7: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u14_to_i8 :: U14 -> I8+u14_to_i8 x = if x < 0 || x > 127 then error "u14_to_i8: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u14_to_i12 :: U14 -> I12+u14_to_i12 x = if x < 0 || x > 2047 then error "u14_to_i12: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u14_to_i14 :: U14 -> I14+u14_to_i14 x = if x < 0 || x > 8191 then error "u14_to_i14: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral'+u14_to_i16 :: U14 -> I16+u14_to_i16 = fromIntegral++-- | Type specialised 'fromIntegral'+u14_to_i24 :: U14 -> I24+u14_to_i24 = fromIntegral++-- | Type specialised 'fromIntegral'+u14_to_i32 :: U14 -> I32+u14_to_i32 = fromIntegral++-- | Type specialised 'fromIntegral'+u14_to_i64 :: U14 -> I64+u14_to_i64 = fromIntegral++-- | Type specialised 'fromIntegral' with out-of-range error.+u16_to_u4 :: U16 -> U4+u16_to_u4 x = if x < 0 || x > 15 then error "u16_to_u4: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u16_to_u7 :: U16 -> U7+u16_to_u7 x = if x < 0 || x > 127 then error "u16_to_u7: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u16_to_u8 :: U16 -> U8+u16_to_u8 x = if x < 0 || x > 255 then error "u16_to_u8: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u16_to_u12 :: U16 -> U12+u16_to_u12 x = if x < 0 || x > 4095 then error "u16_to_u12: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u16_to_u14 :: U16 -> U14+u16_to_u14 x = if x < 0 || x > 16383 then error "u16_to_u14: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral'+u16_to_u24 :: U16 -> U24+u16_to_u24 = fromIntegral++-- | Type specialised 'fromIntegral'+u16_to_u32 :: U16 -> U32+u16_to_u32 = fromIntegral++-- | Type specialised 'fromIntegral'+u16_to_u64 :: U16 -> U64+u16_to_u64 = fromIntegral++-- | Type specialised 'fromIntegral' with out-of-range error.+u16_to_i4 :: U16 -> I4+u16_to_i4 x = if x < 0 || x > 7 then error "u16_to_i4: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u16_to_i7 :: U16 -> I7+u16_to_i7 x = if x < 0 || x > 63 then error "u16_to_i7: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u16_to_i8 :: U16 -> I8+u16_to_i8 x = if x < 0 || x > 127 then error "u16_to_i8: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u16_to_i12 :: U16 -> I12+u16_to_i12 x = if x < 0 || x > 2047 then error "u16_to_i12: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u16_to_i14 :: U16 -> I14+u16_to_i14 x = if x < 0 || x > 8191 then error "u16_to_i14: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u16_to_i16 :: U16 -> I16+u16_to_i16 x = if x < 0 || x > 32767 then error "u16_to_i16: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral'+u16_to_i24 :: U16 -> I24+u16_to_i24 = fromIntegral++-- | Type specialised 'fromIntegral'+u16_to_i32 :: U16 -> I32+u16_to_i32 = fromIntegral++-- | Type specialised 'fromIntegral'+u16_to_i64 :: U16 -> I64+u16_to_i64 = fromIntegral++-- | Type specialised 'fromIntegral' with out-of-range error.+u24_to_u4 :: U24 -> U4+u24_to_u4 x = if x < 0 || x > 15 then error "u24_to_u4: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u24_to_u7 :: U24 -> U7+u24_to_u7 x = if x < 0 || x > 127 then error "u24_to_u7: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u24_to_u8 :: U24 -> U8+u24_to_u8 x = if x < 0 || x > 255 then error "u24_to_u8: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u24_to_u12 :: U24 -> U12+u24_to_u12 x = if x < 0 || x > 4095 then error "u24_to_u12: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u24_to_u14 :: U24 -> U14+u24_to_u14 x = if x < 0 || x > 16383 then error "u24_to_u14: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u24_to_u16 :: U24 -> U16+u24_to_u16 x = if x < 0 || x > 65535 then error "u24_to_u16: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral'+u24_to_u32 :: U24 -> U32+u24_to_u32 = fromIntegral++-- | Type specialised 'fromIntegral'+u24_to_u64 :: U24 -> U64+u24_to_u64 = fromIntegral++-- | Type specialised 'fromIntegral' with out-of-range error.+u24_to_i4 :: U24 -> I4+u24_to_i4 x = if x < 0 || x > 7 then error "u24_to_i4: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u24_to_i7 :: U24 -> I7+u24_to_i7 x = if x < 0 || x > 63 then error "u24_to_i7: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u24_to_i8 :: U24 -> I8+u24_to_i8 x = if x < 0 || x > 127 then error "u24_to_i8: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u24_to_i12 :: U24 -> I12+u24_to_i12 x = if x < 0 || x > 2047 then error "u24_to_i12: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u24_to_i14 :: U24 -> I14+u24_to_i14 x = if x < 0 || x > 8191 then error "u24_to_i14: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u24_to_i16 :: U24 -> I16+u24_to_i16 x = if x < 0 || x > 32767 then error "u24_to_i16: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u24_to_i24 :: U24 -> I24+u24_to_i24 x = if x < 0 || x > 8388607 then error "u24_to_i24: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral'+u24_to_i32 :: U24 -> I32+u24_to_i32 = fromIntegral++-- | Type specialised 'fromIntegral'+u24_to_i64 :: U24 -> I64+u24_to_i64 = fromIntegral++-- | Type specialised 'fromIntegral' with out-of-range error.+u32_to_u4 :: U32 -> U4+u32_to_u4 x = if x < 0 || x > 15 then error "u32_to_u4: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u32_to_u7 :: U32 -> U7+u32_to_u7 x = if x < 0 || x > 127 then error "u32_to_u7: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u32_to_u8 :: U32 -> U8+u32_to_u8 x = if x < 0 || x > 255 then error "u32_to_u8: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u32_to_u12 :: U32 -> U12+u32_to_u12 x = if x < 0 || x > 4095 then error "u32_to_u12: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u32_to_u14 :: U32 -> U14+u32_to_u14 x = if x < 0 || x > 16383 then error "u32_to_u14: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u32_to_u16 :: U32 -> U16+u32_to_u16 x = if x < 0 || x > 65535 then error "u32_to_u16: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u32_to_u24 :: U32 -> U24+u32_to_u24 x = if x < 0 || x > 16777215 then error "u32_to_u24: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral'+u32_to_u64 :: U32 -> U64+u32_to_u64 = fromIntegral++-- | Type specialised 'fromIntegral' with out-of-range error.+u32_to_i4 :: U32 -> I4+u32_to_i4 x = if x < 0 || x > 7 then error "u32_to_i4: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u32_to_i7 :: U32 -> I7+u32_to_i7 x = if x < 0 || x > 63 then error "u32_to_i7: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u32_to_i8 :: U32 -> I8+u32_to_i8 x = if x < 0 || x > 127 then error "u32_to_i8: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u32_to_i12 :: U32 -> I12+u32_to_i12 x = if x < 0 || x > 2047 then error "u32_to_i12: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u32_to_i14 :: U32 -> I14+u32_to_i14 x = if x < 0 || x > 8191 then error "u32_to_i14: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u32_to_i16 :: U32 -> I16+u32_to_i16 x = if x < 0 || x > 32767 then error "u32_to_i16: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u32_to_i24 :: U32 -> I24+u32_to_i24 x = if x < 0 || x > 8388607 then error "u32_to_i24: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u32_to_i32 :: U32 -> I32+u32_to_i32 x = if x < 0 || x > 2147483647 then error "u32_to_i32: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral'+u32_to_i64 :: U32 -> I64+u32_to_i64 = fromIntegral++-- | Type specialised 'fromIntegral' with out-of-range error.+u64_to_u4 :: U64 -> U4+u64_to_u4 x = if x < 0 || x > 15 then error "u64_to_u4: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u64_to_u7 :: U64 -> U7+u64_to_u7 x = if x < 0 || x > 127 then error "u64_to_u7: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u64_to_u8 :: U64 -> U8+u64_to_u8 x = if x < 0 || x > 255 then error "u64_to_u8: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u64_to_u12 :: U64 -> U12+u64_to_u12 x = if x < 0 || x > 4095 then error "u64_to_u12: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u64_to_u14 :: U64 -> U14+u64_to_u14 x = if x < 0 || x > 16383 then error "u64_to_u14: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u64_to_u16 :: U64 -> U16+u64_to_u16 x = if x < 0 || x > 65535 then error "u64_to_u16: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u64_to_u24 :: U64 -> U24+u64_to_u24 x = if x < 0 || x > 16777215 then error "u64_to_u24: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u64_to_u32 :: U64 -> U32+u64_to_u32 x = if x < 0 || x > 4294967295 then error "u64_to_u32: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u64_to_i4 :: U64 -> I4+u64_to_i4 x = if x < 0 || x > 7 then error "u64_to_i4: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u64_to_i7 :: U64 -> I7+u64_to_i7 x = if x < 0 || x > 63 then error "u64_to_i7: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u64_to_i8 :: U64 -> I8+u64_to_i8 x = if x < 0 || x > 127 then error "u64_to_i8: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u64_to_i12 :: U64 -> I12+u64_to_i12 x = if x < 0 || x > 2047 then error "u64_to_i12: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u64_to_i14 :: U64 -> I14+u64_to_i14 x = if x < 0 || x > 8191 then error "u64_to_i14: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u64_to_i16 :: U64 -> I16+u64_to_i16 x = if x < 0 || x > 32767 then error "u64_to_i16: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u64_to_i24 :: U64 -> I24+u64_to_i24 x = if x < 0 || x > 8388607 then error "u64_to_i24: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u64_to_i32 :: U64 -> I32+u64_to_i32 x = if x < 0 || x > 2147483647 then error "u64_to_i32: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+u64_to_i64 :: U64 -> I64+u64_to_i64 x = if x < 0 || x > 9223372036854775807 then error "u64_to_i64: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i4_to_u4 :: I4 -> U4+i4_to_u4 x = if x < 0 then error "i4_to_u4: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i4_to_u7 :: I4 -> U7+i4_to_u7 x = if x < 0 then error "i4_to_u7: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i4_to_u8 :: I4 -> U8+i4_to_u8 x = if x < 0 then error "i4_to_u8: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i4_to_u12 :: I4 -> U12+i4_to_u12 x = if x < 0 then error "i4_to_u12: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i4_to_u14 :: I4 -> U14+i4_to_u14 x = if x < 0 then error "i4_to_u14: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i4_to_u16 :: I4 -> U16+i4_to_u16 x = if x < 0 then error "i4_to_u16: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i4_to_u24 :: I4 -> U24+i4_to_u24 x = if x < 0 then error "i4_to_u24: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i4_to_u32 :: I4 -> U32+i4_to_u32 x = if x < 0 then error "i4_to_u32: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i4_to_u64 :: I4 -> U64+i4_to_u64 x = if x < 0 then error "i4_to_u64: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral'+i4_to_i7 :: I4 -> I7+i4_to_i7 = fromIntegral++-- | Type specialised 'fromIntegral'+i4_to_i8 :: I4 -> I8+i4_to_i8 = fromIntegral++-- | Type specialised 'fromIntegral'+i4_to_i12 :: I4 -> I12+i4_to_i12 = fromIntegral++-- | Type specialised 'fromIntegral'+i4_to_i14 :: I4 -> I14+i4_to_i14 = fromIntegral++-- | Type specialised 'fromIntegral'+i4_to_i16 :: I4 -> I16+i4_to_i16 = fromIntegral++-- | Type specialised 'fromIntegral'+i4_to_i24 :: I4 -> I24+i4_to_i24 = fromIntegral++-- | Type specialised 'fromIntegral'+i4_to_i32 :: I4 -> I32+i4_to_i32 = fromIntegral++-- | Type specialised 'fromIntegral'+i4_to_i64 :: I4 -> I64+i4_to_i64 = fromIntegral++-- | Type specialised 'fromIntegral' with out-of-range error.+i7_to_u4 :: I7 -> U4+i7_to_u4 x = if x < 0 || x > 15 then error "i7_to_u4: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i7_to_u7 :: I7 -> U7+i7_to_u7 x = if x < 0 then error "i7_to_u7: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i7_to_u8 :: I7 -> U8+i7_to_u8 x = if x < 0 then error "i7_to_u8: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i7_to_u12 :: I7 -> U12+i7_to_u12 x = if x < 0 then error "i7_to_u12: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i7_to_u14 :: I7 -> U14+i7_to_u14 x = if x < 0 then error "i7_to_u14: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i7_to_u16 :: I7 -> U16+i7_to_u16 x = if x < 0 then error "i7_to_u16: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i7_to_u24 :: I7 -> U24+i7_to_u24 x = if x < 0 then error "i7_to_u24: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i7_to_u32 :: I7 -> U32+i7_to_u32 x = if x < 0 then error "i7_to_u32: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i7_to_u64 :: I7 -> U64+i7_to_u64 x = if x < 0 then error "i7_to_u64: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i7_to_i4 :: I7 -> I4+i7_to_i4 x = if x < -8 || x > 7 then error "i7_to_i4: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral'+i7_to_i8 :: I7 -> I8+i7_to_i8 = fromIntegral++-- | Type specialised 'fromIntegral'+i7_to_i12 :: I7 -> I12+i7_to_i12 = fromIntegral++-- | Type specialised 'fromIntegral'+i7_to_i14 :: I7 -> I14+i7_to_i14 = fromIntegral++-- | Type specialised 'fromIntegral'+i7_to_i16 :: I7 -> I16+i7_to_i16 = fromIntegral++-- | Type specialised 'fromIntegral'+i7_to_i24 :: I7 -> I24+i7_to_i24 = fromIntegral++-- | Type specialised 'fromIntegral'+i7_to_i32 :: I7 -> I32+i7_to_i32 = fromIntegral++-- | Type specialised 'fromIntegral'+i7_to_i64 :: I7 -> I64+i7_to_i64 = fromIntegral++-- | Type specialised 'fromIntegral' with out-of-range error.+i8_to_u4 :: I8 -> U4+i8_to_u4 x = if x < 0 || x > 15 then error "i8_to_u4: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i8_to_u7 :: I8 -> U7+i8_to_u7 x = if x < 0 || x > 127 then error "i8_to_u7: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i8_to_u8 :: I8 -> U8+i8_to_u8 x = if x < 0 then error "i8_to_u8: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i8_to_u12 :: I8 -> U12+i8_to_u12 x = if x < 0 then error "i8_to_u12: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i8_to_u14 :: I8 -> U14+i8_to_u14 x = if x < 0 then error "i8_to_u14: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i8_to_u16 :: I8 -> U16+i8_to_u16 x = if x < 0 then error "i8_to_u16: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i8_to_u24 :: I8 -> U24+i8_to_u24 x = if x < 0 then error "i8_to_u24: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i8_to_u32 :: I8 -> U32+i8_to_u32 x = if x < 0 then error "i8_to_u32: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i8_to_u64 :: I8 -> U64+i8_to_u64 x = if x < 0 then error "i8_to_u64: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i8_to_i4 :: I8 -> I4+i8_to_i4 x = if x < -8 || x > 7 then error "i8_to_i4: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i8_to_i7 :: I8 -> I7+i8_to_i7 x = if x < -64 || x > 63 then error "i8_to_i7: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral'+i8_to_i12 :: I8 -> I12+i8_to_i12 = fromIntegral++-- | Type specialised 'fromIntegral'+i8_to_i14 :: I8 -> I14+i8_to_i14 = fromIntegral++-- | Type specialised 'fromIntegral'+i8_to_i16 :: I8 -> I16+i8_to_i16 = fromIntegral++-- | Type specialised 'fromIntegral'+i8_to_i24 :: I8 -> I24+i8_to_i24 = fromIntegral++-- | Type specialised 'fromIntegral'+i8_to_i32 :: I8 -> I32+i8_to_i32 = fromIntegral++-- | Type specialised 'fromIntegral'+i8_to_i64 :: I8 -> I64+i8_to_i64 = fromIntegral++-- | Type specialised 'fromIntegral' with out-of-range error.+i12_to_u4 :: I12 -> U4+i12_to_u4 x = if x < 0 || x > 15 then error "i12_to_u4: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i12_to_u7 :: I12 -> U7+i12_to_u7 x = if x < 0 || x > 127 then error "i12_to_u7: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i12_to_u8 :: I12 -> U8+i12_to_u8 x = if x < 0 || x > 255 then error "i12_to_u8: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i12_to_u12 :: I12 -> U12+i12_to_u12 x = if x < 0 then error "i12_to_u12: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i12_to_u14 :: I12 -> U14+i12_to_u14 x = if x < 0 then error "i12_to_u14: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i12_to_u16 :: I12 -> U16+i12_to_u16 x = if x < 0 then error "i12_to_u16: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i12_to_u24 :: I12 -> U24+i12_to_u24 x = if x < 0 then error "i12_to_u24: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i12_to_u32 :: I12 -> U32+i12_to_u32 x = if x < 0 then error "i12_to_u32: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i12_to_u64 :: I12 -> U64+i12_to_u64 x = if x < 0 then error "i12_to_u64: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i12_to_i4 :: I12 -> I4+i12_to_i4 x = if x < -8 || x > 7 then error "i12_to_i4: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i12_to_i7 :: I12 -> I7+i12_to_i7 x = if x < -64 || x > 63 then error "i12_to_i7: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i12_to_i8 :: I12 -> I8+i12_to_i8 x = if x < -128 || x > 127 then error "i12_to_i8: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral'+i12_to_i14 :: I12 -> I14+i12_to_i14 = fromIntegral++-- | Type specialised 'fromIntegral'+i12_to_i16 :: I12 -> I16+i12_to_i16 = fromIntegral++-- | Type specialised 'fromIntegral'+i12_to_i24 :: I12 -> I24+i12_to_i24 = fromIntegral++-- | Type specialised 'fromIntegral'+i12_to_i32 :: I12 -> I32+i12_to_i32 = fromIntegral++-- | Type specialised 'fromIntegral'+i12_to_i64 :: I12 -> I64+i12_to_i64 = fromIntegral++-- | Type specialised 'fromIntegral' with out-of-range error.+i14_to_u4 :: I14 -> U4+i14_to_u4 x = if x < 0 || x > 15 then error "i14_to_u4: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i14_to_u7 :: I14 -> U7+i14_to_u7 x = if x < 0 || x > 127 then error "i14_to_u7: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i14_to_u8 :: I14 -> U8+i14_to_u8 x = if x < 0 || x > 255 then error "i14_to_u8: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i14_to_u12 :: I14 -> U12+i14_to_u12 x = if x < 0 || x > 4095 then error "i14_to_u12: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i14_to_u14 :: I14 -> U14+i14_to_u14 x = if x < 0 then error "i14_to_u14: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i14_to_u16 :: I14 -> U16+i14_to_u16 x = if x < 0 then error "i14_to_u16: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i14_to_u24 :: I14 -> U24+i14_to_u24 x = if x < 0 then error "i14_to_u24: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i14_to_u32 :: I14 -> U32+i14_to_u32 x = if x < 0 then error "i14_to_u32: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i14_to_u64 :: I14 -> U64+i14_to_u64 x = if x < 0 then error "i14_to_u64: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i14_to_i4 :: I14 -> I4+i14_to_i4 x = if x < -8 || x > 7 then error "i14_to_i4: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i14_to_i7 :: I14 -> I7+i14_to_i7 x = if x < -64 || x > 63 then error "i14_to_i7: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i14_to_i8 :: I14 -> I8+i14_to_i8 x = if x < -128 || x > 127 then error "i14_to_i8: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i14_to_i12 :: I14 -> I12+i14_to_i12 x = if x < -2048 || x > 2047 then error "i14_to_i12: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral'+i14_to_i16 :: I14 -> I16+i14_to_i16 = fromIntegral++-- | Type specialised 'fromIntegral'+i14_to_i24 :: I14 -> I24+i14_to_i24 = fromIntegral++-- | Type specialised 'fromIntegral'+i14_to_i32 :: I14 -> I32+i14_to_i32 = fromIntegral++-- | Type specialised 'fromIntegral'+i14_to_i64 :: I14 -> I64+i14_to_i64 = fromIntegral++-- | Type specialised 'fromIntegral' with out-of-range error.+i16_to_u4 :: I16 -> U4+i16_to_u4 x = if x < 0 || x > 15 then error "i16_to_u4: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i16_to_u7 :: I16 -> U7+i16_to_u7 x = if x < 0 || x > 127 then error "i16_to_u7: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i16_to_u8 :: I16 -> U8+i16_to_u8 x = if x < 0 || x > 255 then error "i16_to_u8: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i16_to_u12 :: I16 -> U12+i16_to_u12 x = if x < 0 || x > 4095 then error "i16_to_u12: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i16_to_u14 :: I16 -> U14+i16_to_u14 x = if x < 0 || x > 16383 then error "i16_to_u14: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i16_to_u16 :: I16 -> U16+i16_to_u16 x = if x < 0 then error "i16_to_u16: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i16_to_u24 :: I16 -> U24+i16_to_u24 x = if x < 0 then error "i16_to_u24: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i16_to_u32 :: I16 -> U32+i16_to_u32 x = if x < 0 then error "i16_to_u32: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i16_to_u64 :: I16 -> U64+i16_to_u64 x = if x < 0 then error "i16_to_u64: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i16_to_i4 :: I16 -> I4+i16_to_i4 x = if x < -8 || x > 7 then error "i16_to_i4: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i16_to_i7 :: I16 -> I7+i16_to_i7 x = if x < -64 || x > 63 then error "i16_to_i7: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i16_to_i8 :: I16 -> I8+i16_to_i8 x = if x < -128 || x > 127 then error "i16_to_i8: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i16_to_i12 :: I16 -> I12+i16_to_i12 x = if x < -2048 || x > 2047 then error "i16_to_i12: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i16_to_i14 :: I16 -> I14+i16_to_i14 x = if x < -8192 || x > 8191 then error "i16_to_i14: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral'+i16_to_i24 :: I16 -> I24+i16_to_i24 = fromIntegral++-- | Type specialised 'fromIntegral'+i16_to_i32 :: I16 -> I32+i16_to_i32 = fromIntegral++-- | Type specialised 'fromIntegral'+i16_to_i64 :: I16 -> I64+i16_to_i64 = fromIntegral++-- | Type specialised 'fromIntegral' with out-of-range error.+i24_to_u4 :: I24 -> U4+i24_to_u4 x = if x < 0 || x > 15 then error "i24_to_u4: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i24_to_u7 :: I24 -> U7+i24_to_u7 x = if x < 0 || x > 127 then error "i24_to_u7: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i24_to_u8 :: I24 -> U8+i24_to_u8 x = if x < 0 || x > 255 then error "i24_to_u8: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i24_to_u12 :: I24 -> U12+i24_to_u12 x = if x < 0 || x > 4095 then error "i24_to_u12: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i24_to_u14 :: I24 -> U14+i24_to_u14 x = if x < 0 || x > 16383 then error "i24_to_u14: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i24_to_u16 :: I24 -> U16+i24_to_u16 x = if x < 0 || x > 65535 then error "i24_to_u16: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i24_to_u24 :: I24 -> U24+i24_to_u24 x = if x < 0 then error "i24_to_u24: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i24_to_u32 :: I24 -> U32+i24_to_u32 x = if x < 0 then error "i24_to_u32: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i24_to_u64 :: I24 -> U64+i24_to_u64 x = if x < 0 then error "i24_to_u64: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i24_to_i4 :: I24 -> I4+i24_to_i4 x = if x < -8 || x > 7 then error "i24_to_i4: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i24_to_i7 :: I24 -> I7+i24_to_i7 x = if x < -64 || x > 63 then error "i24_to_i7: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i24_to_i8 :: I24 -> I8+i24_to_i8 x = if x < -128 || x > 127 then error "i24_to_i8: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i24_to_i12 :: I24 -> I12+i24_to_i12 x = if x < -2048 || x > 2047 then error "i24_to_i12: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i24_to_i14 :: I24 -> I14+i24_to_i14 x = if x < -8192 || x > 8191 then error "i24_to_i14: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i24_to_i16 :: I24 -> I16+i24_to_i16 x = if x < -32768 || x > 32767 then error "i24_to_i16: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral'+i24_to_i32 :: I24 -> I32+i24_to_i32 = fromIntegral++-- | Type specialised 'fromIntegral'+i24_to_i64 :: I24 -> I64+i24_to_i64 = fromIntegral++-- | Type specialised 'fromIntegral' with out-of-range error.+i32_to_u4 :: I32 -> U4+i32_to_u4 x = if x < 0 || x > 15 then error "i32_to_u4: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i32_to_u7 :: I32 -> U7+i32_to_u7 x = if x < 0 || x > 127 then error "i32_to_u7: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i32_to_u8 :: I32 -> U8+i32_to_u8 x = if x < 0 || x > 255 then error "i32_to_u8: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i32_to_u12 :: I32 -> U12+i32_to_u12 x = if x < 0 || x > 4095 then error "i32_to_u12: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i32_to_u14 :: I32 -> U14+i32_to_u14 x = if x < 0 || x > 16383 then error "i32_to_u14: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i32_to_u16 :: I32 -> U16+i32_to_u16 x = if x < 0 || x > 65535 then error "i32_to_u16: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i32_to_u24 :: I32 -> U24+i32_to_u24 x = if x < 0 || x > 16777215 then error "i32_to_u24: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i32_to_u32 :: I32 -> U32+i32_to_u32 x = if x < 0 then error "i32_to_u32: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i32_to_u64 :: I32 -> U64+i32_to_u64 x = if x < 0 then error "i32_to_u64: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i32_to_i4 :: I32 -> I4+i32_to_i4 x = if x < -8 || x > 7 then error "i32_to_i4: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i32_to_i7 :: I32 -> I7+i32_to_i7 x = if x < -64 || x > 63 then error "i32_to_i7: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i32_to_i8 :: I32 -> I8+i32_to_i8 x = if x < -128 || x > 127 then error "i32_to_i8: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i32_to_i12 :: I32 -> I12+i32_to_i12 x = if x < -2048 || x > 2047 then error "i32_to_i12: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i32_to_i14 :: I32 -> I14+i32_to_i14 x = if x < -8192 || x > 8191 then error "i32_to_i14: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i32_to_i16 :: I32 -> I16+i32_to_i16 x = if x < -32768 || x > 32767 then error "i32_to_i16: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i32_to_i24 :: I32 -> I24+i32_to_i24 x = if x < -8388608 || x > 8388607 then error "i32_to_i24: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral'+i32_to_i64 :: I32 -> I64+i32_to_i64 = fromIntegral++-- | Type specialised 'fromIntegral' with out-of-range error.+i64_to_u4 :: I64 -> U4+i64_to_u4 x = if x < 0 || x > 15 then error "i64_to_u4: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i64_to_u7 :: I64 -> U7+i64_to_u7 x = if x < 0 || x > 127 then error "i64_to_u7: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i64_to_u8 :: I64 -> U8+i64_to_u8 x = if x < 0 || x > 255 then error "i64_to_u8: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i64_to_u12 :: I64 -> U12+i64_to_u12 x = if x < 0 || x > 4095 then error "i64_to_u12: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i64_to_u14 :: I64 -> U14+i64_to_u14 x = if x < 0 || x > 16383 then error "i64_to_u14: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i64_to_u16 :: I64 -> U16+i64_to_u16 x = if x < 0 || x > 65535 then error "i64_to_u16: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i64_to_u24 :: I64 -> U24+i64_to_u24 x = if x < 0 || x > 16777215 then error "i64_to_u24: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i64_to_u32 :: I64 -> U32+i64_to_u32 x = if x < 0 || x > 4294967295 then error "i64_to_u32: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i64_to_u64 :: I64 -> U64+i64_to_u64 x = if x < 0 then error "i64_to_u64: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i64_to_i4 :: I64 -> I4+i64_to_i4 x = if x < -8 || x > 7 then error "i64_to_i4: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i64_to_i7 :: I64 -> I7+i64_to_i7 x = if x < -64 || x > 63 then error "i64_to_i7: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i64_to_i8 :: I64 -> I8+i64_to_i8 x = if x < -128 || x > 127 then error "i64_to_i8: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i64_to_i12 :: I64 -> I12+i64_to_i12 x = if x < -2048 || x > 2047 then error "i64_to_i12: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i64_to_i14 :: I64 -> I14+i64_to_i14 x = if x < -8192 || x > 8191 then error "i64_to_i14: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i64_to_i16 :: I64 -> I16+i64_to_i16 x = if x < -32768 || x > 32767 then error "i64_to_i16: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i64_to_i24 :: I64 -> I24+i64_to_i24 x = if x < -8388608 || x > 8388607 then error "i64_to_i24: OUT-OF-RANGE" else fromIntegral x++-- | Type specialised 'fromIntegral' with out-of-range error.+i64_to_i32 :: I64 -> I32+i64_to_i32 x = if x < -2147483648 || x > 2147483647 then error "i64_to_i32: OUT-OF-RANGE" else fromIntegral x
+ Music/Theory/Math/Nichomachus.hs view
@@ -0,0 +1,53 @@+{- | Nichomachus of Gerasa (Νικόμαχος) c.60-c.120++<https://pdfs.semanticscholar.org/5dac/8842ad857c822ab854ede3decadfe0464f15.pdf>+-}+module Music.Theory.Math.Nichomachus where++{- | a-b = b-c ; b = a+c / 2++> arithmetic_mean 2 6 == 4+> arithmetic_mean 1 2 == (1+2)/2 -- 3/2+-}+arithmetic_mean :: Fractional a => a -> a -> a+arithmetic_mean a c = (a + c) / 2++{- | a/b = b/c ; b = sqrt ac++> geometric_mean 1 4 == 2+> geometric_mean 1 2 == sqrt (1*2) -- sqrt 2+-}+geometric_mean :: Floating a => a -> a -> a+geometric_mean a c = sqrt (a * c)++{- | a-b / a = b-c / c ; 2ac / a+c++> harmonic_mean 2 6 == 3+> harmonic_mean 1 2 == (2*1*2)/(1+2) -- 4/3+-}+harmonic_mean :: Fractional a => a -> a -> a+harmonic_mean a c = (2 * a * c) / (a + c) -- OR -- 2 / (1/a + 1/c)++{- | a-b / c = b-c / a ; a-b / b-c = c/a ; aa+cc / a+c++> cont_harmonic_mean 3 6 == 5+> cont_harmonic_mean 1 2 == (1*1+2*2)/(1+2) -- 5/3+-}+cont_harmonic_mean :: Fractional a => a -> a -> a+cont_harmonic_mean a c = (a * a + c * c) / (a + c)++{- | a-b / c = b-c / b ; a-b / b-c = c/b ; c - a + (sqrt (5aa - 2ac + cc)) / 2++> cont_geometric_mean 2 5 == 4+> cont_geometric_mean 1 2 == (2-1+sqrt(5*1*1-2*1*2+2*2))/2 -- (1+sqrt 5)/2 -- GOLDEN RATIO -- 1.6180+-}+cont_geometric_mean :: Floating a => a -> a -> a+cont_geometric_mean a c = (c - a + sqrt (5 * a * a - 2 * a * c + c * c)) / 2++{- | a-b / c = b-c / b ; a-b / b-c = c/b ; a - c + (sqrt (aa - 2ac + 5cc)) / 2++> subcont_geometric_mean 1 6 == 4+> subcont_geometric_mean 1 2 == (-1 + sqrt 17) / 2 -- 1.5616+-}+subcont_geometric_mean :: Floating a => a -> a -> a+subcont_geometric_mean a c = (a - c + sqrt (a * a - 2 * a * c + 5 * c * c)) / 2
− Music/Theory/Math/OEIS.hs 
@@ -1,27 +0,0 @@--- | The On-Line Encyclopedia of Integer Sequences, <http://oeis.org/>-module Music.Theory.Math.OEIS where---- | <http://oeis.org/A000290>------ The squares of the non-negative integers.------ > import Data.List--- > [0,1,4,9,16,25,36,49,64,81,100] `isInfixOf` a000290-a000290 :: Integral n => [n]-a000290 = let square n = n * n in map square [0..]---- | <http://oeis.org/A002267>-a002267 :: Num n => [n]-a002267 = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, 71]---- | <http://oeis.org/A126709>------ Loh-Shu magic square, attributed to the legendary Fu Xi (Fuh-Hi).-a126709 :: Num n => [n]-a126709 = [4, 9, 2, 3, 5, 7, 8, 1, 6]---- | <http://oeis.org/A126710>------ Jaina inscription of the twelfth or thirteenth century, Khajuraho, India.-a126710 :: Num n => [n]-a126710 = [7, 12, 1, 14, 2, 13, 8, 11, 16, 3, 10, 5, 9, 6, 15, 4]
+ Music/Theory/Math/Oeis.hs view
@@ -0,0 +1,1478 @@+-- | The On-Line Encyclopedia of Integer Sequences, <http://oeis.org/>+module Music.Theory.Math.Oeis where++import Data.Bits {- base -}+import Data.Char {- base -}+import Data.List {- base -}+import Data.Ratio {- base -}++import qualified Data.Set as Set {- containers -}++import qualified Data.MemoCombinators as Memo {- data-memocombinators -}++import qualified Music.Theory.Math as Math {- hmt-base -}++import qualified Music.Theory.Math.Prime as Prime {- hmt -}++{- | <http://oeis.org/A000005>++d(n) (also called tau(n) or sigma_0(n)), the number of divisors of n. (Formerly M0246 N0086)++[1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 2, 6, 2, 4, 4, 5, 2, 6, 2, 6, 4, 4, 2, 8, 3, 4, 4, 6, 2, 8, 2, 6, 4, 4, 4, 9, 2, 4, 4, 8, 2, 8, 2, 6, 6, 4, 2, 10, 3, 6, 4, 6, 2, 8, 4, 8, 4, 4, 2, 12, 2, 4, 6, 7, 4, 8, 2, 6, 4, 8, 2, 12, 2, 4, 6, 6, 4, 8, 2, 10, 5, 4, 2, 12, 4, 4, 4, 8, 2, 12, 4, 6, 4, 4, 4, 12, 2, 6, 6, 9, 2, 8, 2, 8] `isPrefixOf` a000005+-}+a000005 :: Integral n => [n]+a000005 = map (product . map (+ 1) . a124010_row) [1..]++{- | <http://oeis.org/A000010>++Euler totient function phi(n): count numbers <= n and prime to n.++> [1,1,2,2,4,2,6,4,6,4,10,4,12,6,8,8,16,6,18,8,12,10,22,8,20,12] `isPrefixOf` a000010+-}+a000010 :: Integral n => [n]+a000010 = map a000010_n [1 ..]++a000010_n :: Integral n => n -> n+a000010_n n = genericLength (filter (==1) (map (gcd n) [1..n]))++{- | <http://oeis.org/A000012>++The simplest sequence of positive numbers: the all 1's sequence.+-}+a000012 :: Num n => [n]+a000012 = repeat 1++{- | <https://oeis.org/A000031>++Number of n-bead necklaces with 2 colors when turning over is not allowed; also number of output sequences from a simple n-stage cycling shift register; also number of binary irreducible polynomials whose degree divides n.++> [1,2,3,4,6,8,14,20,36,60,108,188,352,632,1182,2192,4116,7712,14602,27596] `isPrefixOf` a000031+-}+a000031 :: Integral n => [n]+a000031 = map a000031_n [0..]++a000031_n :: Integral n => n -> n+a000031_n n =+  if n == 0+  then 1+  else let divs = a027750_row n+       in ((`div` n) . sum . zipWith (*) (map a000010_n divs) . map (2 ^) . reverse) divs++{- | <http://oeis.org/A000032>++Lucas numbers beginning at 2: L(n) = L(n-1) + L(n-2), L(0) = 2, L(1) = 1. (Formerly M0155)++> [2,1,3,4,7,11,18,29,47,76,123,199,322,521,843,1364,2207,3571,5778,9349,15127] `isPrefixOf` a000032+-}+a000032 :: Num n => [n]+a000032 = 2 : 1 : zipWith (+) a000032 (tail a000032)++{- | <http://oeis.org/A000040>++The prime numbers.++> [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103] `isPrefixOf` a000040+-}+a000040 :: Integral n => [n]+a000040 =+  let base = [2, 3, 5, 7, 11, 13, 17]+      larger = p0 : filter prime more+      prime n = all ((> 0) . mod n) (takeWhile (\x -> x*x <= n) larger)+      _ : p0 : more = roll (makeWheels base)+      roll (n,rs) = [n * k + r | k <- [0..], r <- rs]+      makeWheels = foldl nextSize (1,[1])+      nextSize (size,bs) p = (size * p,[r | k <- [0..p-1], b <- bs, let r = size*k+b, mod r p > 0])+  in base ++ larger++{- | <http://oeis.org/A000041>++a(n) is the number of partitions of n (the partition numbers).++[1,1,2,3,5,7,11,15,22,30,42,56,77,101,135,176,231,297,385,490,627,792,1002,1255] `isPrefixOf` a000041+-}+a000041 :: Num n => [n]+a000041 =+  let p_m = Memo.memo2 Memo.integral Memo.integral p+      p _ 0 = 1+      p k m = if m < k then 0 else p_m k (m - k) + p_m (k + 1) m+  in map (p_m 1) [0::Integer ..]++{- | <http://oeis.org/A000045>++Fibonacci numbers++> [0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,6765,10946] `isPrefixOf` a000045+-}+a000045 :: Num n => [n]+a000045 = 0 : 1 : zipWith (+) a000045 (tail a000045)++{- | <http://oeis.org/A000051>++a(n) = 2^n + 1++> [2,3,5,9,17,33,65,129,257,513,1025,2049,4097,8193,16385,32769,65537,131073] `isPrefixOf` a000051+-}+a000051 :: Num n => [n]+a000051 = iterate (subtract 1 . (* 2)) 2++{- | <http://oeis.org/A000071>++a(n) = Fibonacci(n) - 1.++> [0,0,1,2,4,7,12,20,33,54,88,143,232,376,609,986,1596,2583,4180,6764,10945,17710] `isPrefixOf` a000071+-}+a000071 :: Num n => [n]+a000071 = map (subtract 1) (tail a000045)++{- | <http://oeis.org/A000073>++Tribonacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) for n >= 3 with a(0) = a(1) = 0 and a(2) = 1.++> [0,0,1,1,2,4,7,13,24,44,81,149,274,504,927,1705,3136,5768,10609,19513,35890] `isPrefixOf` a000073+-}+a000073 :: Num n => [n]+a000073 = 0 : 0 : 1 : zipWith (+) a000073 (tail (zipWith (+) a000073 (tail a000073)))++{- | <http://oeis.org/A000078>++Tetranacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4) with a(0)=a(1)=a(2)=0, a(3)=1.++> [0,0,0,1,1,2,4,8,15,29,56,108,208,401,773,1490,2872,5536,10671,20569,39648] `isPrefixOf` a000078+-}+a000078 :: Num n => [n]+a000078 =+  let f xs = let y = (sum . head . transpose . take 4 . tails) xs in y : f (y:xs)+  in 0 : 0 : 0 : f [0, 0, 0, 1]++{- | <http://oeis.org/A000079>++Powers of 2: a(n) = 2^n. (Formerly M1129 N0432)++> [1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384,32768,65536] `isPrefixOf` a000079+> [1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384,32768,65536] `isPrefixOf` map (2 ^) [0..]+-}+a000079 :: Num n => [n]+a000079 = iterate (* 2) 1++{- | <http://oeis.org/A000085>++Number of self-inverse permutations on n letters, also known as involutions; number of standard Young tableaux with n cells.++> [1,1,2,4,10,26,76,232,764,2620,9496,35696,140152,568504,2390480,10349536] `isPrefixOf` a000085+-}+a000085 :: Integral n => [n]+a000085 = 1 : 1 : zipWith (+) (zipWith (*) [1..] a000085) (tail a000085)++{- | <http://oeis.org/A000108>++Catalan numbers: C(n) = binomial(2n,n)/(n+1) = (2n)!/(n!(n+1)!).++> [1,1,2,5,14,42,132,429,1430,4862,16796,58786,208012,742900,2674440,9694845] `isPrefixOf` a000108+-}+a000108 :: Num n => [n]+a000108 = map last (iterate (scanl1 (+) . (++ [0])) [1])++{- | <http://oeis.org/A000120>++1's-counting sequence: number of 1's in binary expansion of n (or the binary weight of n).++> [0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,1,2,2,3,2,3,3] `isPrefixOf` a000120+-}+a000120 :: Integral i => [i]+a000120 = let r = [0] : (map . map) (+ 1) (scanl1 (++) r) in concat r++{- | <http://oeis.org/A000142>++Factorial numbers: n! = 1*2*3*4*...*n+(order of symmetric group S_n, number of permutations of n letters).++> [1,1,2,6,24,120,720,5040,40320,362880,3628800,39916800,479001600,6227020800] `isPrefixOf` a000142+-}+a000142 :: (Enum n, Num n) => [n]+a000142 = 1 : zipWith (*) [1..] a000142++{- | https://oeis.org/A000201++Lower Wythoff sequence (a Beatty sequence): a(n) = floor(n*phi), where phi = (1+sqrt(5))/2 = A001622++> [1,3,4,6,8,9,11,12,14,16,17,19,21,22,24,25,27,29,30,32,33,35,37,38,40,42] `isPrefixOf` a000201++> import Sound.SC3.Plot {- hsc3-plot -}+> plot_p1_imp [take 128 a000201 :: [Int]]+-}+a000201 :: Integral n => [n]+a000201 =+  let f (x:xs) (y:ys) = y : f xs (delete (x + y) ys)+      f _ _ = error "a000201"+  in f [1..] [1..]++{- | <https://oeis.org/A000204>++Lucas numbers (beginning with 1): L(n) = L(n-1) + L(n-2) with L(1) = 1, L(2) = 3++> [1,3,4,7,11,18,29,47,76,123,199,322,521,843,1364,2207,3571,5778,9349,15127] `isPrefixOf` a000204+-}+a000204 :: Num n => [n]+a000204 = 1 : 3 : zipWith (+) a000204 (tail a000204)++{- | <http://oeis.org/A000213>++Tribonacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) with a(0)=a(1)=a(2)=1.++[1,1,1,3,5,9,17,31,57,105,193,355,653,1201,2209,4063,7473,13745,25281,46499]  `isPrefixOf` a000213+-}+a000213 :: Num n => [n]+a000213 = 1 : 1 : 1 : zipWith (+) a000213 (tail (zipWith (+) a000213 (tail a000213)))++{- | <https://oeis.org/A000217>++Triangular numbers: a(n) = binomial(n+1,2) = n(n+1)/2 = 0 + 1 + 2 + ... + n.++> [0,1,3,6,10,15,21,28,36,45,55,66,78,91,105,120,136,153,171,190,210,231,253,276] `isPrefixOf` a000217+-}+a000217 :: (Enum n,Num n) => [n]+a000217 = scanl1 (+) [0..]++{- | <http://oeis.org/A000225>++a(n) = 2^n - 1 (Sometimes called Mersenne numbers, although that name is usually reserved for A001348)++> [0,1,3,7,15,31,63,127,255,511,1023,2047,4095,8191,16383,32767,65535] `isPrefixOf` a000225+-}+a000225 :: Num n => [n]+a000225 = iterate ((+ 1) . (* 2)) 0++{- | <http://oeis.org/000285>++a(0) = 1, a(1) = 4, and a(n) = a(n-1) + a(n-2) for n >= 2. (Formerly M3246 N1309)++> [1,4,5,9,14,23,37,60,97,157,254,411,665,1076,1741,2817,4558,7375,11933,19308] `isPrefixOf` a000285+-}+a000285 :: Num n => [n]+a000285 = 1 : 4 : zipWith (+) a000285 (tail a000285)++{- | <http://oeis.org/A000290>++The squares of the non-negative integers.++> [0,1,4,9,16,25,36,49,64,81,100] `isPrefixOf` a000290+-}+a000290 :: Integral n => [n]+a000290 = let square n = n * n in map square [0..]++{- | <https://oeis.org/A000292>++Tetrahedral (or triangular pyramidal) numbers: a(n) = C(n+2,3) = n*(n+1)*(n+2)/6.++> [0,1,4,10,20,35,56,84,120,165,220,286,364,455,560,680,816,969,1140,1330,1540] `isPrefixOf` a000292+-}+a000292 :: (Enum n,Num n) => [n]+a000292 = scanl1 (+) a000217++{- | <http://oeis.org/A000384>++Hexagonal numbers: a(n) = n*(2*n-1). (Formerly M4108 N1705)++> [0,1,6,15,28,45,66,91,120,153,190,231,276,325,378,435,496,561,630,703,780,861] `isPrefixOf` a000384+-}+a000384 :: Integral n => [n]+a000384 = scanl (+) 0 a016813++{- | <http://oeis.org/A000578>++The cubes: a(n) = n^3.++> [0,1,8,27,64,125,216,343,512,729,1000,1331,1728,2197,2744,3375,4096,4913,5832] `isPrefixOf` a000578+-}+a000578 :: Num n => [n]+a000578 =+  0 : 1 : 8 :+  zipWith (+) (map (+ 6) a000578) (map (* 3) (tail (zipWith (-) (tail a000578) a000578)))++{- | <http://oeis.org/A000583>++Fourth powers: a(n) = n^4.++> [0,1,16,81,256,625,1296,2401,4096,6561,10000,14641,20736,28561,38416,50625] `isPrefixOf` a000583+-}+a000583 :: Integral n => [n]+a000583 = scanl (+) 0 a005917++{- | <http://oeis.org/A000670>++Fubini numbers: number of preferential arrangements of n labeled elements; or number of weak orders on n labeled elements; or number of ordered partitions of [n].++> [1,1,3,13,75,541,4683,47293,545835,7087261,102247563,1622632573,28091567595] `isPrefixOf` a000670+-}+a000670 :: Integral n => [n]+a000670 =+  let f xs (bs:bss) = let y = sum (zipWith (*) xs bs) in y : f (y : xs) bss+      f _ _ = error "a000670d"+  in 1 : f [1] (map tail (tail a007318_tbl))++{- | <https://oeis.org/A000796>++Decimal expansion of Pi (or digits of Pi).++> [3,1,4,1,5,9,2,6,5,3,5,8,9,7,9,3,2,3,8,4,6,2,6,4,3,3,8,3,2,7,9,5,0,2,8,8,4,1,9] `isPrefixOf` a000796++> pi :: Data.Number.Fixed.Fixed Data.Number.Fixed.Prec500 {- numbers -}+-}+a000796 :: Integral n => [n]+a000796 =+  let gen _ [] = error "A000796"+      gen z (x:xs) =+        let lb = approx z 3+            approx (a,b,c) n = div (a * n + b) c+            mult (a,b,c) (d,e,f) = (a * d,a * e + b * f,c * f)+        in if lb /= approx z 4+           then gen (mult z x) xs+        else lb : gen (mult (10,-10 * lb,1) z) (x:xs)+  in map fromInteger (gen (1,0,1) [(n,a*d,d) | (n,d,a) <- map (\k -> (k,2 * k + 1,2)) [1..]])++{- | <https://oeis.org/A000930>++Narayana's cows sequence.++> [1,1,1,2,3,4,6,9,13,19,28,41,60] `isPrefixOf` a000930+-}+a000930 :: Num n => [n]+a000930 = 1 : 1 : 1 : zipWith (+) a000930 (drop 2 a000930)++{- | <https://oeis.org/A000931>++Padovan sequence (or Padovan numbers): a(n) = a(n-2) + a(n-3) with a(0) = 1, a(1) = a(2) = 0.++> [1,0,0,1,0,1,1,1,2,2,3,4,5,7,9,12,16,21,28,37,49,65,86,114,151,200,265] `isPrefixOf` a000931+-}+a000931 :: Num n => [n]+a000931 = 1 : 0 : 0 : zipWith (+) a000931 (tail a000931)++{- | <https://oeis.org/A001008>++Numerators of harmonic numbers H(n) = Sum_{i=1..n} 1/i++[1,3,11,25,137,49,363,761,7129,7381,83711,86021,1145993,1171733,1195757,2436559] `isPrefixOf` a001008+-}+a001008 :: Integral i => [i]+a001008 = map numerator (scanl1 (+) (map (1 %) [1..]))++{- | <http://oeis.org/A001037>++Number of degree-n irreducible polynomials over GF(2); number of+n-bead necklaces with beads of 2 colors when turning over is not+allowed and with primitive period n; number of binary Lyndon words of+length n.++> [1,2,1,2,3,6,9,18,30,56,99,186,335,630,1161,2182,4080,7710,14532,27594,52377,99858,190557,364722,698870] `isPrefixOf` a001037+-}+a001037 :: Integral n => [n]+a001037 = map a001037_n [0..]++a001037_n :: Integral n => n -> n+a001037_n n = if n == 0 then 1 else (sum (map (\d -> (2 ^ d) * a008683_n (n `div` d)) (a027750_row n))) `div` n++{- | <http://oeis.org/A001113>++Decimal expansion of e.++> [2,7,1,8,2,8,1,8,2,8,4,5,9,0,4,5,2,3,5,3,6,0,2,8,7,4,7,1,3,5,2,6,6,2,4,9,7,7,5] `isPrefixOf` a001113++> exp 1 :: Data.Number.Fixed.Fixed Data.Number.Fixed.Prec500 {- numbers -}+-}+a001113 :: Integral n => [n]+a001113 =+  let gen _ [] = error "A001113"+      gen z (x:xs) =+        let lb = approx z 1+            approx (a,b,c) n = div (a * n + b) c+            mult (a,b,c) (d,e,f) = (a * d,a * e + b * f,c * f)+        in if lb /= approx z 2+           then gen (mult z x) xs+           else lb : gen (mult (10,-10 * lb,1) z) (x:xs)+  in gen (1,0,1) [(n,a * d,d) | (n,d,a) <- map (\k -> (1,k,1)) [1..]]++{- | <https://oeis.org/A001147>++Double factorial of odd numbers: a(n) = (2*n-1)!! = 1*3*5*...*(2*n-1). (Formerly M3002 N1217)++> [1,1,3,15,105,945,10395,135135,2027025,34459425,654729075,13749310575] `isPrefixOf` a001147+-}+a001147 :: Integral t => [t]+a001147 = 1 : zipWith (*) [1, 3 ..] a001147++{- | <https://oeis.org/A001156>++Number of partitions of n into squares.++> [1,1,1,1,2,2,2,2,3,4,4,4,5,6,6,6,8,9,10,10,12,13,14,14,16,19,20,21,23,26,27,28] `isPrefixOf` a001156+-}+a001156 :: Num n => [n]+a001156 =+  let p _ 0 = 1+      p ks'@(k:ks) m = if m < k then 0 else p ks' (m - k) + p ks m+      p _ _ = error "A001156"+  in map (p (tail a000290)) [0::Integer ..]++{- | <https://oeis.org/A001333>++Numerators of continued fraction convergents to sqrt(2).++[1,1,3,7,17,41,99,239,577,1393,3363,8119,19601,47321,114243,275807,665857] `isPrefixOf` a001333+-}+a001333 :: Num n => [n]+a001333 = 1 : 1 : zipWith (+) a001333 (map (* 2) (tail a001333))++{- | <http://oeis.org/A001622>++Decimal expansion of golden ratio phi (or tau) = (1 + sqrt(5))/2.++> [1,6,1,8,0,3,3,9,8,8,7,4,9,8,9,4,8,4,8,2,0,4,5,8,6,8,3,4,3,6,5,6,3,8,1,1,7,7,2] `isPrefixOf` a001622++> a001622_k :: Data.Number.Fixed.Fixed Data.Number.Fixed.Prec500 {- numbers -}+-}+a001622 :: Num n => [n]+a001622 = map (fromIntegral . digitToInt) "161803398874989484820458683436563811772030917980576286213544862270526046281890244970720720418939113748475408807538689175212663386222353693179318006076672635443338908659593958290563832266131992829026788067520876689250171169620703222104321626954862629631361443814975870122034080588795445474924618569536486444924104432077134494704956584678850987433944221254487706647809158846074998871240076521705751797883416625624940758906970400028121042762177111777805315317141011704666599146697987317613560067087480711" ++ error "A001622"++a001622_k :: Floating n => n+a001622_k = (1 + sqrt 5) / 2++{- |  <http://oeis.org/A001644>++a(n) = a(n-1) + a(n-2) + a(n-3), a(0)=3, a(1)=1, a(2)=3.++[3,1,3,7,11,21,39,71,131,241,443,815,1499,2757,5071,9327,17155,31553,58035,106743] `isPrefixOf` a001644+-}+a001644 :: Num n => [n]+a001644 = 3 : 1 : 3 : zipWith3 (((+) .) . (+)) a001644 (tail a001644) (drop 2 a001644)++{- | <https://oeis.org/A001653>++Numbers k such that 2*k^2 - 1 is a square.++> [1, 5, 29, 169, 985, 5741, 33461, 195025, 1136689, 6625109, 38613965, 225058681, 1311738121, 7645370045, 44560482149] `isPrefixOf` a001653++-}+a001653 :: [Integer]+a001653 = 1 : 5 : zipWith (-) (map (* 6) (tail a001653)) a001653++{- | <http://oeis.org/A001687>++a(n) = a(n-2) + a(n-5).++[0,1,0,1,0,1,1,1,2,1,3,2,4,4,5,7,7,11,11,16,18,23,29,34,45,52,68,81,102,126,154] `isPrefixOf` a001687+-}+a001687 :: Num n => [n]+a001687 = 0 : 1 : 0 : 1 : 0 : zipWith (+) a001687 (drop 3 a001687)++{- | <https://oeis.org/A001950>++Upper Wythoff sequence (a Beatty sequence): a(n) = floor(n*phi^2), where phi = (1+sqrt(5))/2++> [2,5,7,10,13,15,18,20,23,26,28,31,34,36,39,41,44,47,49,52,54,57,60,62,65] `isPrefixOf` a001950+-}+a001950 :: Integral n => [n]+a001950 = zipWith (+) a000201 [1..]++-- | <http://oeis.org/A002267>+--+-- The 15 supersingular primes.+a002267 :: Num n => [n]+a002267 = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, 71]++{- | <https://oeis.org/A002487>++Stern's diatomic series (or Stern-Brocot sequence)++> [0,1,1,2,1,3,2,3,1,4,3,5,2,5,3,4,1,5,4,7,3,8,5,7,2,7,5,8,3,7,4,5] `isPrefixOf` a002487+-}+a002487 :: Num n => [n]+a002487 =+  let f (a:a') (b:b') = a + b : a : f a' b'+      f _ _ = error "a002487"+      x = 1 : 1 : f (tail x) x+  in 0 : x++{- | <https://oeis.org/A002858>++Ulam numbers: a(1) = 1; a(2) = 2; for n>2, a(n) = least number > a(n-1) which is a unique sum of two distinct earlier terms.++> [1, 2, 3, 4, 6, 8, 11, 13, 16, 18, 26, 28, 36, 38, 47, 48, 53, 57, 62, 69, 72, 77, 82, 87, 97, 99, 102, 106, 114, 126] `isPrefixOf` a002858+-}+a002858 :: [Integer]+a002858 = 1 : 2 : ulam 2 2 a002858++ulam :: Int -> Integer -> [Integer] -> [Integer]+ulam n u us =+  let u' = f (0 :: Integer) (u + 1) us'+      f 2 z _                         = f 0 (z + 1) us'+      f e z (v:vs) | z - v <= v       = if e == 1 then z else f 0 (z + 1) us'+                   | z - v `elem` us' = f (e + 1) z vs+                   | otherwise        = f e z vs+      f _ _ []                        = error "ulam?"+      us' = take n us+  in u' : ulam (n + 1) u' us++{- | <http://oeis.org/A003108>++Number of partitions of n into cubes.++> [1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,4,4,4,5,5,5,5,5,6,6,6,7,7,7,7] `isPrefixOf` a003108+-}+a003108 :: Num n => [n]+a003108 =+  let p _ 0 = 1+      p ks'@(k:ks) m = if m < k then 0 else p ks' (m - k) + p ks m+      p _ _ = error "A003108"+  in map (p (tail a000578)) [0::Integer ..]++a003215_n :: Num n => n -> n+a003215_n n = 3 * n * (n + 1) + 1++{- | <http://oeis.org/A003215>++Hex (or centered hexagonal) numbers: 3*n*(n+1)+1 (crystal ball sequence for hexagonal lattice).++> [1,7,19,37,61,91,127,169,217,271,331,397,469,547,631,721,817,919,1027,1141] `isPrefixOf` a003215+-}+a003215 :: (Enum n,Num n) => [n]+a003215 = map a003215_n [0..]++-- | <http://oeis.org/A003269>+--+-- > [0,1,1,1,1,2,3,4,5,7,10,14,19,26,36,50,69,95,131,181,250,345,476,657] `isPrefixOf` a003269+a003269 :: Num n => [n]+a003269 = 0 : 1 : 1 : 1 : zipWith (+) a003269 (drop 3 a003269)++{- | <http://oeis.org/A003520>++a(n) = a(n-1) + a(n-5); a(0) = ... = a(4) = 1.++> [1,1,1,1,1,2,3,4,5,6,8,11,15,20,26,34,45,60,80,106,140,185,245,325,431] `isPrefixOf` a003520+-}+a003520 :: Num n => [n]+a003520 = 1 : 1 : 1 : 1 : 1 : zipWith (+) a003520 (drop 4 a003520)++{- | <http://oeis.org/A003462>++a(n) = (3^n - 1)/2. (Formerly M3463)++[0, 1, 4, 13, 40, 121, 364, 1093, 3280, 9841, 29524, 88573, 265720, 797161, 2391484, 7174453] `isPrefixOf` a003462+-}+a003462 :: [Integer]+a003462 = iterate ((+ 1) . (* 3)) 0++a003462_n :: Integer -> Integer+a003462_n = (`div` 2) . (subtract 1) . (3 ^)++{- | <http://oeis.org/A003586>++3-smooth numbers: numbers of the form 2^i*3^j with i, j >= 0++[1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 128, 144, 162] `isPrefixOf` a003586+-}+a003586 :: [Integer]+a003586 =+  let smooth s = let (x, s') = Set.deleteFindMin s in x : smooth (Set.insert (3 * x) (Set.insert (2 * x) s'))+  in  smooth (Set.singleton 1)++{- | <https://oeis.org/A003849>++The infinite Fibonacci word (start with 0, apply 0->01, 1->0, take limit).++> [0,1,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,1,0,0,1,0,1,0] `isPrefixOf` a003849+-}+a003849 :: Num n => [n]+a003849 =+  let fws = [1] : [0] : zipWith (++) fws (tail fws)+  in tail (concat fws)++{- | <http://oeis.org/A004001>++Hofstadter-Conway sequence: a(n) = a(a(n-1)) + a(n-a(n-1)) with a(1) = a(2) = 1.++> [1,1,2,2,3,4,4,4,5,6,7,7,8,8,8,8,9,10,11,12,12,13,14,14,15,15,15,16,16,16,16,16] `isPrefixOf` a004001++> plot_p1_ln [take 250 a004001]+> plot_p1_ln [zipWith (-) a004001 (map (`div` 2) [1 .. 2000])]++-}+a004001 :: [Int]+a004001 =+  let h n x =+        let x' = a004001 !! (x - 1) + a004001 !! (n - x - 1)+        in x' : h (n + 1) x'+  in 1 : 1 : h 3 1++{- | <http://oeis.org/A004718>++Per Nørgård's "infinity sequence"++> take 32 a004718 == [0,1,-1,2,1,0,-2,3,-1,2,0,1,2,-1,-3,4,1,0,-2,3,0,1,-1,2,-2,3,1,0,3,-2,-4,5]++> plot_p1_imp [take 1024 a004718]++<https://www.tandfonline.com/doi/abs/10.1080/17459737.2017.1299807>+<https://arxiv.org/pdf/1402.3091.pdf>++-}+a004718 :: Num n => [n]+a004718 = 0 : concat (transpose [map (+ 1) a004718, map negate (tail a004718)])++{- | <http://oeis.org/A005185>++Hofstadter Q-sequence: a(1) = a(2) = 1; a(n) = a(n-a(n-1)) + a(n-a(n-2)) for n > 2.++> [1,1,2,3,3,4,5,5,6,6,6,8,8,8,10,9,10,11,11,12,12,12,12,16,14,14,16,16,16,16,20] `isPrefixOf` a005185+-}+a005185 :: [Int]+a005185 =+  let ix n = a005185 !! (n - 1)+      zadd = zipWith (+)+      zsub = zipWith (-)+  in 1 : 1 : zadd (map ix (zsub [3..] a005185)) (map ix (zsub [3..] (tail a005185)))++{- | <https://oeis.org/A005448>++Centered triangular numbers: a(n) = 3n(n-1)/2 + 1.++> [1,4,10,19,31,46,64,85,109,136,166,199,235,274,316,361,409,460,514,571,631,694] `isPrefixOf` a005448++> map a005448_n [1 .. 1000] `isPrefixOf` a005448+-}+a005448 :: Integral n => [n]+a005448 = 1 : zipWith (+) a005448 [3,6 ..]++a005448_n :: Integral n => n -> n+a005448_n n = 3 * n * (n - 1) `div` 2 + 1++{- | <http://oeis.org/A005728>++Number of fractions in Farey series of order n.++> [1,2,3,5,7,11,13,19,23,29,33,43,47,59,65,73,81,97,103,121,129,141,151] `isPrefixOf` a005728+-}+a005728 :: Integral i => [i]+a005728 =+  let phi n = genericLength (filter (==1) (map (gcd n) [1..n]))+      f n = if n == 0 then 1 else f (n - 1) + phi n+  in map f [0::Integer ..]++{- | <http://oeis.org/A005811>++Number of runs in binary expansion of n (n>0); number of 1's in Gray code for n++> take 32 a005811 == [0,1,2,1,2,3,2,1,2,3,4,3,2,3,2,1,2,3,4,3,4,5,4,3,2,3,4,3,2,3,2,1]+-}+a005811 :: Integral n => [n]+a005811 =+  let f (x:xs) = x : f (xs ++ [x + x `mod` 2, x + 1 - x `mod` 2])+      f _ = error "A005811"+  in 0 : f [1]++{- | <http://oeis.org/A005917>++Rhombic dodecahedral numbers: a(n) = n^4 - (n - 1)^4.++> [1,15,65,175,369,671,1105,1695,2465,3439,4641,6095,7825,9855,12209,14911,17985] `isPrefixOf` a005917+-}+a005917 :: Integral n => [n]+a005917 =+  let f x ws = let (us,vs) = splitAt x ws in us : f (x + 2) vs+  in map sum (f 1 [1, 3 ..])++{- | <https://oeis.org/A006003>++a(n) = n*(n^2 + 1)/2.++> [0,1,5,15,34,65,111,175,260,369,505,671,870,1105,1379,1695,2056,2465,2925,3439] `isPrefixOf` a006003++> map a006003_n [0 .. 1000] `isPrefixOf` a006003+-}+a006003 :: Integral n => [n]+a006003 = scanl (+) 0 a005448++a006003_n :: Integral n => n -> n+a006003_n n = n * (n ^ (2::Int) + 1) `div` 2++{- | <http://oeis.org/A006046>++Total number of odd entries in first n rows of Pascal's triangle: a(0) = 0, a(1) = 1, a(2k) = 3*a(k), a(2k+1) = 2*a(k) + a(k+1).++> [0,1,3,5,9,11,15,19,27,29,33,37,45,49,57,65,81,83,87,91,99,103,111,119,135,139] `isPrefixOf` a006046++> import Sound.SC3.Plot {- hsc3-plot -}+> plot_p1_ln [take 250 a006046]+> let t = log 3 / log 2+> plot_p1_ln [zipWith (/) (map fromIntegral a006046) (map (\n -> n ** t) [0.0,1 .. 200])]+-}+a006046 :: [Int]+a006046 = map (sum . concat) (inits a047999_tbl)++{- | <http://oeis.org/A006052>++Number of magic squares of order n composed of the numbers from 1 to n^2, counted up to rotations and reflections.++> [1,0,1,880,275305224] == a006052+-}+a006052 :: Integral n => [n]+a006052 = [1,0,1,880,275305224]++{- | <http://oeis.org/A006842>++Triangle read by rows: row n gives numerators of Farey series of order n.++> [0,1,0,1,1,0,1,1,2,1,0,1,1,1,2,3,1,0,1,1,1,2,1,3,2,3,4,1,0,1,1,1,1,2,1,3] `isPrefixOf` a006842+> plot_p1_imp [take 200 (a006842 :: [Int])]+> plot_p1_pt [take 10000 (a006842 :: [Int])]+-}+a006842 :: Integral i => [i]+a006842 = map numerator (concatMap Math.farey [1..])++{- | <http://oeis.org/A006843>++Triangle read by rows: row n gives denominators of Farey series of order n++> [1,1,1,2,1,1,3,2,3,1,1,4,3,2,3,4,1,1,5,4,3,5,2,5,3,4,5,1,1,6,5,4,3,5,2,5] `isPrefixOf` a006843+> plot_p1_imp [take 200 (a006843 :: [Int])]+> plot_p1_pt [take 10000 (a006843 :: [Int])]+-}+a006843 :: Integral i => [i]+a006843 = map denominator (concatMap Math.farey [1..])++{- | <https://oeis.org/A007318>++Pascal's triangle read by rows++[[1],[1,1],[1,2,1],[1,3,3,1],[1,4,6,4,1],[1,5,10,10,5,1]] `isPrefixOf` a007318_tbl+-}+a007318 :: Integral i => [i]+a007318 = concat a007318_tbl++a007318_tbl :: Integral i => [[i]]+a007318_tbl =+  let f r = zipWith (+) (0 : r) (r ++ [0])+  in iterate f [1]++{- | <https://oeis.org/A008277>++Triangle of Stirling numbers of the second kind, S2(n,k), n >= 1, 1 <= k <= n.++[1,1,1,1,3,1,1,7,6,1,1,15,25,10,1,1,31,90,65,15,1,1,63,301,350,140,21,1] `isPrefixOf` a008277+-}+a008277 :: (Enum n,Num n) => [n]+a008277 = concat a008277_tbl++a008277_tbl :: (Enum n,Num n) => [[n]]+a008277_tbl = map tail a048993_tbl++{- | <http://oeis.org/A008278>++Triangle of Stirling numbers of 2nd kind, S(n,n-k+1), n >= 1, 1<=k<=n.++[1,1,1,1,3,1,1,6,7,1,1,10,25,15,1,1,15,65,90,31,1,1,21,140,350,301,63,1] `isPrefixOf` a008278+-}+a008278 :: (Enum n,Num n) => [n]+a008278 = concat a008278_tbl++a008278_tbl :: (Enum n,Num n) => [[n]]+a008278_tbl =+  let f p =+        let q = reverse (zipWith (*) [1..] (reverse p))+        in zipWith (+) (0 : q) (p ++ [0])+  in iterate f [1]++{- | <http://oeis.org/A008683>++Möbius (or Moebius) function mu(n). mu(1) = 1; mu(n) = (-1)^k if n is the product of k different primes; otherwise mu(n) = 0.++> [1,-1,-1,0,-1,1,-1,0,0,1,-1,0,-1,1,1,0,-1,0,-1,0,1,1,-1,0,0,1,0,0,-1,-1,-1,0,1] `isPrefixOf` a008683+-}+a008683 :: Integral n => [n]+a008683 = map a008683_n [1..]++a008683_n :: Integral n => n -> n+a008683_n =+  let mu [] = 1+      mu (1:es) = - mu es+      mu _ = 0+  in mu . snd . unzip . Prime.prime_factors_m ++{- | <http://oeis.org/A010049>++Second-order Fibonacci numbers.++> [0,1,1,3,5,10,18,33,59,105,185,324,564,977,1685,2895,4957,8462,14406,24465,41455] `isInfixOf` a010049+-}+a010049 :: Num n => [n]+a010049 =+  let c us (v:vs) = sum (zipWith (*) us (1 : reverse us)) : c (v:us) vs+      c _ _ = error "A010049"+  in uncurry c (splitAt 1 a000045)++{- | <https://oeis.org/A010060>++Thue-Morse sequence: let A_k denote the first 2^k terms; then A_0 = 0 and for k >= 0, A_{k+1} = A_k B_k, where B_k is obtained from A_k by interchanging 0's and 1's.++[0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0] `isPrefixOf` a010060++-}+a010060 :: [Integer]+a010060 =+  let interleave (x:xs) ys = x : interleave ys xs+      interleave [] _ = error "a010060?"+   in 0 : interleave (map (1 -) a010060) (tail a010060)++{- | <https://oeis.org/A014081>++a(n) is the number of occurrences of '11' in binary expansion of n.++> [0, 0, 0, 1, 0, 0, 1, 2, 0, 0, 0, 1, 1, 1, 2, 3, 0, 0, 0, 1, 0, 0, 1, 2, 1, 1, 1, 2, 2, 2, 3, 4, 0, 0, 0, 1, 0, 0, 1, 2] `isPrefixOf` a014081++-}+a014081 :: (Integral i, Bits i) => [i]+a014081 = map (\n -> a000120 !! (n .&. div n 2)) [0..]++{- | <https://oeis.org/A014577>++The regular paper-folding sequence (or dragon curve sequence).++> [1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1] `isPrefixOf` a014577+-}+a014577 :: Integral i => [i]+a014577 =+  let f n = if n `rem` 2 == 1 then f (n `quot` 2) else 1 - (n `div` 2 `rem` 2)+  in map f [0..]++{- | <http://oeis.org/A016813>++a(n) = 4*n + 1.++> [1,5,9,13,17,21,25,29,33,37,41,45,49,53,57,61,65,69,73,77,81,85,89,93,97,101] `isPrefixOf` a016813+-}+a016813 :: Integral n => [n]+a016813 = [1, 5 ..]++{- | <http://oeis.org/A017817>++a(n) = a(n-3) + a(n-4), with a(0)=1, a(1)=a(2)=0, a(3)=1++> [1,0,0,1,1,0,1,2,1,1,3,3,2,4,6,5,6,10,11,11,16,21,22,27,37,43,49,64,80,92] `isPrefixOf` a017817+-}+a017817 :: Num n => [n]+a017817 = 1 : 0 : 0 : 1 : zipWith (+) a017817 (tail a017817)++{- | <http://oeis.org/A020695>++Pisot sequence E(2,3).++> [2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,6765,10946,17711] `isPrefixOf` a020695+-}+a020695 :: Num n => [n]+a020695 = drop 3 a000045++{- | <https://oeis.org/A020985>++The Rudin-Shapiro or Golay-Rudin-Shapiro sequence (coefficients of the Shapiro polynomials).		45++> [1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1] `isPrefixOf` a020985+-}+a020985 :: [Integer]+a020985 =+  let f (x:xs) w = x : x*w : f xs (0 - w)+      f [] _ = error "a020985?"+  in 1 : 1 : f (tail a020985) (-1)++{- | <http://oeis.org/A022095>++Fibonacci sequence beginning 1, 5.++> [1,5,6,11,17,28,45,73,118,191,309,500,809,1309,2118,3427,5545,8972,14517,23489] `isPrefixOf` a022095+-}+a022095 :: Num n => [n]+a022095 = 1 : 5 : zipWith (+) a022095 (tail a022095)++{- | <http://oeis.org/A022096>++Fibonacci sequence beginning 1, 6.++> [1,6,7,13,20,33,53,86,139,225,364,589,953,1542,2495,4037,6532,10569,17101,27670] `isPrefixOf` a022096+-}+a022096 :: Num n => [n]+a022096 = 1 : 6 : zipWith (+) a022096 (tail a022096)++{- | <https://oeis.org/A027750>++Triangle read by rows in which row n lists the divisors of n.++> [1,1,2,1,3,1,2,4,1,5,1,2,3,6,1,7,1,2,4,8,1,3,9,1,2,5,10,1,11,1,2,3,4,6,12,1,13] `isPrefixOf` a027750+-}+a027750 :: Integral n => [n]+a027750 = concatMap a027750_row [1..]++a027750_row :: Integral n => n -> [n]+a027750_row n = filter ((== 0) . (mod n)) [1..n]++{- | <http://oeis.org/A027934>++a(0)=0, a(1)=1, a(2)=2; for n > 2, a(n) = 3*a(n-1) - a(n-2) - 2*a(n-3).++> [0,1,2,5,11,24,51,107,222,457,935,1904,3863,7815,15774,31781,63939,128488] `isPrefixOf` a027934+-}+a027934 :: Num n => [n]+a027934 =+  let f x y z = 3 * x - y - 2 * z+  in 0 : 1 : 2 : zipWith3 f (drop 2 a027934) (tail a027934) a027934++{- | <http://oeis.org/A029635>++The (1,2)-Pascal triangle (or Lucas triangle) read by rows.++> [2,1,2,1,3,2,1,4,5,2,1,5,9,7,2,1,6,14,16,9,2,1,7,20,30,25,11,2,1,8,27,50,55,36] `isPrefixOf` a029635+> take 7 a029635_tbl == [[2],[1,2],[1,3,2],[1,4,5,2],[1,5,9,7,2],[1,6,14,16,9,2],[1,7,20,30,25,11,2]]+-}+a029635 :: Num i => [i]+a029635 = concat a029635_tbl++a029635_tbl :: Num i => [[i]]+a029635_tbl =+  let f r = zipWith (+) (0 : r) (r ++ [0])+  in [2] : iterate f [1,2]++{- | <http://oeis.org/A030308>++Triangle T(n,k): Write n in base 2, reverse order of digits, to get the n-th row++> take 9 a030308 == [[0],[1],[0,1],[1,1],[0,0,1],[1,0,1],[0,1,1],[1,1,1],[0,0,0,1]]+-}+a030308 :: (Eq n,Num n) => [[n]]+a030308 =+   let f l = case l of+         [] -> [1]+         0:b -> 1 : b+         1:b -> 0 : f b+         _ -> error "A030308"+   in iterate f [0]++{- | <https://oeis.org/A033622>++Good sequence of increments for Shell sort (best on big values).++[1, 5, 19, 41, 109, 209, 505, 929, 2161, 3905, 8929, 16001, 36289, 64769, 146305, 260609, 587521] `isPrefixOf` a033622+-}+a033622 :: [Integer]+a033622 = map a033622_n [0..]++a033622_n :: Integer -> Integer+a033622_n n =+  if even n+  then 9 * 2 ^ n - 9 * 2 ^ ( n `div` 2) + 1+  else 8 * 2 ^ n - 6 * 2 ^ ((n + 1 )`div` 2) + 1++{- | <http://oeis.org/A033812>++The Loh-Shu 3 X 3 magic square, lexicographically largest variant when read by columns.+-}+a033812 :: Num n => [n]+a033812 = [8, 1, 6, 3, 5, 7, 4, 9, 2]++{- | <http://oeis.org/A034968>++Minimal number of factorials that add to n.++> [0,1,1,2,2,3,1,2,2,3,3,4,2,3,3,4,4,5,3,4,4,5,5,6,1,2,2,3,3,4,2,3,3,4,4,5,3,4,4] `isPrefixOf` a034968+-}+a034968 :: Integral n => [n]+a034968 =+  let f i s n = if n == 0 then s else f (i + 1) (s + rem n i) (quot n i)+  in map (f 2 0) [0 ..]++{- | <https://oeis.org/A036562>++a(n) = 4^(n+1) + 3*2^n + 1++[1, 8, 23, 77, 281, 1073, 4193, 16577, 65921, 262913, 1050113, 4197377, 16783361, 67121153] `isPrefixOf` a036562+-}+a036562 :: [Integer]+a036562 = 1 : map a036562_n [0..]++a036562_n :: Integer -> Integer+a036562_n n = 4^(n+1) + 3*2^n + 1++{- | <http://oeis.org/A046042>++Number of partitions of n into fourth powers.++> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3] `isPrefixOf` a046042+-}+a046042 :: Num n => [n]+a046042 =+  let p _ 0 = 1+      p ks'@(k:ks) m = if m < k then 0 else p ks' (m - k) + p ks m+      p _ _ = error "A046042"+  in map (p (tail a000583)) [1::Integer ..]++{- | <http://oeis.org/A047999>++Sierpiński's triangle (or gasket): triangle, read by rows, formed by reading Pascal's triangle mod 2.++> [1,1,1,1,0,1,1,1,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,1,0,1,0,1,1,1,1,1,1,1,1,1,1,0,0] `isPrefixOf` a047999+-}+a047999 :: [Int]+a047999 = concat a047999_tbl++a047999_tbl :: [[Int]]+a047999_tbl = iterate (\r -> zipWith xor (0 : r) (r ++ [0])) [1]++{- | <https://oeis.org/A048993>++Triangle of Stirling numbers of 2nd kind, S(n,k), n >= 0, 0 <= k <= n.++> [1,0,1,0,1,1,0,1,3,1,0,1,7,6,1,0,1,15,25,10,1,0,1,31,90,65,15,1] `isPrefixOf` a048993+-}+a048993 :: (Enum n,Num n) => [n]+a048993 = concat a048993_tbl++a048993_tbl :: (Enum n,Num n) => [[n]]+a048993_tbl = iterate (\row -> 0 : zipWith (+) row (zipWith (*) [1..] (tail row)) ++ [1]) [1]++{- | <http://oeis.org/A049455>++Triangle read by rows, numerator of fractions of a variant of the Farey series.++> [0,1,0,1,1,0,1,1,2,1,0,1,1,2,1,3,2,3,1,0,1,1,2,1,3,2,3,1,4,3,5,2,5,3,4,1,0] `isPrefixOf` a049455+> plot_p1_imp [take 200 (a049455 :: [Int])]+> plot_p1_pt [take 10000 (a049455 :: [Int])]+-}+a049455 :: Integral n => [n]+a049455 = map fst (concat Math.stern_brocot_tree_lhs)++{- | <http://oeis.org/A049456>++Triangle read by rows, denominator of fractions of a variant of the Farey series.++[1,1,1,2,1,1,3,2,3,1,1,4,3,5,2,5,3,4,1,1,5,4,7,3,8,5,7,2,7,5,8,3,7,4,5,1,1,6,5,9] `isPrefixOf` a049456+> plot_p1_imp [take 200 (a049456 :: [Int])]+> plot_p1_pt [take 10000 (a049456 :: [Int])]+-}+a049456 :: Integral n => [n]+a049456 = map snd (concat Math.stern_brocot_tree_lhs)++{- | <http://oeis.org/A053121>++Catalan triangle (with 0's) read by rows.++> [1,0,1,1,0,1,0,2,0,1,2,0,3,0,1,0,5,0,4,0,1,5,0,9,0,5,0,1,0,14,0,14,0,6,0,1,14,0] `isPrefixOf` a053121+> take 7 a053121_tbl == [[1],[0,1],[1,0,1],[0,2,0,1],[2,0,3,0,1],[0,5,0,4,0,1],[5,0,9,0,5,0,1]]+-}+a053121 :: Num n => [n]+a053121 = concat a053121_tbl++a053121_tbl :: Num n => [[n]]+a053121_tbl = iterate (\row -> zipWith (+) (0 : row) (tail row ++ [0, 0])) [1]++{- | <http://oeis.org/A058265>++Decimal expansion of the tribonacci constant t, the real root of x^3 - x^2 - x - 1.++> [1,8,3,9,2,8,6,7,5,5,2,1,4,1,6,1,1,3,2,5,5,1,8,5,2,5,6,4,6,5,3,2,8,6,6,0,0,4,2] `isPrefixOf` a058265++> a058265_k :: Data.Number.Fixed.Fixed Data.Number.Fixed.Prec500 {- numbers -}+-}+a058265 :: Num n => [n]+a058265 = map (fromIntegral . digitToInt) "183928675521416113255185256465328660042417874609759224677875863940420322208196642573843541942830701414197982685924097416417845074650743694383154582049951379624965553964461366612154027797267811894104121160922328215595607181671218236598665227337853781569698925211739579141322872106187898408525495693114534913498534595761750359652213238142472727224173581877000697905510254904496571074252654772281100659893755563630933305282623575385197199429914530082546639774729005870059744813919316728258488396263329709" ++ error "A058265"++-- | A058265 as 'Floating' calculation, see "Data.Number.Fixed".+a058265_k :: Floating n => n+a058265_k = (1/3) * (1 + (19 + 3 * sqrt 33) ** (1/3) + (19 - 3 * sqrt 33)  ** (1/3))++{- | <http://oeis.org/A060588>++If the final two digits of n written in base 3 are the same then this digit, otherwise mod 3-sum of these two digits.++> [0,2,1,2,1,0,1,0,2,0,2,1,2,1,0,1,0,2,0,2,1,2,1,0,1,0,2,0,2,1,2,1,0,1,0,2,0,2,1] `isPrefixOf` a060588a+-}+a060588a :: Integral n => [n]+a060588a = map a060588a_n [0..]++a060588a_n :: Integral n => n -> n+a060588a_n n = (-n - floor (fromIntegral n / (3::Double))) `mod` 3++{- | <http://oeis.org/A061654>++a(n) = (3*16^n + 2)/5++> [1,10,154,2458,39322,629146,10066330,161061274,2576980378,41231686042] `isPrefixOf` a061654+-}+a061654 :: Integral n => [n]+a061654 = map a061654_n [0 ..]++a061654_n :: Integral n => n -> n+a061654_n n = (3 * 16^n + 2) `div` 5++{- | <http://oeis.org/A071996>++a(1) = 0, a(2) = 1, a(n) = a(floor(n/3)) + a(n - floor(n/3)).++> [0,1,1,1,1,2,2,3,3,3,4,4,4,4,4,5,5,6,6,6,6,6,7,8,8,9,9,9,9,9,9,9,10,11,12,12,12] `isPrefixOf` a071996++> plot_p1_ln [take 50 a000201 :: [Int]]+> plot_p1_imp [map length (take 250 (group a071996))]+-}+a071996 :: Integral n => [n]+a071996 =+  let f n =+        case n of+          0 -> error "A071996"+          1 -> 0+          2 -> 1+          _ -> let m = floor (fromIntegral n / (3::Double)) in f m + f (n - m)+  in map f [1::Int ..]++{- | <http://oeis.org/A073334>++The "rhythmic infinity system" of Danish composer Per Nørgård++> take 24 a073334 == [3,5,8,5,8,13,8,5,8,13,21,13,8,13,8,5,8,13,21,13,21,34,21,13]+> plot_p1_imp [take 200 (a073334 :: [Int])]+-}+a073334 :: Num n => [n]+a073334 =+  let f n = a000045 !! ((a005811 !! n) + 4)+  in 3 : map f [1..]++{- | <https://oeis.org/A080843>++Tribonacci word: limit S(infinity), where S(0) = 0, S(1) = 0,1, S(2) = 0,1,0,2 and for n >= 0, S(n+3) = S(n+2) S(n+1) S(n).++> [0,1,0,2,0,1,0,0,1,0,2,0,1,0,1,0,2,0,1,0,0,1,0,2,0,1,0,2,0,1,0,0,1,0,2,0,1,0,1] `isPrefixOf` a080843+-}+a080843 :: Integral n => [n]+a080843 =+  let rw n = case n of {0 -> [0,1];1 -> [0,2];2 -> [0];_ -> error "A080843"}+      unf = let f n l = case l of {[] -> error "A080843";x:xs -> drop n x ++ f (length x) xs} in f 0+  in unf (iterate (concatMap rw) [0])++{- | <http://oeis.org/A080992>++Entries in Durer's magic square.++> [16,3,2,13,5,10,11,8,9,6,7,12,4,15,14,1] == a080992+-}+a080992 :: Num n => [n]+a080992 =+  [16,03,02,13+  ,05,10,11,08+  ,09,06,07,12+  ,04,15,14,01]++{- | <http://oeis.org/A083866>++Positions of zeros in Per Nørgård's infinity sequence (A004718).++> take 24 a083866 == [0,5,10,17,20,27,34,40,45,54,65,68,75,80,85,90,99,105,108,119,130,136,141,150]+-}+a083866 :: (Enum n,Num n) => [n]+a083866 = map snd (filter ((== (0::Int)) . fst) (zip a004718 [0..]))++{- | <http://oeis.org/A095660>++Pascal (1,3) triangle.++> [3,1,3,1,4,3,1,5,7,3,1,6,12,10,3,1,7,18,22,13,3,1,8,25,40,35,16,3,1,9,33,65,75] `isPrefixOf` a095660+> take 6 a095660_tbl == [[3],[1,3],[1,4,3],[1,5,7,3],[1,6,12,10,3],[1,7,18,22,13,3]]+-}+a095660 :: Num i => [i]+a095660 = concat a095660_tbl++a095660_tbl :: Num i => [[i]]+a095660_tbl =+  let f r = zipWith (+) (0 : r) (r ++ [0])+  in [3] : iterate f [1,3]++{- | <http://oeis.org/A095666>++Pascal (1,4) triangle.++> [4,1,4,1,5,4,1,6,9,4,1,7,15,13,4,1,8,22,28,17,4,1,9,30,50,45,21,4,1,10,39,80,95] `isPrefixOf` a095666+> take 6 a095666_tbl == [[4],[1,4],[1,5,4],[1,6,9,4],[1,7,15,13,4],[1,8,22,28,17,4]]+-}+a095666 :: Num i => [i]+a095666 = concat a095666_tbl++a095666_tbl :: Num i => [[i]]+a095666_tbl =+  let f r = zipWith (+) (0 : r) (r ++ [0])+  in [4] : iterate f [1,4]++{- | <http://oeis.org/A096940>++Pascal (1,5) triangle.++> [5,1,5,1,6,5,1,7,11,5,1,8,18,16,5,1,9,26,34,21,5,1,10,35,60,55,26,5,1,11,45,95] `isPrefixOf` a096940+> take 6 a096940_tbl == [[5],[1,5],[1,6,5],[1,7,11,5],[1,8,18,16,5],[1,9,26,34,21,5]]+-}+a096940 :: Num i => [i]+a096940 = concat a096940_tbl++a096940_tbl :: Num i => [[i]]+a096940_tbl =+  let f r = zipWith (+) (0 : r) (r ++ [0])+  in [5] : iterate f [1,5]++{- | <http://oeis.org/A105809>++A Fibonacci-Pascal matrix.++> [1,1,1,2,2,1,3,4,3,1,5,7,7,4,1,8,12,14,11,5,1,13,20,26,25,16,6,1,21,33,46,51,41] `isPrefixOf` a105809+-}+a105809 :: Num n => [n]+a105809 = concat a105809_tbl++a105809_tbl :: Num n => [[n]]+a105809_tbl =+  let f (u:_, vs) = (vs, zipWith (+) (u : vs) (vs ++ [0]))+      f _ = error "A105809"+  in map fst (iterate f ([1], [1, 1]))++{- | <http://oeis.org/A124010>++Triangle in which first row is 0, n-th row (n>1) lists the (ordered)+prime signature of n, that is, the exponents of distinct prime factors+in factorization of n.++> [0,1,1,2,1,1,1,1,3,2,1,1,1,2,1,1,1,1,1,1,4,1,1,2,1,2,1,1,1,1,1,1,3,1,2,1,1,3,2,1,1,1,1,1,1,5,1] `isPrefixOf` a124010+-}+a124010 :: Integral n => [n]+a124010 = concatMap a124010_row [1..]++a124010_row :: Integral n => n -> [n]+a124010_row n =+  let f u w =+        case (u, w) of+          (1, _) -> []+          (_, p:ps) ->+            let h v e =+                  let (v', m) = divMod v p+                  in if m == 0+                     then h v' (e + 1)+                     else if e > 0+                          then e : f v ps+                          else f v ps+            in h u 0+          _ -> error "a124010"+  in if n == 1 then [0] else f n a000040++{- | <https://oeis.org/A124472>++Benjamin Franklin's 16 X 16 magic square read by rows.++> [200,217,232,249,8,25,40,57,72,89,104,121,136,153,168,185,58,39,26,7,250,231] `isPrefixOf` a124472+-}+a124472 :: Num n => [n]+a124472 =+  concat+  [[200,217,232,249,8,25,40,57,72,89,104,121,136,153,168,185]+  ,[58,39,26,7,250,231,218,199,186,167,154,135,122,103,90,71]+  ,[198,219,230,251,6,27,38,59,70,91,102,123,134,155,166,187]+  ,[60,37,28,5,252,229,220,197,188,165,156,133,124,101,92,69]+  ,[201,216,233,248,9,24,41,56,73,88,105,120,137,152,169,184]+  ,[55,42,23,10,247,234,215,202,183,170,151,138,119,106,87,74]+  ,[203,214,235,246,11,22,43,54,75,86,107,118,139,150,171,182]+  ,[53,44,21,12,245,236,213,204,181,172,149,140,117,108,85,76]+  ,[205,212,237,244,13,20,45,52,77,84,109,116,141,148,173,180]+  ,[51,46,19,14,243,238,211,206,179,174,147,142,115,110,83,78]+  ,[207,210,239,242,15,18,47,50,79,82,111,114,143,146,175,178]+  ,[49,48,17,16,241,240,209,208,177,176,145,144,113,112,81,80]+  ,[196,221,228,253,4,29,36,61,68,93,100,125,132,157,164,189]+  ,[62,35,30,3,254,227,222,195,190,163,158,131,126,99,94,67]+  ,[194,223,226,255,2,31,34,63,66,95,98,127,130,159,162,191]+  ,[64,33,32,1,256,225,224,193,192,161,160,129,128,97,96,65]]++{- | <http://oeis.org/A125519>++A 4 x 4 permutation-free magic square.+-}+a125519 :: Num n => [n]+a125519 = [831,326,267,574,584,257,316,841,158,683,742,415,425,732,673,168]++{- | <http://oeis.org/A126275>++Moment of inertia of all magic squares of order n.++> [5,60,340,1300,3885,9800,21840,44280,83325,147620,248820,402220,627445,949200] `isPrefixOf` a126275+-}+a126275 :: Integral n => [n]+a126275 = map a126275_n [2..]++a126275_n :: Integral n => n -> n+a126275_n n = (n ^ (2::Int) * (n ^ (4::Int) - 1)) `div` 12++{- | <http://oeis.org/A126276>++Moment of inertia of all magic cubes of order n.++> [18,504,5200,31500,136710,471968,1378944,3547800,8258250,17728920,35603568] `isPrefixOf` a126276+-}+a126276 :: Integral n => [n]+a126276 = map a126276_n [2..]++a126276_n :: Integral n => n -> n+a126276_n n = (n ^ (3::Int) * (n ^ (3::Int) + 1) * (n ^ (2::Int) - 1)) `div` 12++{- | <http://oeis.org/A126651>++A 7 x 7 magic square.+-}+a126651 :: Num n => [n]+a126651 =+  [71,  1, 51, 32, 50,  2, 80+  ,21, 41, 61, 56, 26, 13, 69+  ,31, 81, 11, 20, 62, 65, 17+  ,34, 40, 60, 43, 28, 64, 18+  ,48, 42, 22, 54, 39, 75,  7+  ,33, 53, 15, 68, 16, 44, 58+  ,49, 29, 67, 14, 66, 24, 38]++{- | <http://oeis.org/A126652>++A 3 X 3 magic square with magic sum 75: the Loh-Shu square A033812 multiplied by 5.++> a126652 == map (* 5) a033812+-}+a126652 :: Num n => [n]+a126652 = [40, 5, 30, 15, 25, 35, 20, 45, 10]++{- | <http://oeis.org/A126653>++A 3 X 3 magic square with magic sum 45: the Loh-Shu square A033812 multiplied by 3.++> a126653 == map (* 3) a033812+-}+a126653 :: Num n => [n]+a126653 = [24, 3, 18, 9, 15, 21, 12, 27, 6]++{- | <http://oeis.org/A126654>++A 3 x 3 magic square.+-}+a126654 :: Num n => [n]+a126654 = [32, 4, 24, 12, 20, 28, 16, 36, 8]++{- | <http://oeis.org/A126709>++The Loh-Shu 3 x 3 magic square, variant 2.++Loh-Shu magic square, attributed to the legendary Fu Xi (Fuh-Hi).+-}+a126709 :: Num n => [n]+a126709 =+  [4,9,2+  ,3,5,7+  ,8,1,6]++{- | <http://oeis.org/A126710>++Jaina inscription of the twelfth or thirteenth century, Khajuraho, India.+-}+a126710 :: Num n => [n]+a126710 =+  [ 7,12, 1,14+  , 2,13, 8,11+  ,16, 3,10, 5+  , 9, 6,15, 4]++{- | <http://oeis.org/A126976>++A 6 x 6 magic square read by rows.++Agrippa (Magic Square of the Sun)+-}+a126976 :: Num n => [n]+a126976 =+  [06,32,03,34,35,01+  ,07,11,27,28,08,30+  ,19,14,16,15,23,24+  ,18,20,22,21,17,13+  ,25,29,10,09,26,12+  ,36,05,33,04,02,31]++{- | <https://oeis.org/A212804>++Expansion of (1 - x)/(1 - x - x^2).++[1,0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,6765,10946] `isPrefixOf` a212804+-}+a212804 :: Integral n => [n]+a212804 = 1 : a000045++{- | <https://oeis.org/A245553>++A Rauzy fractal sequence: trajectory of 1 under morphism 1 -> 2,3; 2 -> 3; 3 -> 1.++> [1,2,3,2,3,3,1,2,3,3,1,3,1,1,2,3,2,3,3,1,3,1,1,2,3,3,1,1,2,3,1,2,3,2,3,3,1,2,3] `isPrefixOf` a245553+-}+a245553 :: Integral n => [n]+a245553 =+  let rw n = case n of {1 -> [2,3];2 -> [3];3 -> [1];_ -> error "A245553"}+      jn x = x ++ concatMap rw x+      unf = let f n l = case l of {[] -> error "A245553";x:xs -> drop n x ++ f (length x) xs} in f 0+  in unf (iterate jn [1])++{- | <http://oeis.org/A255723>++Another variant of Per Nørgård's "infinity sequence"++> take 24 a255723 == [0,-2,-1,2,-2,-4,1,0,-1,-3,0,1,2,0,-3,4,-2,-4,1,0,-4,-6,3,-2]+> plot_p1_imp [take 400 (a255723 :: [Int])]+-}+a255723 :: Num n => [n]+a255723 = 0 : concat (transpose [map (subtract 2) a255723+                                ,map (-1 -) a255723+                                ,map (+ 2) a255723+                                ,tail a255723])++{- | <http://oeis.org/A256184>++First of two variations by Per Nørgård of his "infinity sequence"++> take 24 a256184 == [0,-2,-1,2,-4,-3,1,-3,-2,-2,0,1,4,-6,-5,3,-5,-4,-1,-1,0,3,-5,-4]+-}+a256184 :: Num n => [n]+a256184 = 0 : concat (transpose [map (subtract 2) a256184+                                ,map (subtract 1) a256184+                                ,map negate (tail a256184)])++{- | <http://oeis.org/A256185>++Second of two variations by Per Nørgård of his "infinity sequence"++> take 24 a256185 == [0,-3,-2,3,-6,1,2,-5,0,-3,0,-5,6,-9,4,-1,-2,-3,-2,-1,-4,5,-8,3]+-}+a256185 :: Num n => [n]+a256185 = 0 : concat (transpose [map (subtract 3) a256185+                                ,map (-2 -) a256185+                                ,map negate (tail a256185)])++{- | <http://oeis.org/A270876>++Number of magic tori of order n composed of the numbers from 1 to n^2.++> [1,0,1,255,251449712] == a270876+-}+a270876 :: Integral n => [n]+a270876 = [1,0,1,255,251449712]++{- | <http://oeis.org/A320872>++For all possible 3 X 3 magic squares made of primes, in order of increasing magic sum, list the lexicographically smallest representative of each equivalence class (modulo symmetries of the square), as a row of the 9 elements (3 rows of 3 elements each).+-}+a320872 :: Num n => [n]+a320872 =+  [17, 89,  71,  113,  59,  5, 47, 29, 101+  ,41, 89,  83,  113,  71, 29, 59, 53, 101+  ,37, 79,  103, 139,  73,  7, 43, 67, 109+  ,29, 131, 107, 167,  89, 11, 71, 47, 149+  ,43, 127, 139, 199, 103,  7, 67, 79, 163+  ,37, 151, 139, 211, 109,  7, 79, 67, 181+  ,43, 181, 157, 241, 127, 13, 97, 73, 211]
+ Music/Theory/Math/Prime.hs view
@@ -0,0 +1,234 @@+-- | Prime number related functions.+module Music.Theory.Math.Prime where++import Data.List {- base -}+import Data.Maybe {- base -}+import Data.Ratio {- base -}++import qualified Data.Numbers.Primes as Primes {- primes -}++import qualified Music.Theory.Function as Function {- hmt -}+import qualified Music.Theory.List as List {- hmt -}+import qualified Music.Theory.Math as Math {- hmt -}+import qualified Music.Theory.Unicode as Unicode {- hmt -}++-- | Alias for 'Primes.primes'.+--+-- > take 12 primes_list == [2,3,5,7,11,13,17,19,23,29,31,37]+primes_list :: Integral i => [i]+primes_list = Primes.primes++-- | Give zero-index of prime, or Nothing if value is not prime.+--+-- > map prime_k [2,3,5,7,11,13,17,19,23,29,31,37] == map Just [0 .. 11]+-- > map prime_k [1,4,6,8,9,10,12,14,15,16,18,20,21,22] == replicate 14 Nothing+prime_k :: Integral a => a -> Maybe Int+prime_k i = if Primes.isPrime i then Just (List.findIndex_err (== i) primes_list) else Nothing++-- | 'maybe' 'error' of 'prime_k'+--+-- > prime_k_err 13 == 5+prime_k_err :: Integral a => a -> Int+prime_k_err = fromMaybe (error "prime_k: not prime?") . prime_k++{- | Generate list of factors of /n/ from /x/.++> factor primes_list 315 == [3,3,5,7]+> Primes.primeFactors 315 == [3,3,5,7]++As a special case 1 gives the empty list.++> factor primes_list 1 == []+> Primes.primeFactors 1 == []+-}+factor :: Integral i => [i] -> i -> [i]+factor x n =+    case x of+      [] -> error "factor: null primes_list input"+      i:x' -> if n < i+              then [] -- ie. prime factors of 1...+              else if i * i > n+                   then [n]+                   else if rem n i == 0+                        then i : factor x (quot n i)+                        else factor x' n++-- | 'factor' of 'primes_list'.+--+-- > map prime_factors [-1,0,1] == [[],[],[]]+-- > map prime_factors [1,4,231,315] == [[],[2,2],[3,7,11],[3,3,5,7]]+-- > map Primes.primeFactors [1,4,231,315] == [[],[2,2],[3,7,11],[3,3,5,7]]+prime_factors :: Integral i => i -> [i]+prime_factors = factor primes_list++-- | 'maximum' of 'prime_factors'+--+-- > map prime_limit [243,125] == [3,5]+-- > map prime_limit [0,1] == [1,1]+prime_limit :: Integral i => i -> i+prime_limit x = if x < 2 then 1 else maximum (prime_factors x)++-- | Collect number of occurences of each element of a sorted list.+--+-- > multiplicities [1,1,1,2,2,3] == [(1,3),(2,2),(3,1)]+multiplicities :: Eq t => [t] -> [(t,Int)]+multiplicities = List.generic_histogram_by (==) Nothing++-- | Pretty printer for histogram (multiplicites).+--+-- > multiplicities_pp [(3,2),(5,1),(7,1)] == "3×2 5×1 7×1"+multiplicities_pp :: Show t => [(t,Int)] -> String+multiplicities_pp =+  let f (x,y) = show x ++ "×" ++ show y+  in unwords . map f++-- | 'multiplicities' of 'Primes.primeFactors'.+--+-- > prime_factors_m 1 == []+-- > prime_factors_m 315 == [(3,2),(5,1),(7,1)]+prime_factors_m :: Integral i => i -> [(i,Int)]+prime_factors_m = multiplicities . Primes.primeFactors++-- | 'multiplicities_pp' of 'prime_factors_m'.+prime_factors_m_pp :: (Show i,Integral i) => i -> String+prime_factors_m_pp = multiplicities_pp . prime_factors_m++-- | Prime factors of /n/ and /d/.+rat_prime_factors :: Integral i => (i,i) -> ([i],[i])+rat_prime_factors = Function.bimap1 Primes.primeFactors++-- | 'Ratio' variant of 'rat_prime_factors'+rational_prime_factors :: Integral i => Ratio i -> ([i],[i])+rational_prime_factors = rat_prime_factors . Math.rational_nd++{- | Variant that writes factors of numerator as positive and factors for denominator as negative.+     Sorted by absolute value.++> rat_prime_factors_sgn (3 * 5 * 7 * 11,1) == [3,5,7,11]+> rat_prime_factors_sgn (3 * 5,7 * 11) == [3,5,-7,-11]+> rat_prime_factors_sgn (3 * 7,5) == [3,-5,7]+-}+rat_prime_factors_sgn :: Integral i => (i,i) -> [i]+rat_prime_factors_sgn r = let (n,d) = rat_prime_factors r in sortOn abs (n ++ map negate d)++-- | Rational variant.+--+-- > rational_prime_factors_sgn (2 * 2 * 2 * 1/3 * 1/3 * 1/3 * 1/3 * 5) == [2,2,2,-3,-3,-3,-3,5]+rational_prime_factors_sgn :: Integral i => Ratio i -> [i]+rational_prime_factors_sgn = rat_prime_factors_sgn . Math.rational_nd++-- | The largest prime factor of n/d.+rat_prime_limit :: Integral i => (i,i) -> i+rat_prime_limit = uncurry max . Function.bimap1 prime_limit++-- | The largest prime factor of /n/.+--+-- > rational_prime_limit (243/125) == 5+rational_prime_limit :: Integral i => Ratio i -> i+rational_prime_limit = rat_prime_limit . Math.rational_nd++-- | Merge function for 'rat_prime_factors_m'+rat_pf_merge :: Ord t => [(t,Int)] -> [(t,Int)] -> [(t,Int)]+rat_pf_merge p q =+  case (p,q) of+    (_,[]) -> p+    ([],_) -> map (\(i,j) -> (i,-j)) q+    ((a,b):p',(c,d):q') ->+      if a < c+      then (a,b) : rat_pf_merge p' q+      else if a > c+           then (c,-d) : rat_pf_merge p q'+           else if b /= d+                then (a,b-d) : rat_pf_merge p' q'+                else rat_pf_merge p' q'++{- | Collect the prime factors in a rational number given as a+numerator/ denominator pair (n,m). Prime factors are listed in+ascending order with their positive or negative multiplicities,+depending on whether the prime factor occurs in the numerator or the+denominator (after cancelling out common factors).++> rat_prime_factors_m (1,1) == []+> rat_prime_factors_m (16,15) == [(2,4),(3,-1),(5,-1)]+> rat_prime_factors_m (10,9) == [(2,1),(3,-2),(5,1)]+> rat_prime_factors_m (81,64) == [(2,-6),(3,4)]+> rat_prime_factors_m (27,16) == [(2,-4),(3,3)]+> rat_prime_factors_m (12,7) == [(2,2),(3,1),(7,-1)]+> rat_prime_factors_m (5,31) == [(5,1),(31,-1)]+-}+rat_prime_factors_m :: Integral i => (i,i) -> [(i,Int)]+rat_prime_factors_m (n,d) = rat_pf_merge (prime_factors_m n) (prime_factors_m d)++-- | 'Ratio' variant of 'rat_prime_factors_m'+rational_prime_factors_m :: Integral i => Ratio i -> [(i,Int)]+rational_prime_factors_m = rat_prime_factors_m . Math.rational_nd++-- | Variant of 'rat_prime_factors_m' giving results in a list.+--+-- > rat_prime_factors_l (1,1) == []+-- > rat_prime_factors_l (2^5,9) == [5,-2]+-- > rat_prime_factors_l (2*2*3,7) == [2,1,0,-1]+-- > rat_prime_factors_l (3*3,11*13) == [0,2,0,0,-1,-1]+rat_prime_factors_l :: Integral i => (i,i) -> [Int]+rat_prime_factors_l x =+  case rat_prime_factors_m x of+    [] -> []+    r -> let lm = maximum (map fst r)+         in map (\i -> fromMaybe 0 (lookup i r)) (List.take_until (== lm) primes_list)++-- | 'Ratio' variant of 'rat_prime_factors_l'+--+-- > map rational_prime_factors_l [1/31,256/243] == [[0,0,0,0,0,0,0,0,0,0,-1],[8,-5]]+rational_prime_factors_l :: Integral i => Ratio i -> [Int]+rational_prime_factors_l = rat_prime_factors_l . Math.rational_nd++-- | Variant of 'rational_prime_factors_l' padding table to /k/ places.+--   It is an error for /k/ to indicate a prime less than the limit of /x/.+--+-- > map (rat_prime_factors_t 6) [(5,13),(12,7)] == [[0,0,1,0,0,-1],[2,1,0,-1,0,0]]+-- > rat_prime_factors_t 3 (9,7) == undefined+rat_prime_factors_t :: (Integral i,Show i) => Int -> (i,i) -> [Int]+rat_prime_factors_t k = List.pad_right_err 0 k . rat_prime_factors_l++-- | 'Ratio' variant of 'rat_prime_factors_t'+rational_prime_factors_t :: (Integral i,Show i) => Int -> Ratio i -> [Int]+rational_prime_factors_t n = rat_prime_factors_t n . Math.rational_nd++-- | Condense factors list to include only indicated places.+--   It is an error if a deleted factor has a non-zero entry in the table.+--+-- > rat_prime_factors_l (12,7) == [2,1,0,-1]+-- > rat_prime_factors_c [2,3,5,7] (12,7) == [2,1,0,-1]+-- > rat_prime_factors_c [2,3,7] (12,7) == [2,1,-1]+rat_prime_factors_c :: (Integral i,Show i) => [i] -> (i,i) -> [Int]+rat_prime_factors_c fc r =+  let t = rat_prime_factors_l r+      k = map prime_k_err fc+      f (ix,e) = if ix `notElem` k+                 then (if e > 0 then error "rat_prime_factors_c: non-empty factor" else Nothing)+                 else Just e+  in mapMaybe f (zip [0..] t)++-- | 'Ratio' variant of 'rat_prime_factors_t'+--+-- > map (rational_prime_factors_c [3,5,31]) [3,5,31]+rational_prime_factors_c :: (Integral i,Show i) => [i] -> Ratio i -> [Int]+rational_prime_factors_c fc = rat_prime_factors_c fc . Math.rational_nd++-- | Pretty printer for prime factors.  sup=superscript ol=overline+prime_factors_pp :: [Integer] -> String+prime_factors_pp = intercalate [Unicode.middle_dot] . map show++{- | Pretty printer for prime factors.  sup=superscript ol=overline++> prime_factors_pp_sup_ol True [2,2,-3,5] == "2²·3̅·5"+> prime_factors_pp_sup_ol False [-2,-2,-2,3,3,5,5,5,5] == "-2³·3²·5⁴"+-}+prime_factors_pp_sup_ol :: Bool -> [Integer] -> String+prime_factors_pp_sup_ol ol =+  let mk x = if x < 0 && ol then Unicode.overline (show (- x)) else show x+      f x = let x0 = head x+                n = length x+            in if n == 1 then mk x0 else mk x0 ++ Unicode.int_show_superscript n+  in intercalate [Unicode.middle_dot] . map f . group+
− Music/Theory/Maybe.hs 
@@ -1,84 +0,0 @@--- | Extensions to "Data.Maybe".-module Music.Theory.Maybe where--import Data.Maybe {- base -}---- | Variant with error text.-from_just :: String -> Maybe a -> a-from_just err = fromMaybe (error err)---- | Variant of unzip.------ > let r = ([Just 1,Nothing,Just 3],[Just 'a',Nothing,Just 'c'])--- > in maybe_unzip [Just (1,'a'),Nothing,Just (3,'c')] == r-maybe_unzip :: [Maybe (a,b)] -> ([Maybe a],[Maybe b])-maybe_unzip =-    let f x = case x of-                Nothing -> (Nothing,Nothing)-                Just (i,j) -> (Just i,Just j)-    in unzip . map f---- | Replace 'Nothing' elements with last 'Just' value.  This does not--- alter the length of the list.------ > maybe_latch 1 [Nothing,Just 2,Nothing,Just 4] == [1,2,2,4]-maybe_latch :: a -> [Maybe a] -> [a]-maybe_latch i x =-    case x of-      [] -> []-      Just e:x' -> e : maybe_latch e x'-      Nothing:x' -> i : maybe_latch i x'---- | Variant requiring initial value is not 'Nothing'.------ > maybe_latch1 [Just 1,Nothing,Nothing,Just 4] == [1,1,1,4]-maybe_latch1 :: [Maybe a] -> [a]-maybe_latch1 = maybe_latch (error "maybe_latch1")---- | 'map' of 'fmap'.------ > maybe_map negate [Nothing,Just 2] == [Nothing,Just (-2)]-maybe_map :: (a -> b) -> [Maybe a] -> [Maybe b]-maybe_map = map . fmap---- | If either is 'Nothing' then 'False', else /eq/ of values.-maybe_eq_by :: (t -> u -> Bool) -> Maybe t -> Maybe u -> Bool-maybe_eq_by eq_fn p q =-    case (p,q) of-      (Just p',Just q') -> eq_fn p' q'-      _ -> False---- | Join two values, either of which may be missing.-maybe_join' :: (s -> t) -> (s -> s -> t) -> Maybe s -> Maybe s -> Maybe t-maybe_join' f g p q =-    case (p,q) of-      (Nothing,_) -> fmap f q-      (_,Nothing) -> fmap f p-      (Just p',Just q') -> Just (p' `g` q')---- | 'maybe_join'' of 'id'-maybe_join :: (t -> t -> t) -> Maybe t -> Maybe t -> Maybe t-maybe_join = maybe_join' id---- | Apply predicate inside 'Maybe'.------ > maybe_predicate even (Just 3) == Nothing-maybe_predicate :: (a -> Bool) -> Maybe a -> Maybe a-maybe_predicate f i =-    case i of-      Nothing -> Nothing-      Just j -> if f j then Just j else Nothing---- | 'map' of 'maybe_predicate'.------ > let r = [Nothing,Nothing,Nothing,Just 4]--- > in maybe_filter even [Just 1,Nothing,Nothing,Just 4] == r-maybe_filter :: (a -> Bool) -> [Maybe a] -> [Maybe a]-maybe_filter = map . maybe_predicate---- | Variant of 'Data.List.filter' that retains 'Nothing' as a--- placeholder for removed elements.------ > filter_maybe even [1..4] == [Nothing,Just 2,Nothing,Just 4]-filter_maybe :: (a -> Bool) -> [a] -> [Maybe a]-filter_maybe f = maybe_filter f . map Just
Music/Theory/Meter/Barlow_1987.hs view
@@ -3,53 +3,55 @@ -- Translated by Henning Lohner. module Music.Theory.Meter.Barlow_1987 where -import Data.List-import Data.Numbers.Primes {- primes -}+import Data.List {- base -} --import Debug.Trace -import Music.Theory.Math (R)+import qualified Data.Numbers.Primes as P {- primes -} +import qualified Music.Theory.Math as T {- hmt-base -}+ traceShow :: a -> b -> b traceShow _ x = x  -- | One indexed variant of 'genericIndex'. ----- > map (at [11..13]) [1..3] == [11,12,13]-at :: (Integral n) => [a] -> n -> a-at x i = x `genericIndex` (i - 1)+-- > map (at1 [11..13]) [1..3] == [11,12,13]+at1 :: Integral n => [a] -> n -> a+at1 x i = x `genericIndex` (i - 1) --- | Variant of 'at' with boundary rules and specified error message.+-- | Variant of 'at1' with boundary rules and specified error message. ----- > map (at' 'x' [11..13]) [0..4] == [1,11,12,13,1]--- > at' 'x' [0] 3 == undefined-at' :: (Num a,Show a,Integral n,Show n,Show m) => m -> [a] -> n -> a-at' m x i =+-- > map (at1_bnd_err 'x' [11..13]) [0..4] == [1,11,12,13,1]+-- > at1_bnd_err 'x' [0] 3 == undefined+at1_bnd_err :: (Num a,Show a,Integral n,Show n,Show m) => m -> [a] -> n -> a+at1_bnd_err m x i =     let n = genericLength x     in if i == 0 || i == n + 1        then 1 -- error (show ("at':==",m,x,i))        else if i < 0 || i > n + 1-            then error (show ("at'",m,x,i))+            then error (show ("at1_bnd_err",m,x,i))             else x `genericIndex` (i - 1)  -- | Variant of 'mod' with input constraints. ----- > mod' (-1) 2 == 1-mod' :: (Integral a,Show a) => a -> a -> a-mod' a b =+-- > mod_pos_err (-1) 2 == 1+-- > mod_pos_err 1 (-2) == undefined+mod_pos_err :: (Integral a,Show a) => a -> a -> a+mod_pos_err a b =     let r = mod a b     in if r < 0 || r >= b-       then error (show ("mod'",a,b,r))+       then error (show ("mod_pos_err",a,b,r))        else r --- | Specialised variant of 'fromIntegral'.-to_r :: Integral n => n -> R+-- | Type-specialised variant of 'fromIntegral'.+to_r :: Integral n => n -> Double to_r = fromIntegral  -- | Variant on 'div' with input constraints.-div' :: (Integral a,Show a) => String -> a -> a -> a-div' m i j =+div_pos_err :: (Integral a,Show a) => String -> a -> a -> a+div_pos_err m i j =     if i < 0 || j < 0-    then error (show ("div'",m,i,j))+    then error (show ("div_pos_err",m,i,j))     else truncate (to_r i / to_r j)  -- | A stratification is a tree of integral subdivisions.@@ -76,23 +78,24 @@ lower_psi q z n =     let s8 r =             let s1 = product q-                s2 = (n - 2) `mod'` s1-                s3 = let f k = at' "s3" q (z + 1 - k)+                s2 = (n - 2) `mod_pos_err` s1+                s3 = let f k = at1_bnd_err "s3" q (z + 1 - k)                      in product (map f [0 .. r])-                s4 = 1 + div' "s4" s2 s3-                c = at' "c" q (z - r)-                s5 = s4 `mod'` c+                s4 = 1 + div_pos_err "s4" s2 s3+                c = at1_bnd_err "c" q (z - r)+                s5 = s4 `mod_pos_err` c                 s6 = upper_psi c (1 + s5)-                s7 = let f = at' "s7" q+                s7 = let f = at1_bnd_err "s7" q                      in product (map f [0 .. z - r - 1])             in traceShow ("lower_psi:s",s1,s2,s3,s4,s5,s6,s7) (s7 * s6)     in traceShow ("lower_psi",q,z,n) (sum (map s8 [0 .. z - 1])) --- | The first /n/th primes, reversed.+-- | The first /n/ primes, reversed. -- -- > reverse_primes 14 == [43,41,37,31,29,23,19,17,13,11,7,5,3,2]+-- > length (reverse_primes 14) == 14 reverse_primes :: Integral n => n -> [n]-reverse_primes n = reverse (genericTake n primes)+reverse_primes n = reverse (genericTake n P.primes)  -- | Generate prime stratification for /n/. --@@ -105,7 +108,7 @@     let go x k =             case x of               p:x' -> if k `rem` p == 0-                      then p : go x (div' "ps" k p)+                      then p : go x (div_pos_err "ps" k p)                       else go x' k               [] -> []     in go (reverse_primes 14)@@ -125,8 +128,8 @@     else if p == 2          then p - n          else if n == p - 1-              then div' "upper_psi" p 4-              else let n' = n - div' "n'" n p+              then div_pos_err "upper_psi" p 4+              else let n' = n - div_pos_err "n'" n p                        s = prime_stratification (p - 1)                        q = lower_psi s (genericLength s) n'                        q' = to_r q@@ -179,7 +182,7 @@ -- @(0,1)@. -- -- relative_indispensibilities [3,2] == [1,0,0.6,0.2,0.8,0.4]-relative_indispensibilities :: (Integral n,Show n) => Stratification n -> [R]+relative_indispensibilities :: (Integral n,Show n) => Stratification n -> [Double] relative_indispensibilities = relative_to_length . indispensibilities  -- | Align two meters (given as stratifications) to least common@@ -209,7 +212,7 @@ -- | Type pairing a stratification and a tempo. type S_MM t = ([t],t) --- | Variant of 'div' that requires 'mod' be @0@.+-- | Variant of 'div' that requires 'mod_pos_err be @0@. whole_div :: Integral a => a -> a -> a whole_div i j =     case i `divMod` j of@@ -242,18 +245,6 @@         s2' = s2 ++ prime_stratification (t `whole_div` t2)     in (s1',s2') --- | Arithmetic mean (average) of a list.------ > mean [0..5] == 2.5-mean :: Fractional a => [a] -> a-mean x = sum x / fromIntegral (length x)---- | Square of /n/.------ > square 5 == 25-square :: Num a => a -> a-square n = n * n- -- | Composition of 'prolong_stratifications' and 'align_meters'. -- -- > align_s_mm indispensibilities ([2,2,3],5) ([3,5],4)@@ -274,15 +265,15 @@ upper_psi' h n =     if h > 3     then let omega x = if x == 0 then 0 else 1-             h4 = div' "h4" h 4+             h4 = div_pos_err "h4" h 4              n' = n - 1 + omega (h - n)              p = prime_stratification (h - 1)              x0 = lower_psi p (genericLength p) n'-             x1 = x0 + omega (div' "z" x0 h4)+             x1 = x0 + omega (div_pos_err "z" x0 h4)              x2 = omega (h - n - 1)              x3 = x2 + h4 * (1 - x2)          in traceShow ("upper_psi'",h,n,n',x0,x1,x2,x3) (x1 * x3)-    else (h + n - 2) `mod'` h+    else (h + n - 2) `mod_pos_err` h  -- | The /MPS/ limit equation given on p.58. --@@ -301,9 +292,9 @@ -- > mean_square_product [(2,3),(4,5)] == (6^2 + 20^2) / 2^2 mean_square_product :: Fractional n => [(n,n)] -> n mean_square_product x =-    let f = square . uncurry (*)+    let f = T.square . uncurry (*)         n = fromIntegral (length x)-    in sum (map f x) / square n+    in sum (map f x) / T.square n  -- | An incorrect attempt at the description in paragraph two of p.58 -- of the /CMJ/ paper.@@ -311,7 +302,7 @@ -- > let p ~= q = abs (p - q) < 1e-4 -- > metrical_affinity [2,3] 1 [3,2] 1 ~= 0.0324 -- > metrical_affinity [2,2,3] 20 [3,5] 16 ~= 0.0028-metrical_affinity :: (Integral n,Show n) => [n] -> n -> [n] -> n -> R+metrical_affinity :: (Integral n,Show n) => [n] -> n -> [n] -> n -> Double metrical_affinity s1 v1 s2 v2 =     let (s1',s2') = prolong_stratifications (s1,v1) (s2,v2)         i1 = relative_indispensibilities s1'@@ -331,7 +322,7 @@ -- > metrical_affinity' [2,2,2] 1 [3,2,2] 1 ~= 0.45872 -- -- > metrical_affinity' [3,2,2] 3 [2,2,3] 2 ~= 0.10282-metrical_affinity' :: (Integral t,Show t) => [t] -> t -> [t] -> t -> R+metrical_affinity' :: (Integral t,Show t) => [t] -> t -> [t] -> t -> Double metrical_affinity' s1 v1 s2 v2 =     let (s1',s2') = prolong_stratifications (s1,v1) (s2,v2)         ix :: (Integer -> x) -> Integer -> x@@ -339,20 +330,20 @@                    1 -> f 1                    2 -> f 2                    _ -> error (show ("ix",i))-        s = ix (at [s1,s2])-        v = ix (at [v1,v2])+        s = ix (at1 [s1,s2])+        v = ix (at1 [v1,v2])         u = ix (genericLength . s)-        s' = ix (at [s1',s2'])+        s' = ix (at1 [s1',s2'])         z = ix (genericLength . s')-        q i j = s i `at` j+        q i j = s i `at1` j         omega_u i = product (map (q i) [1::Int .. u i])         omega_z _ = lcm (v 1 * omega_u 1) (v 2 * omega_u 2)         omega_0 = lcm (product (s' 1)) (product (s' 2))-        x0 n i = lower_psi (s' i) (z i) (1 + ((n - 1) `mod'` omega_z i))-        x1 n = square (product (map (x0 n) [1,2]))+        x0 n i = lower_psi (s' i) (z i) (1 + ((n - 1) `mod_pos_err` omega_z i))+        x1 n = T.square (product (map (x0 n) [1,2]))         x2 = sum (map x1 [1 .. omega_0])         x3 = 18 * x2 - 2-        x4 i = square (omega_z i - 1)+        x4 i = T.square (omega_z i - 1)         x5 = product (map x4 [1::Integer,2])         x6 = 7 * omega_0 * x5         x7 = to_r x3 / to_r x6
Music/Theory/Metric/Buchler_1998.hs view
@@ -3,13 +3,14 @@ -- thesis, University of Rochester, 1998 module Music.Theory.Metric.Buchler_1998 where +import Data.Int {- base -} import Data.List {- base -} import Data.Ratio {- base -}  import qualified Music.Theory.List as T-import qualified Music.Theory.Z12.Forte_1973 as T+import qualified Music.Theory.Z as T+import qualified Music.Theory.Z.Forte_1973 as T import qualified Music.Theory.Set.List as T-import Music.Theory.Z12 (Z12)  -- | Predicate for list with cardinality /n/. of_c :: Integral n => n -> [a] -> Bool@@ -18,7 +19,7 @@ -- | Set classes of cardinality /n/. -- -- > sc_table_n 2 == [[0,1],[0,2],[0,3],[0,4],[0,5],[0,6]]-sc_table_n :: (Integral n) => n -> [[Z12]]+sc_table_n :: (Integral n) => n -> [[Int8]] sc_table_n n = filter (of_c n) (map snd T.sc_table)  -- | Minima and maxima of ICV of SCs of cardinality /n/.@@ -27,7 +28,7 @@ icv_minmax :: (Integral n, Integral b) => n -> ([b], [b]) icv_minmax n =     let t = sc_table_n n-        i = transpose (map T.icv t)+        i = transpose (map (T.z_icv T.z12) t)     in (map minimum i,map maximum i)  data R = MIN | MAX deriving (Eq,Show)@@ -43,10 +44,10 @@       MAX -> "-"  -- | 'SATV' element measure with given funtion.-satv_f :: (Integral n) => ((n,n,n) -> D n) -> [Z12] -> [D n]+satv_f :: (Integral n) => ((n,n,n) -> D n) -> [Int8] -> [D n] satv_f f p =     let n = length p-        i = T.icv p+        i = T.z_icv T.z12 p         (l,r) = icv_minmax n     in map f (zip3 l i r) @@ -68,7 +69,7 @@ -- -- > satv_e_pp (satv_a [0,1,2,6,7,8]) == "<-1,+2,+0,+0,-1,-0>" -- > satv_e_pp (satv_a [0,1,2,3,4]) == "<-0,-1,-2,+0,+0,+0>"-satv_a :: Integral i => [Z12] -> [D i]+satv_a :: Integral i => [Int8] -> [D i] satv_a =     let f (l,i,r) = let l' = abs (i - l)                         r' = abs (i - r)@@ -81,7 +82,7 @@ -- -- > satv_e_pp (satv_b [0,1,2,6,7,8]) == "<+4,-4,-5,-4,+4,+3>" -- > satv_e_pp (satv_b [0,1,2,3,4]) == "<+4,+3,+2,-3,-4,-2>"-satv_b :: Integral i => [Z12] -> [D i]+satv_b :: Integral i => [Int8] -> [D i] satv_b =     let f (l,i,r) = let l' = abs (i - l)                         r' = abs (i - r)@@ -102,7 +103,7 @@ -- > satv_pp (satv [0,1,2,3,4,6]) == "(<-1,-2,-2,+0,+1,+1>,<+4,+4,+3,-4,-4,-2>)" -- > satv_pp (satv [0,1,3,6,8]) == "(<+1,-2,-2,+0,-1,-1>,<-3,+2,+2,-3,+3,+1>)" -- > satv_pp (satv [0,2,3,5,7,9]) == "(<+1,-2,-2,+0,-1,+1>,<-4,+4,+3,-4,+4,-2>)"-satv :: Integral i => [Z12] -> SATV i+satv :: Integral i => [Int8] -> SATV i satv p = (satv_a p,satv_b p)  -- | 'SATV' reorganised by 'R'.@@ -120,7 +121,7 @@ -- | Sum of numerical components of @a@ and @b@ parts of 'SATV'. -- -- > satv_n_sum (satv [0,1,2,6,7,8]) == [5,6,5,4,5,3]--- > satv_n_sum (satv [0,3,6,9]) = [3,3,4,3,3,2]+-- > satv_n_sum (satv [0,3,6,9]) == [3,3,4,3,3,2] satv_n_sum :: Num c => SATV c -> [c] satv_n_sum (i,j) = zipWith (+) (map snd i) (map snd j) @@ -148,7 +149,7 @@ -- > satsim [0,1,2,3,4] [0,1,4,5,7] == 8/21 -- > satsim [0,1,2,3,4] [0,2,4,6,8] == 4/7 -- > satsim [0,1,4,5,7] [0,2,4,6,8] == 4/7-satsim :: Integral a => [Z12] -> [Z12] -> Ratio a+satsim :: Integral a => [Int8] -> [Int8] -> Ratio a satsim p q =     let i = satv p         j = satv q@@ -161,7 +162,7 @@ -- | Table of 'satsim' measures for all @SC@ pairs. -- -- > length satsim_table == 24310-satsim_table :: Integral i => [(([Z12],[Z12]),Ratio i)]+satsim_table :: Integral i => [(([Int8],[Int8]),Ratio i)] satsim_table =     let f (i,j) = ((i,j),satsim i j)         t = filter ((`notElem` [0,1,12]) . length) (map snd T.sc_table)
Music/Theory/Metric/Morris_1980.hs view
@@ -2,19 +2,21 @@ -- Sets\". Perspectives of New Music, 18(2):445-460, 1980. module Music.Theory.Metric.Morris_1980 where -import Data.Ratio-import Music.Theory.Z12-import Music.Theory.Z12.Forte_1973+import Data.Int {- base -}+import Data.Ratio {- base -} +import Music.Theory.Z {- hmt -}+import Music.Theory.Z.Forte_1973 {- hmt -}+ -- | SIM ----- > icv [0,1,3,6] == [1,1,2,0,1,1] && icv [0,2,4,7] == [0,2,1,1,2,0]+-- > icv 12 [0,1,3,6] == [1,1,2,0,1,1] && icv 12 [0,2,4,7] == [0,2,1,1,2,0] -- > sim [0,1,3,6] [0,2,4,7] == 6 -- > sim [0,1,2,4,5,8] [0,1,3,7] == 9-sim :: Integral a => [Z12] -> [Z12] -> a+sim :: Integral a => [Int8] -> [Int8] -> a sim r s =-    let r' = icv r-        s' = icv s+    let r' = z_icv z12 r+        s' = z_icv z12 s         t = zipWith (-) r' s'     in sum (map abs t) @@ -25,8 +27,8 @@ -- > asim [0,1,2,3,4] [0,1,4,5,7] == 2/5 -- > asim [0,1,2,3,4] [0,2,4,6,8] == 3/5 -- > asim [0,1,4,5,7] [0,2,4,6,8] == 3/5-asim :: (Integral n) => [Z12] -> [Z12] -> Ratio n+asim :: (Integral n) => [Int8] -> [Int8] -> Ratio n asim r s =-    let r' = icv r-        s' = icv s+    let r' = z_icv z12 r+        s' = z_icv z12 s     in sim r s % (sum r' + sum s')
Music/Theory/Metric/Polansky_1996.hs view
@@ -1,15 +1,16 @@--- | Larry Polansky. \"Morphological Metrics\". Journal of New Music--- Research, 25(4):289-368, 1996.+-- | Larry Polansky. \"Morphological Metrics\".+-- Journal of New Music Research, 25(4):289-368, 1996. module Music.Theory.Metric.Polansky_1996 where -import Data.List-import Data.Maybe-import Data.Ratio-import qualified Music.Theory.Contour.Polansky_1992 as C-import qualified Music.Theory.List as L+import Data.List {- base -}+import Data.Maybe {- base -}+import Data.Ratio {- base -} --- | Distance function, ordinarily /n/ below is in 'Num', 'Fractional'--- or 'Real'.+import qualified Music.Theory.List as L {- hmt-base -}++import qualified Music.Theory.Contour.Polansky_1992 as C {- hmt -}++-- | Distance function, ordinarily /n/ below is in 'Num', 'Fractional' or 'Real'. type Interval a n = (a -> a -> n)  -- | 'fromIntegral' '.' '-'.@@ -21,43 +22,43 @@ dif_r i j = realToFrac (i - j)  -- | 'abs' '.' /f/.-abs_dif :: Num n => Interval a n -> a -> a -> n-abs_dif f i j = abs (i `f` j)+abs_of :: Num n => Interval a n -> a -> a -> n+abs_of f i j = abs (i `f` j)  -- | Square. sqr :: Num a => a -> a sqr n = n * n  -- | 'sqr' '.' /f/.-sqr_dif :: Num n => Interval a n -> a -> a -> n-sqr_dif f i j = sqr (i `f` j)+sqr_of :: Num n => Interval a n -> a -> a -> n+sqr_of f i j = sqr (i `f` j)  -- | 'sqr' '.' 'abs' '.' /f/.-sqr_abs_dif :: Num n => Interval a n -> a -> a -> n-sqr_abs_dif f i = sqr . abs_dif f i+sqr_abs_of :: Num n => Interval a n -> a -> a -> n+sqr_abs_of f i = sqr . abs_of f i  -- | 'sqrt' '.' 'abs' '.' /f/.-sqrt_abs_dif :: Floating c => Interval a c -> a -> a -> c-sqrt_abs_dif f i = sqrt . abs_dif f i+sqrt_abs_of :: Floating c => Interval a c -> a -> a -> c+sqrt_abs_of f i = sqrt . abs_of f i  -- | City block metric, p.296 -- -- > city_block_metric (-) (1,2) (3,5) == 2+3 city_block_metric :: Num n => Interval a n -> (a,a) -> (a,a) -> n-city_block_metric f (x1,x2) (y1,y2) = abs_dif f x1 y1 + abs_dif f x2 y2+city_block_metric f (x1,x2) (y1,y2) = abs_of f x1 y1 + abs_of f x2 y2  -- | Two-dimensional euclidean metric, p.297. -- -- > euclidean_metric_2 (-) (1,2) (3,5) == sqrt (4+9) euclidean_metric_2 :: Floating n => Interval a n -> (a,a) -> (a,a) -> n-euclidean_metric_2 f (x1,x2) (y1,y2) = sqrt (sqr_dif f x1 y1 + sqr_dif f x2 y2)+euclidean_metric_2 f (x1,x2) (y1,y2) = sqrt (sqr_of f x1 y1 + sqr_of f x2 y2)  -- | /n/-dimensional euclidean metric -- -- > euclidean_metric_l (-) [1,2] [3,5] == sqrt (4+9) -- > euclidean_metric_l (-) [1,2,3] [2,4,6] == sqrt (1+4+9) euclidean_metric_l :: Floating c => Interval b c -> [b] -> [b] -> c-euclidean_metric_l f p = sqrt . sum . zipWith (sqr_dif f) p+euclidean_metric_l f p = sqrt . sum . zipWith (sqr_of f) p  -- | Cube root. --@@ -89,19 +90,12 @@     let g i j = abs (i `f` j) ** n     in nthrt n (sum (zipWith g p q)) --- | Integration with /f/.------ > d_dx (-) [0,2,4,1,0] == [2,2,-3,-1]--- > d_dx (-) [2,3,0,4,1] == [1,-3,4,-3]-d_dx :: Interval a n -> [a] -> [n]-d_dx f l = zipWith f (tail l) l---- | 'map' 'abs' '.' 'd_dx'.+-- | 'map' 'abs' '.' 'L.d_dx_by'. -- -- > d_dx_abs (-) [0,2,4,1,0] == [2,2,3,1] -- > d_dx_abs (-) [2,3,0,4,1] == [1,3,4,3] d_dx_abs :: Num n => Interval a n -> [a] -> [n]-d_dx_abs f = map abs . d_dx f+d_dx_abs f = map abs . L.d_dx_by f  -- | Ordered linear magnitude (no delta), p.300 --@@ -114,11 +108,11 @@  -- | Ordered linear magintude (general form) p.302 ----- > olm_general (abs_dif (-)) [0,2,4,1,0] [2,3,0,4,1] == 1.25--- > olm_general (abs_dif (-)) [1,5,12,2,9,6] [7,6,4,9,8,1] == 4.6+-- > olm_general (abs_of (-)) [0,2,4,1,0] [2,3,0,4,1] == 1.25+-- > olm_general (abs_of (-)) [1,5,12,2,9,6] [7,6,4,9,8,1] == 4.6 olm_general :: Fractional n => Interval a n -> [a] -> [a] -> n olm_general f p q =-    let r = zipWith (-) (d_dx f p) (d_dx f q)+    let r = zipWith (-) (L.d_dx_by f p) (L.d_dx_by f q)         z = sum (map abs r)     in z / (fromIntegral (length p) - 1) @@ -149,8 +143,8 @@  -- | Ordered linear magintude (generalised-interval form) p.305 ----- > olm (abs_dif dif_r) (abs_ix_dif dif_r) (const 1) [1,5,12,2,9,6] [7,6,4,9,8,1] == 4.6--- > olm (abs_dif dif_r) (abs_ix_dif dif_r) maximum [1,5,12,2,9,6] [7,6,4,9,8,1] == 0.46+-- > olm (abs_of dif_r) (abs_ix_dif dif_r) (const 1) [1,5,12,2,9,6] [7,6,4,9,8,1] == 4.6+-- > olm (abs_of dif_r) (abs_ix_dif dif_r) maximum [1,5,12,2,9,6] [7,6,4,9,8,1] == 0.46 olm :: Fractional a => Psi a -> Delta n a  -> ([a] -> a) -> [n] -> [n] -> a olm psi delta maxint m n =     let l = length m@@ -163,11 +157,11 @@ -- > olm_no_delta [0,2,4,1,0] [2,3,0,4,1] == 1.25 -- > olm_no_delta [1,6,2,5,11] [3,15,13,2,9] == 4.5 olm_no_delta :: (Real a,Real n,Fractional n) => [a] -> [a] -> n-olm_no_delta = olm (abs_dif dif_r) (abs_ix_dif dif_r) (const 1)+olm_no_delta = olm (abs_of dif_r) (abs_ix_dif dif_r) (const 1)  -- > olm_no_delta_squared [0,2,4,1,0] [2,3,0,4,1] == sum (map sqrt [3,5,7,8]) / 4 olm_no_delta_squared :: Floating a => [a] -> [a] -> a-olm_no_delta_squared = olm (sqrt_abs_dif (-)) (sqr_abs_ix_dif (-)) (const 1)+olm_no_delta_squared = olm (sqrt_abs_of (-)) (sqr_abs_ix_dif (-)) (const 1)  second_order :: (Num n) => ([n] -> [n] -> t) -> [n] -> [n] -> t second_order f p q = f (d_dx_abs (-) p) (d_dx_abs (-) q)@@ -187,12 +181,12 @@ second_order_binonial_coefficient :: Fractional a => a -> a second_order_binonial_coefficient n = ((n * n) - n) / 2 --- | 'd_dx' of 'flip' 'compare'.+-- | 'L.d_dx_by' of 'flip' 'compare'. -- -- > direction_interval [5,9,3,2] == [LT,GT,GT] -- > direction_interval [2,5,6,6] == [LT,LT,EQ] direction_interval :: Ord i => [i] -> [Ordering]-direction_interval = d_dx (flip compare)+direction_interval = L.d_dx_by (flip compare)  -- | Histogram of list of 'Ordering's. --@@ -219,7 +213,7 @@     let (i,j,k) = direction_vector m         (p,q,r) = direction_vector n         z = (i + j + k) * 2-    in (abs_dif (-) i p + abs_dif (-) j q + abs_dif (-) k r) % z+    in (abs_of (-) i p + abs_of (-) j q + abs_of (-) k r) % z  -- | Ordered linear direction, p.312 --@@ -256,27 +250,24 @@     let (i,j,k) = ord_hist (concat (C.half_matrix_f compare m))         (p,q,r) = ord_hist (concat (C.half_matrix_f compare n))         z = (i + j + k) * 2-    in (abs_dif (-) i p + abs_dif (-) j q + abs_dif (-) k r) % z+    in (abs_of (-) i p + abs_of (-) j q + abs_of (-) k r) % z  -- | 'C.half_matrix_f', Fig.9, p.318 ----- > let r = [[2,3,1,4]--- >           ,[1,3,6]--- >             ,[4,7]--- >               ,[3]]--- > in combinatorial_magnitude_matrix (abs_dif (-)) [5,3,2,6,9] == r+-- > let r = [[2,3,1,4],[1,3,6],[4,7],[3]]+-- > combinatorial_magnitude_matrix (abs_of (-)) [5,3,2,6,9] == r combinatorial_magnitude_matrix :: Interval a n -> [a] -> [[n]] combinatorial_magnitude_matrix = C.half_matrix_f  -- | Unordered linear magnitude (simplified), p.320-321 -- -- > let r = abs (sum [5,4,3,6] - sum [12,2,11,7]) / 4--- > in ulm_simplified (abs_dif (-)) [1,6,2,5,11] [3,15,13,2,9] == r+-- > ulm_simplified (abs_of (-)) [1,6,2,5,11] [3,15,13,2,9] == r ----- > ulm_simplified (abs_dif (-)) [1,5,12,2,9,6] [7,6,4,9,8,1] == 3+-- > ulm_simplified (abs_of (-)) [1,5,12,2,9,6] [7,6,4,9,8,1] == 3 ulm_simplified :: Fractional n => Interval a n -> [a] -> [a] -> n ulm_simplified f p q =-    let g = abs . sum . d_dx f+    let g = abs . sum . L.d_dx_by f     in abs (g p - g q) / fromIntegral (length p - 1)  ocm_zcm :: Fractional n => Interval a n -> [a] -> [a] -> (n, n, [n])@@ -291,8 +282,8 @@  -- | Ordered combinatorial magnitude (OCM), p.323 ----- > ocm (abs_dif (-)) [1,6,2,5,11] [3,15,13,2,9] == 5.2--- > ocm (abs_dif (-)) [1,5,12,2,9,6] [7,6,4,9,8,1] == 3.6+-- > ocm (abs_of (-)) [1,6,2,5,11] [3,15,13,2,9] == 5.2+-- > ocm (abs_of (-)) [1,5,12,2,9,6] [7,6,4,9,8,1] == 3.6 ocm :: Fractional n => Interval a n -> [a] -> [a] -> n ocm f p q =     let (z,c,_) = ocm_zcm f p q@@ -300,8 +291,8 @@  -- | Ordered combinatorial magnitude (OCM), p.323 ----- > ocm_absolute_scaled (abs_dif (-)) [1,6,2,5,11] [3,15,13,2,9] == 0.4--- > ocm_absolute_scaled (abs_dif (-)) [1,5,12,2,9,6] [7,6,4,9,8,1] == 54/(15*11)+-- > ocm_absolute_scaled (abs_of (-)) [1,6,2,5,11] [3,15,13,2,9] == 0.4+-- > ocm_absolute_scaled (abs_of (-)) [1,5,12,2,9,6] [7,6,4,9,8,1] == 54/(15*11) ocm_absolute_scaled :: (Ord n,Fractional n) => Interval a n -> [a] -> [a] -> n ocm_absolute_scaled f p q =     let (z,c,m) = ocm_zcm f p q
− Music/Theory/Monad.hs 
@@ -1,10 +0,0 @@--- | Monad functions.-module Music.Theory.Monad where--repeatM_ :: (Monad m) => m a -> m ()-repeatM_ = sequence_ . repeat--iterateM_ :: (Monad m) => st -> (st -> m st) -> m ()-iterateM_ st f = do-  st' <- f st-  iterateM_ st' f
− Music/Theory/Ord.hs 
@@ -1,38 +0,0 @@--- | 'Ordering' functions-module Music.Theory.Ord where---- | Specialised 'fromEnum'.-ord_to_int :: Ordering -> Int-ord_to_int = fromEnum---- | Specialised 'toEnum'.-int_to_ord :: Int -> Ordering-int_to_ord = toEnum---- | Invert 'Ordering'.------ > map ord_invert [LT,EQ,GT] == [GT,EQ,LT]-ord_invert :: Ordering -> Ordering-ord_invert x =-    case x of-      LT -> GT-      EQ -> EQ-      GT -> LT---- | Given 'Ordering', re-order pair,-order_pair :: Ordering -> (t,t) -> (t,t)-order_pair o (x,y) =-    case o of-      LT -> (x,y)-      EQ -> (x,y)-      GT -> (y,x)---- | Sort a pair of equal type values using given comparison function.------ > sort_pair compare ('b','a') == ('a','b')-sort_pair :: (t -> t -> Ordering) -> (t,t) -> (t,t)-sort_pair fn (x,y) = order_pair (fn x y) (x,y)---- | Variant where the comparison function may not compute a value.-sort_pair_m :: (t -> t -> Maybe Ordering) -> (t,t) -> Maybe (t,t)-sort_pair_m fn (x,y) = fmap (`order_pair` (x,y)) (fn x y)
Music/Theory/Parse.hs view
@@ -1,8 +1,10 @@+-- | Parsing utilities module Music.Theory.Parse where  import Data.Maybe {- base -} -import qualified Text.ParserCombinators.Parsec as P {- parsec -}+import qualified Text.Parsec as P {- parsec -}+import qualified Text.Parsec.String as P {- parsec -}  -- | A 'Char' parser. type P a = P.GenParser Char () a@@ -14,3 +16,12 @@ -- | Parse 'Integral'. parse_int :: Integral i => P i parse_int = fmap (fromInteger . read) (P.many1 P.digit)++run_parser :: P t -> String -> Either P.ParseError t+run_parser p = P.runParser p () ""++run_parser_maybe :: P t -> String -> Maybe t+run_parser_maybe p = either (const Nothing) Just . run_parser p++run_parser_error :: P c -> String -> c+run_parser_error p = either (error . show) id . run_parser p
− Music/Theory/Permutations.hs 
@@ -1,162 +0,0 @@--- | Permutation functions.-module Music.Theory.Permutations where--import qualified Data.Permute as P {- permutation -}-import Numeric (showHex) {- base -}--import qualified Music.Theory.List as L---- | Factorial function.------ > (factorial 13,maxBound::Int)-factorial :: (Ord a, Num a) => a -> a-factorial n = if n <= 1 then 1 else n * factorial (n - 1)---- | Number of /k/ element permutations of a set of /n/ elements.------ > (nk_permutations 4 3,nk_permutations 13 3) == (24,1716)-nk_permutations :: Integral a => a -> a -> a-nk_permutations n k = factorial n  `div` factorial (n - k)---- | Number of /nk/ permutations where /n/ '==' /k/.------ > map n_permutations [1..8] == [1,2,6,24,120,720,5040,40320]--- > n_permutations 16 `div` 1000000 == 20922789-n_permutations :: (Integral a) => a -> a-n_permutations n = nk_permutations n n---- | Generate the permutation from /p/ to /q/, ie. the permutation--- that, when applied to /p/, gives /q/.------ > apply_permutation (permutation [0,1,3] [1,0,3]) [0,1,3] == [1,0,3]-permutation :: (Eq a) => [a] -> [a] -> P.Permute-permutation p q =-    let n = length p-        f x = L.elem_index_unique x p-    in P.listPermute n (map f q)---- | Apply permutation /f/ to /p/.------ > let p = permutation [1..4] [4,3,2,1]--- > in apply_permutation p [1..4] == [4,3,2,1]-apply_permutation :: P.Permute -> [a] -> [a]-apply_permutation f p = map (p !!) (P.elems f)---- | Composition of 'apply_permutation' and 'from_cycles'.------ > apply_permutation_c [[0,3],[1,2]] [1..4] == [4,3,2,1]--- > apply_permutation_c [[0,2],[1],[3,4]] [1..5] == [3,2,1,5,4]--- > apply_permutation_c [[0,1,4],[2,3]] [1..5] == [2,5,4,3,1]--- > apply_permutation_c [[0,1,3],[2,4]] [1..5] == [2,4,5,1,3]-apply_permutation_c :: [[Int]] -> [a] -> [a]-apply_permutation_c = apply_permutation . from_cycles---- | True if the inverse of /p/ is /p/.------ > non_invertible (permutation [0,1,3] [1,0,3]) == True------ > let p = permutation [1..4] [4,3,2,1]--- > in non_invertible p == True && P.cycles p == [[0,3],[1,2]]-non_invertible :: P.Permute -> Bool-non_invertible p = p == P.inverse p---- | Generate a permutation from the cycles /c/.------ > apply_permutation (from_cycles [[0,1,2,3]]) [1..4] == [2,3,4,1]-from_cycles :: [[Int]] -> P.Permute-from_cycles c = P.cyclesPermute (sum (map length c)) c---- | Generate all permutations of size /n/.------ > map one_line (permutations_n 3) == [[1,2,3],[1,3,2]--- >                                    ,[2,1,3],[2,3,1]--- >                                    ,[3,1,2],[3,2,1]]-permutations_n :: Int -> [P.Permute]-permutations_n n =-    let f p = let r = P.next p-              in maybe [p] (\np -> p : f np) r-    in f (P.permute n)---- | Composition of /q/ then /p/.------ > let {p = from_cycles [[0,2],[1],[3,4]]--- >     ;q = from_cycles [[0,1,4],[2,3]]--- >     ;r = p `compose` q}--- > in apply_permutation r [1,2,3,4,5] == [2,4,5,1,3]-compose :: P.Permute -> P.Permute -> P.Permute-compose p q =-    let n = P.size q-        i = [1 .. n]-        j = apply_permutation p i-        k = apply_permutation q j-    in permutation i k---- | Two line notation of /p/.------ > two_line (permutation [0,1,3] [1,0,3]) == ([1,2,3],[2,1,3])-two_line :: P.Permute -> ([Int],[Int])-two_line p =-    let n = P.size p-        i = [1..n]-    in (i,apply_permutation p i)---- | One line notation of /p/.------ > one_line (permutation [0,1,3] [1,0,3]) == [2,1,3]------ > map one_line (permutations_n 3) == [[1,2,3],[1,3,2]--- >                                    ,[2,1,3],[2,3,1]--- >                                    ,[3,1,2],[3,2,1]]-one_line :: P.Permute -> [Int]-one_line = snd . two_line---- | Variant of 'one_line' that produces a compact string.------ > one_line_compact (permutation [0,1,3] [1,0,3]) == "213"------ > let p = permutations_n 3--- > in unwords (map one_line_compact p) == "123 132 213 231 312 321"-one_line_compact :: P.Permute -> String-one_line_compact =-    let f n = if n >= 0 && n <= 15-              then showHex n ""-              else error "one_line_compact:not(0-15)"-    in concatMap f . one_line---- | Multiplication table of symmetric group /n/.------ > unlines (map (unwords . map one_line_compact) (multiplication_table 3))------ @--- ==> 123 132 213 231 312 321---     132 123 312 321 213 231---     213 231 123 132 321 312---     231 213 321 312 123 132---     312 321 132 123 231 213---     321 312 231 213 132 123--- @-multiplication_table :: Int -> [[P.Permute]]-multiplication_table n =-    let ps = permutations_n n-        f p = map (compose p) ps-    in map f ps--{--let q = permutation [1..4] [2,3,4,1] -- [[0,1,2,3]]-(q,non_invertible q,P.cycles q,apply_permutation q [1..4])--let p = permutation [1..5] [3,2,1,5,4] -- [[0,2],[1],[3,4]]-let q = permutation [1..5] [2,5,4,3,1] -- [[0,1,4],[2,3]]-let r = permutation [1..5] [2,4,5,1,3] -- [[0,1,3],[2,4]]-(non_invertible p,P.cycles p,apply_permutation p [1..5])-(non_invertible q,P.cycles q,apply_permutation q [1..5])-(non_invertible r,P.cycles r,apply_permutation r [1..5])--map P.cycles (permutations_n 3)-map P.cycles (permutations_n 4)-partition not (map non_invertible (permutations_n 4))--import Data.List {- base -}-putStrLn $ unlines $ map unwords $ permutations ["A0","A1","B0"]---}
Music/Theory/Permutations/List.hs view
@@ -2,38 +2,45 @@ module Music.Theory.Permutations.List where  import Data.List {- base -}+ import qualified Math.Combinatorics.Multiset as C {- multiset-comb -} -import qualified Music.Theory.Permutations as P {- hmt -}+import qualified Music.Theory.Permutations as P {- hmt-base -}  -- | Generate all permutations. ----- > permutations [0,3] == [[0,3],[3,0]]--- > length (permutations [1..5]) == P.n_permutations 5-permutations :: [a] -> [[a]]-permutations i =+-- > permutations_l [0,3] == [[0,3],[3,0]]+-- > length (permutations_l [1..5]) == P.n_permutations 5+permutations_l :: [a] -> [[a]]+permutations_l i =     let f p = P.apply_permutation p i     in map f (P.permutations_n (length i)) +-- | /k/-element permutations of a set of /n/-elements.+--+-- > permutations_nk_l 3 2 "abc" == ["ab","ac","ba","bc","ca","cb"]+permutations_nk_l :: Eq e => Int -> Int -> [e] -> [[e]]+permutations_nk_l n k e =+  if length e /= n+  then error "permutations_nk_l"+  else nub (map (take k) (permutations_l e))+ -- | Generate all distinct permutations of a multi-set. -- -- > multiset_permutations [0,1,1] == [[0,1,1],[1,1,0],[1,0,1]]-multiset_permutations :: (Ord a) => [a] -> [[a]]+multiset_permutations :: Ord a => [a] -> [[a]] multiset_permutations = C.permutations . C.fromList -factorial :: (Enum a, Num a) => a -> a-factorial n = product [1..n]- -- | Calculate number of permutations of a multiset. ----- > let r = factorial 11 `div` product (map factorial [1,4,4,2])--- > in multiset_permutations_n "MISSISSIPPI" == r+-- > let r = P.factorial 11 `div` product (map P.factorial [1,4,4,2])+-- > multiset_permutations_n "MISSISSIPPI" == r -- -- > multiset_permutations_n "MISSISSIPPI" == 34650 -- > length (multiset_permutations "MISSISSIPPI") == 34650 multiset_permutations_n :: Ord a => [a] -> Int multiset_permutations_n x =     let occ = map length . group . sort-        n = factorial (length x)-        d = product $ map factorial $ occ x+        n = P.factorial (length x)+        d = product $ map P.factorial $ occ x     in n `div` d
Music/Theory/Permutations/Morris_1984.hs view
@@ -5,33 +5,41 @@ -- <http://www.cccbr.org.uk/bibliography/> module Music.Theory.Permutations.Morris_1984 where -import Data.Char {- base -} import Data.List {- base -} import Data.List.Split {- split -} import Data.Maybe {- base -} -import qualified Music.Theory.List as T {- hmt -}-import qualified Music.Theory.Permutations as T {- hmt -}+import qualified Music.Theory.List as T {- hmt-base -}+import qualified Music.Theory.Permutations as T {- hmt-base -}+import qualified Music.Theory.Tuple as T {- hmt-base -}  -- | A change either swaps all adjacent bells, or holds a subset of bells. data Change = Swap_All | Hold [Int] deriving (Eq,Show) --- | A method is a sequence of changes, if symmetrical only have the+-- | A method is a sequence of changes, if symmetrical only half the -- changes are given and the lead end.-data Method = Method [Change] (Maybe Change) deriving (Eq,Show)+data Method = Method [Change] (Maybe [Change]) deriving (Eq,Show) --- | Compete list of 'Change's at 'Method', writing out symmetries.+-- | Maximum hold value at 'Method'+method_limit :: Method -> Int+method_limit (Method p q) =+  let f c = case c of+              Swap_All -> 0+              Hold i -> maximum i+  in maximum (map f (p ++ fromMaybe [] q))++-- | Complete list of 'Change's at 'Method', writing out symmetries. method_changes :: Method -> [Change] method_changes (Method p q) =     case q of       Nothing -> p-      Just q' -> p ++ tail (reverse p) ++ [q']+      Just le -> p ++ tail (reverse p) ++ le  -- | Parse a change notation. -- -- > map parse_change ["-","x","38"] == [Swap_All,Swap_All,Hold [3,8]] parse_change :: String -> Change-parse_change s = if is_swap_all s then Swap_All else Hold (to_abbrev s)+parse_change s = if is_swap_all s then Swap_All else Hold (map nchar_to_int s)  -- | Separate changes. --@@ -40,58 +48,64 @@ split_changes :: String -> [String] split_changes = filter (/= ".") . split (dropInitBlank (oneOf "-x.")) --- | Parse 'Method' from the sequence of changes with possible lead end.------ > parse_method ("-38-14-1258-36-14-58-16-78",Just "12")-parse_method :: (String,Maybe String) -> Method+-- | Place notation, sequence of changes with possible lead end.+type Place = (String,Maybe String)++-- | Parse 'Method' given 'PLACE' notation.+parse_method :: Place -> Method parse_method (p,q) =-    let c = map parse_change (split_changes p)-        le = fmap parse_change q-    in Method c le+    let f = map parse_change . split_changes+    in Method (f p) (fmap f q) --- > map is_swap_all ["-","x","38"] == [True,True,False]-is_swap_all :: String -> Bool-is_swap_all s =-    case s of-      [c] -> c `elem` "-x"-      _ -> False+-- | Parse string into 'Place'.+--+-- > parse_method (parse_place "-38-14-1258-36-14-58-16-78,12")+parse_place :: String -> Place+parse_place txt =+  case splitOn "," txt of+    [p] -> (p,Nothing)+    [p,q] -> (p,Just q)+    _ -> error "parse_place?" --- | Swap elemets of two-tuple (pair).+-- | - or x? ----- > swap_pair (1,2) == (2,1)-swap_pair :: (s,t) -> (t,s)-swap_pair (p,q) = (q,p)+-- > map is_swap_all ["-","x","38"] == [True,True,False]+is_swap_all :: String -> Bool+is_swap_all = flip elem ["-","x"]  -- | Flatten list of pairs. -- -- > flatten_pairs [(1,2),(3,4)] == [1..4] flatten_pairs :: [(a,a)] -> [a]-flatten_pairs l =-    case l of-      [] -> []-      (p,q):l' -> p : q : flatten_pairs l'+flatten_pairs = concatMap T.t2_to_list  -- | Swap all adjacent pairs at list. -- -- > swap_all [1 .. 8] == [2,1,4,3,6,5,8,7] swap_all :: [a] -> [a]-swap_all = flatten_pairs . map swap_pair . T.adj2 2+swap_all = flatten_pairs . map T.p2_swap . T.adj2 2  numeric_spelling_tbl :: [(Char,Int)]-numeric_spelling_tbl = zip "1234567890ETABCD" [1 .. 16]+numeric_spelling_tbl = zip "1234567890ETABCDFGHJKL" [1 .. 22] --- | Parse abbreviated 'Hold' notation, characters are hexedecimal.+-- | Parse abbreviated 'Hold' notation, characters are NOT hexadecimal. ----- > to_abbrev "380ETA" == [3,8,10,11,12,13]-to_abbrev :: String -> [Int]-to_abbrev = map (fromMaybe (error "to_abbrev") . flip lookup numeric_spelling_tbl)+-- > map nchar_to_int "380ETA" == [3,8,10,11,12,13]+nchar_to_int :: Char -> Int+nchar_to_int = fromMaybe (error "nchar_to_int") . flip lookup numeric_spelling_tbl +-- | Inverse of 'nchar_to_int'.+--+-- > map int_to_nchar [3,8,10,11,12,13] == "380ETA"+int_to_nchar :: Int -> Char+int_to_nchar = flip T.reverse_lookup_err numeric_spelling_tbl+ -- | Given a 'Hold' notation, generate permutation cycles. -- -- > let r = [Right (1,2),Left 3,Right (4,5),Right (6,7),Left 8]--- > in gen_swaps 8 [3,8] == r+-- > gen_swaps 8 [3,8] == r ----- > let r = [Left 1,Left 2,Right (3,4),Right (5,6),Right (7,8)]+-- > r = [Left 1,Left 2,Right (3,4),Right (5,6),Right (7,8)] -- > gen_swaps 8 [1,2] == r gen_swaps :: (Num t, Ord t) => t -> [t] -> [Either t (t,t)] gen_swaps k =@@ -125,7 +139,7 @@ -- | One-indexed permutation cycles to zero-indexed. -- -- > let r = [[0],[1],[2,3],[4,5],[6,7]]--- > in to_zero_indexed [[1],[2],[3,4],[5,6],[7,8]] == r+-- > to_zero_indexed [[1],[2],[3,4],[5,6],[7,8]] == r to_zero_indexed :: Enum t => [[t]] -> [[t]] to_zero_indexed = map (map pred) @@ -135,7 +149,7 @@ swap_abbrev :: Int -> [Int] -> [a] -> [a] swap_abbrev k a =     let c = to_zero_indexed (swaps_to_cycles (gen_swaps k a))-        p = T.from_cycles c+        p = T.from_cycles_zero_indexed c     in T.apply_permutation p  -- | Apply a 'Change'.@@ -151,7 +165,7 @@ -- > let r = ([1,2,4,5,3] -- >         ,[[1,2,3,4,5],[2,1,3,4,5],[2,3,1,4,5],[3,2,4,1,5],[3,4,2,5,1] -- >          ,[4,3,2,5,1],[4,2,3,1,5],[2,4,1,3,5],[2,1,4,3,5],[1,2,4,3,5]])--- > in apply_method cambridgeshire_slow_course_doubles [1..5] == r+-- > apply_method cambridgeshire_slow_course_doubles [1..5] == r apply_method :: Method -> [a] -> ([a],[[a]]) apply_method m l =     let k = length l@@ -172,60 +186,69 @@     in rec l []  -- | 'concat' of 'closed_method' with initial sequence appended.-closed_method' :: Eq a => Method -> [a] -> [[a]]-closed_method' m l = concat (closed_method m l) ++ [l]+closed_method_lp :: Eq a => Method -> [a] -> [[a]]+closed_method_lp m l = concat (closed_method m l) ++ [l] +-- | 'closed_method' of 'parse_method'+closed_place :: Eq t => Place -> [t] -> [[[t]]]+closed_place pl = closed_method (parse_method pl)+ -- * Methods --- | <https://rsw.me.uk/blueline/methods/view/Cambridgeshire_Slow_Course_Doubles>+-- | <https://rsw.me.uk/blueline/methods/view/Cambridgeshire_Place_Doubles> ----- > length (closed_method cambridgeshire_slow_course_doubles [1..5]) == 3+-- > length (closed_place cambridgeshire_place_doubles_pl [1..5]) == 3+cambridgeshire_place_doubles_pl :: Place+cambridgeshire_place_doubles_pl = ("345.145.5.1.345",Just "123")++-- | 'parse_method' of 'cambridgeshire_place_doubles_pl' cambridgeshire_slow_course_doubles :: Method-cambridgeshire_slow_course_doubles =-    let a = ("345.145.5.1.345",Just "123")-    in parse_method a+cambridgeshire_slow_course_doubles = parse_method cambridgeshire_place_doubles_pl --- | Double Cambridge Cyclic Bob Minor.------ <https://rsw.me.uk/blueline/methods/view/Double_Cambridge_Cyclic_Bob_Minor>+-- | <https://rsw.me.uk/blueline/methods/view/Double_Cambridge_Cyclic_Bob_Minor> ----- > length (closed_method double_cambridge_cyclic_bob_minor [1..6]) == 5+-- > length (closed_place double_cambridge_cyclic_bob_minor_pl [1..6]) == 5+double_cambridge_cyclic_bob_minor_pl :: Place+double_cambridge_cyclic_bob_minor_pl = ("-14-16-56-36-16-12",Nothing)++-- | 'parse_method' of 'double_cambridge_cyclic_bob_minor_pl' double_cambridge_cyclic_bob_minor :: Method-double_cambridge_cyclic_bob_minor =-    let a = ("-14-16-56-36-16-12",Nothing)-    in parse_method a+double_cambridge_cyclic_bob_minor = parse_method double_cambridge_cyclic_bob_minor_pl --- | Hammersmith Bob Triples------ <https://rsw.me.uk/blueline/methods/view/Hammersmith_Bob_Triples>+-- | <https://rsw.me.uk/blueline/methods/view/Hammersmith_Bob_Triples> ----- > length (closed_method hammersmith_bob_triples [1..7]) == 6+-- > length (closed_place hammersmith_bob_triples_pl [1..7]) == 6+hammersmith_bob_triples_pl :: Place+hammersmith_bob_triples_pl = ("7.1.5.123.7.345.7",Just "127")+ hammersmith_bob_triples :: Method-hammersmith_bob_triples =-    let a = ("7.1.5.123.7.345.7",Just "127")-    in parse_method a+hammersmith_bob_triples = parse_method hammersmith_bob_triples_pl  -- | <https://rsw.me.uk/blueline/methods/view/Cambridge_Surprise_Major> ----- > length (closed_method cambridge_surprise_major [1..8]) == 7+-- > length (closed_place cambridge_surprise_major_pl [1..8]) == 7+cambridge_surprise_major_pl :: Place+cambridge_surprise_major_pl = ("-38-14-1258-36-14-58-16-78",Just "12")+ cambridge_surprise_major :: Method-cambridge_surprise_major =-    let a = ("-38-14-1258-36-14-58-16-78",Just "12")-    in parse_method a+cambridge_surprise_major = parse_method cambridge_surprise_major_pl  -- | <https://rsw.me.uk/blueline/methods/view/Smithsonian_Surprise_Royal> ----- > let m = closed_method smithsonian_surprise_royal [1..10]--- > (length m,nub (map length m),sum (map length m)) == (9,[40],360)+-- > let c = closed_place smithsonian_surprise_royal_pl [1..10]+-- > (length c,nub (map length c),sum (map length c)) == (9,[40],360)+smithsonian_surprise_royal_pl :: Place+smithsonian_surprise_royal_pl = ("-30-14-50-16-3470-18-1456-50-16-70",Just "12")+ smithsonian_surprise_royal :: Method-smithsonian_surprise_royal =-    let a = ("-30-14-50-16-3470-18-1456-50-16-70",Just "12")-    in parse_method a+smithsonian_surprise_royal = parse_method smithsonian_surprise_royal_pl  -- | <https://rsw.me.uk/blueline/methods/view/Ecumenical_Surprise_Maximus> ----- > let m = closed_method ecumenical_surprise_maximus [1..12]--- > (length m,nub (map length m),sum (map length m)) == (11,[48],528)+-- > c = closed_place ecumenical_surprise_maximus_pl [1..12]+-- > (length c,nub (map length c),sum (map length c)) == (11,[48],528)+ecumenical_surprise_maximus_pl :: Place+ecumenical_surprise_maximus_pl = ("x3Tx14x5Tx16x7Tx1238x149Tx50x16x7Tx18.90.ET",Just "12")+ ecumenical_surprise_maximus :: Method-ecumenical_surprise_maximus =-  parse_method ("x3Tx14x5Tx16x7Tx1238x149Tx50x16x7Tx18.90.ET",Just "12")+ecumenical_surprise_maximus = parse_method ecumenical_surprise_maximus_pl
Music/Theory/Pitch.hs view
@@ -7,17 +7,23 @@ import Data.Maybe {- base -} import Text.Printf {- base -} +import qualified Text.Parsec as P {- parsec -}+ import qualified Music.Theory.List as T {- hmt -} import qualified Music.Theory.Math as T {- hmt -}+import qualified Music.Theory.Math.Convert as T {- hmt -}+import qualified Music.Theory.Parse as T {- hmt -} import qualified Music.Theory.Pitch.Note as T {- hmt -}+import qualified Music.Theory.Show as T {- hmt -}+import qualified Music.Theory.Tuning as T {- hmt -} --- * Octave & pitch-class (generic)+-- * Octave pitch-class (generic)  -- | 'Octave' and 'PitchClass' duple. type Octave_PitchClass i = (i,i)  -- | Normalise 'Octave_PitchClass' value, ie. ensure pitch-class is in (0,11).-octave_pitchclass_nrm :: Integral i => Octave_PitchClass i -> Octave_PitchClass i+octave_pitchclass_nrm :: (Ord i,Num i) => Octave_PitchClass i -> Octave_PitchClass i octave_pitchclass_nrm (o,pc) =     if pc > 11     then octave_pitchclass_nrm (o+1,pc-12)@@ -28,80 +34,125 @@ -- | Transpose 'Octave_PitchClass' value. octave_pitchclass_trs :: Integral i => i -> Octave_PitchClass i -> Octave_PitchClass i octave_pitchclass_trs n (o,pc) =-    let pc' = fromIntegral pc-        k = pc' + n+    let k = pc + n         (i,j) = k `divMod` 12-    in (fromIntegral o + fromIntegral i,fromIntegral j)+    in (o + i,j)  -- | 'Octave_PitchClass' value to integral /midi/ note number.-octave_pitchclass_to_midi :: Integral i => Octave_PitchClass i -> i+--+-- > map octave_pitchclass_to_midi [(-1,9),(8,0)] == map (+ 9) [0,99]+octave_pitchclass_to_midi :: Num i => Octave_PitchClass i -> i octave_pitchclass_to_midi (o,pc) = 60 + ((o - 4) * 12) + pc  -- | Inverse of 'octave_pitchclass_to_midi'.-midi_to_octave_pitchclass :: Integral i => i -> Octave_PitchClass i-midi_to_octave_pitchclass n = (n - 12) `divMod` 12+--+-- > map midi_to_octave_pitchclass [0,36,60,84,91] == [(-1,0),(2,0),(4,0),(6,0),(6,7)]+midi_to_octave_pitchclass :: (Integral m,Integral i) => m -> Octave_PitchClass i+midi_to_octave_pitchclass n = (fromIntegral n - 12) `divMod` 12 +{- | One-indexed piano key number (for standard 88 key piano) to pitch class.+     This has the mnemonic that 49 maps to (4,9).++> map pianokey_to_octave_pitchclass [1,49,88] == [(0,9),(4,9),(8,0)]+-}+pianokey_to_octave_pitchclass :: (Integral m,Integral i) => m -> Octave_PitchClass i+pianokey_to_octave_pitchclass = midi_to_octave_pitchclass . (+) 20+ -- * Octave & PitchClass --- | Pitch classes are modulo twelve integers.+-- | Pitch classes are modulo twelve integers (0-11) type PitchClass = Int  -- | Octaves are integers, the octave of middle C is @4@. type Octave = Int  -- | 'Octave' and 'PitchClass' duple.-type OctPC = (Octave,PitchClass)+type OctPc = (Octave,PitchClass)  -- | Translate from generic octave & pitch-class duple.-to_octpc :: (Integral pc, Integral oct) => (oct,pc) -> OctPC-to_octpc (oct,pc) = (fromIntegral oct,fromIntegral pc)+octave_pitchclass_to_octpc :: (Integral pc, Integral oct) => (oct,pc) -> OctPc+octave_pitchclass_to_octpc (oct,pc) = (fromIntegral oct,fromIntegral pc) --- | Normalise 'OctPC'.+-- | Normalise 'OctPc'. -- -- > octpc_nrm (4,16) == (5,4)-octpc_nrm :: OctPC -> OctPC+octpc_nrm :: OctPc -> OctPc octpc_nrm = octave_pitchclass_nrm --- | Transpose 'OctPC'.+-- | Transpose 'OctPc'. -- -- > octpc_trs 7 (4,9) == (5,4) -- > octpc_trs (-11) (4,9) == (3,10)-octpc_trs :: Int -> OctPC -> OctPC+octpc_trs :: Int -> OctPc -> OctPc octpc_trs = octave_pitchclass_trs  -- | Enumerate range, inclusive. -- -- > octpc_range ((3,8),(4,1)) == [(3,8),(3,9),(3,10),(3,11),(4,0),(4,1)]-octpc_range :: (OctPC,OctPC) -> [OctPC]+octpc_range :: (OctPc,OctPc) -> [OctPc] octpc_range (l,r) =     let (l',r') = (octpc_to_midi l,octpc_to_midi r)     in map midi_to_octpc [l' .. r'] --- * Midi note number+-- * Midi note number (0 - 127) --- | Midi note number+{- | Midi note number (0 - 127).+     Midi data values are unsigned 7-bit integers, however using an unsigned type would be problematic.+     It would make transposition, for instance, awkward.+     x - 12 would transpose down an octave, but the transposition interval itself could not be negative.+-} type Midi = Int --- | 'OctPC' value to integral /midi/ note number.+-- | Type conversion+midi_to_int :: Midi -> Int+midi_to_int = id++-- | Type-specialise /f/, ie. round, ceiling, truncate+double_to_midi :: (Double -> Midi) -> Double -> Midi+double_to_midi = T.double_to_int++-- | 'OctPc' value to integral /midi/ note number. ----- > map octpc_to_midi [(0,0),(2,6),(4,9),(9,0)] == [12,42,69,120]+-- > map octpc_to_midi [(0,0),(2,6),(4,9),(6,2),(9,0)] == [12,42,69,86,120] -- > map octpc_to_midi [(0,9),(8,0)] == [21,108]-octpc_to_midi :: OctPC -> Midi+octpc_to_midi :: OctPc -> Midi octpc_to_midi = octave_pitchclass_to_midi  -- | Inverse of 'octpc_to_midi'. -- -- > map midi_to_octpc [40,69] == [(2,4),(4,9)]-midi_to_octpc :: Midi -> OctPC+midi_to_octpc :: Midi -> OctPc midi_to_octpc = midi_to_octave_pitchclass  -- * Octave & fractional pitch-class +-- | (octave,pitch-class) to fractional octave.+--   This is an odd notation, but can be useful for writing pitch data where a float is required.+--   Note this is not a linear octave, for that see 'Sound.SC3.Common.Math.oct_to_cps'.+--+-- > map octpc_to_foct [(4,0),(4,7),(5,11)] == [4.00,4.07,5.11]+octpc_to_foct :: (Integral i, Fractional r) => (i,i) -> r+octpc_to_foct (o,pc) = fromIntegral o + (fromIntegral pc / 100)++-- | Inverse of 'octpc_to_foct'.+--+-- > map foct_to_octpc [3.11,4.00,4.07,5.11] == [(3,11),(4,0),(4,7),(5,11)]+foct_to_octpc :: (Integral i, RealFrac r) => r -> (i,i)+foct_to_octpc x =+  let (p,q) = T.integral_and_fractional_parts x+  in (p,round (q * 100))++-- | 'octpc_to_midi' of 'foct_to_octpc'.+foct_to_midi :: (Integral i, RealFrac r) => r -> i+foct_to_midi = octave_pitchclass_to_midi . foct_to_octpc++-- * FMIDI+ -- | Fractional midi note number. type FMidi = Double  -- | Fractional octave pitch-class (octave is integral, pitch-class is fractional).-type FOctPC = (Int,Double)+type FOctPc = (Int,Double)  -- | 'fromIntegral' of 'octpc_to_midi'. octpc_to_fmidi :: (Integral i,Num n) => Octave_PitchClass i -> n@@ -126,11 +177,22 @@ fmidi_in_octave :: RealFrac f => Octave -> f -> f fmidi_in_octave o m = let (_,pc) = fmidi_to_foctpc m in foctpc_to_fmidi (o,pc) +-- | Print fractional midi note number as ET12 pitch with cents detune in parentheses.+--+-- > fmidi_et12_cents_pp T.pc_spell_ks 66.5 == "F♯4(+50)"+fmidi_et12_cents_pp :: Spelling PitchClass -> FMidi -> String+fmidi_et12_cents_pp sp =+    let f (m,c) =+            let d = T.num_diff_str (round c :: Int)+                d' = if null d then "" else "(" ++ d ++ ")"+            in pitch_pp (midi_to_pitch sp m) ++ d'+    in f . midi_detune_normalise . fmidi_to_midi_detune+ -- * Pitch  -- | Common music notation pitch value.-data Pitch = Pitch {note :: T.Note_T-                   ,alteration :: T.Alteration_T+data Pitch = Pitch {note :: T.Note+                   ,alteration :: T.Alteration                    ,octave :: Octave}            deriving (Eq,Show) @@ -139,8 +201,8 @@  -- | Simplify 'Pitch' to standard 12ET by deleting quarter tones. ----- > let p = Pitch A QuarterToneSharp 4--- > in alteration (pitch_clear_quarter_tone p) == Sharp+-- > let p = Pitch T.A T.QuarterToneSharp 4+-- > alteration (pitch_clear_quarter_tone p) == T.Sharp pitch_clear_quarter_tone :: Pitch -> Pitch pitch_clear_quarter_tone p =     let Pitch n a o = p@@ -150,7 +212,7 @@ -- -- > pitch_to_octpc (Pitch F Sharp 4) == (4,6) pitch_to_octpc :: Integral i => Pitch -> Octave_PitchClass i-pitch_to_octpc = midi_to_octave_pitchclass . pitch_to_midi+pitch_to_octpc = midi_to_octave_pitchclass . T.int_id . pitch_to_midi  -- | Is 'Pitch' 12-ET. pitch_is_12et :: Pitch -> Bool@@ -194,12 +256,12 @@ -- * Spelling  -- | Function to spell a 'PitchClass'.-type Spelling n = n -> (T.Note_T,T.Alteration_T)+type Spelling n = n -> (T.Note,T.Alteration)  -- | Variant of 'Spelling' for incomplete functions.-type Spelling_M i = i -> Maybe (T.Note_T,T.Alteration_T)+type Spelling_M i = i -> Maybe (T.Note,T.Alteration) --- | Given 'Spelling' function translate from 'OctPC' notation to 'Pitch'.+-- | Given 'Spelling' function translate from 'OctPc' notation to 'Pitch'. -- -- > octpc_to_pitch T.pc_spell_sharp (4,6) == Pitch T.F T.Sharp 4 octpc_to_pitch :: Integral i => Spelling i -> Octave_PitchClass i -> Pitch@@ -209,28 +271,20 @@  -- | Midi note number to 'Pitch'. --+-- > import Music.Theory.Pitch.Spelling.Table as T -- > let r = ["C4","E♭4","F♯4"]--- > in map (pitch_pp . midi_to_pitch pc_spell_ks) [60,63,66] == r-midi_to_pitch :: Integral i => Spelling i -> i -> Pitch+-- > map (pitch_pp . midi_to_pitch T.pc_spell_ks) [60,63,66] == r+midi_to_pitch :: (Integral i,Integral k) => Spelling k -> i -> Pitch midi_to_pitch sp = octpc_to_pitch sp . midi_to_octave_pitchclass --- | Print fractional midi note number as ET12 pitch with cents detune in parentheses.------ > fmidi_et12_cents_pp 66.5 == "F♯4(+50)"-fmidi_et12_cents_pp :: Spelling PitchClass -> Double -> String-fmidi_et12_cents_pp sp =-    let f (m,c) =-            let d = T.num_diff_str (round c :: Int)-                d' = if null d then "" else "(" ++ d ++ ")"-            in pitch_pp (midi_to_pitch sp m) ++ d'-    in f . midi_detune_normalise . fmidi_to_midi_detune+{- | Fractional midi note number to 'Pitch'. --- | Fractional midi note number to 'Pitch'.------ > fmidi_to_pitch pc_spell_ks 69.25 == Nothing+> p = Pitch T.B T.ThreeQuarterToneFlat 4+> map (fmidi_to_pitch T.pc_spell_ks) [69.25,69.5] == [Nothing,Just p]+-} fmidi_to_pitch :: RealFrac n => Spelling PitchClass -> n -> Maybe Pitch fmidi_to_pitch sp m =-    let m' = round m+    let m' = T.real_round_int m         (Pitch n a o) = midi_to_pitch sp m'         q = m - fromIntegral m'     in case T.alteration_edit_quarter_tone q a of@@ -239,11 +293,11 @@  -- | Erroring variant. ----- > import Music.Theory.Pitch.Spelling--- > pitch_pp (fmidi_to_pitch_err pc_spell_ks 65.5) == "F𝄲4"--- > pitch_pp (fmidi_to_pitch_err pc_spell_ks 66.5) == "F𝄰4"--- > pitch_pp (fmidi_to_pitch_err pc_spell_ks 67.5) == "A𝄭4"--- > pitch_pp (fmidi_to_pitch_err pc_spell_ks 69.5) == "B𝄭4"+-- > import Music.Theory.Pitch.Spelling as T+-- > pitch_pp (fmidi_to_pitch_err T.pc_spell_ks 65.5) == "F𝄲4"+-- > pitch_pp (fmidi_to_pitch_err T.pc_spell_ks 66.5) == "F𝄰4"+-- > pitch_pp (fmidi_to_pitch_err T.pc_spell_ks 67.5) == "A𝄭4"+-- > pitch_pp (fmidi_to_pitch_err T.pc_spell_ks 69.5) == "B𝄭4" fmidi_to_pitch_err :: (Show n,RealFrac n) => Spelling Int -> n -> Pitch fmidi_to_pitch_err sp m = fromMaybe (error (show ("fmidi_to_pitch",m))) (fmidi_to_pitch sp m) @@ -251,10 +305,9 @@ -- -- > import Music.Theory.Pitch.Name as T -- > import Music.Theory.Pitch.Spelling as T------ > pitch_tranpose T.pc_spell_ks 2 T.ees5 == T.f5-pitch_tranpose :: (RealFrac n,Show n) => Spelling Int -> n -> Pitch -> Pitch-pitch_tranpose sp n p =+-- > pitch_transpose_fmidi T.pc_spell_ks 2 T.ees5 == T.f5+pitch_transpose_fmidi :: (RealFrac n,Show n) => Spelling Int -> n -> Pitch -> Pitch+pitch_transpose_fmidi sp n p =     let m = pitch_to_fmidi p     in fmidi_to_pitch_err sp (m + n) @@ -264,8 +317,9 @@  -- | Octave displacement of /m2/ that is nearest /m1/. ----- > let {p = octpc_to_fmidi (2,1);q = map octpc_to_fmidi [(4,11),(4,0),(4,1)]}--- > in map (fmidi_in_octave_nearest p) q == [35,36,37]+-- > let p = octpc_to_fmidi (2,1)+-- > let q = map octpc_to_fmidi [(4,11),(4,0),(4,1)]+-- > map (fmidi_in_octave_nearest p) q == [35,36,37] fmidi_in_octave_nearest :: RealFrac n => n -> n -> n fmidi_in_octave_nearest m1 m2 =     let m2' = fmidi_in_octave (fmidi_octave m1) m2@@ -290,45 +344,51 @@ fmidi_in_octave_below :: RealFrac a => a -> a -> a fmidi_in_octave_below p q = let r = fmidi_in_octave_nearest p q in if r > p then r - 12 else r -cps_in_octave' :: Floating f => (f -> f -> f) -> f -> f -> f-cps_in_octave' f p = fmidi_to_cps . f (cps_to_fmidi p) . cps_to_fmidi+-- | CPS form of binary /fmidi/ function /f/.+lift_fmidi_binop_to_cps :: Floating f => (f -> f -> f) -> f -> f -> f+lift_fmidi_binop_to_cps f p = T.fmidi_to_cps . f (cps_to_fmidi p) . cps_to_fmidi  -- | CPS form of 'fmidi_in_octave_nearest'. -- -- > map cps_octave [440,256] == [4,4] -- > round (cps_in_octave_nearest 440 256) == 512 cps_in_octave_nearest :: (Floating f,RealFrac f) => f -> f -> f-cps_in_octave_nearest = cps_in_octave' fmidi_in_octave_nearest+cps_in_octave_nearest = lift_fmidi_binop_to_cps fmidi_in_octave_nearest --- | Raise or lower the frequency /q/ by octaves until it is in the--- octave starting at /p/.+-- | CPS form of 'fmidi_in_octave_above'. ----- > cps_in_octave_above 55.0 392.0 == 98.0-cps_in_octave_above :: (Ord a, Fractional a) => a -> a -> a-cps_in_octave_above p =-    let go q = if q > p * 2 then go (q / 2) else if q < p then go (q * 2) else q-    in go---- > cps_in_octave_above' 55.0 392.0 == 97.99999999999999-cps_in_octave_above' :: (Floating f,RealFrac f) => f -> f -> f-cps_in_octave_above' = cps_in_octave' fmidi_in_octave_above+-- > cps_in_octave_above 55.0 392.0 == 97.99999999999999+cps_in_octave_above :: (Floating f,RealFrac f) => f -> f -> f+cps_in_octave_above = lift_fmidi_binop_to_cps fmidi_in_octave_above +-- | CPS form of 'fmidi_in_octave_above'. cps_in_octave_below :: (Floating f,RealFrac f) => f -> f -> f-cps_in_octave_below = cps_in_octave' fmidi_in_octave_below+cps_in_octave_below = lift_fmidi_binop_to_cps fmidi_in_octave_below +-- | Direct implementation of 'cps_in_octave_above'.+--   Raise or lower the frequency /q/ by octaves until it is in the+--   octave starting at /p/.+--+-- > cps_in_octave_above_direct 55.0 392.0 == 98.0+cps_in_octave_above_direct :: (Ord a, Fractional a) => a -> a -> a+cps_in_octave_above_direct p q =+  let f = cps_in_octave_above_direct p+  in if q > p * 2 then f (q / 2) else if q < p then f (q * 2) else q+ -- | Set octave of /p2/ so that it nearest to /p1/. --+-- > import Music.Theory.Pitch -- > import Music.Theory.Pitch.Name as T------ > let {r = ["B1","C2","C#2"];f = pitch_in_octave_nearest T.cis2}--- > in map (pitch_pp_iso . f) [T.b4,T.c4,T.cis4] == r+-- > let r = ["B1","C2","C#2"]+-- > let f = pitch_in_octave_nearest T.cis2+-- > map (pitch_pp_iso . f) [T.b4,T.c4,T.cis4] == r pitch_in_octave_nearest :: Pitch -> Pitch -> Pitch pitch_in_octave_nearest p1 p2 =     let f = pitch_to_fmidi :: Pitch -> Double         o = fmidi_octave (fmidi_in_octave_nearest (f p1) (f p2))     in p2 {octave = o} --- | Raise 'Note_T' of 'Pitch', account for octave transposition.+-- | Raise 'Note' of 'Pitch', account for octave transposition. -- -- > pitch_note_raise (Pitch B Natural 3) == Pitch C Natural 4 pitch_note_raise :: Pitch -> Pitch@@ -337,7 +397,7 @@     then Pitch minBound a (o + 1)     else Pitch (succ n) a o --- | Lower 'Note_T' of 'Pitch', account for octave transposition.+-- | Lower 'Note' of 'Pitch', account for octave transposition. -- -- > pitch_note_lower (Pitch C Flat 4) == Pitch B Flat 3 pitch_note_lower :: Pitch -> Pitch@@ -349,9 +409,9 @@ -- | Rewrite 'Pitch' to not use @3/4@ tone alterations, ie. re-spell -- to @1/4@ alteration. ----- > let {p = Pitch A ThreeQuarterToneFlat 4--- >     ;q = Pitch G QuarterToneSharp 4}--- > in pitch_rewrite_threequarter_alteration p == q+-- > let p = Pitch T.A T.ThreeQuarterToneFlat 4+-- > let q = Pitch T.G T.QuarterToneSharp 4+-- > pitch_rewrite_threequarter_alteration p == q pitch_rewrite_threequarter_alteration :: Pitch -> Pitch pitch_rewrite_threequarter_alteration (Pitch n a o) =     case a of@@ -361,81 +421,63 @@  -- | Apply function to 'octave' of 'PitchClass'. ----- > pitch_edit_octave (+ 1) (Pitch A Natural 4) == Pitch A Natural 5+-- > pitch_edit_octave (+ 1) (Pitch T.A T.Natural 4) == Pitch T.A T.Natural 5 pitch_edit_octave :: (Octave -> Octave) -> Pitch -> Pitch pitch_edit_octave f (Pitch n a o) = Pitch n a (f o)  -- * Frequency (CPS) --- | /Midi/ note number to cycles per second, given frequency of ISO A4.-midi_to_cps_f0 :: (Integral i,Floating f) => f -> i -> f-midi_to_cps_f0 f0 = fmidi_to_cps_f0 f0 . fromIntegral---- | 'midi_to_cps_f0' 440.------ > map midi_to_cps [60,69] == [261.6255653005986,440.0]-midi_to_cps :: (Integral i,Floating f) => i -> f-midi_to_cps = midi_to_cps_f0 440---- | Fractional /midi/ note number to cycles per second, given frequency of ISO A4.-fmidi_to_cps_f0 :: Floating a => a -> a -> a-fmidi_to_cps_f0 f0 i = f0 * (2 ** ((i - 69) * (1 / 12)))---- | 'fmidi_to_cps_f0' 440.------ > map fmidi_to_cps [69,69.1] == [440.0,442.5488940698553]-fmidi_to_cps :: Floating a => a -> a-fmidi_to_cps = fmidi_to_cps_f0 440+-- | 'fmidi_to_cps' of 'pitch_to_fmidi', given (k0,f0).+pitch_to_cps_k0 :: Floating n => (n,n) -> Pitch -> n+pitch_to_cps_k0 o = T.fmidi_to_cps_k0 o . pitch_to_fmidi  -- | 'fmidi_to_cps' of 'pitch_to_fmidi', given frequency of ISO A4. pitch_to_cps_f0 :: Floating n => n -> Pitch -> n-pitch_to_cps_f0 f0 = fmidi_to_cps_f0 f0 . pitch_to_fmidi+pitch_to_cps_f0 f0 = pitch_to_cps_k0 (69,f0) --- | 'pitch_to_cps_f0' 440.+-- | 'pitch_to_cps_k0' (60,440). pitch_to_cps :: Floating n => Pitch -> n-pitch_to_cps = pitch_to_cps_f0 440+pitch_to_cps = pitch_to_cps_k0 (69,440)  -- | Frequency (cps = cycles per second) to fractional /midi/ note -- number, given frequency of ISO A4 (mnn = 69).-cps_to_fmidi_f0 :: Floating a => a -> a -> a-cps_to_fmidi_f0 f0 a = (logBase 2 (a * (1 / f0)) * 12) + 69+cps_to_fmidi_k0 :: Floating a => (a,a) -> a -> a+cps_to_fmidi_k0 (k0,f0) a = (logBase 2 (a * (1 / f0)) * 12) + k0 --- | 'cps_to_fmidi_f0' @440@.+-- | 'cps_to_fmidi_k0' @(69,440)@. -- -- > cps_to_fmidi 440 == 69 -- > cps_to_fmidi (fmidi_to_cps 60.25) == 60.25 cps_to_fmidi :: Floating a => a -> a-cps_to_fmidi = cps_to_fmidi_f0 440+cps_to_fmidi = cps_to_fmidi_k0 (69,440) --- | Frequency (cycles per second) to /midi/ note number, ie. 'round'--- of 'cps_to_fmidi'.+-- | Frequency (cycles per second) to /midi/ note number,+-- ie. 'round' of 'cps_to_fmidi'. -- -- > map cps_to_midi [261.6,440] == [60,69] cps_to_midi :: (Integral i,Floating f,RealFrac f) => f -> i cps_to_midi = round . cps_to_fmidi --- | 'midi_to_cps_f0' of 'octpc_to_midi', given frequency of ISO A4.-octpc_to_cps_f0 :: (Integral i,Floating n) => n -> Octave_PitchClass i -> n-octpc_to_cps_f0 f0 = midi_to_cps_f0 f0 . octave_pitchclass_to_midi+-- | 'midi_to_cps_f0' of 'octpc_to_midi', given (k0,f0)+octpc_to_cps_k0 :: (Integral i,Floating n) => (n,n) -> Octave_PitchClass i -> n+octpc_to_cps_k0 o = T.midi_to_cps_k0 o . octave_pitchclass_to_midi --- | 'octpc_to_cps_f0' 440.------ > octpc_to_cps (4,9) == 440+{- | 'octpc_to_cps_k0' (69,440).++> map (round . octpc_to_cps) [(-1,0),(0,0),(4,9),(9,0)] == [8,16,440,8372]+-} octpc_to_cps :: (Integral i,Floating n) => Octave_PitchClass i -> n-octpc_to_cps = octpc_to_cps_f0 440+octpc_to_cps = octpc_to_cps_k0 (69,440)  -- | 'midi_to_octpc' of 'cps_to_midi'. cps_to_octpc :: (Floating f,RealFrac f,Integral i) => f -> Octave_PitchClass i-cps_to_octpc = midi_to_octave_pitchclass . cps_to_midi+cps_to_octpc = midi_to_octave_pitchclass . T.real_round_int . cps_to_fmidi  cps_octave :: (Floating f,RealFrac f) => f -> Octave cps_octave = fst . cps_to_octpc  -- * MIDI detune (cents) --- | Midi note number with cents detune.-type Midi_Detune' c = (Int,c)- -- | Is cents in (-50,+50]. -- -- > map cents_is_normal [-250,-75,75,250] == replicate 4 False@@ -443,45 +485,60 @@ cents_is_normal c = c > (-50) && c <= 50  -- | 'cents_is_normal' of 'snd'.-midi_detune_is_normal :: (Num c, Ord c) => Midi_Detune' c -> Bool+midi_detune_is_normal :: (Num c, Ord c) => (x,c) -> Bool midi_detune_is_normal = cents_is_normal . snd  -- | In normal form the detune is in the range (-50,+50] instead of [0,100) or wider. -- -- > map midi_detune_normalise [(60,-250),(60,-75),(60,75),(60,250)]-midi_detune_normalise :: (Ord c,Num c) => Midi_Detune' c -> Midi_Detune' c-midi_detune_normalise (m,c) =-    if c > 50-    then midi_detune_normalise (m + 1,c - 100)-    else if c > (-50)-         then (m,c)-         else midi_detune_normalise (m - 1,c + 100)+midi_detune_normalise :: (Num m,Ord c,Num c) => (m,c) -> (m,c)+midi_detune_normalise =+  let recur (m,c) =+        if c > 50+        then recur (m + 1,c - 100)+        else if c > (-50)+             then (m,c)+             else recur (m - 1,c + 100)+  in recur +-- | In normal-positive form the detune is in the range (0,+100].+--+-- > map midi_detune_normalise_positive [(60,-250),(60,-75),(60,75),(60,250)]+midi_detune_normalise_positive :: (Num m,Ord m,Ord c,Num c) => (m,c) -> (m,c)+midi_detune_normalise_positive =+  let recur (m,c) =+        if c < 0+        then recur (m - 1,c + 100)+        else if c > 100+        then recur (m + 1,c - 100)+        else (m,c)+  in recur+ -- | Inverse of 'cps_to_midi_detune', given frequency of ISO @A4@.-midi_detune_to_cps_f0 :: Real c => Double -> Midi_Detune' c -> Double-midi_detune_to_cps_f0 f0 (m,c) = fmidi_to_cps_f0 f0 (fromIntegral m + (realToFrac c / 100))+midi_detune_to_cps_f0 :: (Integral m,Real c) => Double -> (m,c) -> Double+midi_detune_to_cps_f0 f0 (m,c) = T.fmidi_to_cps_f0 f0 (fromIntegral m + (realToFrac c / 100))  -- | Inverse of 'cps_to_midi_detune'. -- -- > map midi_detune_to_cps [(69,0),(68,100)] == [440,440]-midi_detune_to_cps :: Real c => Midi_Detune' c -> Double+midi_detune_to_cps :: (Integral m,Real c) => (m,c) -> Double midi_detune_to_cps = midi_detune_to_cps_f0 440  -- | 'Midi_Detune' to fractional midi note number. -- -- > midi_detune_to_fmidi (60,50.0) == 60.50-midi_detune_to_fmidi :: Real c => Midi_Detune' c -> Double+midi_detune_to_fmidi :: (Integral m,Real c) => (m,c) -> Double midi_detune_to_fmidi (mnn,c) = fromIntegral mnn + (realToFrac c / 100)  -- | 'Midi_Detune' to 'Pitch', detune must be precisely at a notateable Pitch. ----- > let p = Pitch {note = C, alteration = QuarterToneSharp, octave = 4}--- > in midi_detune_to_pitch T.pc_spell_ks (midi_detune_nearest_24et (60,35)) == p-midi_detune_to_pitch :: Real c => Spelling Int -> Midi_Detune' c -> Pitch+-- > let p = Pitch {note = T.C, alteration = T.QuarterToneSharp, octave = 4}+-- > midi_detune_to_pitch T.pc_spell_ks (midi_detune_nearest_24et (60,35)) == p+midi_detune_to_pitch :: (Integral m,Real c) => Spelling Int -> (m,c) -> Pitch midi_detune_to_pitch sp = fmidi_to_pitch_err sp . cps_to_fmidi . midi_detune_to_cps  -- | Midi note number with real-valued cents detune.-type Midi_Detune = Midi_Detune' Double+type Midi_Detune = (Midi,Double)  -- | Fractional midi note number to 'Midi_Detune'. --@@ -506,7 +563,7 @@ -- * MIDI cents  -- | Midi note number with integral cents detune.-type Midi_Cents = Midi_Detune' Int+type Midi_Cents = (Midi,Int)  midi_detune_to_midi_cents :: Midi_Detune -> Midi_Cents midi_detune_to_midi_cents (m,c) = (m,round c)@@ -517,41 +574,86 @@ midi_cents_pp :: Midi_Cents -> String midi_cents_pp (m,c) = if cents_is_normal c then printf "%d.%02d" m c else error "midi_cents_pp" +-- * 24ET++{- | The 24ET pitch-class universe, with /sharp/ spellings, in octave '4'.++> length pc24et_univ == 24++> let r = "C C𝄲 C♯ C𝄰 D D𝄲 D♯ D𝄰 E E𝄲 F F𝄲 F♯ F𝄰 G G𝄲 G♯ G𝄰 A A𝄲 A♯ A𝄰 B B𝄲"+> unwords (map pitch_class_pp pc24et_univ) == r++-}+pc24et_univ :: [Pitch]+pc24et_univ =+    let a = [T.Natural,T.QuarterToneSharp,T.Sharp,T.ThreeQuarterToneSharp]+        f (n,k) = map (\i -> Pitch n (a !! i) 4) [0 .. k - 1]+    in concatMap f (zip T.note_seq [4,4,2,4,4,4,2])++-- | 'genericIndex' into 'pc24et_univ'.+--+-- > pitch_class_pp (pc24et_to_pitch 13) == "F𝄰"+pc24et_to_pitch :: Integral i => i -> Pitch+pc24et_to_pitch = genericIndex pc24et_univ++-- * Pitch, rational alteration.++-- | Generalised pitch, given by a generalised alteration.+data Pitch_R = Pitch_R T.Note T.Alteration_R Octave+               deriving (Eq,Show)++-- | Pretty printer for 'Pitch_R'.+pitch_r_pp :: Pitch_R -> String+pitch_r_pp (Pitch_R n (_,a) o) = show n ++ a ++ show o++-- | 'Pitch_R' printed without octave.+pitch_r_class_pp :: Pitch_R -> String+pitch_r_class_pp = T.dropWhileRight isDigit . pitch_r_pp+ -- * Parsers +-- | Parser for single digit ISO octave (C4 = middle-C)+p_octave_iso :: T.P Octave+p_octave_iso = fmap digitToInt P.digit++-- | Parser for single digit ISO octave with default value in case of no parse.+p_octave_iso_opt :: Octave -> T.P Octave+p_octave_iso_opt def_o = do+  o <- P.optionMaybe p_octave_iso+  return (fromMaybe def_o o)++-- | Parser for ISO pitch notation.+p_iso_pitch_strict :: T.P Pitch+p_iso_pitch_strict = do+  n <- T.p_note_t+  a <- T.p_alteration_t_iso True+  o <- p_octave_iso+  return (Pitch  n a o)++-- | Parser for extended form of ISO pitch notation.+p_iso_pitch_oct :: Octave -> T.P Pitch+p_iso_pitch_oct def_o = do+  n <- T.p_note_t_ci -- ISO is requires upper case note names+  a <- T.p_alteration_t_iso False -- ISO does not allow ##+  o <- p_octave_iso_opt def_o -- ISO requires octave+  return (Pitch  n a o)+ -- | Parse possible octave from single integer. ----- > map (parse_octave 2) ["","4","x","11"]-parse_octave :: Num a => a -> String -> Maybe a-parse_octave def_o o =-    case o of-      [] -> Just def_o-      [n] -> if isDigit n-             then Just (fromIntegral (digitToInt n))-             else Nothing-      _ -> Nothing+-- > map (parse_octave 2) ["","4","x","11"] == [2,4,2,1]x+parse_octave :: Octave -> String -> Octave+parse_octave def_o = T.run_parser_error (p_octave_iso_opt def_o) --- | Slight generalisation of ISO pitch representation.  Allows octave+-- | Generalisation of ISO pitch representation.  Allows octave -- to be elided, pitch names to be lower case, and double sharps -- written as @##@. -- -- See <http://www.musiccog.ohio-state.edu/Humdrum/guide04.html> ----- > let r = [Pitch C Natural 4,Pitch A Flat 5,Pitch F DoubleSharp 6]--- > in mapMaybe (parse_iso_pitch_oct 4) ["C","Ab5","f##6",""] == r+-- > let r = [Pitch T.C T.Natural 4,Pitch T.A T.Flat 5,Pitch T.F T.DoubleSharp 6]+-- > mapMaybe (parse_iso_pitch_oct 4) ["C","Ab5","f##6",""] == r parse_iso_pitch_oct :: Octave -> String -> Maybe Pitch-parse_iso_pitch_oct def_o s =-    let mk n a o = case T.parse_note_t True n of-                   Nothing -> Nothing-                   Just n' -> fmap (Pitch n' a) (parse_octave def_o o)-    in case s of-         [] -> Nothing-         n:'b':'b':o -> mk n T.DoubleFlat o-         n:'#':'#':o -> mk n T.DoubleSharp o-         n:'x':o -> mk n T.DoubleSharp o-         n:'b':o -> mk n T.Flat o-         n:'#':o -> mk n T.Sharp o-         n:o -> mk n T.Natural o+parse_iso_pitch_oct def_o = T.run_parser_maybe (p_iso_pitch_oct def_o)  -- | Variant of 'parse_iso_pitch_oct' requiring octave. parse_iso_pitch :: String -> Maybe Pitch@@ -590,11 +692,12 @@  -- | Sequential list of /n/ pitch class names starting from /k/. ----- > unwords (pitch_class_names_12et 0 12) == "C C♯ D E♭ E F F♯ G A♭ A B♭ B"--- > pitch_class_names_12et 11 2 == ["B","C"]+-- > import Music.Theory.Pitch.Spelling.Table+-- > unwords (pitch_class_names_12et pc_spell_ks 0 12) == "C C♯ D E♭ E F F♯ G A♭ A B♭ B"+-- > pitch_class_names_12et pc_spell_ks 11 2 == ["B","C"] pitch_class_names_12et :: Integral n => Spelling n -> n -> n -> [String] pitch_class_names_12et sp k n =-    let f = pitch_class_pp . midi_to_pitch sp+    let f = pitch_class_pp . midi_to_pitch sp . T.from_integral_to_int     in map f [60 + k .. 60 + k + n - 1]  -- | Pretty printer for 'Pitch' (ISO, ASCII, see 'alteration_iso').@@ -605,6 +708,28 @@ pitch_pp_iso :: Pitch -> String pitch_pp_iso (Pitch n a o) = show n ++ T.alteration_iso a ++ show o +-- | Lilypond octave syntax.+ly_octave_tbl :: [(Octave, String)]+ly_octave_tbl =+  [(-1,",,,,")+  ,( 0,",,,")+  ,( 1,",,")+  ,( 2,",")+  ,( 3,"")+  ,( 4,"'")+  ,( 5,"''")+  ,( 6,"'''")+  ,( 7,"''''")+  ,( 8,"'''''")]++-- | Lookup 'ly_octave_tbl'.+octave_pp_ly :: Octave -> String+octave_pp_ly o = T.lookup_err o ly_octave_tbl++-- | Parse lilypond octave indicator.+octave_parse_ly :: String -> Maybe Octave+octave_parse_ly s = T.reverse_lookup s ly_octave_tbl+ -- | Pretty printer for 'Pitch' (ASCII, see 'alteration_tonh'). -- -- > pitch_pp_hly (Pitch E Flat 4) == "ees4"@@ -631,39 +756,34 @@          (T.E,T.Flat) -> "Es" ++ o'          _ -> show n ++ T.alteration_tonh a ++ o' --- * 24ET--{-  The 24ET pitch-class universe, with /sharp/ spellings, in octave '4'.--> length pc24et_univ == 24+-- * Parsers -> let r = "C C𝄲 C♯ C𝄰 D D𝄲 D♯ D𝄰 E E𝄲 F F𝄲 F♯ F𝄰 G G𝄲 G♯ G𝄰 A A𝄲 A♯ A𝄰 B B𝄲"-> in unwords (map pitch_class_pp pc24et_univ) == r+p_octave_ly :: T.P Octave+p_octave_ly =+    fmap+    (fromMaybe (error "p_octave_ly") . octave_parse_ly)+    (P.many1 (P.oneOf ",'")) --}-pc24et_univ :: [Pitch]-pc24et_univ =-    let a = [T.Natural,T.QuarterToneSharp,T.Sharp,T.ThreeQuarterToneSharp]-        f (n,k) = map (\i -> Pitch n (a !! i) 4) [0 .. k - 1]-    in concatMap f (zip T.note_seq [4,4,2,4,4,4,2])+p_pitch_ly :: T.P Pitch+p_pitch_ly = do+  (n,a) <- T.p_note_alteration_ly+  o <- P.optionMaybe p_octave_ly+  return (Pitch n (fromMaybe T.Natural a) (fromMaybe 3 o)) --- | 'genericIndex' into 'pc24et_univ'.+-- | Run 'p_pitch_ly'. ----- > pitch_class_pp (pc24et_to_pitch 13) == "F𝄰"-pc24et_to_pitch :: Integral i => i -> Pitch-pc24et_to_pitch = genericIndex pc24et_univ---- * Pitch, rational alteration.---- | Generalised pitch, given by a generalised alteration.-data Pitch_R = Pitch_R T.Note_T T.Alteration_R Octave-               deriving (Eq,Show)---- | Pretty printer for 'Pitch_R'.-pitch_r_pp :: Pitch_R -> String-pitch_r_pp (Pitch_R n (_,a) o) = show n ++ a ++ show o+-- > map (pitch_pp . pitch_parse_ly_err) ["c","d'","ees,","fisis''"] == ["C3","D4","E♭2","F𝄪5"]+pitch_parse_ly_err :: String -> Pitch+pitch_parse_ly_err = T.run_parser_error p_pitch_ly --- | 'Pitch_R' printed without octave.-pitch_r_class_pp :: Pitch_R -> String-pitch_r_class_pp = T.dropWhileRight isDigit . pitch_r_pp+-- | Parser for hly notation.+p_pitch_hly :: T.P Pitch+p_pitch_hly = do+  (n,a) <- T.p_note_alteration_ly+  fmap (Pitch n (fromMaybe T.Natural a)) p_octave_iso +-- | Run 'p_pitch_hly'.+--+-- > map (pitch_pp . pitch_parse_hly) ["ees4","fih3","b6"] == ["E♭4","F𝄲3","B6"]+pitch_parse_hly :: String -> Pitch+pitch_parse_hly = T.run_parser_error p_pitch_hly
+ Music/Theory/Pitch/Bark.hs view
@@ -0,0 +1,69 @@+-- | Zwicker, E. (1961) "Subdivision of the audible frequency range into critical bands"+--   The Journal of the Acoustical Society of America, Volume 33, Issue 2, p. 248 (1961)+--+-- <https://ccrma.stanford.edu/courses/120-fall-2003/lecture-5.html>+module Music.Theory.Pitch.Bark where++-- * TABLES++-- | Center freqencies of Bark scale critical bands (hz).+bark_center :: Num n => [n]+bark_center =+  [50,150,250,350,450,570,700,840,1000,1170+  ,1370,1600,1850,2150,2500,2900,3400,4000,4800,5800+  ,7000,8500,10500,13500]++-- | Edge freqencies of Bark scale critical bands (hz).+bark_edge :: Num n => [n]+bark_edge =+  [0,100,200,300,400,510,630,770,920,1080,1270+  ,1480,1720,2000,2320,2700,3150,3700,4400,5300,6400+  ,7700,9500,12000,15500]++-- | Bandwidths of Bark scale critical bands (hz).+bark_bandwidth :: Num n => [n]+bark_bandwidth = let c = bark_edge in zipWith (-) (tail c) c++-- * FUNCTIONS++-- | Zwicker & Terhardt (1980)+--+-- > map (round . cps_to_bark_zwicker) bark_centre == concat [[0..7],[9..15],[15..19],[21..24]]+-- > let f = [0,100 .. 8000] in Sound.SC3.Plot.plot_p2_ln [zip f (map cps_to_bark_zwicker f)]+cps_to_bark_zwicker :: Floating a => a -> a+cps_to_bark_zwicker x = 13 * atan (0.00076 * x) + 3.5 * atan ((x / 7500) ** 2)++-- | Traunmüller, Hartmut.+--   "Analytical Expressions for the Tonotopic Sensory Scale."+--   Journal of the Acoustical Society of America. Vol. 88, Issue 1, 1990, pp. 97-100.+--+-- > r = concat [[0,1],[3,4],[4],[6..9],[9,10],[12],[12..17],[19,20],[20..23]]+-- > map (round . cps_to_bark_traunmuller) bark_centre == r+-- > let f = [0,100 .. 8000] in Sound.SC3.Plot.plot_p2_ln [zip f (map cps_to_bark_traunmuller f)]+cps_to_bark_traunmuller :: (Fractional n,Ord n) => n -> n+cps_to_bark_traunmuller x =+  let y = ((26.81 * x) / (1960 + x)) - 0.53+  in if y < 2 then y + 0.15 * (2 - y) else if y > 20.1 then y + 0.22 * (y - 20.1) else y++-- | Traunmüller (1990)+--+-- > Sound.SC3.Plot.plot_p2_ln [zip (map bark_to_cps_traunmuller [0..23]) [0..23]]+bark_to_cps_traunmuller :: (Fractional n,Ord n) => n -> n+bark_to_cps_traunmuller y =+  let f x = 1960 * ((x + 0.53) / (26.28 - x))+  in if y < 2 then f ((y - 0.3) / 0.85) else if y > 20.1 then f ((y + 4.422) / 1.22) else f y++-- | Wang, Sekey & Gersho (1992)+--+-- > map (round . cps_to_bark_wsg) bark_centre == concat [[0..9],[9..21],[23]]+-- > let f = [0,100 .. 8000] in Sound.SC3.Plot.plot_p2_ln [zip f (map cps_to_bark_wsg f)]+cps_to_bark_wsg :: Floating a => a -> a+cps_to_bark_wsg x = 6 * asinh (x / 600)++-- | Wang, Sekey & Gersho (1992)+--+-- > r = [100,204,313,430,560,705,870,1059,1278,1532,1828,2176,2584,3065,3630,4297,5083,6011,7106,8399]+-- > map (round . bark_to_cps_wsg) [1 .. 20] == r+-- > Sound.SC3.Plot.plot_p2_ln [zip (map bark_to_cps_wsg [0..23]) [0..23]]+bark_to_cps_wsg :: Floating a => a -> a+bark_to_cps_wsg x = 600 * sinh (x / 6)
Music/Theory/Pitch/Chord.hs view
@@ -3,15 +3,16 @@ import Data.List {- base -} import Data.Maybe {- base -} -import qualified Text.ParserCombinators.Parsec as P {- parsec -}+import qualified Text.Parsec as P {- parsec -}  import qualified Music.Theory.Key as T {- hmt -} import qualified Music.Theory.List as T {- hmt -}+import qualified Music.Theory.Parse as T {- hmt -} import qualified Music.Theory.Pitch.Note as T {- hmt -} -type PC = (T.Note_T,T.Alteration_T)+type Pc = (T.Note,T.Alteration) -pc_pp :: (T.Note_T, T.Alteration_T) -> [Char]+pc_pp :: Pc -> [Char] pc_pp (n,a) = T.note_pp n : T.alteration_iso a  -- | D = dominant, M = major@@ -61,25 +62,25 @@ chord_type_pcset = snd . chord_type_dat  -- (root,mode,extensions,bass)-data Chord = CH PC Chord_Type (Maybe Extension) (Maybe PC)+data Chord = Chord Pc Chord_Type (Maybe Extension) (Maybe Pc)              deriving (Show)  chord_pcset :: Chord -> (Maybe Int,[Int])-chord_pcset (CH pc ty ex bs) =+chord_pcset (Chord pc ty ex bs) =     let get = m_error "chord_pcset" . T.note_alteration_to_pc         pc' = get pc         ty' = chord_type_pcset ty         ex' = fmap extension_to_pc ex         bs' = fmap get bs         ch = map ((`mod` 12) . (+ pc')) (ty' ++ maybe [] return ex')-        ch' = maybe ch (flip delete ch) bs'+        ch' = maybe ch (`delete` ch) bs'     in (bs',ch') -bass_pp :: PC -> String+bass_pp :: Pc -> String bass_pp = ('/' :) . pc_pp  chord_pp :: Chord -> String-chord_pp (CH pc ty ex bs) =+chord_pp (Chord pc ty ex bs) =     let (pre_ty,post_ty) = if is_suspended ty                            then (Nothing,Just ty)                            else (Just ty,Nothing)@@ -89,33 +90,19 @@               ,maybe "" chord_type_pp post_ty               ,maybe "" bass_pp bs] -type P a = P.GenParser Char () a- m_error :: String -> Maybe a -> a m_error txt = fromMaybe (error txt) -p_note_t :: P T.Note_T-p_note_t =-    fmap-    (m_error "p_note_t" . T.parse_note_t False)-    (P.oneOf "ABCDEFG")--p_alteration_t_iso :: P T.Alteration_T-p_alteration_t_iso =-    fmap-    (m_error "p_alteration_t_iso" . T.symbol_to_alteration_iso)-    (P.oneOf "b#x")--p_pc :: P PC+p_pc :: T.P Pc p_pc = do-  n <- p_note_t-  a <- P.optionMaybe p_alteration_t_iso+  n <- T.p_note_t+  a <- P.optionMaybe (T.p_alteration_t_iso True)   return (n,fromMaybe T.Natural a) -p_mode_m :: P T.Mode_T+p_mode_m :: T.P T.Mode p_mode_m = P.option T.Major_Mode (P.char 'm' >> return T.Minor_Mode) -p_chord_type :: P Chord_Type+p_chord_type :: T.P Chord_Type p_chord_type =     let m = P.char 'm' >> return Minor         au = P.char '+' >> return Augmented@@ -126,16 +113,16 @@         sus4 = P.try (P.string "sus4" >> return Suspended_4)     in P.option Major (P.choice [dm7,dm,hdm,au,sus2,sus4,m]) -p_extension :: P Extension+p_extension :: T.P Extension p_extension =     let d7 = P.char '7' >> return D7         m7 = P.try (P.string "M7" >> return M7)     in P.choice [d7,m7] -p_bass :: P (Maybe PC)+p_bass :: T.P (Maybe Pc) p_bass = P.optionMaybe (P.char '/' >> p_pc) -p_chord :: P Chord+p_chord :: T.P Chord p_chord = do   pc <- p_pc   ty <- p_chord_type@@ -147,8 +134,10 @@                (Major,Suspended_4) -> Suspended_4                (_,Major) -> ty -- ie. nothing                _ -> error ("trailing type not sus2 or sus4: " ++ show ty')-  return (CH pc ty'' ex b)+  return (Chord pc ty'' ex b) +-- | Parse chord.+-- -- > let ch = words "CmM7 C#o EbM7 Fo7 Gx/D C/E GØ/F Bbsus4/C E7sus2" -- > let c = map parse_chord ch -- > map chord_pp c == ch
Music/Theory/Pitch/Note.hs view
@@ -4,62 +4,72 @@ import Data.Char {- base -} import Data.Maybe {- base -} +import qualified Text.Parsec as P {- parsec -}+ import qualified Music.Theory.List as T {- hmt -}+import qualified Music.Theory.Parse as T {- hmt -} --- * Note_T+-- * Note  -- | Enumeration of common music notation note names (@C@ to @B@).-data Note_T = C | D | E | F | G | A | B+data Note = C | D | E | F | G | A | B               deriving (Eq,Enum,Bounded,Ord,Read,Show)  -- | Note sequence as usually understood, ie. 'C' - 'B'.-note_seq :: [Note_T]+note_seq :: [Note] note_seq = [C .. B]  -- | Char variant of 'show'.-note_pp :: Note_T -> Char+note_pp :: Note -> Char note_pp = head . show --- | Table of 'Note_T' and corresponding pitch-classes.-note_pc_tbl :: Num i => [(Note_T,i)]+-- | Note name in lilypond syntax (ie. lower case).+note_pp_ly :: Note -> String+note_pp_ly = map toLower . show++-- | Table of 'Note' and corresponding pitch-classes.+note_pc_tbl :: Num i => [(Note,i)] note_pc_tbl = zip [C .. B] [0,2,4,5,7,9,11] --- | Transform 'Note_T' to pitch-class number.+-- | Transform 'Note' to pitch-class number. -- -- > map note_to_pc [C,E,G] == [0,4,7]-note_to_pc :: Num i => Note_T -> i-note_to_pc n = fromMaybe (error "note_to_pc") (lookup n note_pc_tbl)+note_to_pc :: Num i => Note -> i+note_to_pc n = T.lookup_err_msg "note_to_pc" n note_pc_tbl  -- | Inverse of 'note_to_pc'. -- -- > mapMaybe pc_to_note [0,4,7] == [C,E,G]-pc_to_note :: (Eq i,Num i) => i -> Maybe Note_T+pc_to_note :: (Eq i,Num i) => i -> Maybe Note pc_to_note i = T.reverse_lookup i note_pc_tbl --- | Modal transposition of 'Note_T' value.+-- | Modal transposition of 'Note' value. -- -- > note_t_transpose C 2 == E-note_t_transpose :: Note_T -> Int -> Note_T+note_t_transpose :: Note -> Int -> Note note_t_transpose x n =     let x' = fromEnum x-        n' = fromEnum (maxBound::Note_T) + 1+        n' = fromEnum (maxBound::Note) + 1     in toEnum ((x' + n) `mod` n')  -- | Parser from 'Char', case insensitive flag. -- -- > mapMaybe (parse_note True) "CDEFGab" == [C,D,E,F,G,A,B]-parse_note_t :: Bool -> Char -> Maybe Note_T+parse_note_t :: Bool -> Char -> Maybe Note parse_note_t ci c =     let tbl = zip "CDEFGAB" [C,D,E,F,G,A,B]     in lookup (if ci then toUpper c else c) tbl --- | Inclusive set of 'Note_T' within indicated interval.  This is not+char_to_note_t :: Bool -> Char -> Note+char_to_note_t ci = fromMaybe (error "char_to_note_t") . parse_note_t ci++-- | Inclusive set of 'Note' within indicated interval.  This is not -- equal to 'enumFromTo' which is not circular. -- -- > note_span E B == [E,F,G,A,B] -- > note_span B D == [B,C,D] -- > enumFromTo B D == []-note_span :: Note_T -> Note_T -> [Note_T]+note_span :: Note -> Note -> [Note] note_span n1 n2 =     let fn x = toEnum (x `mod` 7)         n1' = fromEnum n1@@ -70,7 +80,7 @@ -- * Alteration  -- | Enumeration of common music notation note alterations.-data Alteration_T =+data Alteration =     DoubleFlat   | ThreeQuarterToneFlat | Flat | QuarterToneFlat   | Natural@@ -79,7 +89,7 @@     deriving (Eq,Enum,Bounded,Ord,Show)  -- | Generic form.-generic_alteration_to_diff :: Integral i => Alteration_T -> Maybe i+generic_alteration_to_diff :: Integral i => Alteration -> Maybe i generic_alteration_to_diff a =     case a of       DoubleFlat -> Just (-2)@@ -89,30 +99,30 @@       DoubleSharp -> Just 2       _ -> Nothing --- | Transform 'Alteration_T' to semitone alteration.  Returns+-- | Transform 'Alteration' to semitone alteration.  Returns -- 'Nothing' for non-semitone alterations. -- -- > map alteration_to_diff [Flat,QuarterToneSharp] == [Just (-1),Nothing]-alteration_to_diff :: Alteration_T -> Maybe Int+alteration_to_diff :: Alteration -> Maybe Int alteration_to_diff = generic_alteration_to_diff --- | Is 'Alteration_T' 12-ET.-alteration_is_12et :: Alteration_T -> Bool+-- | Is 'Alteration' 12-ET.+alteration_is_12et :: Alteration -> Bool alteration_is_12et = isJust . alteration_to_diff --- | Transform 'Alteration_T' to semitone alteration.+-- | Transform 'Alteration' to semitone alteration. -- -- > map alteration_to_diff_err [Flat,Sharp] == [-1,1]-alteration_to_diff_err :: Integral i => Alteration_T -> i+alteration_to_diff_err :: Integral i => Alteration -> i alteration_to_diff_err =     let err = error "alteration_to_diff: quarter tone"     in fromMaybe err . generic_alteration_to_diff --- | Transform 'Alteration_T' to fractional semitone alteration,+-- | Transform 'Alteration' to fractional semitone alteration, -- ie. allow quarter tones. -- -- > alteration_to_fdiff QuarterToneSharp == 0.5-alteration_to_fdiff :: Fractional n => Alteration_T -> n+alteration_to_fdiff :: Fractional n => Alteration -> n alteration_to_fdiff a =     case a of       ThreeQuarterToneFlat -> -1.5@@ -121,12 +131,12 @@       ThreeQuarterToneSharp -> 1.5       _ -> fromInteger (alteration_to_diff_err a) --- | Transform fractional semitone alteration to 'Alteration_T',+-- | Transform fractional semitone alteration to 'Alteration', -- ie. allow quarter tones. -- -- > map fdiff_to_alteration [-0.5,0.5] == [Just QuarterToneFlat -- >                                       ,Just QuarterToneSharp]-fdiff_to_alteration :: (Fractional n,Eq n) => n -> Maybe Alteration_T+fdiff_to_alteration :: (Fractional n,Eq n) => n -> Maybe Alteration fdiff_to_alteration d =     case d of       -2 -> Just DoubleFlat@@ -140,29 +150,29 @@       2 -> Just DoubleSharp       _ -> undefined --- | Raise 'Alteration_T' by a quarter tone where possible.+-- | Raise 'Alteration' by a quarter tone where possible. -- -- > alteration_raise_quarter_tone Flat == Just QuarterToneFlat -- > alteration_raise_quarter_tone DoubleSharp == Nothing-alteration_raise_quarter_tone :: Alteration_T -> Maybe Alteration_T+alteration_raise_quarter_tone :: Alteration -> Maybe Alteration alteration_raise_quarter_tone a =     if a == maxBound then Nothing else Just (toEnum (fromEnum a + 1)) --- | Lower 'Alteration_T' by a quarter tone where possible.+-- | Lower 'Alteration' by a quarter tone where possible. -- -- > alteration_lower_quarter_tone Sharp == Just QuarterToneSharp -- > alteration_lower_quarter_tone DoubleFlat == Nothing-alteration_lower_quarter_tone :: Alteration_T -> Maybe Alteration_T+alteration_lower_quarter_tone :: Alteration -> Maybe Alteration alteration_lower_quarter_tone a =     if a == minBound then Nothing else Just (toEnum (fromEnum a - 1)) --- | Edit 'Alteration_T' by a quarter tone where possible, @-0.5@+-- | Edit 'Alteration' by a quarter tone where possible, @-0.5@ -- lowers, @0@ retains, @0.5@ raises. -- -- > import Data.Ratio -- > alteration_edit_quarter_tone (-1 % 2) Flat == Just ThreeQuarterToneFlat alteration_edit_quarter_tone :: (Fractional n,Eq n) =>-                                n -> Alteration_T -> Maybe Alteration_T+                                n -> Alteration -> Maybe Alteration alteration_edit_quarter_tone n a =     case n of       -0.5 -> alteration_lower_quarter_tone a@@ -170,10 +180,10 @@       0.5 -> alteration_raise_quarter_tone a       _ -> Nothing --- | Simplify 'Alteration_T' to standard 12ET by deleting quarter tones.+-- | Simplify 'Alteration' to standard 12ET by deleting quarter tones. -- -- > Data.List.nub (map alteration_clear_quarter_tone [minBound..maxBound])-alteration_clear_quarter_tone :: Alteration_T -> Alteration_T+alteration_clear_quarter_tone :: Alteration -> Alteration alteration_clear_quarter_tone x =     case x of       ThreeQuarterToneFlat -> Flat@@ -182,7 +192,8 @@       ThreeQuarterToneSharp -> Sharp       _ -> x -alteration_symbol_tbl :: [(Alteration_T,Char)]+-- | Table of Unicode characters for alterations.+alteration_symbol_tbl :: [(Alteration,Char)] alteration_symbol_tbl =     [(DoubleFlat,'𝄫')     ,(ThreeQuarterToneFlat,'𝄭')@@ -200,26 +211,43 @@ -- UP@. -- -- > map alteration_symbol [minBound .. maxBound] == "𝄫𝄭♭𝄳♮𝄲♯𝄰𝄪"-alteration_symbol :: Alteration_T -> Char+alteration_symbol :: Alteration -> Char alteration_symbol a = fromMaybe (error "alteration_symbol") (lookup a alteration_symbol_tbl)  -- | Inverse of 'alteration_symbol'. -- -- > mapMaybe symbol_to_alteration "♭♮♯" == [Flat,Natural,Sharp]-symbol_to_alteration :: Char -> Maybe Alteration_T+symbol_to_alteration :: Char -> Maybe Alteration symbol_to_alteration c = T.reverse_lookup c alteration_symbol_tbl --- | Variant of 'symbol_to_alteration' that /also/ recognises @b@ for 'Flat'--- and @#@ for 'Sharp' and 'x' for double sharp.-symbol_to_alteration_iso :: Char -> Maybe Alteration_T-symbol_to_alteration_iso c =+-- | ISO alteration notation.  When not strict extended to allow ## for x.+symbol_to_alteration_iso :: Bool -> String -> Maybe Alteration+symbol_to_alteration_iso strict txt =+    case txt of+      "bb" -> Just DoubleFlat+      "b" -> Just Flat+      "#" -> Just Sharp+      "##" -> if strict then Nothing else Just DoubleSharp+      "x" -> Just DoubleSharp+      "" -> Just Natural+      _ -> Nothing++symbol_to_alteration_iso_err :: Bool -> String -> Alteration+symbol_to_alteration_iso_err strict =+  fromMaybe (error "symbol_to_alteration_iso") .+  symbol_to_alteration_iso strict++-- | 'symbol_to_alteration' extended to allow single character ISO notations.+symbol_to_alteration_unicode_plus_iso :: Char -> Maybe Alteration+symbol_to_alteration_unicode_plus_iso c =     case c of       'b' -> Just Flat       '#' -> Just Sharp       'x' -> Just DoubleSharp       _ -> symbol_to_alteration c -alteration_iso_tbl :: [(Alteration_T,String)]+-- | ISO alteration table, strings not characters because of double flat.+alteration_iso_tbl :: [(Alteration,String)] alteration_iso_tbl =     [(DoubleFlat,"bb")     ,(Flat,"b")@@ -232,57 +260,72 @@ -- -- > mapMaybe alteration_iso_m [Flat .. Sharp] == ["b","","#"] -- > mapMaybe alteration_iso_m [DoubleFlat,DoubleSharp] == ["bb","x"]-alteration_iso_m :: Alteration_T -> Maybe String+alteration_iso_m :: Alteration -> Maybe String alteration_iso_m a = lookup a alteration_iso_tbl  -- | The @ISO@ ASCII spellings for alterations.-alteration_iso :: Alteration_T -> String+alteration_iso :: Alteration -> String alteration_iso =     let qt = error "alteration_iso: quarter tone"     in fromMaybe qt . alteration_iso_m  -- | The /Tonhöhe/ ASCII spellings for alterations.+alteration_tonh_tbl :: [(Alteration, String)]+alteration_tonh_tbl =+  [(DoubleFlat,"eses")+  ,(ThreeQuarterToneFlat,"eseh")+  ,(Flat,"es")+  ,(QuarterToneFlat,"eh")+  ,(Natural,"")+  ,(QuarterToneSharp,"ih")+  ,(Sharp,"is")+  ,(ThreeQuarterToneSharp,"isih")+  ,(DoubleSharp,"isis")]++-- | The /Tonhöhe/ ASCII spellings for alterations. -- -- See <http://www.musiccog.ohio-state.edu/Humdrum/guide04.html> and -- <http://lilypond.org/doc/v2.16/Documentation/notation/writing-pitches> -- -- > map alteration_tonh [Flat .. Sharp] == ["es","eh","","ih","is"]-alteration_tonh :: Alteration_T -> String-alteration_tonh a =-    case a of-      DoubleFlat -> "eses"-      ThreeQuarterToneFlat -> "eseh"-      Flat -> "es"-      QuarterToneFlat -> "eh"-      Natural -> ""-      QuarterToneSharp -> "ih"-      Sharp -> "is"-      ThreeQuarterToneSharp -> "isih"-      DoubleSharp -> "isis"+alteration_tonh :: Alteration -> String+alteration_tonh a = T.lookup_err a alteration_tonh_tbl +-- | Inverse of 'alteration_tonh'.+--+-- > mapMaybe tonh_to_alteration ["es","eh","","ih","is"] == [Flat .. Sharp]+tonh_to_alteration :: String -> Maybe Alteration+tonh_to_alteration s = T.reverse_lookup s alteration_tonh_tbl++tonh_to_alteration_err :: String -> Alteration+tonh_to_alteration_err = fromMaybe (error "tonh_to_alteration") . tonh_to_alteration+ -- * 12-ET -note_alteration_to_pc :: (Note_T,Alteration_T) -> Maybe Int+-- | Note and alteration to pitch-class, or not.+note_alteration_to_pc :: (Note,Alteration) -> Maybe Int note_alteration_to_pc (n,a) =     let n_pc = note_to_pc n     in fmap ((`mod` 12) . (+ n_pc)) (alteration_to_diff a) +-- | Error variant.+-- -- > map note_alteration_to_pc_err [(A,DoubleSharp),(B,Sharp),(C,Flat),(C,DoubleFlat)]-note_alteration_to_pc_err :: (Note_T, Alteration_T) -> Int+note_alteration_to_pc_err :: (Note, Alteration) -> Int note_alteration_to_pc_err = fromMaybe (error "note_alteration_to_pc") . note_alteration_to_pc  -- | Note & alteration sequence in key-signature spelling.-note_alteration_ks :: [(Note_T, Alteration_T)]+note_alteration_ks :: [(Note, Alteration)] note_alteration_ks =     [(C,Natural),(C,Sharp),(D,Natural),(E,Flat),(E,Natural),(F,Natural)     ,(F,Sharp),(G,Natural),(A,Flat),(A,Natural),(B,Flat),(B,Natural)]  -- | Table connecting pitch class number with 'note_alteration_ks'.-pc_note_alteration_ks_tbl :: Integral i => [((Note_T,Alteration_T),i)]+pc_note_alteration_ks_tbl :: Integral i => [((Note,Alteration),i)] pc_note_alteration_ks_tbl = zip note_alteration_ks [0..11]  -- | 'T.reverse_lookup' of 'pc_note_alteration_ks_tbl'.-pc_to_note_alteration_ks :: Integral i => i -> Maybe (Note_T,Alteration_T)+pc_to_note_alteration_ks :: Integral i => i -> Maybe (Note,Alteration) pc_to_note_alteration_ks i = T.reverse_lookup i pc_note_alteration_ks_tbl  -- * Rational Alteration@@ -291,9 +334,42 @@ -- and a string representation of the alteration. type Alteration_R = (Rational,String) --- | Transform 'Alteration_T' to 'Alteration_R'.+-- | Transform 'Alteration' to 'Alteration_R'. -- -- > let r = [(-1,"♭"),(0,"♮"),(1,"♯")]--- > in map alteration_t' [Flat,Natural,Sharp] == r-alteration_r :: Alteration_T -> Alteration_R+-- > map alteration_r [Flat,Natural,Sharp] == r+alteration_r :: Alteration -> Alteration_R alteration_r a = (alteration_to_fdiff a,[alteration_symbol a])++-- * Parsers++-- | Parser for ISO note name, upper case.+--+-- > map (T.run_parser_error p_note_t . return) "ABCDEFG"+p_note_t :: T.P Note+p_note_t = fmap (char_to_note_t False) (P.oneOf "ABCDEFG")++-- | Note name in lower case (not ISO)+p_note_t_lc :: T.P Note+p_note_t_lc = fmap (char_to_note_t True) (P.oneOf "abcdefg")++-- | Case-insensitive note name (not ISO).+p_note_t_ci :: T.P Note+p_note_t_ci = fmap (char_to_note_t True) (P.oneOf "abcdefgABCDEFG")++-- | Parser for ISO alteration name.+--+-- > map (T.run_parser_error p_alteration_t_iso) (words "bb b # x ##")+p_alteration_t_iso :: Bool -> T.P Alteration+p_alteration_t_iso strict = fmap (symbol_to_alteration_iso_err strict) (P.many (P.oneOf "b#x"))++-- > map (T.run_parser_error p_alteration_t_tonh) ["eses","es","is","isis"]+p_alteration_t_tonh :: T.P Alteration+p_alteration_t_tonh = fmap tonh_to_alteration_err (P.many1 (P.oneOf "ehis"))++-- > map (T.run_parser_error p_note_alteration_ly) ["c","ees","fis","aeses"]+p_note_alteration_ly :: T.P (Note,Maybe Alteration)+p_note_alteration_ly = do+  n <- p_note_t_lc+  a <- P.optionMaybe p_alteration_t_tonh+  return (n,a)
Music/Theory/Pitch/Note/Name.hs view
@@ -6,7 +6,7 @@  import Music.Theory.Pitch.Note -ceses,deses,eeses,feses,geses,aeses,beses :: (Note_T,Alteration_T)+ceses,deses,eeses,feses,geses,aeses,beses :: (Note,Alteration) ceses = (C,DoubleFlat) deses = (D,DoubleFlat) eeses = (E,DoubleFlat)@@ -15,7 +15,7 @@ aeses = (A,DoubleFlat) beses = (B,DoubleFlat) -ceseh,deseh,eeseh,feseh,geseh,aeseh,beseh :: (Note_T,Alteration_T)+ceseh,deseh,eeseh,feseh,geseh,aeseh,beseh :: (Note,Alteration) ceseh = (C,ThreeQuarterToneFlat) deseh = (D,ThreeQuarterToneFlat) eeseh = (E,ThreeQuarterToneFlat)@@ -24,7 +24,7 @@ aeseh = (A,ThreeQuarterToneFlat) beseh = (B,ThreeQuarterToneFlat) -ces,des,ees,fes,ges,aes,bes :: (Note_T,Alteration_T)+ces,des,ees,fes,ges,aes,bes :: (Note,Alteration) ces = (C,Flat) des = (D,Flat) ees = (E,Flat)@@ -33,7 +33,7 @@ aes = (A,Flat) bes = (B,Flat) -ceh,deh,eeh,feh,geh,aeh,beh :: (Note_T,Alteration_T)+ceh,deh,eeh,feh,geh,aeh,beh :: (Note,Alteration) ceh = (C,QuarterToneFlat) deh = (D,QuarterToneFlat) eeh = (E,QuarterToneFlat)@@ -42,7 +42,7 @@ aeh = (A,QuarterToneFlat) beh = (B,QuarterToneFlat) -c,d,e,f,g,a,b :: (Note_T,Alteration_T)+c,d,e,f,g,a,b :: (Note,Alteration) c = (C,Natural) d = (D,Natural) e = (E,Natural)@@ -51,7 +51,7 @@ a = (A,Natural) b = (B,Natural) -cih,dih,eih,fih,gih,aih,bih :: (Note_T,Alteration_T)+cih,dih,eih,fih,gih,aih,bih :: (Note,Alteration) cih = (C,QuarterToneSharp) dih = (D,QuarterToneSharp) eih = (E,QuarterToneSharp)@@ -60,7 +60,7 @@ aih = (A,QuarterToneSharp) bih = (B,QuarterToneSharp) -cis,dis,eis,fis,gis,ais,bis :: (Note_T,Alteration_T)+cis,dis,eis,fis,gis,ais,bis :: (Note,Alteration) cis = (C,Sharp) dis = (D,Sharp) eis = (E,Sharp)@@ -69,7 +69,7 @@ ais = (A,Sharp) bis = (B,Sharp) -cisih,disih,eisih,fisih,gisih,aisih,bisih :: (Note_T,Alteration_T)+cisih,disih,eisih,fisih,gisih,aisih,bisih :: (Note,Alteration) cisih = (C,ThreeQuarterToneSharp) disih = (D,ThreeQuarterToneSharp) eisih = (E,ThreeQuarterToneSharp)@@ -78,7 +78,7 @@ aisih = (A,ThreeQuarterToneSharp) bisih = (B,ThreeQuarterToneSharp) -cisis,disis,eisis,fisis,gisis,aisis,bisis :: (Note_T,Alteration_T)+cisis,disis,eisis,fisis,gisis,aisis,bisis :: (Note,Alteration) cisis = (C,DoubleSharp) disis = (D,DoubleSharp) eisis = (E,DoubleSharp)
Music/Theory/Pitch/Spelling.hs view
@@ -6,7 +6,7 @@ import qualified Music.Theory.Pitch.Spelling.Key as T {- hmt -} import qualified Music.Theory.Pitch.Spelling.Table as T {- hmt -} -spell_octpc_set :: [T.OctPC] -> [T.Pitch]+spell_octpc_set :: [T.OctPc] -> [T.Pitch] spell_octpc_set o =   case T.octpc_spell_implied_key o of     Just r -> r@@ -15,5 +15,5 @@         Just r -> r         Nothing -> map T.octpc_to_pitch_ks o -spell_midi_set :: [T.Midi] -> [T.Pitch]-spell_midi_set = spell_octpc_set . map T.midi_to_octpc+spell_midi_set :: Integral i => [i] -> [T.Pitch]+spell_midi_set = spell_octpc_set . map T.midi_to_octave_pitchclass
Music/Theory/Pitch/Spelling/Cluster.hs view
@@ -14,12 +14,12 @@ cluster_normal_order :: [T.PitchClass] -> [T.PitchClass] cluster_normal_order =     let with_bounds x = ((last x - head x) `mod` 12,x)-    in snd . head . sort . map with_bounds . T.rotations+    in snd . minimum . map with_bounds . T.rotations  -- | Normal order starting in indicated octave. -- -- > cluster_normal_order_octpc 3 [0,1,11] == [(3,11),(4,0),(4,1)]-cluster_normal_order_octpc :: T.Octave -> [T.PitchClass] -> [T.OctPC]+cluster_normal_order_octpc :: T.Octave -> [T.PitchClass] -> [T.OctPc] cluster_normal_order_octpc o pc =     let pc_n = cluster_normal_order pc         pc_0 = head pc_n@@ -36,7 +36,7 @@ -- -- > let f (p,q) = (p == map T.note_alteration_to_pc_err q) -- > in all f spell_cluster_table-spell_cluster_table :: [([T.PitchClass],[(T.Note_T,T.Alteration_T)])]+spell_cluster_table :: [([T.PitchClass],[(T.Note,T.Alteration)])] spell_cluster_table =     [([0,1,2,3],[bis,cis,d,ees])     ,([0,1,2],[bis,cis,d])@@ -130,13 +130,13 @@     ,([9,10],[a,bes])     ,([9],[a])] -spell_cluster :: [T.PitchClass] -> Maybe [(T.Note_T,T.Alteration_T)]+spell_cluster :: [T.PitchClass] -> Maybe [(T.Note,T.Alteration)] spell_cluster = flip lookup spell_cluster_table --- | Spell an arbitrary sequence of 'T.OctPC' values.+-- | Spell an arbitrary sequence of 'T.OctPc' values. -- -- > fmap (map T.pitch_pp_iso) (spell_cluster_octpc [(3,11),(4,3),(4,11),(5,1)])-spell_cluster_octpc :: [T.OctPC] -> Maybe [T.Pitch]+spell_cluster_octpc :: [T.OctPc] -> Maybe [T.Pitch] spell_cluster_octpc o =     let p = cluster_normal_order (sort (nub (map snd o)))         na_f na =@@ -150,7 +150,7 @@ -- in octave @4@. -- -- > let f = (fmap (map T.pitch_pp) . spell_cluster_c4)--- > in map f [[11,0],[11]] == [Just ["B3","C4"],Just ["B4"]]+-- > map f [[11,0],[11],[0,11]] == [Just ["B3","C4"],Just ["B4"],Nothing] -- -- > fmap (map T.pitch_pp) (spell_cluster_c4 [10,11]) == Just ["A♯4","B4"] spell_cluster_c4 :: [T.PitchClass] -> Maybe [T.Pitch]@@ -159,7 +159,7 @@         oct = map fst (cluster_normal_order_octpc o_0 p)     in case spell_cluster p of          Nothing -> Nothing-         Just na -> Just (map (\((n,alt),o) -> T.Pitch n alt o) (zip na oct))+         Just na -> Just (zipWith (\(n,alt) o -> T.Pitch n alt o) na oct)  -- | Variant of 'spell_cluster_c4' that runs 'pitch_edit_octave'.  An -- octave of @4@ is the identitiy, @3@ an octave below, @5@ an octave@@ -177,17 +177,19 @@ -- -- > import Data.Maybe ----- > let {f n = if n >= 11 then 3 else 4--- >     ;g = map T.pitch_pp .fromJust . spell_cluster_f f--- >     ;r = [["B3","C4"],["B3"],["C4"],["A♯4","B4"]]}--- > in map g [[11,0],[11],[0],[10,11]] == r+-- > let f n = if n >= 11 then 3 else 4+-- > let g = map T.pitch_pp .fromJust . spell_cluster_f f+-- > let r = [["B3","C4"],["B3"],["C4"],["A♯4","B4"]]+-- > map g [[11,0],[11],[0],[10,11]] == r+--+-- > map (spell_cluster_f (const 4)) [[0,11],[11,0],[6,7],[7,6]] spell_cluster_f :: (T.PitchClass -> T.Octave) -> [T.PitchClass] -> Maybe [T.Pitch] spell_cluster_f o_f p =     let fn r = case r of                 [] -> []                 l:_ -> let (o,n) = T.pitch_to_octpc l                            oct_f = (+ (o_f n - o))-                       in (map (T.pitch_edit_octave oct_f) r)+                       in map (T.pitch_edit_octave oct_f) r     in fmap fn (spell_cluster_c4 p)  -- | Variant of 'spell_cluster_c4' that runs 'pitch_edit_octave' so
Music/Theory/Pitch/Spelling/Key.hs view
@@ -16,14 +16,14 @@                      else Just T.pc_spell_sharp  -- > map pcset_spell_implied_key [[0,1],[4,10],[3,9],[3,11]]-pcset_spell_implied_key :: Integral i => [i] -> Maybe [(T.Note_T, T.Alteration_T)]+pcset_spell_implied_key :: Integral i => [i] -> Maybe [(T.Note, T.Alteration)] pcset_spell_implied_key x =     case pcset_spell_implied_key_f x of       Just f -> Just (map f x)       Nothing -> Nothing  -- > map octpc_spell_implied_key [[(3,11),(4,1)],[(3,11),(4,10)]]-octpc_spell_implied_key :: [T.OctPC] -> Maybe [T.Pitch]+octpc_spell_implied_key :: [T.OctPc] -> Maybe [T.Pitch] octpc_spell_implied_key x =     let f o (n,a) = T.Pitch n a o     in fmap (zipWith f (map fst x)) (pcset_spell_implied_key (map snd x))
Music/Theory/Pitch/Spelling/Table.hs view
@@ -3,10 +3,10 @@  import Data.Maybe {- base -} -import Music.Theory.Pitch {- hmt -}+import qualified Music.Theory.Pitch as T {- hmt -} import Music.Theory.Pitch.Note {- hmt -} -type Spelling_Table i = [(i,(Note_T,Alteration_T))]+type Spelling_Table i = [(i,(Note,Alteration))]  -- | Spelling table for natural (♮) notes only. pc_spell_natural_tbl :: Integral i => Spelling_Table i@@ -48,54 +48,58 @@       ,(8,(A,Flat)) -- 3♭/3♯       ,(10,(B,Flat))] -- 1♭ -pc_spell_tbl :: Integral i => Spelling_Table i -> Spelling i+pc_spell_tbl :: Integral i => Spelling_Table i -> T.Spelling i pc_spell_tbl tbl = fromMaybe (error "pc_spell_tbl") . flip lookup tbl  -- | Spell using indicated table prepended to and 'pc_spell_natural_tbl' and 'pc_spell_ks_tbl'-pc_spell_tbl_ks :: Integral i => Spelling_Table i -> Spelling i+pc_spell_tbl_ks :: Integral i => Spelling_Table i -> T.Spelling i pc_spell_tbl_ks tbl = pc_spell_tbl (tbl ++ pc_spell_natural_tbl ++ pc_spell_ks_tbl)  -- | Spelling for natural (♮) notes only. -- -- > map pc_spell_natural_m [0,1] == [Just (C,Natural),Nothing]-pc_spell_natural_m :: Integral i => Spelling_M i+pc_spell_natural_m :: Integral i => T.Spelling_M i pc_spell_natural_m = flip lookup pc_spell_natural_tbl  -- | Erroring variant of 'pc_spell_natural_m'. -- -- > map pc_spell_natural [0,5,7] == [(C,Natural),(F,Natural),(G,Natural)]-pc_spell_natural :: Integral i => Spelling i+pc_spell_natural :: Integral i => T.Spelling i pc_spell_natural = pc_spell_tbl pc_spell_natural_tbl  -- | Lookup 'pc_spell_ks_tbl'. -- -- > map pc_spell_ks [6,8] == [(F,Sharp),(A,Flat)]-pc_spell_ks :: Integral i => Spelling i+pc_spell_ks :: Integral i => T.Spelling i pc_spell_ks = pc_spell_tbl_ks []  -- | Use always sharp (♯) spelling. -- -- > map pc_spell_sharp [6,8] == [(F,Sharp),(G,Sharp)] -- > Data.List.nub (map (snd . pc_spell_sharp) [1,3,6,8,10]) == [Sharp]-pc_spell_sharp :: Integral i => Spelling i+pc_spell_sharp :: Integral i => T.Spelling i pc_spell_sharp = pc_spell_tbl (pc_spell_sharp_tbl ++ pc_spell_natural_tbl)  -- | Use always flat (♭) spelling. -- -- >  map pc_spell_flat [6,8] == [(G,Flat),(A,Flat)] -- >  Data.List.nub (map (snd . pc_spell_flat) [1,3,6,8,10]) == [Flat]-pc_spell_flat :: Integral i => Spelling i+pc_spell_flat :: Integral i => T.Spelling i pc_spell_flat = pc_spell_tbl (pc_spell_flat_tbl ++ pc_spell_natural_tbl) -octpc_to_pitch_ks :: Integral i => Octave_PitchClass i -> Pitch-octpc_to_pitch_ks = octpc_to_pitch pc_spell_ks+octpc_to_pitch_ks :: Integral i => T.Octave_PitchClass i -> T.Pitch+octpc_to_pitch_ks = T.octpc_to_pitch pc_spell_ks --- | 'midi_to_pitch' 'T.pc_spell_ks'.-midi_to_pitch_ks :: Integral i => i -> Pitch-midi_to_pitch_ks = midi_to_pitch pc_spell_ks+-- | 'T.midi_to_pitch' 'pc_spell_ks'.+midi_to_pitch_ks :: Integral i => i -> T.Pitch+midi_to_pitch_ks = T.midi_to_pitch (pc_spell_ks :: T.Spelling Int) -fmidi_to_pitch_ks :: (Show n,RealFrac n) => n -> Pitch-fmidi_to_pitch_ks = fmidi_to_pitch_err pc_spell_ks+fmidi_to_pitch_ks :: (Show n,RealFrac n) => n -> T.Pitch+fmidi_to_pitch_ks = T.fmidi_to_pitch_err pc_spell_ks -midi_detune_to_pitch_ks :: Real c => Midi_Detune' c -> Pitch-midi_detune_to_pitch_ks = midi_detune_to_pitch pc_spell_ks+midi_detune_to_pitch_ks :: (Integral m,Real c) => (m,c) -> T.Pitch+midi_detune_to_pitch_ks = T.midi_detune_to_pitch pc_spell_ks++-- | 'T.midi_to_pitch' 'pc_spell_sharp'+midi_to_pitch_sharp :: Integral i => i -> T.Pitch+midi_to_pitch_sharp = T.midi_to_pitch (pc_spell_sharp :: T.Spelling Int)
Music/Theory/Random/I_Ching.hs view
@@ -1,14 +1,18 @@-{-# Language BinaryLiterals #-}-+-- | YIJING / I-CHING module Music.Theory.Random.I_Ching where  import Control.Monad {- base -} import Data.Maybe {- base -}+import Data.Int {- base -} import System.Random {- random -} -import qualified Music.Theory.Bits as T {- hmt -}-import qualified Music.Theory.Tuple as T {- hmt -}+import qualified Music.Theory.Bits as T {- hmt-base -}+import qualified Music.Theory.Read as T {- hmt-base -}+import qualified Music.Theory.Tuple as T {- hmt-base -}+import qualified Music.Theory.Unicode as T {- hmt-base -} +-- * LINE+ -- | Line, indicated as sum. data Line = L6 | L7 | L8 | L9 deriving (Eq,Show) @@ -19,23 +23,25 @@ -} type Line_Stat = (Line,(Rational,Rational,String,String,String)) +-- | I-CHING chart as sequence of 4 'Line_Stat'. i_ching_chart :: [Line_Stat] i_ching_chart =     [(L6,(1/16,2/16,"old yin","yin changing into yang","---x---"))+    ,(L7,(5/16,6/16,"young yang","yang unchanging","-------"))     ,(L8,(7/16,6/16,"young yin","yin unchanging","--- ---"))-    ,(L9,(3/16,2/16,"old yang","yang changing into yin","---o---"))-    ,(L7,(5/16,6/16,"young yang","yang unchanging","-------"))]+    ,(L9,(3/16,2/16,"old yang","yang changing into yin","---o---"))]  -- | Lines L6 and L7 are unbroken (since L6 is becoming L7). line_unbroken :: Line -> Bool line_unbroken n = n `elem` [L6,L7] +-- | If /b/ then L7 else L8. line_from_bit :: Bool -> Line line_from_bit b = if b then L7 else L8  -- | Seven character ASCII string for line. line_ascii_pp :: Line -> String-line_ascii_pp n = fromMaybe (error "line_ascii_pp") (fmap T.p5_fifth (lookup n i_ching_chart))+line_ascii_pp n = maybe (error "line_ascii_pp") T.p5_fifth (lookup n i_ching_chart)  -- | Is line (ie. sum) moving (ie. 6 or 9). line_is_moving :: Line -> Bool@@ -49,16 +55,11 @@       L9 -> Just L8       _ -> Nothing -type Hexagram = [Line]---- | Hexagrams are drawn upwards.-hexagram_pp :: Hexagram -> String-hexagram_pp = unlines . reverse . map line_ascii_pp- {- | Sequence of sum values assigned to ascending four bit numbers.+     Sequence is in ascending probablity, ie: 1×6,3×9,5×7,7×8. -> import  Music.Theory.Bits {- hmt -}-> zip (map (gen_bitseq_pp 4) [0::Int .. 15]) (map line_ascii_pp_err four_coin_sequence)+> import Music.Theory.Bits {- hmt -}+> zip (map (gen_bitseq_pp 4) [0::Int .. 15]) (map line_ascii_pp four_coin_sequence)  -} four_coin_sequence :: [Line]@@ -68,6 +69,15 @@     ,L7,L8,L8,L8     ,L8,L8,L8,L8] +-- * HEXAGRAM++-- | Sequence of 6 'Line'.+type Hexagram = [Line]++-- | Hexagrams are drawn upwards.+hexagram_pp :: Hexagram -> String+hexagram_pp = unlines . reverse . map line_ascii_pp+ -- | Generate hexagram (ie. sequence of six lines given by sum) using 'four_coin_sequence'. -- -- > four_coin_gen_hexagram >>= putStrLn . hexagram_pp@@ -88,7 +98,7 @@     let f n = fromMaybe n (line_complement n)     in if hexagram_has_complement h then Just (map f h) else Nothing --- | Names of hexagrams, in King Wen order.+-- | Names of hexagrams, in King Wen order (see also data/csv/combinatorics/yijing.csv) -- -- > length hexagram_names == 64 hexagram_names :: [(String,String)]@@ -163,30 +173,47 @@ -- > import Data.List.Split {- split -} -- > mapM_ putStrLn (chunksOf 8 hexagram_unicode_sequence) hexagram_unicode_sequence :: [Char]-hexagram_unicode_sequence = map toEnum [0x4DC0 .. 0x4DFF]+hexagram_unicode_sequence = map (toEnum . fst) T.yijing_tbl -hexagram_to_binary :: Hexagram -> Int+-- | Binary form of 'Hexagram'.+hexagram_to_binary :: Hexagram -> Int8 hexagram_to_binary = T.pack_bitseq . map line_unbroken --- > let h = hexagram_from_binary 0b100010--- > putStrLn (hexagram_pp h)--- > gen_bitseq_pp 6 (hexagram_to_binary h) == "100010"-hexagram_from_binary :: Int -> Hexagram+-- | Show binary form.+hexagram_to_binary_str :: Hexagram -> String+hexagram_to_binary_str = T.gen_bitseq_pp 6 . hexagram_to_binary++-- | Inverse of 'hexagram_to_binary'.+hexagram_from_binary :: Int8 -> Hexagram hexagram_from_binary = map line_from_bit . T.gen_bitseq 6 +-- | Read binary form.+--+-- > let h = hexagram_from_binary_str "100010"+-- > putStrLn (hexagram_pp h)+-- > hexagram_to_binary_str h == "100010"+hexagram_from_binary_str :: String -> Hexagram+hexagram_from_binary_str = hexagram_from_binary . T.read_bin_err++-- * TRIGRAM++-- | Unicode sequence of trigrams (unicode order).+-- -- > import Data.List {- base -} -- > putStrLn (intersperse ' ' trigram_unicode_sequence) trigram_unicode_sequence :: [Char]-trigram_unicode_sequence = map toEnum [0x2630 .. 0x2637]+trigram_unicode_sequence = map (toEnum . fst) T.bagua_tbl --- > map p8_third trigram_chart == [7,6,5,4,3,2,1,0]-trigram_chart :: Num i => [(i, Char, i, Char, String, Char, String, Char)]+-- | (INDEX,UNICODE,BIT-SEQUENCE,NAME,NAME-TRANSLITERATION,NATURE-IMAGE,DIRECTION,ANIMAL)+--+-- > map (T.read_bin_err . T.p8_third) trigram_chart == [7,6,5,4,3,2,1,0]+trigram_chart :: [(Int, Char, String, Char, String, Char, String, Char)] trigram_chart =-    [(1,'☰',0b111,'乾',"qián",'天',"NW",'馬')-    ,(2,'☱',0b110,'兌',"duì",'澤',"W",'羊')-    ,(3,'☲',0b101,'離',"lí",'火',"S",'雉')-    ,(4,'☳',0b100,'震',"zhèn",'雷',"E",'龍')-    ,(5,'☴',0b011,'巽',"xùn",'風',"SE",'雞')-    ,(6,'☵',0b010,'坎',"kǎn",'水',"N",'豕')-    ,(7,'☶',0b001,'艮',"gèn",'山',"NE",'狗')-    ,(8,'☷',0b000,'坤',"kūn",'地',"SW",'牛')]+    [(1,'☰',"111",'乾',"qián",'天',"NW",'馬')+    ,(2,'☱',"110",'兌',"duì",'澤',"W",'羊')+    ,(3,'☲',"101",'離',"lí",'火',"S",'雉')+    ,(4,'☳',"100",'震',"zhèn",'雷',"E",'龍')+    ,(5,'☴',"011",'巽',"xùn",'風',"SE",'雞')+    ,(6,'☵',"010",'坎',"kǎn",'水',"N",'豕')+    ,(7,'☶',"001",'艮',"gèn",'山',"NE",'狗')+    ,(8,'☷',"000",'坤',"kūn",'地',"SW",'牛')]
+ Music/Theory/Random/Jones_1981.hs view
@@ -0,0 +1,60 @@+-- | Kevin Jones. "Compositional Applications of Stochastic Processes".+--   Computer Music Journal, 5(2):45-58, 1981.+module Music.Theory.Random.Jones_1981 where++import Data.List {- base -}+import Data.Maybe {- base -}+import System.Random {- random -}++-- * Stochastic Finite State Grammars++data G a = T a | P (G a) (G a) deriving (Eq,Show)++type Rule k a = k -> a -> Maybe (a,a)+type Probablities k r = (r,[(k,r)])+type SFSG k a r = (Rule k a,Probablities k r)++-- > p_verify (1/2,[('a',1/4),('b',1/4)]) == True+p_verify :: (Eq a,Num a) => Probablities k a -> Bool+p_verify (t,k) = sum (t : map snd k) == 1++p_select :: (Ord a, Num a) => Probablities k a -> a -> Maybe (Maybe k)+p_select (t,k) =+  let windex w n = findIndex (n <) (scanl1 (+) w)+      (kk,kn) = unzip k+      f i = case i of+              0 -> Nothing+              _ -> Just (kk !! (i - 1))+  in fmap f . windex (t : kn)++-- > let p = (1/2,[('a',1/4),('b',1/4)])+-- > map (p_select_err p) [0,0.5,0.75] == [Nothing,Just 'a',Just 'b']+p_select_err :: (Ord a, Num a) => Probablities k a -> a -> Maybe k+p_select_err p = fromMaybe (error "p_select") . p_select p++g_collect :: G a -> [a]+g_collect g =+  case g of+    T e -> [e]+    P p q -> g_collect p ++ g_collect q++unfold :: (RandomGen g,Random r,Ord r,Num r) => SFSG k a r -> a -> g -> (G a,g)+unfold (r,p) st g =+  let (n,g') = randomR (0,1) g+  in case p_select_err p n of+       Nothing -> (T st,g')+       Just k ->+         case r k st of+           Nothing -> (T st,g')+           Just (i,j) ->+             let (i',g'') = unfold (r,p) i g'+                 (j',g''') = unfold (r,p) j g''+             in (P i' j',g''')++sfsg_chain :: (RandomGen g,Random r,Ord r,Num r) => SFSG k a r -> a -> g -> [G a]+sfsg_chain gr st g =+  let (x,g') = unfold gr st g+  in x : sfsg_chain gr st g'++sfsg_chain_n :: (RandomGen g,Random r,Ord r,Num r) => Int -> SFSG k a r -> a -> g -> [G a]+sfsg_chain_n n gr st = take n . sfsg_chain gr st
− Music/Theory/Read.hs 
@@ -1,147 +0,0 @@--- | Read functions.-module Music.Theory.Read where--import Data.Char {- base -}-import Data.List {- base -}-import Data.Maybe {- base -}-import Data.Ratio {- base -}-import Numeric {- base -}---- | Transform 'ReadS' function into precise 'Read' function.--- Requires using all the input to produce a single token.  The only--- exception is a singular trailing white space character.-reads_to_read_precise :: ReadS t -> (String -> Maybe t)-reads_to_read_precise f s =-    case f s of-      [(r,[])] -> Just r-      [(r,[c])] -> if isSpace c then Just r else Nothing-      _ -> Nothing---- | Error variant of 'reads_to_read_precise'.-reads_to_read_precise_err :: String -> ReadS t -> String -> t-reads_to_read_precise_err err f =-    fromMaybe (error ("reads_to_read_precise_err:" ++ err)) .-    reads_to_read_precise f---- | 'reads_to_read_precise' of 'reads'.--- space character.-read_maybe :: Read a => String -> Maybe a-read_maybe = reads_to_read_precise reads---- | Variant of 'read_maybe' with default value.------ > map (read_def 0) ["2","2:","2\n"] == [2,0,2]-read_def :: Read a => a -> String -> a-read_def x s = maybe x id (read_maybe s)---- | Variant of 'read_maybe' that errors on 'Nothing'.-read_err :: Read a => String -> a-read_err s = maybe (error ("read_err: " ++ s)) id (read_maybe s)---- | Variant of 'reads' requiring exact match, no trailing white space.------ > map reads_exact ["1.5","2,5"] == [Just 1.5,Nothing]-reads_exact :: Read a => String -> Maybe a-reads_exact s =-    case reads s of-      [(r,"")] -> Just r-      _ -> Nothing---- | Variant of 'reads_exact' that errors on failure.-reads_exact_err :: Read a => String -> String -> a-reads_exact_err err_txt str =-    let err = error ("reads: " ++ err_txt ++ ": " ++ str)-    in fromMaybe err (reads_exact str)---- * Type specific variants---- | Allow commas as thousand separators.------ > let r = [Just 123456,Just 123456,Nothing,Just 123456789]--- > in map read_integral_allow_commas_maybe ["123456","123,456","1234,56","123,456,789"]-read_integral_allow_commas_maybe :: Read i => String -> Maybe i-read_integral_allow_commas_maybe s =-    let c = filter ((== ',') . fst) (zip (reverse s) [0..])-    in if null c-       then read_maybe s-       else if map snd c `isPrefixOf` [3::Int,7..]-            then read_maybe (filter (not . (== ',')) s)-            else Nothing--read_integral_allow_commas_err :: (Integral i,Read i) => String -> i-read_integral_allow_commas_err s =-    let err = error ("read_integral_allow_commas: misplaced commas: " ++ s)-    in fromMaybe err (read_integral_allow_commas_maybe s)--read_int_allow_commas :: String -> Int-read_int_allow_commas = read_integral_allow_commas_err---- | Read a ratio where the division is given by @/@ instead of @%@--- and the integers allow commas.------ > map read_ratio_with_div_err ["123,456/7","123,456,789"] == [123456/7,123456789]-read_ratio_with_div_err :: (Integral i, Read i) => String -> Ratio i-read_ratio_with_div_err s =-    let f = read_integral_allow_commas_err-    in case break (== '/') s of-         (n,'/':d) -> f n % f d-         _ -> read_integral_allow_commas_err s % 1---- | Read 'Ratio', allow commas for thousand separators.------ > read_ratio_allow_commas_err "327,680" "177,147" == 327680 / 177147-read_ratio_allow_commas_err :: (Integral i,Read i) => String -> String -> Ratio i-read_ratio_allow_commas_err n d = let f = read_integral_allow_commas_err in f n % f d---- | Delete trailing @.@, 'read' fails for @700.@.-delete_trailing_point :: String -> String-delete_trailing_point s =-    case reverse s of-      '.':s' -> reverse s'-      _ -> s---- | 'read_err' disallows trailing decimal points.------ > map read_fractional_allow_trailing_point_err ["123.","123.4"] == [123.0,123.4]-read_fractional_allow_trailing_point_err :: Read n => String -> n-read_fractional_allow_trailing_point_err = read_err . delete_trailing_point---- * Plain type specialisations---- | Type specialised 'read_maybe'.------ > map read_maybe_int ["2","2:","2\n"] == [Just 2,Nothing,Just 2]-read_maybe_int :: String -> Maybe Int-read_maybe_int = read_maybe---- | Type specialised 'read_err'.-read_int :: String -> Int-read_int = read_err---- | Type specialised 'read_maybe'.-read_maybe_double :: String -> Maybe Double-read_maybe_double = read_maybe---- | Type specialised 'read_err'.-read_double :: String -> Double-read_double = read_err---- | Type specialised 'read_maybe'.------ > map read_maybe_rational ["1","1%2","1/2"] == [Nothing,Just (1/2),Nothing]-read_maybe_rational :: String -> Maybe Rational-read_maybe_rational = read_maybe---- | Type specialised 'read_err'.------ > read_rational "1%4"-read_rational :: String -> Rational-read_rational = read_err---- * Numeric variants---- | Error variant of 'readHex'.------ > read_hex_err "F0B0" == 61616-read_hex_err :: (Eq n,Num n) => String -> n-read_hex_err = reads_to_read_precise_err "readHex" readHex
Music/Theory/Set/List.hs view
@@ -3,9 +3,10 @@  import Control.Monad {- base -} import Data.List {- base -}+ import qualified Math.Combinatorics.Multiset as M {- multiset-comb -} -import qualified Music.Theory.List as T {- hmt -}+import qualified Music.Theory.List as T {- hmt-base -}  -- | 'sort' then 'nub'. --@@ -28,9 +29,9 @@  -- | Variant where result is sorted and the empty set is not given. ----- > powerset' [1,2,3] == [[1],[2],[3],[1,2],[1,3],[2,3],[1,2,3]]-powerset' :: Ord a => [a] -> [[a]]-powerset' = tail . T.sort_by_two_stage length id . powerset+-- > powerset_sorted [1,2,3] == [[1],[2],[3],[1,2],[1,3],[2,3],[1,2,3]]+powerset_sorted :: Ord a => [a] -> [[a]]+powerset_sorted = tail . T.sort_by_two_stage_on length id . powerset  -- | Two element subsets. --@@ -41,12 +42,14 @@       [] -> []       x:s' -> [(x,y) | y <- s'] ++ pairs s' --- | Three element subsets.------ > triples [1..4] == [(1,2,3),(1,2,4),(1,3,4),(2,3,4)]------ > let f n = genericLength (triples [1..n]) == nk_combinations n 3--- > in all f [1..15]+{- | Three element subsets.++> triples [1..4] == [(1,2,3),(1,2,4),(1,3,4),(2,3,4)]++> import Music.Theory.Combinations+> let f n = genericLength (triples [1..n]) == nk_combinations n 3+> all f [1..15]+-} triples :: [a] -> [(a,a,a)] triples s =     case s of@@ -62,23 +65,18 @@     then [xs]     else nub (concatMap (expand_set n) [sort (y : xs) | y <- xs]) --- | All distinct multiset partitions, see 'M.partitions'.------ > partitions "aab" == [["aab"],["a","ab"],["b","aa"],["b","a","a"]]------ > partitions "abc" == [["abc"]--- >                     ,["bc","a"],["b","ac"],["c","ab"]--- >                     ,["c","b","a"]]+{- | All distinct multiset partitions, see 'M.partitions'.++> partitions "aab" == [["aab"],["a","ab"],["b","aa"],["b","a","a"]]+> partitions "abc" == [["abc"],["bc","a"],["b","ac"],["c","ab"],["c","b","a"]]+-} partitions :: Eq a => [a] -> [[[a]]] partitions = map (map M.toList . M.toList) . M.partitions . M.fromListEq  {- | Cartesian product of two sets. -> let r = [('a',1),('a',2),('b',1),('b',2),('c',1),('c',2)]-> in cartesian_product "abc" [1,2] == r-+> cartesian_product "abc" [1,2] == [('a',1),('a',2),('b',1),('b',2),('c',1),('c',2)] > cartesian_product "abc" "" == []- -} cartesian_product :: [a] -> [b] -> [(a,b)] cartesian_product p q = [(i,j) | i <- p, j <- q]@@ -94,3 +92,10 @@       [_] -> []       [x,y] -> [[i,j] | i <- x, j <- y]       x:l' -> concatMap (\e -> map (e :) (nfold_cartesian_product l')) x++{- | Generate all distinct cycles, aka necklaces, with elements taken from a multiset.++> concatMap multiset_cycles [replicate i 0 ++ replicate (6 - i) 1 | i <- [0 .. 6]]+-}+multiset_cycles :: Ord t => [t] -> [[t]]+multiset_cycles = M.cycles . M.fromList
Music/Theory/Set/Set.hs view
@@ -2,7 +2,8 @@ module Music.Theory.Set.Set where  import qualified Data.Set as S {- containers -}-import qualified Music.Theory.Set.List as L++import qualified Music.Theory.Set.List as L {- hmt -}  set :: (Ord a) => [a] -> S.Set a set = S.fromList
− Music/Theory/Show.hs 
@@ -1,2 +0,0 @@--- | Show functions.-module Music.Theory.Show where
− Music/Theory/String.hs 
@@ -1,15 +0,0 @@--- | String functions.-module Music.Theory.String where--import Data.Char {- base -}---- | Remove @\r@.-filter_cr :: String -> String-filter_cr = filter (not . (==) '\r')---- | Delete trailing 'Char' where 'isSpace' holds.------ > delete_trailing_whitespace "   str   " == "   str"-delete_trailing_whitespace :: String -> String-delete_trailing_whitespace = reverse . dropWhile isSpace . reverse-
Music/Theory/Tempo_Marking.hs view
@@ -4,16 +4,16 @@ import Data.List {- base -}  import Music.Theory.Duration-import Music.Theory.Duration.RQ+import Music.Theory.Duration.Rq import Music.Theory.Time_Signature  -- | A tempo marking is in terms of a common music notation 'Duration'. type Tempo_Marking = (Duration,Rational) --- | Duration of a RQ value, in seconds, given indicated tempo.+-- | Duration of a Rq value, in seconds, given indicated tempo. -- -- > rq_to_seconds (quarter_note,90) 1 == 60/90-rq_to_seconds :: Tempo_Marking -> RQ -> Rational+rq_to_seconds :: Tempo_Marking -> Rq -> Rational rq_to_seconds (d,n) x =     let d' = duration_to_rq d         s = 60 / n
Music/Theory/Tiling/Canon.hs view
@@ -1,5 +1,6 @@ module Music.Theory.Tiling.Canon where +import Control.Monad {- base -} import Data.List {- base -} import Data.List.Split {- split -} import Text.Printf {- base -}@@ -37,16 +38,17 @@ e_to_seq :: E -> [Int] e_to_seq (s,m,o) = map ((+ o) . (* m)) s --- | Infer 'E' from sequence.------ > e_from_seq [1,5,11] == ([0,2,5],2,1)--- > e_from_seq [4,7] == ([0,1],3,4)--- > e_from_seq [2] == ([0],1,2)+{- | Infer 'E' from sequence.++> e_from_seq [1,5,11] == ([0,2,5],2,1)+> e_from_seq [4,7] == ([0,1],3,4)+> e_from_seq [2] == ([0],1,2)+-} e_from_seq :: [Int] -> E e_from_seq p =-    let i:_ = p+    let i = head p         q = map (+ negate i) p-        _:r = q+        r = tail q         n = if null r then 1 else foldl1 gcd r     in (map (`div` n) q,n,i) @@ -63,7 +65,7 @@ -- | Retrograde of 'T', the result 'T' is sorted. -- -- > let r = [[0,7,14],[1,5,9],[2,4,6],[3,8,13],[10,11,12]]--- > in t_retrograde [[0,7,14],[1,6,11],[2,3,4],[5,9,13],[8,10,12]] == r+-- > t_retrograde [[0,7,14],[1,6,11],[2,3,4],[5,9,13],[8,10,12]] == r t_retrograde :: T -> T t_retrograde t =     let n = maximum (concat t)@@ -72,46 +74,47 @@ -- | The normal form of 'T' is the 'min' of /t/ and it's 't_retrograde'. -- -- > let r = [[0,7,14],[1,5,9],[2,4,6],[3,8,13],[10,11,12]]--- > in t_normal [[0,7,14],[1,6,11],[2,3,4],[5,9,13],[8,10,12]] == r+-- > t_normal [[0,7,14],[1,6,11],[2,3,4],[5,9,13],[8,10,12]] == r t_normal :: T -> T t_normal t = min t (t_retrograde t) --- | Derive set of 'R' from 'T'.------ > let {r = [(21,[0,1,2],[10,8,2,4,7,5,1],[0,1,2,3,5,8,14])]--- >     ;t = [[0,10,20],[1,9,17],[2,4,6],[3,7,11],[5,12,19],[8,13,18],[14,15,16]]}--- > in r_from_t t == r+{- | Derive set of 'R' from 'T'.++> let r = [(21,[0,1,2],[10,8,2,4,7,5,1],[0,1,2,3,5,8,14])]+> let t = [[0,10,20],[1,9,17],[2,4,6],[3,7,11],[5,12,19],[8,13,18],[14,15,16]]+> r_from_t t == r+-} r_from_t :: T -> [R] r_from_t t =     let e = map e_from_seq t         n = maximum (concat t) + 1         t3_1 (i,_,_) = i-        f z = let (s:_,m,o) = unzip3 z in (n,s,m,o)+        f z = let (s,m,o) = unzip3 z in (n,head s,m,o)     in map f (T.group_on t3_1 e)  -- * Construction  -- | 'msum' '.' 'map' 'return'. ----- > observeAll (fromList [1..7]) == [1..7]-fromList :: L.MonadPlus m => [a] -> m a-fromList = L.msum . map return+-- > L.observeAll (fromList [1..7]) == [1..7]+fromList :: MonadPlus m => [a] -> m a+fromList = msum . map return  -- | Search for /perfect/ tilings of the sequence 'S' using -- multipliers from /m/ to degree /n/ with /k/ parts.-perfect_tilings_m :: L.MonadPlus m => [S] -> [Int] -> Int -> Int -> m T+perfect_tilings_m :: MonadPlus m => [S] -> [Int] -> Int -> Int -> m T perfect_tilings_m s m n k =     let rec p q =             if length q == k             then return (sort q)             else do m' <- fromList m-                    L.guard (m' `notElem` p)+                    guard (m' `notElem` p)                     s' <- fromList s                     let i = n - (maximum s' * m') - 1                     o <- fromList [0..i]                     let s'' = e_to_seq (s',m',o)                         q' = concat q-                    L.guard (all (`notElem` q') s'')+                    guard (all (`notElem` q') s'')                     rec (m':p) (s'':q)     in rec [] [] @@ -120,14 +123,12 @@ > perfect_tilings [[0,1]] [1..3] 6 3 == []  > let r = [[[0,7,14],[1,5,9],[2,4,6],[3,8,13],[10,11,12]]]-> in perfect_tilings [[0,1,2]] [1,2,4,5,7] 15 5 == r+> perfect_tilings [[0,1,2]] [1,2,4,5,7] 15 5 == r  > length (perfect_tilings [[0,1,2]] [1..12] 15 5) == 1 -> let r = [[[0,1],[2,5],[3,7],[4,6]]->         ,[[0,1],[2,6],[3,5],[4,7]]->         ,[[0,2],[1,4],[3,7],[5,6]]]-> in perfect_tilings [[0,1]] [1..4] 8 4 == r+> let r = [[[0,1],[2,5],[3,7],[4,6]], [[0,1],[2,6],[3,5],[4,7]] ,[[0,2],[1,4],[3,7],[5,6]]]+> perfect_tilings [[0,1]] [1..4] 8 4 == r  > let r = [[[0,1],[2,5],[3,7],[4,9],[6,8]] >         ,[[0,1],[2,7],[3,5],[4,8],[6,9]]@@ -139,10 +140,10 @@ Johnson 2004, p.2  > let r = [[0,6,12],[1,8,15],[2,11,20],[3,5,7],[4,9,14],[10,13,16],[17,18,19]]-> in perfect_tilings [[0,1,2]] [1,2,3,5,6,7,9] 21 7 == [r]+> perfect_tilings [[0,1,2]] [1,2,3,5,6,7,9] 21 7 == [r]  > let r = [[0,10,20],[1,9,17],[2,4,6],[3,7,11],[5,12,19],[8,13,18],[14,15,16]]-> in perfect_tilings [[0,1,2]] [1,2,4,5,7,8,10] 21 7 == [t_retrograde r]+> perfect_tilings [[0,1,2]] [1,2,4,5,7,8,10] 21 7 == [t_retrograde r]  -} perfect_tilings :: [S] -> [Int] -> Int -> Int -> [T]
Music/Theory/Time/Bel1990/R.hs view
@@ -11,7 +11,7 @@   Centre National de la Recherche Scientifique, 1992. /GRTC 458/   (<http://www.lpl.univ-aix.fr/~belbernard/music/2algorithms.pdf>) -For details see <http://rd.slavepianos.org/t/hmt-texts>.+For details see <http://rohandrape.net/?t=hmt-texts>. -}  module Music.Theory.Time.Bel1990.R where@@ -20,18 +20,18 @@ import Data.Function {- base -} import Data.List {- base -} import Data.Ratio {- base -}-import qualified Text.ParserCombinators.Parsec as P {- parsec -} +import qualified Text.Parsec as P {- parsec -}+ import qualified Music.Theory.List as T-import qualified Music.Theory.Math as T+import qualified Music.Theory.Parse as T+import qualified Music.Theory.Show as T  -- * Bel  -- | Types of 'Par' nodes.-data Par_Mode = Par_Left | Par_Right-              | Par_Min | Par_Max-              | Par_None-              deriving (Eq,Show)+data Par_Mode = Par_Left | Par_Right | Par_Min | Par_Max | Par_None+  deriving (Eq, Show)  -- | The different 'Par' modes are indicated by bracket types. par_mode_brackets :: Par_Mode -> (String,String)@@ -43,6 +43,17 @@       Par_Max -> ("{","}")       Par_None -> ("[","]") +-- | Inverse of par_mode_brackets+par_mode_kind :: (String, String) -> Par_Mode+par_mode_kind brk =+  case brk of+    ("{","}") -> Par_Max+    ("~{","}") -> Par_Min+    ("(",")") -> Par_Left+    ("~(",")") -> Par_Right+    ("[","]") -> Par_None+    _ -> error "par_mode_kind: incoherent par"+ bel_brackets_match :: (Char,Char) -> Bool bel_brackets_match (open,close) =     case (open,close) of@@ -51,25 +62,43 @@       ('[',']') -> True       _ -> False --- | Tempo is rational.  The duration of a 'Term' is the reciprocal of--- the 'Tempo' that is in place at the 'Term'.+{- | Tempo is rational.+The duration of a 'Term' is the reciprocal of the 'Tempo' that is in place at the 'Term'.+-} type Tempo = Rational  -- | Terms are the leaf nodes of the temporal structure.-data Term a = Value a-            | Rest-            | Continue-           deriving (Eq,Show)+data Term a = Value a | Rest | Continue+  deriving (Eq,Show) +-- | Value of Term, else Nothing+term_value :: Term t -> Maybe t+term_value t =+  case t of+    Value x -> Just x+    _ -> Nothing+ -- | Recursive temporal structure.-data Bel a = Node (Term a) -- ^ Leaf node-           | Iso (Bel a) -- ^ Isolate-           | Seq (Bel a) (Bel a) -- ^ Sequence-           | Par Par_Mode (Bel a) (Bel a) -- ^ Parallel-           | Mul Tempo -- ^ Tempo multiplier-           deriving (Eq,Show)+data Bel a =+  Node (Term a) -- ^ Leaf node+  | Iso (Bel a) -- ^ Isolate+  | Seq (Bel a) (Bel a) -- ^ Sequence+  | Par Par_Mode (Bel a) (Bel a) -- ^ Parallel+  | Mul Tempo -- ^ Tempo multiplier+  deriving (Eq,Show) --- | Pretty printer for 'Bel', given pretty printer for the term type.+-- | Given a Par mode, generate either: 1. an Iso, 2. a Par, 3. a series of nested Par.+par_of :: Par_Mode -> [Bel a] -> Bel a+par_of m l =+  case l of+    [] -> error "par_of: null"+    [e] -> Iso e+    lhs : rhs : [] -> Par m lhs rhs+    e : l' -> Par m e (par_of m l')++{- | Pretty printer for 'Bel', given pretty printer for the term type.+Note this does not write nested Par nodes in their simplified form.+-} bel_pp :: (a -> String) -> Bel a -> String bel_pp f b =     case b of@@ -87,13 +116,14 @@ bel_char_pp :: Bel Char -> String bel_char_pp = bel_pp return --- | Analyse a Par node giving (duration,LHS-tempo-*,RHS-tempo-*).------ > par_analyse 1 Par_Left (nseq "cd") (nseq "efg") == (2,1,3/2)--- > par_analyse 1 Par_Right (nseq "cd") (nseq "efg") == (3,2/3,1)--- > par_analyse 1 Par_Min (nseq "cd") (nseq "efg") == (2,1,3/2)--- > par_analyse 1 Par_Max (nseq "cd") (nseq "efg") == (3,2/3,1)--- > par_analyse 1 Par_None (nseq "cd") (nseq "efg") == (3,1,1)+{- | Analyse a Par node giving (duration,LHS-tempo-*,RHS-tempo-*).++> par_analyse 1 Par_Left (nseq "cd") (nseq "efg") == (2,1,3/2)+> par_analyse 1 Par_Right (nseq "cd") (nseq "efg") == (3,2/3,1)+> par_analyse 1 Par_Min (nseq "cd") (nseq "efg") == (2,1,3/2)+> par_analyse 1 Par_Max (nseq "cd") (nseq "efg") == (3,2/3,1)+> par_analyse 1 Par_None (nseq "cd") (nseq "efg") == (3,1,1)+-} par_analyse :: Tempo -> Par_Mode -> Bel a -> Bel a -> (Rational,Rational,Rational) par_analyse t m p q =     let (_,d_p) = bel_tdur t p@@ -133,14 +163,17 @@ -- | Time point. type Time = Rational --- | Voices are named as a sequence of left and right directions--- within nested 'Par' structures.+{- | Voices are named as a sequence of left and right directions within nested 'Par' structures.+l is left and r is right.+-} type Voice = [Char] --- | Linear state.  'Time' is the start time of the term, 'Tempo' is--- the active tempo & therefore the reciprocal of the duration,--- 'Voice' is the part label.-type L_St = (Time,Tempo,Voice)+{- | Linear state.+'Time' is the start time of the term.+'Tempo' is the active tempo & therefore the reciprocal of the duration.+'Voice' is the part label.+-}+type L_St = (Time, Tempo, Voice)  -- | Linear term. type L_Term a = (L_St,Term a)@@ -157,6 +190,18 @@ lterm_end_time :: L_Term a -> Time lterm_end_time e = lterm_time e + lterm_duration e +-- | Voice of 'L_Term'.+lterm_voice :: L_Term t -> Voice+lterm_voice ((_,_,vc),_) = vc++-- | Term of L_Term+lterm_term :: L_Term t -> Term t+lterm_term (_,t) = t++-- | Value of Term of L_Term+lterm_value :: L_Term t -> Maybe t+lterm_value = term_value . lterm_term+ -- | Linear form of 'Bel', an ascending sequence of 'L_Term'. type L_Bel a = [L_Term a] @@ -192,18 +237,25 @@ lbel_tempo_mul :: Rational -> L_Bel a -> L_Bel a lbel_tempo_mul n = map (\((st,tm,vc),e) -> ((st / n,tm * n,vc),e)) --- | After normalisation all start times and durations are integral.+{- | The multiplier that will normalise an L_Bel value.+     After normalisation all start times and durations are integral.+-}+lbel_normalise_multiplier :: L_Bel t -> Rational+lbel_normalise_multiplier b =+  let t = lbel_tempi b+      n = foldl1 lcm (map denominator t) % 1+      m = foldl1 lcm (map (numerator . (* n)) t) % 1+  in n / m++-- | Calculate and apply L_Bel normalisation multiplier. lbel_normalise :: L_Bel a -> L_Bel a-lbel_normalise b =-    let t = lbel_tempi b-        n = foldl1 lcm (map denominator t) % 1-        m = foldl1 lcm (map numerator (map (* n) t)) % 1-    in lbel_tempo_mul (n / m) b+lbel_normalise b = lbel_tempo_mul (lbel_normalise_multiplier b) b --- | All leftmost voices are re-written to the last non-left turning point.------ > map voice_normalise ["","l","ll","lll"] == replicate 4 ""--- > voice_normalise "lllrlrl" == "rlrl"+{- | All leftmost voices are re-written to the last non-left turning point.++> map voice_normalise ["","l","ll","lll"] == replicate 4 ""+> voice_normalise "lllrlrl" == "rlrl"+-} voice_normalise :: Voice -> Voice voice_normalise = dropWhile (== 'l') @@ -271,10 +323,11 @@ (~>) :: Bel a -> Bel a -> Bel a p ~> q = Seq p q --- | 'foldl1' of 'Seq'.------ > lseq [Node Rest] == Node Rest--- > lseq [Node Rest,Node Continue] == Seq (Node Rest) (Node Continue)+{- | 'foldl1' of 'Seq'.++> lseq [Node Rest] == Node Rest+> lseq [Node Rest,Node Continue] == Seq (Node Rest) (Node Continue)+-} lseq :: [Bel a] -> Bel a lseq = foldl1 Seq @@ -311,9 +364,10 @@ bel_parse_pp_ident :: String -> Bool bel_parse_pp_ident s = bel_char_pp (bel_char_parse s) == s --- | Run 'bel_char_parse', and print both 'bel_char_pp' and 'bel_ascii'.------ > bel_ascii_pp "{i{ab,{c[d,oh]e,sr{p,qr}}},{jk,ghjkj}}"+{- | Run 'bel_char_parse', and print both 'bel_char_pp' and 'bel_ascii'.++> bel_ascii_pp "{i{ab,c[d,oh]e,sr{p,qr}},{jk,ghjkj}}"+-} bel_ascii_pp :: String -> IO () bel_ascii_pp s = do   let p = bel_char_parse s@@ -322,55 +376,52 @@  -- * Parsing --- | A 'Char' parser.-type P a = P.GenParser Char () a- -- | Parse 'Rest' 'Term'. -- -- > P.parse p_rest "" "-"-p_rest :: P (Term a)-p_rest = liftM (const Rest) (P.char '-')+p_rest :: T.P (Term a)+p_rest = fmap (const Rest) (P.char '-')  -- | Parse 'Rest' 'Term'. -- -- > P.parse p_nrests "" "3"-p_nrests :: P (Bel a)-p_nrests = liftM nrests p_non_negative_integer+p_nrests :: T.P (Bel a)+p_nrests = fmap nrests p_non_negative_integer  -- | Parse 'Continue' 'Term'. -- -- > P.parse p_continue "" "_"-p_continue :: P (Term a)-p_continue = liftM (const Continue) (P.char '_')+p_continue :: T.P (Term a)+p_continue = fmap (const Continue) (P.char '_')  -- | Parse 'Char' 'Value' 'Term'. -- -- > P.parse p_char_value "" "a"-p_char_value :: P (Term Char)-p_char_value = liftM Value P.lower+p_char_value :: T.P (Term Char)+p_char_value = fmap Value P.lower  -- | Parse 'Char' 'Term'. -- -- > P.parse (P.many1 p_char_term) "" "-_a"-p_char_term :: P (Term Char)+p_char_term :: T.P (Term Char) p_char_term = P.choice [p_rest,p_continue,p_char_value]  -- | Parse 'Char' 'Node'. -- -- > P.parse (P.many1 p_char_node) "" "-_a"-p_char_node :: P (Bel Char)-p_char_node = liftM Node p_char_term+p_char_node :: T.P (Bel Char)+p_char_node = fmap Node p_char_term  -- | Parse non-negative 'Integer'. -- -- > P.parse p_non_negative_integer "" "3"-p_non_negative_integer :: P Integer-p_non_negative_integer = liftM read (P.many1 P.digit)+p_non_negative_integer :: T.P Integer+p_non_negative_integer = fmap read (P.many1 P.digit)  -- | Parse non-negative 'Rational'. -- -- > P.parse (p_non_negative_rational `P.sepBy` (P.char ',')) "" "3%5,2/3"-p_non_negative_rational :: P Rational+p_non_negative_rational :: T.P Rational p_non_negative_rational = do   n <- p_non_negative_integer   _ <- P.oneOf "%/"@@ -381,7 +432,7 @@ -- -- > P.parse p_non_negative_double "" "3.5" -- > P.parse (p_non_negative_double `P.sepBy` (P.char ',')) "" "3.5,7.2,1.0"-p_non_negative_double :: P Double+p_non_negative_double :: T.P Double p_non_negative_double = do   a <- P.many1 P.digit   _ <- P.char '.'@@ -391,16 +442,16 @@ -- | Parse non-negative number as 'Rational'. -- -- > P.parse (p_non_negative_number `P.sepBy` (P.char ',')) "" "7%2,3.5,3"-p_non_negative_number :: P Rational+p_non_negative_number :: T.P Rational p_non_negative_number =     P.choice [P.try p_non_negative_rational-             ,P.try (liftM toRational p_non_negative_double)-             ,P.try (liftM toRational p_non_negative_integer)]+             ,P.try (fmap toRational p_non_negative_double)+             ,P.try (fmap toRational p_non_negative_integer)]  -- | Parse 'Mul'. -- -- > P.parse (P.many1 p_mul) "" "/3*3/2"-p_mul :: P (Bel a)+p_mul :: T.P (Bel a) p_mul = do   op <- P.oneOf "*/"   n <- p_non_negative_number@@ -411,50 +462,43 @@   return (Mul n')  -- | Given parser for 'Bel' /a/, generate 'Iso' parser.-p_iso :: P (Bel a) -> P (Bel a)+p_iso :: T.P (Bel a) -> T.P (Bel a) p_iso f = do   open <- P.oneOf "{(["   iso <- P.many1 f   close <- P.oneOf "})]"-  if bel_brackets_match (open,close)-    then return (Iso (lseq iso))-    else error "p_iso: open/close mismatch"+  when (not (bel_brackets_match (open,close))) (error "p_iso: open/close mismatch")+  return (Iso (lseq iso))  -- | 'p_iso' of 'p_char_bel'. -- -- > P.parse p_char_iso "" "{abcde}"-p_char_iso :: P (Bel Char)+p_char_iso :: T.P (Bel Char) p_char_iso = p_iso p_char_bel  -- | Given parser for 'Bel' /a/, generate 'Par' parser.-p_par :: P (Bel a) -> P (Bel a)+p_par :: T.P (Bel a) -> T.P (Bel a) p_par f = do   tilde <- P.optionMaybe (P.char '~')   open <- P.oneOf "{(["-  lhs <- P.many1 f-  _ <- P.char ','-  rhs <- P.many1 f+  items <- P.sepBy (P.many1 f) (P.char ',')   close <- P.oneOf "})]"-  let m = case (tilde,open,close) of-            (Nothing,'{','}') -> Par_Max-            (Just '~','{','}') -> Par_Min-            (Nothing,'(',')') -> Par_Left-            (Just '~','(',')') -> Par_Right-            (Nothing,'[',']') -> Par_None-            _ -> error "p_par: incoherent par"-  return (Par m (lseq lhs) (lseq rhs))+  let m = par_mode_kind (T.mcons tilde [open], [close])+  return (par_of m (map lseq items)) --- | 'p_par' of 'p_char_bel'.------ > P.parse p_char_par "" "{ab,{c,de}}"--- > P.parse p_char_par "" "{ab,~(c,de)}"-p_char_par :: P (Bel Char)+{- | 'p_par' of 'p_char_bel'.++> p = P.parse p_char_par ""+> p "{ab,{c,de}}" == p "{ab,c,de}"+> p "{ab,~(c,de)}"+-}+p_char_par :: T.P (Bel Char) p_char_par = p_par p_char_bel  -- | Parse 'Bel' 'Char'. -- -- > P.parse (P.many1 p_char_bel) "" "-_a*3"-p_char_bel :: P (Bel Char)+p_char_bel :: T.P (Bel Char) p_char_bel = P.choice [P.try p_char_par,p_char_iso,p_mul,p_nrests,p_char_node]  -- | Run parser for 'Bel' of 'Char'.
− Music/Theory/Time/Duration.hs 
@@ -1,148 +0,0 @@-module Music.Theory.Time.Duration where--import qualified Data.List.Split as S {- split -}-import Text.Printf {- base -}---- | Duration stored as /hours/, /minutes/, /seconds/ and /milliseconds/.-data Duration = Duration {hours :: Int-                         ,minutes :: Int-                         ,seconds :: Int-                         ,milliseconds :: Int}-                deriving (Eq)---- | Convert fractional /seconds/ to integral /(seconds,milliseconds)/.------ > s_sms 1.75 == (1,750)-s_sms :: (RealFrac n,Integral i) => n -> (i,i)-s_sms s =-    let s' = floor s-        ms = round ((s - fromIntegral s') * 1000)-    in (s',ms)---- | Inverse of 's_sms'.------ > sms_s (1,750) == 1.75-sms_s :: (Integral i) => (i,i) -> Double-sms_s (s,ms) = fromIntegral s + fromIntegral ms / 1000---- | 'Read' function for 'Duration' tuple.-read_duration_tuple :: String -> (Int,Int,Int,Int)-read_duration_tuple x =-    let f :: (Int,Int,Double) -> (Int,Int,Int,Int)-        f (h,m,s) = let (s',ms) = s_sms s in (h,m,s',ms)-    in case S.splitOneOf ":" x of-        [h,m,s] -> f (read h,read m,read s)-        [m,s] -> f (0,read m,read s)-        [s] -> f (0,0,read s)-        _ -> error "read_duration_tuple"---- | 'Read' function for 'Duration'.  Allows either @H:M:S.MS@ or--- @M:S.MS@ or @S.MS@.------ > read_duration "01:35:05.250" == Duration 1 35 5 250--- > read_duration    "35:05.250" == Duration 0 35 5 250--- > read_duration       "05.250" == Duration 0 0 5 250-read_duration :: String -> Duration-read_duration = tuple_to_duration id . read_duration_tuple--instance Read Duration where-    readsPrec _ x = [(read_duration x,"")]---- | 'Show' function for 'Duration'.------ > show_duration (Duration 1 35 5 250) == "01:35:05.250"--- > show (Duration 1 15 0 000) == "01:15:00.000"-show_duration :: Duration -> String-show_duration (Duration h m s ms) =-    let f :: Int -> String-        f = printf "%02d"-        g = f . fromIntegral-        s' = sms_s (s,ms)-    in concat [g h,":",g m,":",printf "%06.3f" s']--instance Show Duration where-    show = show_duration--normalise_minutes :: Duration -> Duration-normalise_minutes (Duration h m s ms) =-    let (h',m') = m `divMod` 60-    in Duration (h + h') m' s ms--normalise_seconds :: Duration -> Duration-normalise_seconds (Duration h m s ms) =-    let (m',s') = s `divMod` 60-    in Duration h (m + m') s' ms--normalise_milliseconds :: Duration -> Duration-normalise_milliseconds (Duration h m s ms) =-    let (s',ms') = ms `divMod` 1000-    in Duration h m (s + s') ms'--normalise_duration :: Duration -> Duration-normalise_duration =-    normalise_minutes .-    normalise_seconds .-    normalise_milliseconds---- | Extract 'Duration' tuple applying filter function at each element------ > duration_tuple id (Duration 1 35 5 250) == (1,35,5,250)-duration_to_tuple :: (Int -> a) -> Duration -> (a,a,a,a)-duration_to_tuple f (Duration h m s ms) = (f h,f m,f s,f ms)---- | Inverse of 'duration_to_tuple'.-tuple_to_duration :: (a -> Int) -> (a,a,a,a) -> Duration-tuple_to_duration f (h,m,s,ms) = Duration (f h) (f m) (f s) (f ms)---- > duration_to_hours (read "01:35:05.250") == 1.5847916666666668-duration_to_hours :: Fractional n => Duration -> n-duration_to_hours d =-    let (h,m,s,ms) = duration_to_tuple fromIntegral d-    in h + (m / 60) + (s / (60 * 60)) + (ms / (60 * 60 * 1000))---- > duration_to_minutes (read "01:35:05.250") == 95.0875-duration_to_minutes :: Fractional n => Duration -> n-duration_to_minutes = (* 60) . duration_to_hours---- > duration_to_seconds (read "01:35:05.250") == 5705.25-duration_to_seconds :: Fractional n => Duration -> n-duration_to_seconds = (* 60) . duration_to_minutes---- > hours_to_duration 1.5847916 == Duration 1 35 5 250-hours_to_duration :: RealFrac a => a -> Duration-hours_to_duration n =-    let r = fromIntegral :: RealFrac a => Int -> a-        h = (r . floor) n-        m = (n - h) * 60-        (s,ms) = s_sms ((m - (r . floor) m) * 60)-    in Duration (floor h) (floor m) s ms--minutes_to_duration :: RealFrac a => a -> Duration-minutes_to_duration n = hours_to_duration (n / 60)--seconds_to_duration :: RealFrac a => a -> Duration-seconds_to_duration n = minutes_to_duration (n / 60)--nil_duration :: Duration-nil_duration = Duration 0 0 0 0--negate_duration :: Duration -> Duration-negate_duration (Duration h m s ms) =-    let h' = if h > 0 then -h else h-        m' = if h == 0 && m > 0 then -m else m-        s' = if h == 0 && m == 0 && s > 0 then -s else s-        ms' = if h == 0 && m == 0 && s == 0 then -ms else ms-    in Duration h' m' s' ms'---- > duration_diff (Duration 1 35 5 250) (Duration 0 25 1 125) == Duration 1 10 4 125--- > duration_diff (Duration 0 25 1 125) (Duration 1 35 5 250) == Duration (-1) 10 4 125--- > duration_diff (Duration 0 25 1 125) (Duration 0 25 1 250) == Duration 0 0 0 (-125)-duration_diff :: Duration -> Duration -> Duration-duration_diff p q =-    let f = duration_to_hours :: Duration -> Double-        (p',q') = (f p,f q)-        g = normalise_duration . hours_to_duration-    in case compare p' q' of-         LT -> negate_duration (g (q' - p'))-         EQ -> nil_duration-         GT -> g (p' - q')
+ Music/Theory/Time/KeyKit.hs view
@@ -0,0 +1,236 @@+{- | A sequence structure, courtesy <https://github.com/nosuchtim/keykit>.++A /note/ has a time, a duration and a value.+A /phrase/ is a time-ascending sequence of notes and a /length/.+The length of a phrase is independent of the contents.+The sequence operator, /phrase_append/, sums phrase lengths.+The parallel operator, /phrase_merge/, selects the longer length.++Operations are ordinarily on phrases, notes are operated on indirectly.+The phrase indexing operation, /phrase_at/ returns a phrase of degree one.+-}+module Music.Theory.Time.KeyKit where++import Data.List {- base -}++import qualified Data.List.Ordered as O {- data-ordlist -}++import qualified Music.Theory.Time.Seq as Seq {- hmt -}++-- * Time++type Time = Rational+type Duration = Time+type Length = Time++-- * Note++data Note t =+  Note { note_start_time :: Time, note_duration :: Duration, note_value :: t }+  deriving (Eq, Ord, Show)++note_end_time :: Note t -> Time+note_end_time n = note_start_time n + note_duration n++note_region :: Note t -> (Time, Time)+note_region n = (note_start_time n, note_end_time n)++note_shift_time :: Time -> Note t -> Note t+note_shift_time k (Note t d e) = Note (t + k) d e++note_scale_duration :: Time -> Note t -> Note t+note_scale_duration m (Note t d e) = Note t (d * m) e++note_scale_duration_and_time :: Time -> Note t -> Note t+note_scale_duration_and_time m (Note t d e) = Note (t * m) (d * m) e++note_is_start_in_region :: (Time, Time) -> Note t -> Bool+note_is_start_in_region (t1, t2) (Note t _ _) = t >= t1 && t < t2++note_is_entirely_in_region :: (Time, Time) -> Note t -> Bool+note_is_entirely_in_region (t1, t2) (Note t d _) = t >= t1 && (t + d) < t2++-- * Phrase++-- | It is an un-checked invariant that the note list is in ascending order.+data Phrase t =+  Phrase { phrase_notes :: [Note t], phrase_length :: Length }+  deriving (Eq, Ord, Show)++phrase_values :: Phrase t -> [t]+phrase_values = map note_value . phrase_notes++phrase_set_length :: Phrase t -> Length -> Phrase t+phrase_set_length (Phrase n _) l = Phrase n l++phrase_degree :: Phrase t -> Int+phrase_degree (Phrase n _) = length n++phrase_start_time :: Phrase t -> Time+phrase_start_time (Phrase n _) =+  case n of+    [] -> 0+    n1 : _ -> note_start_time n1++phrase_end_time :: Phrase t -> Time+phrase_end_time (Phrase n _) =+  case n of+    [] -> 0+    _ -> note_start_time (last n)++phrase_duration :: Phrase t -> Duration+phrase_duration p = phrase_end_time p - phrase_start_time p++phrase_maximum :: Ord t => Phrase t -> Note t+phrase_maximum (Phrase n _) = maximum n++phrase_minimum :: Ord t => Phrase t -> Note t+phrase_minimum (Phrase n _) = minimum n++-- | Keykit sets the length to the duration, i.e. ('c,e,g'%2).length is 192.+phrase_at :: Phrase t -> Int -> Phrase t+phrase_at (Phrase n _) k =+  let nt = n !! (k - 1)+  in Phrase [nt] (note_start_time nt + note_duration nt)++phrase_time_at :: Phrase t -> Int -> Time+phrase_time_at (Phrase n _) k = note_start_time (n !! (k - 1))++phrase_clear_at :: Phrase t -> Int -> Phrase t+phrase_clear_at (Phrase n l) k =+  let remove_ix ix list = let (p,q) = splitAt ix list in p ++ tail q+  in Phrase (remove_ix (k - 1) n) l++phrase_at_put :: Ord t => Phrase t -> Int -> Phrase t -> Phrase t+phrase_at_put (Phrase n1 l1) k (Phrase n2 _) =+  let nt = n1 !! (k - 1)+      remove_ix ix list = let (p,q) = splitAt ix list in p ++ tail q+  in Phrase (O.merge (remove_ix (k - 1) n1) (map (note_shift_time (note_start_time nt)) n2)) l1++phrase_is_empty :: Phrase t -> Bool+phrase_is_empty (Phrase n _) = null n++-- | KeyKits p+q+phrase_append :: Ord t => Phrase t -> Phrase t -> Phrase t+phrase_append (Phrase n1 l1) (Phrase n2 l2) = Phrase (O.merge n1 (map (note_shift_time l1) n2)) (l1 + l2)++phrase_append_list :: Ord t => [Phrase t] -> Phrase t+phrase_append_list = foldl1' phrase_append++-- | KeyKits p|q+phrase_merge :: Ord t => Phrase t -> Phrase t -> Phrase t+phrase_merge (Phrase n1 l1) (Phrase n2 l2) = Phrase (O.merge n1 n2) (max l1 l2)++phrase_merge_list :: Ord t => [Phrase t] -> Phrase t+phrase_merge_list p =+  let l = maximum (map phrase_length p)+      n = sort (concatMap phrase_notes p)+  in Phrase n l++phrase_select :: Phrase t -> (Note t -> Bool) -> Phrase t+phrase_select (Phrase n l) f = Phrase (filter f n) l++phrase_partition :: Phrase t -> (Note t -> Bool) -> (Phrase t, Phrase t)+phrase_partition (Phrase n l) f =+  let (n1, n2) = partition f n+  in (Phrase n1 l, Phrase n2 l)++phrase_select_region :: Phrase t -> (Time, Time) -> Phrase t+phrase_select_region p r = phrase_select p (note_is_start_in_region r)++phrase_clear_region :: Phrase t -> (Time, Time) -> Phrase t+phrase_clear_region p r = phrase_select p (not . note_is_start_in_region r)++phrase_select_indices :: Phrase t -> (Int, Int) -> Phrase t+phrase_select_indices (Phrase n l) (i, j) = Phrase (take (j - i + 1) (drop (i - 1) n)) l++phrase_clear_indices :: Phrase t -> (Int, Int) -> Phrase t+phrase_clear_indices (Phrase n l) (i, j) = Phrase (take (i - 1) n ++ drop j n) l++phrase_extract_region :: Phrase t -> (Time, Time) -> Phrase t+phrase_extract_region p (t1, t2) =+  let p' = phrase_select_region p (t1, t2)+  in phrase_set_length (phrase_shift p' (0 - t1)) (t2 - t1)++phrase_delete_region :: Ord t => Phrase t -> (Time, Time) -> Phrase t+phrase_delete_region p (t1, t2) =+  phrase_append+  (phrase_extract_region p (0, t1))+  (phrase_extract_region p (t2, phrase_length p))++phrase_separate :: Phrase t -> Time -> (Phrase t, Phrase t)+phrase_separate p t =+  let (p1, p2) = phrase_partition p (note_is_start_in_region (0, t))+      p1' = phrase_set_length p1 t+      p2' = phrase_set_length (phrase_shift p2 (0 - t)) (phrase_length p - t)+  in (p1', p2')++phrase_reverse :: Phrase t -> Phrase t+phrase_reverse (Phrase n l) =+  let f (Note t d e) = Note (l - t - d) d e+  in Phrase (reverse (map f n)) l++phrase_reorder :: Phrase t -> [Int] -> Phrase t+phrase_reorder (Phrase n l) p =+  let f (Note t d _) i = Note t d (note_value (n !! (i - 1)))+  in Phrase (zipWith f n p) l++phrase_truncate :: Phrase t -> Phrase t+phrase_truncate p = phrase_set_length p (phrase_end_time p)++phrase_trim :: Phrase t -> Phrase t+phrase_trim p =+  let t = phrase_start_time p+  in phrase_truncate (phrase_shift p (0 - t))++-- * Functor++note_map :: (t -> u) -> Note t -> Note u+note_map f (Note t d e) = Note t d (f e)++phrase_value_map :: (t -> u) -> Phrase t -> Phrase u+phrase_value_map f (Phrase n l) = Phrase (map (note_map f) n) l++phrase_note_map :: (Note t -> Note u) -> Phrase t -> Phrase u+phrase_note_map f (Phrase n l) = Phrase (map f n) l++phrase_phrase_map :: Ord u => (Phrase t -> Phrase u) -> Phrase t -> Phrase u+phrase_phrase_map f (Phrase n l) =+  let g (Note t d e) = f (Phrase [Note t d e] (t + d))+  in Phrase (sort (concatMap phrase_notes (map g n))) l++phrase_map :: Ord u => (Note t -> Phrase u) -> Phrase t -> Phrase u+phrase_map f (Phrase n l) = Phrase (sort (concatMap phrase_notes (map f n))) l++phrase_shift :: Phrase t -> Time -> Phrase t+phrase_shift p t = phrase_note_map (note_shift_time t) p++phrase_scale_duration :: Phrase t -> Time -> Phrase t+phrase_scale_duration p m = phrase_note_map (note_scale_duration m) p++phrase_scale_duration_and_time :: Phrase t -> Time -> Phrase t+phrase_scale_duration_and_time p m = phrase_note_map (note_scale_duration_and_time m) p++phrase_scale_to_duration :: Phrase t -> Duration -> Phrase t+phrase_scale_to_duration p d = phrase_scale_duration_and_time p (d / phrase_length p)++phrase_scale_to_region :: Phrase t -> (Time, Duration) -> Phrase t+phrase_scale_to_region p (t1, t2) = phrase_shift (phrase_scale_to_duration p (t2 - t1)) t1++-- * Seq++phrase_to_wseq :: Phrase t -> Seq.Wseq Time t+phrase_to_wseq (Phrase n _) =+  let f (Note tm dur e) = ((tm, dur), e)+  in map f n++useq_to_phrase :: Seq.Useq Time t -> Phrase t+useq_to_phrase = dseq_to_phrase . Seq.useq_to_dseq++dseq_to_phrase :: Seq.Dseq Time t -> Phrase t+dseq_to_phrase = wseq_to_phrase . Seq.dseq_to_wseq 0++wseq_to_phrase :: Seq.Wseq Time t -> Phrase t+wseq_to_phrase sq =+  let f ((t, d), e) = Note t d e+  in Phrase (map f sq) (Seq.wseq_dur sq)
+ Music/Theory/Time/KeyKit/Basic.hs view
@@ -0,0 +1,52 @@+-- | Translations of some functions from <https://github.com/nosuchtim/keykit/blob/master/lib/basic1.k>+module Music.Theory.Time.KeyKit.Basic where++import Data.List {- base -}++import qualified Music.Theory.List as List {- hmt-base -}++import Music.Theory.Time.KeyKit {- hmt -}++{- | Returns an arpeggiated version of the phrase.+One way of describing desc it is that all the notes have been separated and then put back together, back-to-back.++> phrase_arpeggio (wseq_to_phrase (zip (repeat (0,1)) [60, 64, 67]))+-}+phrase_arpeggio :: Phrase t -> Phrase t+phrase_arpeggio (Phrase n l) =+  case n of+    [] -> Phrase n l+    n1 : _ ->+      let t_seq = scanl (+) (note_start_time n1) (map note_duration n)+          n' = zipWith (\t (Note _ d e) -> Note t d e) t_seq n+          l' = note_end_time (last n)+      in Phrase n' l'++-- | Return phrase ph echoed num times, with rtime delay between each echo.+phrase_echo :: Ord t => Phrase t -> Int -> Time -> Phrase t+phrase_echo p n t = phrase_merge_list (map (\i -> phrase_shift p (fromIntegral i * t)) [0 .. n - 1])++{- | Convert a phrase to be in step time, ie. all notes with the same spacing and duration.+Overlapped notes (no matter how small the overlap) are played at the same time.++> phrase_step (wseq_to_phrase [((0, 1), 60), ((5, 2), 64), ((23, 3), 67)]) 1+-}+phrase_step :: Phrase t -> Duration -> Phrase t+phrase_step (Phrase n _) d =+  let g = groupBy (\i j -> note_start_time i == note_start_time j) n+      f l t = map (\(Note _ _ e) -> Note t d e) l+      n' = concat (zipWith f g [0, d ..])+  in Phrase n' (note_end_time (last n'))++{- | This function takes a phrase, splits in in 2 halves (along time) and shuffles the result+(ie. first a note from the first half, then a note from the second half, etc.).+The timing of the original phrase is applied to the result.++> phrase_to_wseq (phrase_shuffle (useq_to_phrase (1,[1..9])))+-}+phrase_shuffle :: Phrase t -> Phrase t+phrase_shuffle (Phrase n l) =+  let (lhs, rhs) = List.split_into_halves (map note_value n)+      f (Note t d _) e = Note t d e+      n' = zipWith f n (concat (transpose [lhs, rhs]))+  in Phrase n' l
+ Music/Theory/Time/KeyKit/Parser.hs view
@@ -0,0 +1,249 @@+-- | KeyKit phrase literal (constant) parser and printer.+module Music.Theory.Time.KeyKit.Parser where++import Data.Maybe {- base -}+import Text.Printf {- base -}++import qualified Text.Parsec as P {- parsec -}+import qualified Text.Parsec.String as String {- parsec -}++-- * Parser setup++-- | A 'Char' parser with no user state.+type P a = String.GenParser Char () a++-- | Run parser and return either an error string or an answer.+kk_parse_either :: P t -> String -> Either String t+kk_parse_either p = either (\m -> Left ("kk_parse: " ++ show m)) Right . P.parse p ""++-- | Run parser and report any error.  Does not delete leading spaces.+kk_parse :: P t -> String -> t+kk_parse p = either (\e -> error e) id . kk_parse_either p++-- | Run p then q, returning result of p.+(>>~) :: Monad m => m t -> m u -> m t+p >>~ q = p >>= \x -> q >> return x++kk_lexeme :: P t -> P t+kk_lexeme p = p >>~ P.many P.space++kk_uint :: P Int+kk_uint = do+  digits <- P.many1 P.digit+  return (read digits)++kk_int :: P Int+kk_int = do+  sign <- P.optionMaybe (P.char '-')+  unsigned <- kk_uint+  return (maybe unsigned (const (negate unsigned)) sign)++-- * Note elements parsers++kk_note_name_p :: P Char+kk_note_name_p = P.oneOf "abcdefg"++kk_midi_note_p :: P Int+kk_midi_note_p = P.char 'p' >> kk_uint++kk_rest_p :: P Char+kk_rest_p = P.char 'r'++kk_accidental_p :: P Char+kk_accidental_p = P.oneOf "+-"++kk_char_to_note_number :: Char -> Int+kk_char_to_note_number c = fromMaybe (error "kk_char_to_note_number?") (lookup c (zip "cdefgab" [0, 2, 4, 5, 7, 9, 11]))++kk_char_to_alteration :: Char -> Int+kk_char_to_alteration c = fromMaybe (error "kk_char_to_alteration?") (lookup c (zip "+-" [1, -1]))++-- > map kk_note_number_to_name [0 .. 11]+kk_note_number_to_name :: Int -> String+kk_note_number_to_name k = fromMaybe (error "kk_note_number_to_name?") (lookup k (zip [0..] (words "c c+ d e- e f f+ g a- a b- b")))++kk_named_note_number_p :: P Int+kk_named_note_number_p = do+  nm <- kk_note_name_p+  ac <- P.optionMaybe kk_accidental_p+  return (kk_char_to_note_number nm + maybe 0 kk_char_to_alteration ac)++kk_note_number_p :: P Int+kk_note_number_p = kk_named_note_number_p P.<|> kk_midi_note_p++-- | The octave key can be elided, ordinarily directly after the note name, ie. c2.+kk_modifier_p :: P (Char, Int)+kk_modifier_p = do+  c <- P.optionMaybe (P.oneOf "ovdct")+  n <- kk_int+  return (fromMaybe 'o' c, n)++kk_modifiers_p :: P [(Char, Int)]+kk_modifiers_p = P.many kk_modifier_p++-- * Contextual note++{- | A note where all fields are optional.+If the note number is absent it indicates a rest.+All other fields infer values from the phrase context.+-}+data Kk_Contextual_Note =+  Kk_Contextual_Note+  {kk_contextual_note_number :: Maybe Int+  ,kk_contextual_note_octave :: Maybe Int+  ,kk_contextual_note_volume :: Maybe Int+  ,kk_contextual_note_duration :: Maybe Int+  ,kk_contextual_note_channel :: Maybe Int+  ,kk_contextual_note_time :: Maybe Int}+  deriving (Eq, Ord, Show)++kk_empty_contextual_note :: Kk_Contextual_Note+kk_empty_contextual_note = Kk_Contextual_Note Nothing Nothing Nothing Nothing Nothing Nothing++kk_empty_contextual_rest :: Int -> Kk_Contextual_Note+kk_empty_contextual_rest n = kk_empty_contextual_note {kk_contextual_note_duration = Just n}++{- | If t is set and is at the end time of the previous note print a preceding comma, else print t annotation.++> c = kk_empty_contextual_note {kk_contextual_note_number = Just 0, kk_contextual_time = Just 96}+> map (\t -> kk_contextual_note_pp (t, c)) [0, 96] == ["ct96",", c"]+-}+kk_contextual_note_pp :: (Int, Kk_Contextual_Note) -> String+kk_contextual_note_pp (t', Kk_Contextual_Note n o v d c t) =+  let f i j = maybe "" ((if i == 'o' then id else (i :)) . show) j+      (pre, t'') = if t == Just t' then (", ","") else ("", f 't' t)+  in case n of+          Nothing -> concat [pre, "r", f 'd' d, t'']+          Just k -> concat [pre, kk_note_number_to_name k, f 'o' o, f 'v' v, f 'd' d, f 'c' c, t'']++{- | If the note number is given as p60, then derive octave of and set it, ignoring any modifier.+Note that in KeyKit c3 is p60 or middle c.+-}+kk_contextual_note_p :: P Kk_Contextual_Note+kk_contextual_note_p = do+  n <- fmap Just kk_note_number_p P.<|> (kk_rest_p >> return Nothing)+  m <- kk_modifiers_p+  _ <- P.many P.space+  let get c = lookup c m+      (n', o) =+        case n of+          Just n'' ->+            if n'' > 11+            then+              let (o', n''') = n'' `divMod` 12+              in (Just n''', Just (o' - 2))+            else (n, get 'o')+          Nothing -> (Nothing, Nothing)+  return (Kk_Contextual_Note n' o (get 'v') (get 'd') (get 'c') (get 't'))++kk_contextual_note_is_rest :: Kk_Contextual_Note -> Bool+kk_contextual_note_is_rest = isNothing . kk_contextual_note_number++kk_comma_p :: P Char+kk_comma_p = kk_lexeme (P.char ',')++-- | A contextual note and an is_parallel? indicator.+kk_contextual_phrase_element_p :: P (Kk_Contextual_Note, Bool)+kk_contextual_phrase_element_p = do+  n <- kk_contextual_note_p+  c <- P.optionMaybe kk_comma_p+  return (n, isNothing c)++kk_contextual_phrase_p :: P [(Kk_Contextual_Note, Bool)]+kk_contextual_phrase_p = P.many kk_contextual_phrase_element_p++-- * Note++-- | A note with all fields required.+data Kk_Note =+  Kk_Note+  {kk_note_number :: Int+  ,kk_note_octave :: Int+  ,kk_note_volume :: Int+  ,kk_note_duration :: Int+  ,kk_note_channel :: Int+  ,kk_note_time :: Int}+  deriving (Eq, Ord, Show)++kk_default_note :: Kk_Note+kk_default_note = Kk_Note 60 3 63 96 1 0++kk_note_to_initial_contextual_note :: Kk_Note -> Kk_Contextual_Note+kk_note_to_initial_contextual_note (Kk_Note n o v d c t) =+  let f i j = if i == j then Nothing else Just i+  in Kk_Contextual_Note (Just n) (f o 3) (f v 63) (f d 96) (f c 1) (f t 0)++kk_note_to_contextual_note :: Kk_Note -> Kk_Note -> (Int, Kk_Contextual_Note)+kk_note_to_contextual_note (Kk_Note _ o' v' d' c' t') (Kk_Note n o v d c t) =+  let f i j = if i == j then Nothing else Just i+  in (t' + d', Kk_Contextual_Note (Just n) (f o o') (f v v') (f d d') (f c c') (f t t'))++-- | Elide octave modifier character.+kk_note_pp :: Kk_Note -> String+kk_note_pp (Kk_Note n o v d c t) = printf "%s%dv%dd%dc%dt%d" (kk_note_number_to_name n) o v d c t++kk_decontextualise_note :: Kk_Note -> Bool -> Kk_Contextual_Note -> Either Kk_Note Int+kk_decontextualise_note (Kk_Note _ o v d c t) is_par (Kk_Contextual_Note k' o' v' d' c' t') =+  let t'' = fromMaybe (if is_par then t else t + d) t'+  in case k' of+    Just k'' -> Left (Kk_Note k'' (fromMaybe o o') (fromMaybe v v') (fromMaybe d d') (fromMaybe c c') t'')+    Nothing -> Right t''++data Kk_Phrase = Kk_Phrase { kk_phrase_notes :: [Kk_Note], kk_phrase_length :: Int } deriving (Eq, Show)++-- | This should, but does not, append a trailing rest as required.+kk_phrase_pp :: Kk_Phrase -> String+kk_phrase_pp (Kk_Phrase n _) = unwords (map kk_note_pp n)++-- | Rests are elided, their duration is accounted for in the time of the following notetaken into account.+kk_decontextualise_phrase :: [(Kk_Contextual_Note, Bool)] -> Kk_Phrase+kk_decontextualise_phrase =+  let f r c p l =+        case l of+          [] -> Kk_Phrase (reverse r) (kk_note_time c + kk_note_duration c)+          (n,p'):l' ->+            case kk_decontextualise_note c p n of+              Left c' -> f (c' : r) c' p' l'+              Right t' -> f r (c {kk_note_time = t'}) p' l'+  in f [] kk_default_note True++-- | In addition to contextual note give end time of previous note, to allow for sequence (comma) notation.+kk_recontextualise_phrase :: Kk_Phrase -> [(Int, Kk_Contextual_Note)]+kk_recontextualise_phrase p =+  let f n0 n =+        case n of+          [] -> []+          n1 : n' -> kk_note_to_contextual_note n0 n1 : f n1 n'+  in case p of+    Kk_Phrase [] l -> [(0, kk_empty_contextual_rest l)]+    Kk_Phrase (n1 : n') _ ->+      let c1 = kk_note_to_initial_contextual_note n1+      in (0, c1) : f n1 n'++{- | Read KeyKit phrase constant.++> let rw = (\p -> (kk_phrase_pp p, kk_phrase_length p)) . kk_phrase_read+> rw "c" == ("c3v63d96c1t0",96)+> rw "c, r" == ("c3v63d96c1t0",192)+> rw "c, r, c3, r, p60" == ("c3v63d96c1t0 c3v63d96c1t192 c3v63d96c1t384",480)+> rw "c, e, g" == ("c3v63d96c1t0 e3v63d96c1t96 g3v63d96c1t192",288)+> rw "c2" == rw "co2"+-}+kk_phrase_read :: String -> Kk_Phrase+kk_phrase_read = kk_decontextualise_phrase . kk_parse kk_contextual_phrase_p++{- | Re-contextualise and print phrase.++> rw = kk_phrase_print . kk_phrase_read+> rw_id i = rw i == i+> rw_id "c"+> rw_id "c e g"+> rw_id "c , e , g"+> rw_id "c e g , c f a , c e g , c e- g"+> rw_id "c , e , g c4t384"+> rw "c, r, c3, r, p60" == "c ct192 ct384"+> rw "c , e , g c4t288" == "c , e , g , c4"+> rw "c r" == "c" -- ?+-}+kk_phrase_print :: Kk_Phrase -> String+kk_phrase_print = unwords . map kk_contextual_note_pp . kk_recontextualise_phrase
− Music/Theory/Time/Notation.hs 
@@ -1,127 +0,0 @@-module Music.Theory.Time.Notation where--import Data.List.Split {- split -}-import Text.Printf {- base -}---- | Fractional seconds.-type FSEC = Double---- | Minutes, seconds as @(min,sec)@-type MinSec n = (n,n)---- | Type specialised.-type MINSEC = (Int,Int)---- | Minutes, seconds, centi-seconds as @(min,sec,csec)@-type MinCsec n = (n,n,n)---- | Type specialised.-type MINCSEC = (Int,Int,Int)---- | 'divMod' by @60@.------ > sec_to_minsec 123 == (2,3)-sec_to_minsec :: Integral n => n -> MinSec n-sec_to_minsec = flip divMod 60---- | Inverse of 'sec_minsec'.------ > minsec_to_sec (2,3) == 123-minsec_to_sec :: Num n => MinSec n -> n-minsec_to_sec (m,s) = m * 60 + s--minsec_binop :: Integral t => (t -> t -> t) -> MinSec t -> MinSec t -> MinSec t-minsec_binop f p q = sec_to_minsec (f (minsec_to_sec p) (minsec_to_sec q))---- | 'minsec_binop' '-', assumes /q/ precedes /p/.------ > minsec_sub (2,35) (1,59) == (0,36)-minsec_sub :: Integral n => MinSec n -> MinSec n -> MinSec n-minsec_sub = minsec_binop (-)---- | 'minsec_binop' 'subtract', assumes /p/ precedes /q/.------ > minsec_diff (1,59) (2,35) == (0,36)-minsec_diff :: Integral n => MinSec n -> MinSec n -> MinSec n-minsec_diff = minsec_binop subtract---- | 'minsec_binop' '+'.------ > minsec_add (1,59) (2,35) == (4,34)-minsec_add :: Integral n => MinSec n -> MinSec n -> MinSec n-minsec_add = minsec_binop (+)---- | 'foldl' of 'minsec_add'------ > minsec_sum [(1,59),(2,35),(4,34)] == (9,08)-minsec_sum :: Integral n => [MinSec n] -> MinSec n-minsec_sum = foldl minsec_add (0,0)---- | Fractional seconds to @(min,sec)@.------ > map fsec_to_minsec [59.49,60,60.51] == [(0,59),(1,0),(1,1)]-fsec_to_minsec :: FSEC -> MINSEC-fsec_to_minsec = sec_to_minsec . round---- | 'MINSEC' pretty printer.------ > map (minsec_pp . fsec_to_minsec) [59,61] == ["00:59","01:01"]-minsec_pp :: MINSEC -> String-minsec_pp (m,s) = printf "%02d:%02d" m s---- * 'MinSec' parser.-minsec_parse :: (Num n,Read n) => String -> MinSec n-minsec_parse x =-    case splitOn ":" x of-      [m,s] -> (read m,read s)-      _ -> error "parse_minsec"---- | Fractional seconds to @(min,sec,csec)@, csec value is 'round'ed.------ > map fsec_to_mincsec [1,1.5,4/3] == [(0,1,0),(0,1,50),(0,1,33)]-fsec_to_mincsec :: FSEC -> MINCSEC-fsec_to_mincsec tm =-    let tm' = floor tm-        (m,s) = sec_to_minsec tm'-        cs = round ((tm - fromIntegral tm') * 100)-    in (m,s,cs)---- | Inverse of 'fsec_mincsec'.-mincsec_to_fsec :: Real n => MinCsec n -> FSEC-mincsec_to_fsec (m,s,cs) = realToFrac m * 60 + realToFrac s + (realToFrac cs / 100)---- > map (mincsec_to_csec . fsec_to_mincsec) [1,6+2/3,123.45] == [100,667,12345]-mincsec_to_csec :: Num n => MinCsec n -> n-mincsec_to_csec (m,s,cs) = m * 60 * 100 + s * 100 + cs---- | Centi-seconds to 'MinCsec'.------ > map csec_to_mincsec [123,12345] == [(0,1,23),(2,3,45)]-csec_to_mincsec :: Integral n => n -> MinCsec n-csec_to_mincsec csec =-    let (m,cs) = csec `divMod` 6000-        (s,cs') = cs `divMod` 100-    in (m,s,cs')---- | 'MINCSEC' pretty printer, concise mode omits centiseconds when zero.------ > map (mincsec_pp_opt True . fsec_to_mincsec) [1,60.5] == ["00:01","01:00.50"]-mincsec_pp_opt :: Bool -> MINCSEC -> String-mincsec_pp_opt concise (m,s,cs) =-  if concise && cs == 0-  then printf "%02d:%02d" m s-  else printf "%02d:%02d.%02d" m s cs---- | 'MINCSEC' pretty printer.------ > let r = ["00:01.00","00:06.67","02:03.45"]--- > map (mincsec_pp . fsec_to_mincsec) [1,6+2/3,123.45] == r-mincsec_pp :: MINCSEC -> String-mincsec_pp = mincsec_pp_opt False--mincsec_binop :: Integral t => (t -> t -> t) -> MinCsec t -> MinCsec t -> MinCsec t-mincsec_binop f p q = csec_to_mincsec (f (mincsec_to_csec p) (mincsec_to_csec q))---- | Given printer, pretty print time span.-span_pp :: (t -> String) -> (t,t) -> String-span_pp f (t1,t2) = concat [f t1," - ",f t2]
Music/Theory/Time/Seq.hs view
@@ -1,60 +1,74 @@ -- | Basic temporal sequence functions. module Music.Theory.Time.Seq where +import Data.Bifunctor {- base -} import Data.Function {- base -} import Data.List {- base -}-import qualified Data.List.Ordered as O {- data-ordlist -}-import qualified Data.Map as M {- containers -} import Data.Maybe {- base -} import Data.Ratio {- base -} import Safe {- safe -} -import Music.Theory.Function {- hmt -}-import qualified Music.Theory.List as T {- hmt -}-import qualified Music.Theory.Math as T {- hmt -}-import qualified Music.Theory.Ord as T {- hmt -}-import qualified Music.Theory.Tuple as T {- hmt -}+import qualified Data.List.Ordered as O {- data-ordlist -}+import qualified Data.Map as Map {- containers -} +import qualified Music.Theory.List as T {- hmt-base -}+import qualified Music.Theory.Math as T {- hmt-base -}+import qualified Music.Theory.Ord as T {- hmt-base -}+import qualified Music.Theory.Tuple as T {- hmt-base -}+ -- * Types  -- | Sequence of elements with uniform duration. type Useq t a = (t,[a]) --- | Duration sequence.  The duration is the /forward/ duration of the--- value, if it has other durations they must be encoded at /a/.+-- | Duration sequence.+-- /t/ indicates the /forward/ duration of the value, ie. the interval to the next value.+-- If there are other durations they must be encoded at /a/.+-- If the sequence does not begin at time zero there must be an /empty/ value for /a/. type Dseq t a = [(t,a)] --- | Inter-offset sequence.  The duration is the interval /before/ the--- value.  To indicate the duration of the final value /a/ must have--- a /nil/ (end of sequence) value.+-- | Inter-offset sequence.+-- /t/ is the interval /before/ the value.+-- Duration can be encoded at /a/, or if implicit /a/ must include an end of sequence value. type Iseq t a = [(t,a)] --- | Pattern sequence.  The duration is a triple of /logical/,--- /sounding/ and /forward/ durations.+-- | Pattern sequence.+-- The duration is a triple of /logical/, /sounding/ and /forward/ durations.+-- These indicate the time the value conceptually takes, the time it actually takes, and the time to the next event.+-- If the sequence does not begin at time zero there must be an /empty/ value for /a/. type Pseq t a = [((t,t,t),a)] --- | Time-point sequence.  To express holes /a/ must have an /empty/--- value.  To indicate the duration of the final value /a/ must have--- a /nil/ (end of sequence) value.+-- | Time-point sequence.+-- /t/ is the start time of the value.+-- To express holes /a/ must have an /empty/ value.+-- Duration can be encoded at /a/, or if implicit /a/ must include an end of sequence value. type Tseq t a = [(t,a)] --- | Window sequence.  The temporal field is (/time/,/duration/).--- Holes exist where @t(n) + d(n)@ '<' @t(n+1)@.  Overlaps exist where--- the same relation is '>'.+-- | Window sequence.+-- /t/ is a duple of /start-time/ and /duration/.+-- Holes exist where /start-time(n) + duration(n) < start-time(n + 1)/.+-- Overlaps exist where the same relation is '>'. type Wseq t a = [((t,t),a)] +-- | Event sequence.+-- /t/ is a triple of /start-time/, /duration/ and /length/.+-- /length/ isn't necessarily the time to the next event, though ordinarily it should not be greater than that interval.+type Eseq t a = [((t,t,t),a)]+ -- * Zip +-- | Construct 'Pseq'. pseq_zip :: [t] -> [t] -> [t] -> [a] -> Pseq t a-pseq_zip l o f a = (zip (zip3 l o f) a)+pseq_zip l o f = zip (zip3 l o f) +-- | Construct 'Wseq'. wseq_zip :: [t] -> [t] -> [a] -> Wseq t a-wseq_zip t d a = (zip (zip t d) a)+wseq_zip t d = zip (zip t d)  -- * Time span --- | Given functions for deriving start and end times calculate time--- span of sequence.+-- | Given functions for deriving start and end times calculate time span of sequence.+--   Requires sequence be finite. -- -- > seq_tspan id id [] == (0,0) -- > seq_tspan id id (zip [0..9] ['a'..]) == (0,9)@@ -63,9 +77,11 @@     (maybe 0 (st . fst) (headMay sq)     ,maybe 0 (et . fst) (lastMay sq)) +-- | 'seq_tspan' for 'Tseq'. tseq_tspan :: Num t => Tseq t a -> (t,t) tseq_tspan = seq_tspan id id +-- | 'seq_tspan' for 'Wseq'. wseq_tspan :: Num t => Wseq t a -> (t,t) wseq_tspan = seq_tspan fst (uncurry (+)) @@ -85,22 +101,25 @@  -- * Duration +-- | Sum durations at 'Dseq', result is the end time of the last element. dseq_dur :: Num t => Dseq t a -> t dseq_dur = sum . map fst +-- | Sum durations at 'Iseq', result is the start time of the last element. iseq_dur :: Num t => Iseq t a -> t iseq_dur = sum . map fst +-- | Sum durations at 'Pseq', result is the end time of the last element. pseq_dur :: Num t => Pseq t a -> t pseq_dur = sum . map (T.t3_third . fst) --- | The interval of 'tseq_tspan'.+-- | The interval of 'tseq_tspan', ie. from the start of the first element to the start of the last. -- -- > tseq_dur (zip [0..] "abcde|") == 5 tseq_dur :: Num t => Tseq t a -> t tseq_dur = uncurry subtract . tseq_tspan --- | The interval of 'wseq_tspan'.+-- | The interval of 'wseq_tspan', ie. from the start of the first element to the end of the last. -- -- > wseq_dur (zip (zip [0..] (repeat 2)) "abcde") == 6 wseq_dur :: Num t => Wseq t a -> t@@ -108,8 +127,7 @@  -- * Window --- | Prefix of sequence where the start time precedes or is at the--- indicate time.+-- | Prefix of sequence where the start time precedes or is at the indicated time. wseq_until :: Ord t => t -> Wseq t a -> Wseq t a wseq_until tm = takeWhile (\((t0,_),_) -> t0 <= tm) @@ -118,7 +136,7 @@ -- edges, ie. [t0,t1].  Halts processing at end of window. -- -- > let r = [((5,1),'e'),((6,1),'f'),((7,1),'g'),((8,1),'h')]--- > in wseq_twindow (5,9) (zip (zip [1..] (repeat 1)) ['a'..]) == r+-- > wseq_twindow (5,9) (zip (zip [1..] (repeat 1)) ['a'..]) == r -- -- > wseq_twindow (1,2) [((1,1),'a'),((1,2),'b')] == [((1,1),'a')] wseq_twindow :: (Num t, Ord t) => (t,t) -> Wseq t a -> Wseq t a@@ -131,7 +149,7 @@ -- of window. -- -- > let sq = [((1,1),'a'),((1,2),'b')]--- > in map (wseq_at sq) [1,2] == [sq,[((1,2),'b')]]+-- > map (wseq_at sq) [1,2] == [sq,[((1,2),'b')]] -- -- > wseq_at (zip (zip [1..] (repeat 1)) ['a'..]) 3 == [((3,1),'c')] wseq_at :: (Num t,Ord t) => Wseq t a -> t -> Wseq t a@@ -145,7 +163,7 @@ -- of window. -- -- > let sq = [((0,2),'a'),((0,4),'b'),((2,4),'c')]--- > in wseq_at_window sq (1,3) == sq+-- > wseq_at_window sq (1,3) == sq -- -- > wseq_at_window (zip (zip [1..] (repeat 1)) ['a'..]) (3,4) == [((3,1),'c'),((4,1),'d')] wseq_at_window :: (Num t, Ord t) => Wseq t a -> (t,t) -> Wseq t a@@ -156,12 +174,15 @@  -- * Append +-- | Type specialised '++' dseq_append :: Dseq t a -> Dseq t a -> Dseq t a dseq_append = (++) +-- | Type specialised '++' iseq_append :: Iseq t a -> Iseq t a -> Iseq t a iseq_append = (++) +-- | Type specialised '++' pseq_append :: Pseq t a -> Pseq t a -> Pseq t a pseq_append = (++) @@ -206,6 +227,10 @@ wseq_merge_set :: Ord t => [Wseq t a] -> Wseq t a wseq_merge_set = T.merge_set_by w_compare +-- | Merge considering only start times.+eseq_merge :: Ord t => Eseq t a -> Eseq t a -> Eseq t a+eseq_merge = O.mergeBy (compare `on` (T.t3_fst . fst))+ -- * Lookup  -- | Locate nodes to the left and right of indicated time.@@ -237,13 +262,17 @@  -- * Lseq -data Interpolation_T = None | Linear-                     deriving (Eq,Enum,Show)+-- | Iterpolation type enumeration.+data Interpolation_T =+  None | Linear+  deriving (Eq,Enum,Show)  -- | Variant of 'Tseq' where nodes have an 'Intepolation_T' value. type Lseq t a = Tseq (t,Interpolation_T) a --- | Linear interpolation.+{- | Linear interpolation.+     The Real constraint on t is to allow conversion from t to e (realToFrac).+-} lerp :: (Fractional t,Real t,Fractional e) => (t,e) -> (t,e) -> t -> e lerp (t0,e0) (t1,e1) t =     let n = t1 - t0@@ -272,41 +301,45 @@  -- * Map, Filter, Find -seq_tmap :: (t -> t') -> [(t,a)] -> [(t',a)]-seq_tmap f = map (\(p,q) -> (f p,q))+-- | 'map' over time (/t/) data.+seq_tmap :: (t1 -> t2) -> [(t1,a)] -> [(t2,a)]+seq_tmap f = map (first f) -seq_map :: (b -> c) -> [(a,b)] -> [(a,c)]-seq_map f = map (\(p,q) -> (p,f q))+-- | 'map' over element (/e/) data.+seq_map :: (e1 -> e2) -> [(t,e1)] -> [(t,e2)]+seq_map f = map (second f) --- | Map /t/ and /e/ simultaneously.-seq_bimap :: (t -> t') -> (e -> e') -> [(t,e)] -> [(t',e')]-seq_bimap f g = map (\(p,q) -> (f p,g q))+-- | 'map' /t/ and /e/ simultaneously.+--+-- > seq_bimap negate succ (zip [1..5] [0..4]) == [(-1,1),(-2,2),(-3,3),(-4,4),(-5,5)]+seq_bimap :: (t1 -> t2) -> (e1 -> e2) -> [(t1,e1)] -> [(t2,e2)]+seq_bimap f = map . bimap f +-- | 'filter' over time (/t/) data. seq_tfilter :: (t -> Bool) -> [(t,a)] -> [(t,a)] seq_tfilter f = filter (f . fst) +-- | 'filter' over element (/e/) data. seq_filter :: (b -> Bool) -> [(a,b)] -> [(a,b)] seq_filter f = filter (f . snd) -seq_find :: (a -> Bool) -> [(t,a)] -> Maybe (t,a)-seq_find f = let f' (_,a) = f a in find f'+-- | 'find' over element (/e/) data.+seq_find :: (e -> Bool) -> [(t,e)] -> Maybe (t,e)+seq_find f = find (f . snd)  -- * Maybe  -- | 'mapMaybe' variant. seq_map_maybe :: (p -> Maybe q) -> [(t,p)] -> [(t,q)] seq_map_maybe f =-    let g (t,e) = maybe Nothing (\e' -> Just (t,e')) (f e)+    let g (t,e) = fmap (\e' -> (t,e')) (f e)     in mapMaybe g  -- | Variant of 'catMaybes'. seq_cat_maybes :: [(t,Maybe q)] -> [(t,q)] seq_cat_maybes = seq_map_maybe id --- | If value is unchanged, according to /f/, replace with 'Nothing'.------ > let r = [(1,'s'),(2,'t'),(4,'r'),(6,'i'),(7,'n'),(9,'g')]--- > in seq_cat_maybes (seq_changed_by (==) (zip [1..] "sttrrinng")) == r+-- | If value is unchanged at subsequent entry, according to /f/, replace with 'Nothing'. seq_changed_by :: (a -> a -> Bool) -> [(t,a)] -> [(t,Maybe a)] seq_changed_by f l =     let recur z sq =@@ -320,6 +353,9 @@          (t,e) : l' -> (t,Just e) : recur e l'  -- | 'seq_changed_by' '=='.+--+-- > let r = [(1,'s'),(2,'t'),(4,'r'),(6,'i'),(7,'n'),(9,'g')]+-- > seq_cat_maybes (seq_changed (zip [1..] "sttrrinng")) == r seq_changed :: Eq a => [(t,a)] -> [(t,Maybe a)] seq_changed = seq_changed_by (==) @@ -327,11 +363,11 @@  -- | Apply /f/ at time points of 'Wseq'. wseq_tmap_st :: (t -> t) -> Wseq t a -> Wseq t a-wseq_tmap_st f = let g (t,d) = (f t,d) in seq_tmap g+wseq_tmap_st f = seq_tmap (first f)  -- | Apply /f/ at durations of elements of 'Wseq'. wseq_tmap_dur :: (t -> t) -> Wseq t a -> Wseq t a-wseq_tmap_dur f = let g (t,d) = (t,f d) in seq_tmap g+wseq_tmap_dur f = seq_tmap (second f)  -- * Partition @@ -339,21 +375,22 @@ -- a sequence into voices. seq_partition :: Ord v => (a -> v) -> [(t,a)] -> [(v,[(t,a)])] seq_partition voice sq =-    let assign m (t,a) = M.insertWith (++) (voice a) [(t,a)] m+    let assign m (t,a) = Map.insertWith (++) (voice a) [(t,a)] m         from_map = sortOn fst .-                   map (\(v,l) -> (v,reverse l)) .-                   M.toList-    in from_map (foldl assign M.empty sq)+                   map (second reverse) .+                   Map.toList+    in from_map (foldl assign Map.empty sq)  -- | Type specialised 'seq_partition'. ----- > let {p = zip [0,1,3,5] (zip (repeat 0) "abcd")--- >     ;q = zip [2,4,6,7] (zip (repeat 1) "ABCD")--- >     ;sq = tseq_merge p q}--- > in tseq_partition fst sq == [(0,p),(1,q)]+-- > let p = zip [0,1,3,5] (zip (repeat 0) "abcd")+-- > let q = zip [2,4,6,7] (zip (repeat 1) "ABCD")+-- > let sq = tseq_merge p q+-- > tseq_partition fst sq == [(0,p),(1,q)] tseq_partition :: Ord v => (a -> v) -> Tseq t a -> [(v,Tseq t a)] tseq_partition = seq_partition +-- | Type specialised 'seq_partition'. wseq_partition :: Ord v => (a -> v) -> Wseq t a -> [(v,Wseq t a)] wseq_partition = seq_partition @@ -381,16 +418,17 @@ coalesce_m :: Monoid t => (t -> t -> Bool) -> [t] -> [t] coalesce_m dec_f = coalesce_f dec_f mappend --- | Form of 'coalesce_f' where the decision predicate is on the--- /element/, and a join function sums the /times/.------ > let r = [(1,'a'),(2,'b'),(3,'c'),(2,'d'),(1,'e')]--- > in seq_coalesce (==) const (useq_to_dseq (1,"abbcccdde")) == r+-- | Form of 'coalesce_t' where the join predicate is on the /element/ only, the /times/ are summed.+coalesce_t :: Num t => ((t,a) -> (t,a) -> Bool) -> (a -> a -> a) -> [(t,a)] -> [(t,a)]+coalesce_t dec_f jn_f = coalesce_f dec_f (\(t1,a1) (t2,a2) -> (t1 + t2,jn_f a1 a2))++{- | Form of 'coalesce_f' where both the decision and join predicates are on the/element/, the /times/ are summed.++> let r = [(1,'a'),(2,'b'),(3,'c'),(2,'d'),(1,'e')]+> seq_coalesce (==) const (useq_to_dseq (1,"abbcccdde")) == r+-} seq_coalesce :: Num t => (a -> a -> Bool) -> (a -> a -> a) -> [(t,a)] -> [(t,a)]-seq_coalesce dec_f jn_f =-    let dec_f' = dec_f `on` snd-        jn_f' (t1,a1) (t2,a2) = (t1 + t2,jn_f a1 a2)-    in coalesce_f dec_f' jn_f'+seq_coalesce dec_f jn_f = coalesce_t (dec_f `on` snd) jn_f  dseq_coalesce :: Num t => (a -> a -> Bool) -> (a -> a -> a) -> Dseq t a -> Dseq t a dseq_coalesce = seq_coalesce@@ -400,12 +438,12 @@ -- 'dseq_coalesce' where the /join/ function is 'const'.  The -- implementation is simpler and non-recursive. ----- > let {d = useq_to_dseq (1,"abbcccdde")--- >     ;r = dseq_coalesce (==) const d}--- > in dseq_coalesce' (==) d == r+-- > let d = useq_to_dseq (1,"abbcccdde")+-- > let r = dseq_coalesce (==) const d+-- > dseq_coalesce' (==) d == r dseq_coalesce' :: Num t => (a -> a -> Bool) -> Dseq t a -> Dseq t a dseq_coalesce' eq =-    let f l = let (t,e:_) = unzip l in (sum t,e)+    let f l = let (t,e) = unzip l in (sum t,head e)     in map f . groupBy (eq `on` snd)  iseq_coalesce :: Num t => (a -> a -> Bool) -> (a -> a -> a) -> Iseq t a -> Iseq t a@@ -422,6 +460,7 @@ tseq_tcoalesce :: Eq t => (a -> a -> a) -> Tseq t a -> Tseq t a tseq_tcoalesce = seq_tcoalesce (==) +-- | Type specialised 'seq_tcoalesce'. wseq_tcoalesce :: ((t,t) -> (t,t) -> Bool) -> (a -> a -> a) -> Wseq t a -> Wseq t a wseq_tcoalesce = seq_tcoalesce @@ -430,7 +469,7 @@ -- | Post-process 'groupBy' of /cmp/ 'on' 'fst'. -- -- > let r = [(0,"a"),(1,"bc"),(2,"de"),(3,"f")]--- > in group_f (==) (zip [0,1,1,2,2,3] ['a'..]) == r+-- > group_f (==) (zip [0,1,1,2,2,3] ['a'..]) == r group_f :: (Eq t,Num t) => (t -> t -> Bool) -> [(t,a)] -> [(t,[a])] group_f cmp =     let f l = let (t,a) = unzip l@@ -442,7 +481,7 @@ -- | Group values at equal time points. -- -- > let r = [(0,"a"),(1,"bc"),(2,"de"),(3,"f")]--- > in tseq_group (zip [0,1,1,2,2,3] ['a'..]) == r+-- > tseq_group (zip [0,1,1,2,2,3] ['a'..]) == r -- -- > tseq_group [(1,'a'),(1,'b')] == [(1,"ab")] -- > tseq_group [(1,'a'),(2,'b'),(2,'c')] == [(1,"a"),(2,"bc")]@@ -452,16 +491,17 @@ -- | Group values where the inter-offset time is @0@ to the left. -- -- > let r = [(0,"a"),(1,"bcd"),(1,"ef")]--- > in iseq_group (zip [0,1,0,0,1,0] ['a'..]) == r+-- > iseq_group (zip [0,1,0,0,1,0] ['a'..]) == r iseq_group :: (Eq t,Num t) => Iseq t a -> Iseq t [a] iseq_group = group_f (\_ d -> d == 0)  -- * Fill  -- | Set durations so that there are no gaps or overlaps.+--   For entries with the same start time this leads to zero durations. ----- > let r = wseq_zip [0,3,5] [3,2,1] "abc"--- > in wseq_fill_dur (wseq_zip [0,3,5] [2,1,1] "abc") == r+-- > let r = wseq_zip [0,3,3,5] [3,0,2,1] "abcd"+-- > wseq_fill_dur (wseq_zip [0,3,3,5] [2,1,2,1] "abcd") == r wseq_fill_dur :: Num t => Wseq t a -> Wseq t a wseq_fill_dur l =     let f (((t1,_),e),((t2,_),_)) = ((t1,t2-t1),e)@@ -479,6 +519,10 @@         t_f n = T.rational_whole_err (n * fromIntegral m)     in map (dseq_tmap t_f) sq +-- | End-time of sequence (ie. sum of durations).+dseq_end :: Num t => Dseq t a -> t+dseq_end = sum . map fst+ -- * Tseq  -- | Given a a default value, a 'Tseq' /sq/ and a list of time-points@@ -497,6 +541,14 @@                                    EQ -> (sq_t,sq_e) : tseq_latch sq_e sq' t'                                    GT -> (t0,def) : tseq_latch def sq t' +-- | End-time of sequence (ie. time of last event).+tseq_end :: Tseq t a -> t+tseq_end = fst . last++-- | Append the value /nil/ at /n/ seconds after the end of the sequence.+tseq_add_nil_after :: Num t => a -> t -> Tseq t a -> Tseq t a+tseq_add_nil_after nil n sq = sq ++ [(tseq_end sq + n,nil)]+ -- * Wseq  -- | Sort 'Wseq' by start time, 'Wseq' ought never to be out of@@ -506,56 +558,91 @@ wseq_sort :: Ord t => Wseq t a -> Wseq t a wseq_sort = sortBy (compare `on` (fst . fst)) --- | Transform 'Wseq' to 'Tseq' by discaring durations.+-- | Transform 'Wseq' to 'Tseq' by discarding durations. wseq_discard_dur :: Wseq t a -> Tseq t a wseq_discard_dur = let f ((t,_),e) = (t,e) in map f -wseq_overlap_f :: (Eq e,Ord t,Num t) =>-                  (e -> e -> Bool) -> (t -> t) -> ((t,t),e) -> Wseq t e -> Maybe (Wseq t e)-wseq_overlap_f eq_fn dur_fn ((t,d),a) sq =-  case find (eq_fn a . snd) sq of-    Nothing -> Nothing-    Just ((t',d'),a') ->-      if t == t'-      then if d <= d'-           then Just sq -- delete LHS-           else Just (((t,d),a) : delete ((t',d'),a') sq) -- delete RHS-      else if t' < t + d-           then Just (((t,dur_fn (t' - t)),a) : sq) -- truncate LHS-           else Nothing+-- | Are /e/ equal and do nodes overlap?+--   Nodes are ascending, and so overlap if:+--   1. they begin at the same time and the first has non-zero duration, or+--   2. the second begins before the first ends.+wseq_nodes_overlap :: (Ord t,Num t) => (e -> e -> Bool) -> ((t,t),e) -> ((t,t),e) -> Bool+wseq_nodes_overlap eq_f ((t1,d1),a1) ((t2,_d2),a2) =+  eq_f a1 a2 && ((t1 == t2 && d1 > 0) || (t2 < (t1 + d1))) --- | Determine if sequence has overlapping equal nodes.-wseq_has_overlaps :: (Ord t, Num t, Eq e) => (e -> e -> Bool) -> Wseq t e -> Bool+-- | Find first node at /sq/ that overlaps with /e0/, if there is one.+--   Note: this could, but does not, halt early, ie. when t2 > (t1 + d1).+wseq_find_overlap_1 :: (Ord t,Num t) => (e -> e -> Bool) -> ((t,t),e) -> Wseq t e -> Bool+wseq_find_overlap_1 eq_f e0 = isJust . find (wseq_nodes_overlap eq_f e0)++-- | Determine if sequence has any overlapping equal nodes, stops after finding first instance.+--+-- > wseq_has_overlaps (==) [] == False+-- > wseq_has_overlaps (==) [((0,1),'x')]+wseq_has_overlaps :: (Ord t, Num t) => (e -> e -> Bool) -> Wseq t e -> Bool wseq_has_overlaps eq_fn =   let recur sq =         case sq of           [] -> False-          h:sq' ->-            case wseq_overlap_f eq_fn id h sq' of-              Nothing -> recur sq'-              Just _ -> True-    in recur+          e0:sq' -> wseq_find_overlap_1 eq_fn e0 sq' || recur sq'+  in recur +{- | Remove overlaps by deleting any overlapping nodes. -{- | Edit durations to ensure that nodes don't overlap.  If equal nodes-     begin simultaneously delete the shorter node.  If a node-     extends into a later node shorten the initial duration (apply /dur_fn/ to iot).+> let sq = [((0,1),'a'),((0,5),'a'),((1,5),'a'),((3,1),'a')]+> wseq_has_overlaps (==) sq == True+> let sq_rw = wseq_remove_overlaps_rm (==) sq+> sq_rw == [((0,1),'a'),((1,5),'a')]+> wseq_has_overlaps (==) sq_rw+-}+wseq_remove_overlaps_rm :: (Ord t,Num t) => (e -> e -> Bool) -> Wseq t e -> Wseq t e+wseq_remove_overlaps_rm eq_f =+  let recur sq =+        case sq of+          [] -> []+          e0:sq' -> e0 : recur (filter (not . wseq_nodes_overlap eq_f e0) sq')+  in recur +{- | Find first instance of overlap of /e/ at /sq/ and re-write durations so nodes don't overlap.+     If equal nodes begin simultaneously delete the shorter node (eithe LHS or RHS).+     If a node extends into a later node shorten the initial (LHS) duration (apply /dur_fn/ to iot).+-}+wseq_remove_overlap_rw_1 :: (Ord t,Num t) =>+                            (e -> e -> Bool) -> (t -> t) -> ((t,t),e) -> Wseq t e -> Maybe (Wseq t e)+wseq_remove_overlap_rw_1 eq_f dur_fn ((t,d),a) sq =+  let n_eq ((t1,d1),e1) ((t2,d2),e2) = t1 == t2 && d1 == d2 && eq_f e1 e2+  in case find (eq_f a . snd) sq of+       Nothing -> Nothing+       Just ((t',d'),a') ->+         if t == t'+         then if d <= d'+         then Just sq -- delete LHS+              else Just (((t,d),a) : deleteBy n_eq ((t',d'),a') sq) -- delete RHS+         else if t' < t + d+              then Just (((t,dur_fn (t' - t)),a) : sq) -- truncate LHS+              else Nothing++{- | Run 'wseq_remove_overlap_rw_1' until sequence has no overlaps.+ > let sq = [((0,1),'a'),((0,5),'a'),((1,5),'a'),((3,1),'a')]-> let r = [((0,1),'a'),((1,2),'a'),((3,1),'a')] > wseq_has_overlaps (==) sq == True-> wseq_remove_overlaps (==) id sq == r-> wseq_has_overlaps (==) (wseq_remove_overlaps (==) id sq) == False+> let sq_rw = wseq_remove_overlaps_rw (==) id sq+> sq_rw == [((0,1),'a'),((1,2),'a'),((3,1),'a')]+> wseq_has_overlaps (==) sq_rw == False +> import qualified Music.Theory.Array.Csv.Midi.Mnd as T {- hmt -}+> let csv_fn = "/home/rohan/uc/the-center-is-between-us/visitants/csv/midi/air.B.1.csv"+> sq <- T.csv_midi_read_wseq csv_fn :: IO (Wseq Double (T.Event Double))+> length sq == 186+> length (wseq_remove_overlaps_rw (==) id sq) == 183 -}-wseq_remove_overlaps :: (Eq e,Ord t,Num t) =>-                        (e -> e -> Bool) -> (t -> t) -> Wseq t e -> Wseq t e-wseq_remove_overlaps eq_fn dur_fn =+wseq_remove_overlaps_rw :: (Ord t,Num t) => (e -> e -> Bool) -> (t -> t) -> Wseq t e -> Wseq t e+wseq_remove_overlaps_rw eq_f dur_fn =   let recur sq =         case sq of           [] -> []           h:sq' ->-            case wseq_overlap_f eq_fn dur_fn h sq' of+            case wseq_remove_overlap_rw_1 eq_f dur_fn h sq' of               Nothing -> h : recur sq'               Just sq'' -> recur sq''     in recur@@ -564,7 +651,7 @@ seq_unjoin :: [(t,[e])] -> [(t,e)] seq_unjoin = let f (t,e) = zip (repeat t) e in concatMap f --- | Type specialised.+-- | Type specialised 'seq_unjoin'. wseq_unjoin :: Wseq t [e] -> Wseq t e wseq_unjoin = seq_unjoin @@ -586,6 +673,10 @@ wseq_concat :: Num t => [Wseq t a] -> Wseq t a wseq_concat = foldl1 wseq_append +-- | Transform sequence to start at time zero.+wseq_zero :: Num t => Wseq t a -> Wseq t a+wseq_zero sq = let t0 = wseq_start sq in wseq_tmap (\(st,du) -> (st - t0,du)) sq+ -- * Begin/End  -- | Container to mark the /begin/ and /end/ of a value.@@ -598,6 +689,8 @@       Begin a -> Begin (f a)       End a -> End (f a) +instance Functor Begin_End where fmap = begin_end_map+ -- | Structural comparison at 'Begin_End', 'Begin' compares less than 'End'. cmp_begin_end :: Begin_End a -> Begin_End b -> Ordering cmp_begin_end p q =@@ -607,6 +700,8 @@       (End _,End _) -> EQ       (End _,Begin _) -> GT +--instance Eq t => Ord (Begin_End t) where compare = cmp_begin_end+ -- | Translate container types. either_to_begin_end :: Either a a -> Begin_End a either_to_begin_end p =@@ -621,6 +716,7 @@       Begin a -> Left a       End a -> Right a +-- | Equivalent to 'partitionEithers'. begin_end_partition :: [Begin_End a] -> ([a],[a]) begin_end_partition =   let f e (p,q) = case e of@@ -628,32 +724,35 @@                     End x -> (p,x:q)   in foldr f ([],[]) --- | Add or delete element from accumulated state.-begin_end_track :: Eq a => [a] -> Begin_End a -> [a]-begin_end_track st e =+-- | Add or delete element from accumulated state given equality function.+begin_end_track_by :: (a -> a -> Bool) -> [a] -> Begin_End a -> [a]+begin_end_track_by eq_f st e =   case e of     Begin x -> x : st-    End x -> delete x st+    End x -> deleteBy eq_f x st --- | Convert 'Wseq' to 'Tseq' transforming elements to 'Begin_End'.---   When merging, /end/ elements precede /begin/ elements at equal times.------ > let {sq = [((0,5),'a'),((2,2),'b')]--- >     ;r = [(0,Begin 'a'),(2,Begin 'b'),(4,End 'b'),(5,End 'a')]}--- > in wseq_begin_end sq == r------ > let {sq = [((0,1),'a'),((1,1),'b'),((2,1),'c')]--- >     ;r = [(0,Begin 'a'),(1,End 'a')--- >          ,(1,Begin 'b'),(2,End 'b')--- >          ,(2,Begin 'c'),(3,End 'c')]}--- > in wseq_begin_end sq == r+-- | 'begin_end_track_by' of '=='.+begin_end_track :: Eq a => [a] -> Begin_End a -> [a]+begin_end_track = begin_end_track_by (==)++{- | Convert 'Wseq' to 'Tseq' transforming elements to 'Begin_End'.+     When merging, /end/ elements precede /begin/ elements at equal times.++> let sq = [((0,5),'a'),((2,2),'b')]+> let r = [(0,Begin 'a'),(2,Begin 'b'),(4,End 'b'),(5,End 'a')]+> wseq_begin_end sq == r++> let sq = [((0,1),'a'),((1,1),'b'),((2,1),'c')]+> let r = [(0,Begin 'a'),(1,End 'a'),(1,Begin 'b'),(2,End 'b'),(2,Begin 'c'),(3,End 'c')]+> wseq_begin_end sq == r+-} wseq_begin_end :: (Num t, Ord t) => Wseq t a -> Tseq t (Begin_End a) wseq_begin_end sq =     let f ((t,d),a) = [(t,Begin a),(t + d,End a)]         g l =             case l of               [] -> []-              e:l' -> tseq_merge_by (T.ord_invert .: cmp_begin_end) e (g l')+              e:l' -> tseq_merge_by (\x -> T.ord_invert . cmp_begin_end x) e (g l')     in g (map f sq)  -- | 'begin_end_to_either' of 'wseq_begin_end'.@@ -662,13 +761,13 @@  -- | Variant that applies /begin/ and /end/ functions to nodes. ----- > let {sq = [((0,5),'a'),((2,2),'b')]--- >     ;r = [(0,'A'),(2,'B'),(4,'b'),(5,'a')]}--- > in wseq_begin_end_f Data.Char.toUpper id sq == r+-- > let sq = [((0,5),'a'),((2,2),'b')]+-- > let r = [(0,'A'),(2,'B'),(4,'b'),(5,'a')]+-- > wseq_begin_end_f Data.Char.toUpper id sq == r wseq_begin_end_f :: (Ord t,Num t) => (a -> b) -> (a -> b) -> Wseq t a -> Tseq t b wseq_begin_end_f f g = tseq_map (either f g) . wseq_begin_end_either --- | Result for each time-point the triple (begin-list,end-list,hold-list).+-- | Generate for each time-point the triple (begin-list,end-list,hold-list). --   The elements of the end-list have been deleted from the hold list. tseq_begin_end_accum :: Eq a => Tseq t [Begin_End a] -> Tseq t ([a],[a],[a]) tseq_begin_end_accum =@@ -678,6 +777,15 @@             in (st',(t,(b,e,st \\ e)))     in snd . mapAccumL f [] +-- | Variant that initially transforms 'Wseq' into non-overlapping begin-end sequence.+--   If the sequence was edited for overlaps this is indicated.+wseq_begin_end_accum :: (Eq e, Ord t, Num t) => Wseq t e -> (Bool, Tseq t ([e],[e],[e]))+wseq_begin_end_accum sq =+  let ol = wseq_has_overlaps (==) sq+      sq_edit = if ol then wseq_remove_overlaps_rw (==) id sq else sq+      a_sq = tseq_begin_end_accum (tseq_group (wseq_begin_end sq_edit))+  in (ol,a_sq)+ tseq_accumulate :: Eq a => Tseq t [Begin_End a] -> Tseq t [a] tseq_accumulate =   let f st (t,e) =@@ -695,9 +803,9 @@ -- | Inverse of 'wseq_begin_end' given a predicate function for locating -- the /end/ node of a /begin/ node. ----- > let {sq = [(0,Begin 'a'),(2,Begin 'b'),(4,End 'b'),(5,End 'a')]--- >     ;r = [((0,5),'a'),((2,2),'b')]}--- > in tseq_begin_end_to_wseq (==) sq == r+-- > let sq = [(0,Begin 'a'),(2,Begin 'b'),(4,End 'b'),(5,End 'a')]+-- > let r = [((0,5),'a'),((2,2),'b')]+-- > tseq_begin_end_to_wseq (==) sq == r tseq_begin_end_to_wseq :: Num t => (a -> a -> Bool) -> Tseq t (Begin_End a) -> Wseq t a tseq_begin_end_to_wseq cmp =     let cmp' x e =@@ -725,31 +833,41 @@ -- /eof/ marker. Productive given indefinite input sequence. -- -- > let r = zip [0,1,3,6,8,9] "abcde|"--- > in dseq_to_tseq 0 '|' (zip [1,2,3,2,1] "abcde") == r+-- > dseq_to_tseq 0 '|' (zip [1,2,3,2,1] "abcde") == r ----- > let {d = zip [1,2,3,2,1] "abcde"--- >     ;r = zip [0,1,3,6,8,9,10] "abcdeab"}--- > in take 7 (dseq_to_tseq 0 undefined (cycle d)) == r+-- > let d = zip [1,2,3,2,1] "abcde"+-- > let r = zip [0,1,3,6,8,9,10] "abcdeab"+-- > take 7 (dseq_to_tseq 0 undefined (cycle d)) == r dseq_to_tseq :: Num t => t -> a -> Dseq t a -> Tseq t a-dseq_to_tseq t0 nil sq =-    let (d,a) = unzip sq-        t = T.dx_d t0 d-        a' = a ++ [nil]-    in zip t a'+dseq_to_tseq t0 nil = T.rezip (T.dx_d t0) (T.snoc nil)  -- | Variant where the /nil/ value is taken from the last element of -- the sequence. -- -- > let r = zip [0,1,3,6,8,9] "abcdee"--- > in dseq_to_tseq_last 0 (zip [1,2,3,2,1] "abcde") == r+-- > dseq_to_tseq_last 0 (zip [1,2,3,2,1] "abcde") == r dseq_to_tseq_last :: Num t => t -> Dseq t a -> Tseq t a dseq_to_tseq_last t0 sq = dseq_to_tseq t0 (snd (last sq)) sq +{- | Variant where the final duration is discarded.++> dseq_to_tseq_discard 0 (zip [1,2,3,2,1] "abcde") == zip [0,1,3,6,8] "abcde"+-}+dseq_to_tseq_discard :: Num t => t -> Dseq t a -> Tseq t a+dseq_to_tseq_discard t0 = T.drop_last . dseq_to_tseq t0 undefined++-- | 'Iseq' to 'Tseq', requires t0.+--+-- > let r = zip [1,3,6,8,9] "abcde"+-- > iseq_to_tseq 0 (zip [1,2,3,2,1] "abcde") == r+iseq_to_tseq :: Num t => t -> Iseq t a -> Tseq t a+iseq_to_tseq t0 = T.rezip (tail . T.dx_d t0) id+ -- | The conversion requires a start time and does not consult the -- /logical/ duration. -- -- > let p = pseq_zip (repeat undefined) (cycle [1,2]) (cycle [1,1,2]) "abcdef"--- > in pseq_to_wseq 0 p == wseq_zip [0,1,2,4,5,6] (cycle [1,2]) "abcdef"+-- > pseq_to_wseq 0 p == wseq_zip [0,1,2,4,5,6] (cycle [1,2]) "abcdef" pseq_to_wseq :: Num t => t -> Pseq t a -> Wseq t a pseq_to_wseq t0 sq =     let (p,a) = unzip sq@@ -762,10 +880,10 @@ -- value is required in case the 'Tseq' does not begin at @0@. -- -- > let r = zip [1,2,3,2,1] "abcde"--- > in tseq_to_dseq undefined (zip [0,1,3,6,8,9] "abcde|") == r+-- > tseq_to_dseq undefined (zip [0,1,3,6,8,9] "abcde|") == r -- -- > let r = zip [1,2,3,2,1] "-abcd"--- > in tseq_to_dseq '-' (zip [1,3,6,8,9] "abcd|") == r+-- > tseq_to_dseq '-' (zip [1,3,6,8,9] "abcd|") == r tseq_to_dseq :: (Ord t,Num t) => a -> Tseq t a -> Dseq t a tseq_to_dseq empty sq =     let (t,a) = unzip sq@@ -774,16 +892,37 @@          [] -> []          t0:_ -> if t0 > 0 then (t0,empty) : zip d a else zip d a +{- | Variant that requires a final duration be provided, and that the Tseq have no end marker.++> let r = zip [1,2,3,2,9] "abcde"+> tseq_to_dseq_final_dur undefined 9 (zip [0,1,3,6,8] "abcde") == r+-}+tseq_to_dseq_final_dur :: (Ord t,Num t) => a -> t -> Tseq t a -> Dseq t a+tseq_to_dseq_final_dur empty dur sq =+  let (t,a) = unzip sq+      d = T.d_dx t ++ [dur]+  in case t of+       [] -> []+       t0:_ -> if t0 > 0 then (t0,empty) : zip d a else zip d a++{- | Variant that requires a total duration be provided, and that the Tseq have no end marker.++> let r = zip [1,2,3,2,7] "abcde"+> tseq_to_dseq_total_dur undefined 15 (zip [0,1,3,6,8] "abcde")+-}+tseq_to_dseq_total_dur :: (Ord t,Num t) => a -> t -> Tseq t a -> Dseq t a+tseq_to_dseq_total_dur empty dur sq = tseq_to_dseq_final_dur empty (dur - tseq_end sq) sq+ -- | The last element of 'Tseq' is required to be an /eof/ marker that -- has no duration and is not represented in the 'Wseq'.  The duration--- of each value is either derived from the value, if an /dur/+-- of each value is either derived from the value, if a /dur/ -- function is given, or else the inter-offset time. -- -- > let r = wseq_zip [0,1,3,6,8] [1,2,3,2,1] "abcde"--- > in tseq_to_wseq Nothing (zip [0,1,3,6,8,9] "abcde|") == r+-- > tseq_to_wseq Nothing (zip [0,1,3,6,8,9] "abcde|") == r -- -- > let r = wseq_zip [0,1,3,6,8] (map fromEnum "abcde") "abcde"--- > in tseq_to_wseq (Just fromEnum) (zip [0,1,3,6,8,9] "abcde|") == r+-- > tseq_to_wseq (Just fromEnum) (zip [0,1,3,6,8,9] "abcde|") == r tseq_to_wseq :: Num t => Maybe (a -> t) -> Tseq t a -> Wseq t a tseq_to_wseq dur_f sq =     let (t,a) = unzip sq@@ -792,7 +931,21 @@               Nothing -> T.d_dx t     in wseq_zip t d a -tseq_to_iseq :: Num t => Tseq t a -> Dseq t a+{- | Translate Tseq to Wseq using inter-offset times, up to indicated total duration, as element durations.++> let r = [((0,1),'a'),((1,2),'b'),((3,3),'c'),((6,2),'d'),((8,3),'e')]+> tseq_to_wseq_iot 11 (zip [0,1,3,6,8] "abcde") == r+-}+tseq_to_wseq_iot :: Num t => t -> Tseq t a -> Wseq t a+tseq_to_wseq_iot total_dur sq =+  let (t, e) = unzip sq+      d = zipWith (-) (tail t ++ [total_dur]) t+  in zip (zip t d) e++-- | Tseq to Iseq.+--+-- > tseq_to_iseq (zip [0,1,3,6,8,9] "abcde|") == zip [0,1,2,3,2,1] "abcde|"+tseq_to_iseq :: Num t => Tseq t a -> Iseq t a tseq_to_iseq =     let recur n p =             case p of@@ -803,7 +956,7 @@ -- | Requires start time. -- -- > let r = zip (zip [0,1,3,6,8,9] [1,2,3,2,1]) "abcde"--- > in dseq_to_wseq 0 (zip [1,2,3,2,1] "abcde") == r+-- > dseq_to_wseq 0 (zip [1,2,3,2,1] "abcde") == r dseq_to_wseq :: Num t => t -> Dseq t a -> Wseq t a dseq_to_wseq t0 sq =     let (d,a) = unzip sq@@ -815,16 +968,16 @@ -- truncated. -- -- > let w = wseq_zip [0,1,3,6,8,9] [1,2,3,2,1] "abcde"--- > in wseq_to_dseq '-' w == zip [1,2,3,2,1] "abcde"+-- > wseq_to_dseq '-' w == zip [1,2,3,2,1] "abcde" -- -- > let w = wseq_zip [3,10] [6,2] "ab"--- > in wseq_to_dseq '-' w == zip [3,6,1,2] "-a-b"+-- > wseq_to_dseq '-' w == zip [3,6,1,2] "-a-b" -- -- > let w = wseq_zip [0,1] [2,2] "ab"--- > in wseq_to_dseq '-' w == zip [1,2] "ab"+-- > wseq_to_dseq '-' w == zip [1,2] "ab" -- -- > let w = wseq_zip [0,0,0] [2,2,2] "abc"--- > in wseq_to_dseq '-' w == zip [0,0,2] "abc"+-- > wseq_to_dseq '-' w == zip [0,0,2] "abc" wseq_to_dseq :: (Num t,Ord t) => a -> Wseq t a -> Dseq t a wseq_to_dseq empty sq =     let f (((st0,d),e),((st1,_),_)) =@@ -839,13 +992,16 @@          ((st,_),_):_ -> if st > 0 then (st,empty) : r else r          [] -> error "wseq_to_dseq" +eseq_to_wseq :: Eseq t a -> Wseq t a+eseq_to_wseq = let f ((t, d, _), e) = ((t, d), e) in map f+ -- * Measures  -- | Given a list of 'Dseq' (measures) convert to a list of 'Tseq' and -- the end time of the overall sequence. -- -- > let r = [[(0,'a'),(1,'b'),(3,'c')],[(4,'d'),(7,'e'),(9,'f')]]--- > in dseql_to_tseql 0 [zip [1,2,1] "abc",zip [3,2,1] "def"] == (10,r)+-- > dseql_to_tseql 0 [zip [1,2,1] "abc",zip [3,2,1] "def"] == (10,r) dseql_to_tseql :: Num t => t -> [Dseq t a] -> (t,[Tseq t a]) dseql_to_tseql =     let f z dv =@@ -856,29 +1012,30 @@  -- * Cycle -wseq_cycle' :: Num t => Wseq t a -> [Wseq t a]-wseq_cycle' sq =+-- | List of cycles of 'Wseq'.+wseq_cycle_ls :: Num t => Wseq t a -> [Wseq t a]+wseq_cycle_ls sq =     let (_,et) = wseq_tspan sq         t_sq = iterate (+ et) 0-    in map (\x -> wseq_tmap (\(t,d) -> (x + t,d)) sq) t_sq+    in map (\x -> wseq_tmap (first (+ x)) sq) t_sq  -- | Only finite 'Wseq' can be cycled, the resulting Wseq is infinite. -- -- > take 5 (wseq_cycle [((0,1),'a'),((3,3),'b')]) wseq_cycle :: Num t => Wseq t a -> Wseq t a-wseq_cycle = concat . wseq_cycle'+wseq_cycle = concat . wseq_cycle_ls  -- | Variant cycling only /n/ times. -- -- > wseq_cycle_n 3 [((0,1),'a'),((3,3),'b')] wseq_cycle_n :: Num t => Int -> Wseq t a -> Wseq t a-wseq_cycle_n n = concat . take n . wseq_cycle'+wseq_cycle_n n = concat . take n . wseq_cycle_ls  -- | 'wseq_until' of 'wseq_cycle'. wseq_cycle_until :: (Num t,Ord t) => t -> Wseq t a -> Wseq t a wseq_cycle_until et = wseq_until et . wseq_cycle --- * Type specialised map+-- * Type specialised maps  dseq_tmap :: (t -> t') -> Dseq t a -> Dseq t' a dseq_tmap = seq_tmap@@ -946,3 +1103,12 @@  wseq_cat_maybes :: Wseq t (Maybe a) -> Wseq t a wseq_cat_maybes = seq_cat_maybes++-- * Maps++{- | Requires but does not check that there are no duplicate time points in Tseq.++> tseq_to_map [(0, 'a'), (0, 'b')] == tseq_to_map [(0, 'b')]+-}+tseq_to_map :: Ord t => Tseq t e -> Map.Map t e+tseq_to_map = Map.fromList
Music/Theory/Time_Signature.hs view
@@ -6,7 +6,7 @@  import Music.Theory.Duration import Music.Theory.Duration.Name-import Music.Theory.Duration.RQ+import Music.Theory.Duration.Rq import Music.Theory.Math  -- | A Time Signature is a /(numerator,denominator)/ pair.@@ -49,26 +49,26 @@       (6,2) -> [dotted_breve]       _ -> error ("ts_whole_note: " ++ show t) --- | Duration of measure in 'RQ'.+-- | Duration of measure in 'Rq'. -- -- > map ts_whole_note_rq [(3,8),(2,2)] == [3/2,4]-ts_whole_note_rq :: Time_Signature -> RQ+ts_whole_note_rq :: Time_Signature -> Rq ts_whole_note_rq = sum . map duration_to_rq . ts_whole_note --- | Duration, in 'RQ', of a measure of indicated 'Time_Signature'.+-- | Duration, in 'Rq', of a measure of indicated 'Time_Signature'. -- -- > map ts_rq [(3,4),(5,8)] == [3,5/2]-ts_rq :: Time_Signature -> RQ+ts_rq :: Time_Signature -> Rq ts_rq (n,d) = (4 * n) % d  -- | 'compare' 'on' 'ts_rq'. ts_compare :: Time_Signature -> Time_Signature -> Ordering ts_compare = compare `on` ts_rq --- | 'Time_Signature' derived from whole note duration in 'RQ' form.+-- | 'Time_Signature' derived from whole note duration in 'Rq' form. -- -- > map rq_to_ts [4,3/2,7/4,6] == [(4,4),(3,8),(7,16),(6,4)]-rq_to_ts :: RQ -> Time_Signature+rq_to_ts :: Rq -> Time_Signature rq_to_ts rq =     let n = numerator rq         d = denominator rq * 4@@ -81,7 +81,7 @@ -- > ts_divisions (2,2) == [2,2] -- > ts_divisions (1,1) == [4] -- > ts_divisions (7,4) == [1,1,1,1,1,1,1]-ts_divisions :: Time_Signature -> [RQ]+ts_divisions :: Time_Signature -> [Rq] ts_divisions (i,j) =     let k = fromIntegral i     in replicate k (recip (j % 4))@@ -123,23 +123,23 @@ -- | A composite time signature is a sequence of 'Time_Signature's. type Composite_Time_Signature = [Time_Signature] --- | The 'RQ' is the 'sum' of 'ts_rq' of the elements.+-- | The 'Rq' is the 'sum' of 'ts_rq' of the elements. -- -- > cts_rq [(3,4),(1,8)] == 3 + 1/2-cts_rq :: Composite_Time_Signature -> RQ+cts_rq :: Composite_Time_Signature -> Rq cts_rq = sum . map ts_rq  -- | The divisions are the 'concat' of the 'ts_divisions' of the -- elements. -- -- > cts_divisions [(3,4),(1,8)] == [1,1,1,1/2]-cts_divisions :: Composite_Time_Signature -> [RQ]+cts_divisions :: Composite_Time_Signature -> [Rq] cts_divisions = concatMap ts_divisions --- | Pulses are 1-indexed, RQ locations are 0-indexed.+-- | Pulses are 1-indexed, Rq locations are 0-indexed. -- -- > map (cts_pulse_to_rq [(2,4),(1,8),(1,4)]) [1 .. 4] == [0,1,2,2 + 1/2]-cts_pulse_to_rq :: Composite_Time_Signature -> Int -> RQ+cts_pulse_to_rq :: Composite_Time_Signature -> Int -> Rq cts_pulse_to_rq cts p =     let dv = cts_divisions cts     in sum (take (p - 1) dv)@@ -149,7 +149,7 @@ -- -- > let r = [(0,1),(1,1),(2,1/2),(2 + 1/2,1)] -- > in map (cts_pulse_to_rqw [(2,4),(1,8),(1,4)]) [1 .. 4] == r-cts_pulse_to_rqw :: Composite_Time_Signature -> Int -> (RQ,RQ)+cts_pulse_to_rqw :: Composite_Time_Signature -> Int -> (Rq,Rq) cts_pulse_to_rqw cts p = (cts_pulse_to_rq cts p,cts_divisions cts !! (p - 1))  -- * Rational Time Signatures@@ -158,11 +158,11 @@ -- the parts are 'Rational'. type Rational_Time_Signature = [(Rational,Rational)] --- | The 'sum' of the RQ of the elements.+-- | The 'sum' of the Rq of the elements. -- -- > rts_rq [(3,4),(1,8)] == 3 + 1/2 -- > rts_rq [(3/2,4),(1/2,8)] == 3/2 + 1/4-rts_rq :: Rational_Time_Signature -> RQ+rts_rq :: Rational_Time_Signature -> Rq rts_rq =     let f (n,d) = (4 * n) / d     in sum . map f@@ -171,7 +171,7 @@ -- -- > rts_divisions [(3,4),(1,8)] == [1,1,1,1/2] -- > rts_divisions [(3/2,4),(1/2,8)] == [1,1/2,1/4]-rts_divisions :: Rational_Time_Signature -> [[RQ]]+rts_divisions :: Rational_Time_Signature -> [[Rq]] rts_divisions =     let f (n,d) = let (ni,nf) = integral_and_fractional_parts n                       rq = recip (d / 4)@@ -181,14 +181,14 @@  -- > rts_derive [1,1,1,1/2] -- > rts_derive [1,1/2,1/4]-rts_derive :: [RQ] -> Rational_Time_Signature+rts_derive :: [Rq] -> Rational_Time_Signature rts_derive = let f rq = (rq,4) in map f --- | Pulses are 1-indexed, RQ locations are 0-indexed.+-- | Pulses are 1-indexed, Rq locations are 0-indexed. -- -- > map (rts_pulse_to_rq [(2,4),(1,8),(1,4)]) [1 .. 4] == [0,1,2,2 + 1/2] -- > map (rts_pulse_to_rq [(3/2,4),(1/2,8),(1/4,4)]) [1 .. 4] == [0,1,3/2,7/4]-rts_pulse_to_rq :: Rational_Time_Signature -> Int -> RQ+rts_pulse_to_rq :: Rational_Time_Signature -> Int -> Rq rts_pulse_to_rq rts p =     let dv = concat (rts_divisions rts)     in sum (take (p - 1) dv)@@ -198,5 +198,5 @@ -- -- > let r = [(0,1),(1,1),(2,1/2),(2 + 1/2,1)] -- > in map (rts_pulse_to_rqw [(2,4),(1,8),(1,4)]) [1 .. 4] == r-rts_pulse_to_rqw :: Rational_Time_Signature -> Int -> (RQ,RQ)+rts_pulse_to_rqw :: Rational_Time_Signature -> Int -> (Rq,Rq) rts_pulse_to_rqw ts p = (rts_pulse_to_rq ts p,concat (rts_divisions ts) !! (p - 1))
Music/Theory/Tuning.hs view
@@ -1,176 +1,173 @@ -- | Tuning theory module Music.Theory.Tuning where -import Data.Fixed (mod') {- base -}-import Data.List {- base -}-import qualified Data.Map as M {- containers -}-import Data.Maybe {- base -}+import qualified Data.Fixed as Fixed {- base -} import Data.Ratio {- base -}-import Safe {- safe -} -import qualified Music.Theory.Either as T {- hmt -}+import qualified Music.Theory.Function as T {- hmt -} import qualified Music.Theory.List as T {- hmt -}-import qualified Music.Theory.Map as T {- hmt -}-import qualified Music.Theory.Pitch as T {- hmt -}-import qualified Music.Theory.Set.List as T {- hmt -}-import qualified Music.Theory.Tuple as T {- hmt -}---- * Types---- | An approximation of a ratio.-type Approximate_Ratio = Double+import qualified Music.Theory.Math as T {- hmt -}+import qualified Music.Theory.Ord as T {- hmt -} --- | A real valued division of a semi-tone into one hundred parts, and--- hence of the octave into @1200@ parts.-type Cents = Double+-- * Math/Floating --- | A tuning specified 'Either' as a sequence of exact ratios, or as--- a sequence of possibly inexact 'Cents'.+-- | Fractional /midi/ note number to cycles per second, given (k0,f0) pair. ----- In both cases, the values are given in relation to the first degree--- of the scale, which for ratios is 1 and for cents 0.-data Tuning = Tuning {tn_ratios_or_cents :: Either [Rational] [Cents]-                     ,tn_octave_ratio :: Rational}-              deriving (Eq,Show)+-- > fmidi_to_cps_k0 (60,256) 69 == 430.5389646099018+fmidi_to_cps_k0 :: Floating a => (a,a) -> a -> a+fmidi_to_cps_k0 (k0,f0) i = f0 * (2 ** ((i - k0) * (1 / 12))) --- | Divisions of octave.+-- | 'fmidi_to_cps_k0' with k0 of 69. ----- > tn_divisions (equal_temperament 12) == 12-tn_divisions :: Tuning -> Int-tn_divisions = either length length . tn_ratios_or_cents---- | 'Maybe' exact ratios of 'Tuning'.-tn_ratios :: Tuning -> Maybe [Rational]-tn_ratios = T.fromLeft . tn_ratios_or_cents---- | 'error'ing variant.-tn_ratios_err :: Tuning -> [Rational]-tn_ratios_err = fromMaybe (error "ratios") . tn_ratios+-- > fmidi_to_cps_f0 440 60 == 261.6255653005986+fmidi_to_cps_f0 :: Floating a => a -> a -> a+fmidi_to_cps_f0 f0 = fmidi_to_cps_k0 (69,f0) --- | Possibly inexact 'Cents' of tuning.-tn_cents :: Tuning -> [Cents]-tn_cents = either (map ratio_to_cents) id . tn_ratios_or_cents+-- | 'fmidi_to_cps_k0' (69,440)+--+-- > map fmidi_to_cps [69,69.1] == [440.0,442.5488940698553]+fmidi_to_cps :: Floating a => a -> a+fmidi_to_cps = fmidi_to_cps_k0 (69,440) --- | 'map' 'round' '.' 'cents'.-tn_cents_i :: Integral i => Tuning -> [i]-tn_cents_i = map round . tn_cents+-- | /Midi/ note number to cycles per second, given frequency of ISO A4.+midi_to_cps_k0 :: (Integral i,Floating f) => (f,f) -> i -> f+midi_to_cps_k0 o = fmidi_to_cps_k0 o . fromIntegral --- | Variant of 'cents' that includes octave at right.-tn_cents_octave :: Tuning -> [Cents]-tn_cents_octave t = tn_cents t ++ [ratio_to_cents (tn_octave_ratio t)]+-- | 'midi_to_cps_k0' (69,440).+--+-- > map (round . midi_to_cps) [59,60,69] == [247,262,440]+midi_to_cps :: (Integral i,Floating f) => i -> f+midi_to_cps = midi_to_cps_k0 (69,440)  -- | Convert from interval in cents to frequency ratio. ----- > map cents_to_ratio [0,701.9550008653874,1200] == [1,3/2,2]-cents_to_ratio :: Floating a => a -> a-cents_to_ratio n = 2 ** (n / 1200)+-- > map cents_to_fratio [0,701.9550008653874,1200] == [1,3/2,2]+-- > map cents_to_fratio [-1800,1800] -- three octaves about zero+cents_to_fratio :: Floating a => a -> a+cents_to_fratio n = 2 ** (n / 1200) --- | Possibly inexact 'Approximate_Ratio's of tuning.-tn_approximate_ratios :: Tuning -> [Approximate_Ratio]-tn_approximate_ratios =-    either (map approximate_ratio) (map cents_to_ratio) .-    tn_ratios_or_cents+-- | Convert from a 'Floating' ratio to /cents/.+--+-- > let r = [0,498,702,1200]+-- > map (round . fratio_to_cents) [1,4/3,3/2,2] == r+fratio_to_cents :: (Real r,Floating n) => r -> n+fratio_to_cents = (1200 *) . logBase 2 . realToFrac --- | Cyclic form, taking into consideration 'octave_ratio'.-tn_approximate_ratios_cyclic :: Tuning -> [Approximate_Ratio]-tn_approximate_ratios_cyclic t =-    let r = tn_approximate_ratios t-        m = realToFrac (tn_octave_ratio t)-        g = iterate (* m) 1-        f n = map (* n) r-    in concatMap f g+-- | Frequency /n/ cents from /f/.+--+-- > import Music.Theory.Pitch {- hmt -}+-- > map (cps_shift_cents 440) [-100,100] == map octpc_to_cps [(4,8),(4,10)]+cps_shift_cents :: Floating a => a -> a -> a+cps_shift_cents f = (* f) . cents_to_fratio --- | Iterate the function /f/ /n/ times, the inital value is /x/.+-- | Interval in /cents/ from /p/ to /q/, ie. 'ratio_to_cents' of /p/ '/' /q/. ----- > recur_n 5 (* 2) 1 == 32--- > take (5 + 1) (iterate (* 2) 1) == [1,2,4,8,16,32]-recur_n :: Integral n => n -> (t -> t) -> t -> t-recur_n n f x = if n < 1 then x else recur_n (n - 1) f (f x)+-- > map (round . cps_difference_cents 440) [412,415,octpc_to_cps (5,2)] == [-114,-101,500]+--+-- > let abs_dif i j = abs (i - j)+-- > cps_difference_cents 440 (fmidi_to_cps 69.1) `abs_dif` 10 < 1e9+cps_difference_cents :: (Real r,Fractional r,Floating n) => r -> r -> n+cps_difference_cents p q = fratio_to_cents (q / p) +-- * Math/Ratio+ -- | Convert a (signed) number of octaves difference of given ratio to a ratio. -- -- > map (oct_diff_to_ratio 2) [-3 .. 3] == [1/8,1/4,1/2,1,2,4,8] -- > map (oct_diff_to_ratio (9/8)) [-3 .. 3] == [512/729,64/81,8/9,1/1,9/8,81/64,729/512] oct_diff_to_ratio :: Integral a => Ratio a -> Int -> Ratio a-oct_diff_to_ratio r n = if n >= 0 then recur_n n (* r) 1 else recur_n (negate n) (/ r) 1+oct_diff_to_ratio r n = if n >= 0 then T.recur_n n (* r) 1 else T.recur_n (negate n) (/ r) 1 --- | Lookup function that allows both negative & multiple octave indices.+-- | 'ratio_to_cents' rounded to nearest multiple of 100, modulo 12. ----- > let map_zip f l = zip l (map f l)--- > map_zip (tn_ratios_lookup werckmeister_vi) [-24 .. 24]-tn_ratios_lookup :: Tuning -> Int -> Maybe Rational-tn_ratios_lookup t n =-    let (o,pc) = n `divMod` tn_divisions t-        o_ratio = oct_diff_to_ratio (tn_octave_ratio t) o-    in fmap (\r -> o_ratio * (r !! pc)) (tn_ratios t)+-- > map (ratio_to_pc 0) [1,4/3,3/2,2] == [0,5,7,0]+ratio_to_pc :: Int -> Rational -> Int+ratio_to_pc n = T.mod12 . (+ n) . round . (/ 100) . ratio_to_cents --- | Lookup function that allows both negative & multiple octave indices.+-- | Fold ratio to lie within an octave, ie. @1@ '<' /n/ '<=' @2@.+--   It is an error for /n/ to be more than one octave outside of this range. ----- > map_zip (tn_approximate_ratios_lookup werckmeister_v) [-24 .. 24]-tn_approximate_ratios_lookup :: Tuning -> Int -> Approximate_Ratio-tn_approximate_ratios_lookup t n =-    let (o,pc) = n `divMod` tn_divisions t-        o_ratio = fromRational (oct_diff_to_ratio (tn_octave_ratio t) o)-    in o_ratio * ((tn_approximate_ratios t) !! pc)+-- > map fold_ratio_to_octave_nonrec [2/3,3/4,4/5,4/7] == [4/3,3/2,8/5,8/7]+fold_ratio_to_octave_nonrec :: (Ord n,Fractional n) => n -> n+fold_ratio_to_octave_nonrec n =+  if n >= 1 && n < 2+  then n+  else if n >= 2 && n < 4+       then n / 2+       else if n < 1 && n >= (1/2)+            then n * 2+            else error "fold_ratio_to_octave_nonrec" --- | 'Maybe' exact ratios reconstructed from possibly inexact 'Cents'--- of 'Tuning'.+-- | Fold ratio until within an octave, ie. @1@ '<' /n/ '<=' @2@.+--   It is an error if /n/ is less than or equal to zero. ----- > :l Music.Theory.Tuning.Werckmeister--- > let r = [1,17/16,9/8,13/11,5/4,4/3,7/5,3/2,11/7,5/3,16/9,15/8]--- > tn_reconstructed_ratios 1e-2 werckmeister_iii == Just r-tn_reconstructed_ratios :: Double -> Tuning -> Maybe [Rational]-tn_reconstructed_ratios epsilon =-    fmap (map (reconstructed_ratio epsilon)) .-    T.fromRight .-    tn_ratios_or_cents+-- > map fold_ratio_to_octave_err [2/2,2/3,3/4,4/5,4/7] == [1/1,4/3,3/2,8/5,8/7]+fold_ratio_to_octave_err :: (Ord n,Fractional n) => n -> n+fold_ratio_to_octave_err =+  let f n =+        if n <= 0+        then error "fold_ratio_to_octave_err?"+        else if n >= 2 then f (n / 2) else if n < 1 then f (n * 2) else n+  in f --- | Convert from a 'Floating' ratio to /cents/.+-- | In /n/ is greater than zero, 'fold_ratio_to_octave_err', else 'Nothing'. ----- > let r = [0,498,702,1200]--- > in map (round . fratio_to_cents) [1,4/3,3/2,2] == r-fratio_to_cents :: (Real r,Floating n) => r -> n-fratio_to_cents = (1200 *) . logBase 2 . realToFrac+-- > map fold_ratio_to_octave [0,1] == [Nothing,Just 1]+fold_ratio_to_octave :: (Ord n,Fractional n) => n -> Maybe n+fold_ratio_to_octave n = if n <= 0 then Nothing else Just (fold_ratio_to_octave_err n) --- | Type specialised 'fratio_to_cents'.-approximate_ratio_to_cents :: Approximate_Ratio -> Cents-approximate_ratio_to_cents = fratio_to_cents+-- | The interval between two pitches /p/ and /q/ given as ratio+-- multipliers of a fundamental is /q/ '/' /p/.  The classes over such+-- intervals consider the 'fold_ratio_to_octave' of both /p/ to /q/+-- and /q/ to /p/ and select the minima at the /cmp_f/.+--+-- > map (ratio_interval_class_by id) [3/2,5/4] == [4/3,5/4]+ratio_interval_class_by :: (Ord t, Integral i) => (Ratio i -> t) -> Ratio i -> Ratio i+ratio_interval_class_by cmp_f i =+    let f = fold_ratio_to_octave_err+    in T.min_by cmp_f (f i) (f (recip i)) +-- | 'ratio_interval_class_by' 'ratio_nd_sum'+--+-- > map ratio_interval_class [2/3,3/2,3/4,4/3] == [3/2,3/2,3/2,3/2]+-- > map ratio_interval_class [7/6,12/7] == [7/6,7/6]+ratio_interval_class :: Integral i => Ratio i -> Ratio i+ratio_interval_class = ratio_interval_class_by T.ratio_nd_sum++-- * Types++-- | An approximation of a ratio.+type Approximate_Ratio = Double+ -- | Type specialised 'fromRational'. approximate_ratio :: Rational -> Approximate_Ratio approximate_ratio = fromRational +-- | A real valued division of a semi-tone into one hundred parts, and+-- hence of the octave into @1200@ parts.+type Cents = Double++-- | Integral cents value.+type Cents_I = Int++-- | Type specialised 'fratio_to_cents'.+approximate_ratio_to_cents :: Approximate_Ratio -> Cents+approximate_ratio_to_cents = fratio_to_cents+ -- | 'approximate_ratio_to_cents' '.' 'approximate_ratio'. --+-- > import Data.Ratio {- base -} -- > map (\n -> (n,round (ratio_to_cents (fold_ratio_to_octave_err (n % 1))))) [1..21] ratio_to_cents :: Integral i => Ratio i -> Cents ratio_to_cents = approximate_ratio_to_cents . realToFrac --- | Construct an exact 'Rational' that approximates 'Cents' to within--- /epsilon/.+-- | Construct an exact 'Rational' that approximates 'Cents' to within /epsilon/. ----- > map (reconstructed_ratio 1e-5) [0,700,1200] == [1,442/295,2]+-- > map (reconstructed_ratio 1e-5) [0,700,1200,1800] == [1,442/295,2,577/204] -- -- > ratio_to_cents (442/295) == 699.9976981706735 reconstructed_ratio :: Double -> Cents -> Rational-reconstructed_ratio epsilon c = approxRational (cents_to_ratio c) epsilon---- | Frequency /n/ cents from /f/.------ > import Music.Theory.Pitch--- > map (cps_shift_cents 440) [-100,100] == map octpc_to_cps [(4,8),(4,10)]-cps_shift_cents :: Floating a => a -> a -> a-cps_shift_cents f = (* f) . cents_to_ratio---- | Interval in /cents/ from /p/ to /q/, ie. 'ratio_to_cents' of /p/--- '/' /q/.------ > cps_difference_cents 440 (octpc_to_cps (5,2)) == 500------ > let abs_dif i j = abs (i - j)--- > in cps_difference_cents 440 (fmidi_to_cps 69.1) `abs_dif` 10 < 1e9-cps_difference_cents :: (Real r,Fractional r,Floating n) => r -> r -> n-cps_difference_cents p q = fratio_to_cents (q / p)+reconstructed_ratio epsilon c = approxRational (cents_to_fratio c) epsilon  -- * Commas @@ -192,174 +189,18 @@ mercators_comma :: Rational mercators_comma = 19383245667680019896796723 / 19342813113834066795298816 --- | Calculate /n/th root of /x/.------ > 12 `nth_root` 2 == twelve_tone_equal_temperament_comma-nth_root :: (Floating a,Eq a) => a -> a -> a-nth_root n x =-    let f (_,x0) = (x0, ((n-1)*x0+x/x0**(n-1))/n)-        e = uncurry (==)-    in fst (until e f (x, x/n))- -- | 12-tone equal temperament comma (ie. 12th root of 2). -- -- > twelve_tone_equal_temperament_comma == 1.0594630943592953 twelve_tone_equal_temperament_comma :: (Floating a,Eq a) => a-twelve_tone_equal_temperament_comma = 12 `nth_root` 2---- * Equal temperaments---- | Make /n/ division equal temperament.-equal_temperament :: Integral n => n -> Tuning-equal_temperament n =-    let c = genericTake n [0,1200 / fromIntegral n ..]-    in Tuning (Right c) 2---- | 12-tone equal temperament.------ > cents equal_temperament_12 == [0,100..1100]-equal_temperament_12 :: Tuning-equal_temperament_12 = equal_temperament (12::Int)---- | 19-tone equal temperament.-equal_temperament_19 :: Tuning-equal_temperament_19 = equal_temperament (19::Int)---- | 31-tone equal temperament.-equal_temperament_31 :: Tuning-equal_temperament_31 = equal_temperament (31::Int)---- | 53-tone equal temperament.-equal_temperament_53 :: Tuning-equal_temperament_53 = equal_temperament (53::Int)---- | 72-tone equal temperament.------ > let r = [0,17,33,50,67,83,100]--- > in take 7 (map round (cents equal_temperament_72)) == r-equal_temperament_72 :: Tuning-equal_temperament_72 = equal_temperament (72::Int)---- | 96-tone equal temperament.-equal_temperament_96 :: Tuning-equal_temperament_96 = equal_temperament (96::Int)---- * Harmonic series---- | Harmonic series to /n/th partial, with indicated octave.------ > harmonic_series 17 2-harmonic_series :: Integer -> Rational -> Tuning-harmonic_series n o = Tuning (Left [1 .. n%1]) o---- | Harmonic series on /n/.-harmonic_series_cps :: (Num t, Enum t) => t -> [t]-harmonic_series_cps n = [n,n * 2 ..]---- | /n/ elements of 'harmonic_series_cps'.------ > let r = [55,110,165,220,275,330,385,440,495,550,605,660,715,770,825,880,935]--- > in harmonic_series_cps_n 17 55 == r-harmonic_series_cps_n :: (Num a, Enum a) => Int -> a -> [a]-harmonic_series_cps_n n = take n . harmonic_series_cps---- | Sub-harmonic series on /n/.-subharmonic_series_cps :: (Fractional t,Enum t) => t -> [t]-subharmonic_series_cps n = map (* n) (map recip [1..])---- | /n/ elements of 'harmonic_series_cps'.------ > let r = [1760,880,587,440,352,293,251,220,196,176,160,147,135,126,117,110,104]--- > in map round (subharmonic_series_cps_n 17 1760) == r-subharmonic_series_cps_n :: (Fractional t,Enum t) => Int -> t -> [t]-subharmonic_series_cps_n n = take n . subharmonic_series_cps---- | /n/th partial of /f1/, ie. one indexed.------ > map (partial 55) [1,5,3] == [55,275,165]-partial :: (Num a, Enum a) => a -> Int -> a-partial f1 k = harmonic_series_cps f1 `at` (k - 1)--fold_ratio_to_octave' :: Integral i => Ratio i -> Ratio i-fold_ratio_to_octave' =-    let rec_f n = if n >= 2 then rec_f (n / 2) else if n < 1 then rec_f (n * 2) else n-    in rec_f---- | Error if input is less than or equal to zero.------ > map fold_ratio_to_octave_err [2/3,3/4] == [4/3,3/2]-fold_ratio_to_octave_err :: Integral i => Ratio i -> Ratio i-fold_ratio_to_octave_err n =-    if n <= 0-    then error "fold_ratio_to_octave"-    else fold_ratio_to_octave' n---- | Fold ratio until within an octave, ie. @1@ '<' /n/ '<=' @2@.------ > map fold_ratio_to_octave [0,1] == [Nothing,Just 1]-fold_ratio_to_octave :: Integral i => Ratio i -> Maybe (Ratio i)-fold_ratio_to_octave n = if n <= 0 then Nothing else Just (fold_ratio_to_octave' n)---- | Sun of numerator & denominator.-ratio_nd_sum :: Num a => Ratio a -> a-ratio_nd_sum r = numerator r + denominator r--min_by :: Ord a => (t -> a) -> t -> t -> t-min_by f p q = if f p <= f q then p else q---- | The interval between two pitches /p/ and /q/ given as ratio--- multipliers of a fundamental is /q/ '/' /p/.  The classes over such--- intervals consider the 'fold_ratio_to_octave' of both /p/ to /q/--- and /q/ to /p/.------ > map ratio_interval_class [2/3,3/2,3/4,4/3] == [3/2,3/2,3/2,3/2]--- > map ratio_interval_class [7/6,12/7] == [7/6,7/6]-ratio_interval_class :: Integral i => Ratio i -> Ratio i-ratio_interval_class i =-    let f = fold_ratio_to_octave_err-    in min_by ratio_nd_sum (f i) (f (recip i))---- | Derivative harmonic series, based on /k/th partial of /f1/.------ > import Music.Theory.Pitch------ > let {r = [52,103,155,206,258,309,361,412,464,515,567,618,670,721,773]--- >     ;d = harmonic_series_cps_derived 5 (octpc_to_cps (1,4))}--- > in map round (take 15 d) == r-harmonic_series_cps_derived :: (Ord a, Fractional a, Enum a) => Int -> a -> [a]-harmonic_series_cps_derived k f1 =-    let f0 = T.cps_in_octave_above f1 (partial f1 k)-    in harmonic_series_cps f0---- | Harmonic series to /n/th harmonic (folded, duplicated removed).------ > harmonic_series_folded_r 17 == [1,17/16,9/8,5/4,11/8,3/2,13/8,7/4,15/8]------ > let r = [0,105,204,386,551,702,841,969,1088]--- > in map (round . ratio_to_cents) (harmonic_series_folded_r 17) == r-harmonic_series_folded_r :: Integer -> [Rational]-harmonic_series_folded_r n = nub (sort (map fold_ratio_to_octave_err [1 .. n%1]))---- | 'ratio_to_cents' variant of 'harmonic_series_folded'.-harmonic_series_folded_c :: Integer -> [Cents]-harmonic_series_folded_c = map ratio_to_cents . harmonic_series_folded_r--harmonic_series_folded :: Integer -> Rational -> Tuning-harmonic_series_folded n o = Tuning (Left (harmonic_series_folded_r n)) o---- | @12@-tone tuning of first @21@ elements of the harmonic series.------ > cents_i harmonic_series_folded_21 == [0,105,204,298,386,471,551,702,841,969,1088]--- > divisions harmonic_series_folded_21 == 11-harmonic_series_folded_21 :: Tuning-harmonic_series_folded_21 = harmonic_series_folded 21 2+twelve_tone_equal_temperament_comma = 12 `T.nth_root` 2  -- * Cents  -- | Give cents difference from nearest 12ET tone. -- -- > let r = [50,-49,-2,0,2,49,50]--- > in map cents_et12_diff [650,651,698,700,702,749,750] == r+-- > map cents_et12_diff [650,651,698,700,702,749,750] == r cents_et12_diff :: Integral n => n -> n cents_et12_diff n =     let m = n `mod` 100@@ -368,7 +209,7 @@ -- | Fractional form of 'cents_et12_diff'. fcents_et12_diff :: Real n => n -> n fcents_et12_diff n =-    let m = n `mod'` 100+    let m = n `Fixed.mod'` 100     in if m > 50 then m - 100 else m  -- | The class of cents intervals has range @(0,600)@.@@ -376,7 +217,7 @@ -- > map cents_interval_class [50,1150,1250] == [50,50,50] -- -- > let r = concat [[0,50 .. 550],[600],[550,500 .. 0]]--- > in map cents_interval_class [1200,1250 .. 2400] == r+-- > map cents_interval_class [1200,1250 .. 2400] == r cents_interval_class :: Integral a => a -> a cents_interval_class n =     let n' = n `mod` 1200@@ -385,7 +226,7 @@ -- | Fractional form of 'cents_interval_class'. fcents_interval_class :: Real a => a -> a fcents_interval_class n =-    let n' = n `mod'` 1200+    let n' = n `Fixed.mod'` 1200     in if n' > 600 then 1200 - n' else n'  -- | Always include the sign, elide @0@.@@ -416,203 +257,34 @@ cents_diff_html :: (Num a, Ord a, Show a) => a -> String cents_diff_html = cents_diff_br ("<SUP>","</SUP>") --- * Midi---- | (/n/ -> /dt/).  Function from midi note number /n/ to--- 'Midi_Detune' /dt/.  The incoming note number is the key pressed,--- which may be distant from the note sounded.-type Midi_Tuning_F = Int -> T.Midi_Detune---- | Variant for tunings that are incomplete.-type Sparse_Midi_Tuning_F = Int -> Maybe T.Midi_Detune---- | Variant for sparse tunings that require state.-type Sparse_Midi_Tuning_ST_F st = st -> Int -> (st,Maybe T.Midi_Detune)---- | Lift 'Midi_Tuning_F' to 'Sparse_Midi_Tuning_F'.-lift_tuning_f :: Midi_Tuning_F -> Sparse_Midi_Tuning_F-lift_tuning_f tn_f = Just . tn_f---- | Lift 'Sparse_Midi_Tuning_F' to 'Sparse_Midi_Tuning_ST_F'.-lift_sparse_tuning_f :: Sparse_Midi_Tuning_F -> Sparse_Midi_Tuning_ST_F st-lift_sparse_tuning_f tn_f st k = (st,tn_f k)---- | (t,c,k) where t=tuning (must have 12 divisions of octave),--- c=cents deviation (ie. constant detune offset), k=midi offset--- (ie. value to be added to incoming midi note number).-type D12_Midi_Tuning = (Tuning,Cents,Int)---- | 'Midi_Tuning_F' for 'D12_Midi_Tuning'.------ > let f = d12_midi_tuning_f (equal_temperament 12,0,0)--- > map f [0..127] == zip [0..127] (repeat 0)-d12_midi_tuning_f :: D12_Midi_Tuning -> Midi_Tuning_F-d12_midi_tuning_f (t,c_diff,k) n =-    let (_,pc) = T.midi_to_octpc (n + k)-        dt = zipWith (-) (tn_cents t) [0,100 .. 1200]-    in if tn_divisions t /= 12-       then error "d12_midi_tuning_f: not d12"-       else case dt `atMay` pc of-              Nothing -> error "d12_midi_tuning_f: pc?"-              Just c -> (n,c + c_diff)---- | (t,f0,k,g) where t=tuning, f0=fundamental frequency, k=midi note--- number for f0, g=gamut-type CPS_Midi_Tuning = (Tuning,Double,Int,Int)---- | 'Midi_Tuning_F' for 'CPS_Midi_Tuning'.  The function is sparse, it is only--- valid for /g/ values from /k/.------ > let f = cps_midi_tuning_f (equal_temperament 72,T.midi_to_cps 59,59,72 * 4)--- > map f [59 .. 59 + 72]-cps_midi_tuning_f :: CPS_Midi_Tuning -> Sparse_Midi_Tuning_F-cps_midi_tuning_f (t,f0,k,g) n =-    let r = tn_approximate_ratios_cyclic t-        m = take g (map (T.cps_to_midi_detune . (* f0)) r)-    in m `atMay` (n - k)---- * Midi tuning tables.+-- * Savart --- | Midi-note-number -> CPS table, possibly sparse.-type MNN_CPS_Table = [(Int,Double)]+-- | Felix Savart (1791-1841), the ratio of 10:1 is assigned a value of 1000 savarts.+type Savarts = Double --- | Generates 'MNN_CPS_Table' given 'Midi_Tuning_F' with keys for all valid @MNN@.+-- | Ratio to savarts. ----- > import Sound.SC3.Plot--- > plot_p2_ln [map (fmap round) (gen_cps_tuning_tbl f)]-gen_cps_tuning_tbl :: Sparse_Midi_Tuning_F -> MNN_CPS_Table-gen_cps_tuning_tbl tn_f =-    let f n = case tn_f n of-                Just r -> Just (n,T.midi_detune_to_cps r)-                Nothing -> Nothing-    in mapMaybe f [0 .. 127]---- * Derived (secondary) tuning table (DTT) lookup.---- | Given an 'MNN_CPS_Table' /tbl/, a list of @CPS@ /c/, and a @MNN@ /m/--- find the @CPS@ in /c/ that is nearest to the @CPS@ in /t/ for /m/.-dtt_lookup :: (Eq k, Num v, Ord v) => [(k,v)] -> [v] -> k -> (Maybe v,Maybe v)-dtt_lookup tbl cps n =-    let f = lookup n tbl-    in (f,fmap (T.find_nearest_err cps) f)---- | Require table be non-sparse.-dtt_lookup_err :: (Eq k, Num v, Ord v) => [(k,v)] -> [v] -> k -> (k,v,v)-dtt_lookup_err tbl cps n =-    case dtt_lookup tbl cps n of-      (Just f,Just g) -> (n,f,g)-      _ -> error "dtt_lookup"---- | Given two tuning tables generate the @dtt@ table.-gen_dtt_lookup_tbl :: MNN_CPS_Table -> MNN_CPS_Table -> MNN_CPS_Table-gen_dtt_lookup_tbl t0 t1 =-    let ix = [0..127]-        cps = sort (map (T.p3_third . dtt_lookup_err t0 (map snd t1)) ix)-    in zip ix cps--gen_dtt_lookup_f :: MNN_CPS_Table -> MNN_CPS_Table -> Midi_Tuning_F-gen_dtt_lookup_f t0 t1 =-    let m = M.fromList (gen_dtt_lookup_tbl t0 t1)-    in T.cps_to_midi_detune . T.map_ix_err m---- * Euler-Fokker genus <http://www.huygens-fokker.org/microtonality/efg.html>---- | Normal form, value with occurences count (ie. exponent in notation above).-type EFG i = [(i,Int)]+-- > fratio_to_savarts 10 == 1000+-- > fratio_to_savarts 2 == 301.02999566398114+fratio_to_savarts :: Floating a => a -> a+fratio_to_savarts r = 1000 * logBase 10 r --- | Degree of EFG, ie. sum of exponents.+-- | Savarts to ratio. ----- > efg_degree [(3,3),(7,2)] == 3 + 2-efg_degree :: EFG i -> Int-efg_degree = sum . map snd+-- > savarts_to_fratio 1000 == 10+-- > savarts_to_fratio 301.02999566398118 == 2+savarts_to_fratio :: Floating a => a -> a+savarts_to_fratio s = 10 ** (s / 1000) --- | Number of tones of EFG, ie. product of increment of exponents.+-- | Savarts to cents. ----- > efg_tones [(3,3),(7,2)] == (3 + 1) * (2 + 1)-efg_tones :: EFG i -> Int-efg_tones = product . map ((+ 1) . snd)+-- > savarts_to_cents 1 == 3.9863137138648352+savarts_to_cents :: Floating a => a -> a+savarts_to_cents s = s * (6 / (5 * logBase 10 2)) --- | Collate a genus given as a multiset into standard form, ie. histogram.+-- | Cents to savarts. ----- > efg_collate [3,3,3,7,7] == [(3,3),(7,2)]-efg_collate :: Ord i => [i] -> EFG i-efg_collate = T.histogram . sort--{- | Factors of EFG given with co-ordinate of grid location.--> efg_factors [(3,3)]--> let r = [([0,0],[]),([0,1],[7]),([0,2],[7,7])->         ,([1,0],[3]),([1,1],[3,7]),([1,2],[3,7,7])->         ,([2,0],[3,3]),([2,1],[3,3,7]),([2,2],[3,3,7,7])->         ,([3,0],[3,3,3]),([3,1],[3,3,3,7]),([3,2],[3,3,3,7,7])]-> in efg_factors [(3,3),(7,2)] == r---}-efg_factors :: EFG i -> [([Int],[i])]-efg_factors efg =-    let k = map (\(_,n) -> [0 .. n]) efg-        k' = if length efg == 1-             then concatMap (map return) k-             else T.nfold_cartesian_product k-        z = map fst efg-        f ix = (ix,concat (zipWith (\n m -> replicate n (z !! m)) ix [0..]))-    in map f k'--{- | Ratios of EFG, taking /n/ as the 1:1 ratio, with indices, folded into one octave.--> let r = sort $ map snd $ efg_ratios 7 [(3,3),(7,2)]-> r == [1/1,9/8,8/7,9/7,21/16,189/128,3/2,27/16,12/7,7/4,27/14,63/32]-> map (round . ratio_to_cents) r == [0,204,231,435,471,675,702,906,933,969,1137,1173]--      0:         1/1          C          0.000 cents-      1:         9/8          D        203.910 cents-      2:         8/7          D+       231.174 cents-      3:         9/7          E+       435.084 cents-      4:        21/16         F-       470.781 cents-      5:       189/128        G-       674.691 cents-      6:         3/2          G        701.955 cents-      7:        27/16         A        905.865 cents-      8:        12/7          A+       933.129 cents-      9:         7/4          Bb-      968.826 cents-     10:        27/14         B+      1137.039 cents-     11:        63/32         C-      1172.736 cents-     12:         2/1          C       1200.000 cents--> let r' = sort $ map snd $ efg_ratios 5 [(5,2),(7,3)]-> r' == [1/1,343/320,35/32,49/40,5/4,343/256,7/5,49/32,8/5,1715/1024,7/4,245/128]-> map (round . ratio_to_cents) r' == [0,120,155,351,386,506,583,738,814,893,969,1124]--> let r'' = sort $ map snd $ efg_ratios 3 [(3,1),(5,1),(7,1)]-> r'' == [1/1,35/32,7/6,5/4,4/3,35/24,5/3,7/4]-> map (round . ratio_to_cents) r'' == [0,155,267,386,498,653,884,969]--> let c0 = [0,204,231,435,471,675,702,906,933,969,1137,1173,1200]-> let c1 = [0,120,155,351,386,506,583,738,814,893,969,1124,1200]-> let c2 = [0,155,267,386,498,653,884,969,1200]-> let f (c',y) = map (\x -> (x,y,x,y + 10)) c'-> map f (zip [c0,c1,c2] [0,20,40])---}-efg_ratios :: Real r => Rational -> EFG r -> [([Int],Rational)]-efg_ratios n =-    let to_r = fold_ratio_to_octave_err . (/ n) . toRational . product-        f (ix,i) = (ix,to_r i)-    in map f . efg_factors--{- | Generate a line drawing, as a set of (x0,y0,x1,y1) 4-tuples.-     h=row height, m=distance of vertical mark from row edge, k=distance between rows--> let e = [[3,3,3],[3,3,5],[3,5,5],[3,5,7],[3,7,7],[5,5,5],[5,5,7],[3,3,7],[5,7,7],[7,7,7]]-> let e = [[3,3,3],[5,5,5],[7,7,7],[3,3,5],[3,5,5],[5,5,7],[5,7,7],[3,7,7],[3,3,7],[3,5,7]]-> let e' = map efg_collate e-> efg_diagram_set (round,25,4,75) e'---}-efg_diagram_set :: (Enum n,Real n) => (Cents -> n,n,n,n) -> [EFG n] -> [(n,n,n,n)]-efg_diagram_set (to_f,h,m,k) e =-    let f = (++ [1200]) . sort . map (to_f . ratio_to_cents . snd) . efg_ratios 1-        g (c,y) = let y' = y + h-                      b = [(0,y,1200,y),(0,y',1200,y')]-                  in b ++ map (\x -> (x,y + m,x,y' - m)) c-    in concatMap g (zip (map f e) [0,k ..])+-- > cents_to_savarts 3.9863137138648352 == 1+-- > cents_to_savarts 1200 == ratio_to_savarts 2+cents_to_savarts :: Floating a => a -> a+cents_to_savarts c = c / (6 / (5 * logBase 10 2))
Music/Theory/Tuning/Alves_1997.hs view
@@ -3,54 +3,58 @@ -- 1997.  <http://www2.hmc.edu/~alves/pleng.html> module Music.Theory.Tuning.Alves_1997 where -import Music.Theory.Tuning+import Music.Theory.Tuning.Type {- hmt -} +-- > import Music.Theory.Tuning {- hmt -} -- > let c = [0,231,498,765,996]--- > in map (round.to_cents_r) alves_slendro_r == c+-- > map (round . ratio_to_cents) alves_slendro_r == c alves_slendro_r :: [Rational] alves_slendro_r = [1,8/7,4/3,14/9,16/9] --- | HMC /slendro/ tuning.------ > cents_i alves_slendro == [0,231,498,765,996]------ > scl <- scl_load "slendro_alves"--- > cents_i (scale_tuning 0.01 scl) == cents_i alves_slendro+{- | HMC /slendro/ tuning.++> cents_i alves_slendro == [0,231,498,765,996]++> import Music.Theory.Tuning.Scala {- hmt -}+> scl <- scl_load "alves_slendro"+> tn_cents_i (scale_to_tuning 0.01 scl) == tn_cents_i alves_slendro+-} alves_slendro :: Tuning-alves_slendro = Tuning (Left alves_slendro_r) 2+alves_slendro = Tuning (Left alves_slendro_r) Nothing  -- > let c = [0,231,316,702,814]--- > in map (round.to_cents_r) alves_pelog_bem_r == c+-- > map (round . ratio_to_cents) alves_pelog_bem_r == c alves_pelog_bem_r :: [Rational] alves_pelog_bem_r = [1,8/7,6/5,3/2,8/5] --- | HMC /pelog bem/ tuning.------ > cents_i alves_pelog_bem == [0,231,316,702,814]------ > scl <- scl_load "pelog_alves"--- > cents_i (scale_tuning 0.01 scl) == [0,231,316,471,702,814,969]+{- | HMC /pelog bem/ tuning.++> tn_cents_i alves_pelog_bem == [0,231,316,702,814]++> scl <- scl_load "alves_pelog"+> tn_cents_i (scale_to_tuning 0.01 scl) == [0,231,316,471,702,814,969]+-} alves_pelog_bem :: Tuning-alves_pelog_bem = Tuning (Left alves_pelog_bem_r) 2+alves_pelog_bem = Tuning (Left alves_pelog_bem_r) Nothing  -- > let c = [0,386,471,857,969]--- > in map (round.to_cents_r) alves_pelog_barang_r == c+-- > map (round . ratio_to_cents) alves_pelog_barang_r == c alves_pelog_barang_r :: [Rational] alves_pelog_barang_r = [1,5/4,21/16,105/64,7/4]  -- | HMC /pelog barang/ tuning. ----- > cents_i alves_pelog_barang == [0,386,471,857,969]+-- > tn_cents_i alves_pelog_barang == [0,386,471,857,969] alves_pelog_barang :: Tuning-alves_pelog_barang = Tuning (Left alves_pelog_barang_r) 2+alves_pelog_barang = Tuning (Left alves_pelog_barang_r) Nothing  -- > let c = [0,386,471,702,969]--- > in map (round.to_cents_r) alves_pelog_23467 == c+-- > map (round . ratio_to_cents) alves_pelog_23467_r == c alves_pelog_23467_r :: [Rational] alves_pelog_23467_r = [1,5/4,21/16,3/2,7/4]  -- | HMC /pelog 2,3,4,6,7/ tuning. ----- > cents_i alves_pelog_23467 == [0,386,471,702,969]+-- > tn_cents_i alves_pelog_23467 == [0,386,471,702,969] alves_pelog_23467 :: Tuning-alves_pelog_23467 = Tuning (Left alves_pelog_23467_r) 2+alves_pelog_23467 = Tuning (Left alves_pelog_23467_r) Nothing
+ Music/Theory/Tuning/Anamark.hs view
@@ -0,0 +1,106 @@+-- | Anamark tuning (TUN) files+--+-- <https://www.mark-henning.de/files/am/Tuning_File_V2_Doc.pdf>+module Music.Theory.Tuning.Anamark where++import Text.Printf {- base -}++import qualified Music.Theory.List as T++-- | Format section string+tun_sec :: String -> String+tun_sec = printf "[%s]"++-- | Format 'String' (text) attribute+tun_attr_txt :: (String,String) -> String+tun_attr_txt (k,v) = printf "%s = \"%s\"" k v++-- | Format 'Int' attribute+tun_attr_int :: (String,Int) -> String+tun_attr_int (k,v) = printf "%s = %d" k v++-- | Format 'Double' attribute+tun_attr_real :: (String,Double) -> String+tun_attr_real (k,v) = printf "%s = %f" k v++-- | TUN V.200 /Scale Begin/ (header) section.+tun_begin :: [String]+tun_begin =+  [tun_sec "Scale Begin"+  ,tun_attr_txt ("Format","AnaMark-TUN")+  ,tun_attr_int ("FormatVersion",200)+  ,tun_attr_txt ("FormatSpecs","http://www.mark-henning.de/eternity/tuningspecs.html")]++-- | Format /Info/ section given Name and ID (the only required fields).+--+-- > tun_info ("name","id")+tun_info :: (String,String) -> [String]+tun_info (nm,k) =+  [tun_sec "Info"+  ,tun_attr_txt ("Name",nm)+  ,tun_attr_txt ("ID",k)]++-- | Format /Tuning/ section given sequence of 128 integral cents values.+--+-- > tun_tuning [0,100.. 12700]+tun_tuning :: [Int] -> [String]+tun_tuning =+  let f k c = printf "note %d = %d" k c+  in (:) (tun_sec "Tuning") . zipWith f [0::Int .. 127]++-- | The default base frequency for /Exact Tuning/ (A4=440)+tun_f0_default :: Double+tun_f0_default = 8.1757989156437073336++-- | Format /Exact Tuning/ section given base frequency and sequence of 128 real cents values.+--+-- > tun_exact_tuning tun_f0_default [0,100.. 12700]+tun_exact_tuning :: Double -> [Double] -> [String]+tun_exact_tuning f0 =+  let f k c = printf "note %d = %f" k c+      hdr = [tun_sec "Exact Tuning"+            ,tun_attr_real ("BaseFreq",f0)]+  in (++) hdr  . zipWith f [0::Int .. 127]++{- | Format /Functional Tuning/ section given base frequency and sequence of 128 real cents values.++This simply sets note zero to /f0/ and increments each note by the difference from the previous note.++> tun_functional_tuning tun_f0_default [0,100.. 12700]+-}+tun_functional_tuning :: Double -> [Double] -> [String]+tun_functional_tuning f0 =+  let f k c = printf "note %d = \"#x=%d %% %f\"" k (k - 1) c+      hdr = [tun_sec "Functional Tuning"+            ,printf "note 0 = \"# %f\"" f0]+  in (++) hdr  . zipWith f [1::Int .. 127] . T.d_dx++-- | Format /Scale End/ section header.+tun_end :: [String]+tun_end =+  [tun_sec "Scale End"]++-- | Synonym for a list of strings.+type TUN = [String]++-- | Version 1 has just the /Tuning/ and /Exact Tuning/.+tun_from_cents_version_one :: (Double, [Double]) -> TUN+tun_from_cents_version_one (f0,c) =+  concat [tun_tuning (map round c)+         ,tun_exact_tuning f0 c]++-- | Version 2 files have, in addition, /Begin/, /Info/, /Functional Tuning/ and /End/ sections.+tun_from_cents_version_two :: (String,String) -> (Double, [Double]) -> TUN+tun_from_cents_version_two (nm,k) (f0,c) =+  concat [tun_begin+         ,tun_info (nm,k)+         ,tun_tuning (map round c)+         ,tun_exact_tuning f0 c+         ,tun_functional_tuning f0 c+         ,tun_end]++-- > t = tun_from_cents_version_one (tun_f0_default,[0,100 .. 12700])+-- > t = tun_from_cents_version_two ("equal-temperament-12","et12") (tun_f0_default,[0,100 .. 12700])+-- > tun_store "/home/rohan/et12.tun" t+tun_store :: FilePath -> TUN -> IO ()+tun_store fn = writeFile fn . unlines
− Music/Theory/Tuning/DB.hs 
@@ -1,62 +0,0 @@--- | DB of locally defined tunings, but for ordinary use see "Music.Theory.Tuning.Scala".-module Music.Theory.Tuning.DB where--import Data.List {- base -}--import Music.Theory.Tuning--import Music.Theory.Tuning.Alves_1997-import Music.Theory.Tuning.Gann_1993-import Music.Theory.Tuning.Polansky_1978-import Music.Theory.Tuning.Polansky_1985c--import Music.Theory.Tuning.DB.Alves-import Music.Theory.Tuning.DB.Gann-import Music.Theory.Tuning.DB.Microtonal_Synthesis-import Music.Theory.Tuning.DB.Riley-import Music.Theory.Tuning.DB.Werckmeister---- | (last-name,first-name,title,year,hmt/tuning,scala/name)-type Named_Tuning = (String,String,String,String,Tuning,String)--named_tuning_t :: Named_Tuning -> Tuning-named_tuning_t (_,_,_,_,t,_) = t--tuning_db :: [Named_Tuning]-tuning_db =-    [("Aaron","Pietro","","1523",pietro_aaron_1523,"meanquar")-    ,("Alves","Bill","Slendro","",alves_slendro,"slendro_alves")-    ,("Alves","Bill","Pelog/Bem","",alves_pelog_bem,"")-    ,("Alves","Bill","Pelog/Barang","",alves_pelog_barang,"")-    ,("Gann","Kyle","Superparticular","1992",gann_superparticular,"gann_super")-    ,("Harrison","Lou","Ditone","",harrison_ditone,"")-    ,("Harrison","Lou","16-tone","",lou_harrison_16,"harrison_16")-    ,("Johnston","Ben","MTP","1977",ben_johnston_mtp_1977,"")-    ,("Johnston","Ben","25-tone","",ben_johnston_25,"johnston_25")-    ,("Kirnberger","Johann Philipp","III","",kirnberger_iii,"kirnberger")-    ,("Malcolm","Alexander","Monochord","1721",five_limit_tuning,"malcolm")-    ,("Partch","Harry","43-tone","",partch_43,"partch_43")-    ,("Polansky","Larry","Piano Study #5","1985",ps5_jpr,"polansky_ps")-    ,("Polansky","Larry","Psaltery","1978",psaltery_o,"")-    ,("Riley","Terry","Harp of New Albion","",riley_albion,"riley_albion")-    ,("Tsuda","Mayumi","13-limit","",mayumi_tsuda,"tsuda13")-    ,("Vallotti","","","1754",vallotti,"vallotti")-    ,("Werckmeister","Andreas","Werckmeister III","",werckmeister_iii,"werck3")-    ,("Werckmeister","Andreas","Werckmeister IV","",werckmeister_iv,"werck4")-    ,("Werckmeister","Andreas","Werckmeister V","",werckmeister_v,"werck5")-    ,("Werckmeister","Andreas","Werckmeister VI","",werckmeister_vi,"werck6")-    ,("Young","La Monte","The Well-Tuned Piano","",lmy_wtp,"young-lm_piano")-    ,("Young","Thomas","","1799",thomas_young_1799,"young2")-    ,("Zarlino","Gioseffo","","1588",zarlino_1588,"zarlino2")-    ,("","","JI/12 7-limit","",septimal_tritone_just_intonation,"ji_12")-    ,("","","ET/12","",equal_temperament_12,"")-    ,("","","ET/19","",equal_temperament_19,"")-    ,("","","ET/31","",equal_temperament_31,"")-    ,("","","ET/53","",equal_temperament_53,"")-    ,("","","ET/72","",equal_temperament_72,"")-    ,("","","ET/96","",equal_temperament_96,"")-    ,("","","Pythagorean/12","",pythagorean_12,"pyth_12")-    ]--tuning_db_lookup_scl :: String -> Maybe Tuning-tuning_db_lookup_scl nm = fmap named_tuning_t (find (\(_,_,_,_,_,scl) -> scl == nm) tuning_db)
− Music/Theory/Tuning/DB/Alves.hs 
@@ -1,26 +0,0 @@--- | Bill Alves.-module Music.Theory.Tuning.DB.Alves where--import Music.Theory.Tuning {- hmt -}---- | Ratios for 'harrison_ditone'.------ > let c = [0,114,204,294,408,498,612,702,816,906,996,1110]--- > in map (round . ratio_to_cents) harrison_ditone_r == c-harrison_ditone_r :: [Rational]-harrison_ditone_r =-    [1,2187/2048 {- 256/243 -}-    ,9/8,32/27-    ,81/64-    ,4/3,729/512-    ,3/2,6561/4096 {- 128/81 -}-    ,27/16,16/9-    ,243/128]---- | Ditone/pythagorean tuning,--- see <http://www.billalves.com/porgitaro/ditonesettuning.html>------ > tn_divisions harrison_ditone == 12--- > tn_cents_i harrison_ditone == [0,114,204,294,408,498,612,702,816,906,996,1110]-harrison_ditone :: Tuning-harrison_ditone = Tuning (Left harrison_ditone_r) 2
− Music/Theory/Tuning/DB/Gann.hs 
@@ -1,130 +0,0 @@--- | Kyle Gann.-module Music.Theory.Tuning.DB.Gann where--import Music.Theory.Tuning {- hmt -}---- * Historical---- | Cents for 'pietro_aaron_1523'.------ > let c = [0,76,193,310,386,503,580,697,773,890,1007,1083]--- > in map round pietro_aaron_1523_c == c------ > map ((+ 60) . (/ 100)) pietro_aaron_1523_c-pietro_aaron_1523_c :: [Cents]-pietro_aaron_1523_c =-    [0,76.0-    ,193.2,310.3-    ,386.3-    ,503.4,579.5-    ,696.8,772.6-    ,889.7,1006.8-    ,1082.9]---- | Pietro Aaron (1523) meantone temperament, see--- <http://www.kylegann.com/histune.html>------ > cents_i pietro_aaron_1523 == [0,76,193,310,386,503,580,697,773,890,1007,1083]------ > import Music.Theory.Tuning.Scala--- > scl <- scl_load "meanquar"--- > cents_i (scale_tuning 0.01 scl) == [0,76,193,310,386,503,579,697,773,890,1007,1083]-pietro_aaron_1523 :: Tuning-pietro_aaron_1523 = Tuning (Right pietro_aaron_1523_c) 2---- | Cents for 'thomas_young_1799'.------ > let c = [0,94,196,298,392,500,592,698,796,894,1000,1092]--- > in map round thomas_young_1799_c == c-thomas_young_1799_c :: [Cents]-thomas_young_1799_c =-    [0,93.9-    ,195.8,297.8-    ,391.7-    ,499.9,591.9-    ,697.9,795.8-    ,893.8,999.8-    ,1091.8]---- | Thomas Young (1799), Well Temperament, <http://www.kylegann.com/histune.html>.------ > cents_i thomas_young_1799 == [0,94,196,298,392,500,592,698,796,894,1000,1092]------ > scl <- scl_load "young2"--- > cents_i (scale_tuning 0.01 scl) == cents_i thomas_young_1799-thomas_young_1799 :: Tuning-thomas_young_1799 = Tuning (Right thomas_young_1799_c) 2---- | Ratios for 'zarlino'.------ > length zarlino_1588_r == 16-zarlino_1588_r :: [Rational]-zarlino_1588_r = [1/1,25/24,10/9,9/8,32/27,6/5,5/4,4/3,25/18,45/32,3/2,25/16,5/3,16/9,9/5,15/8]---- | Gioseffo Zarlino, 1588, see <http://www.kylegann.com/tuning.html>.------ > divisions zarlino_1588 == 16--- > cents_i zarlino_1588 == [0,71,182,204,294,316,386,498,569,590,702,773,884,996,1018,1088]------ > scl <- scl_load "zarlino2"--- > cents_i (scale_tuning 0.01 scl) == cents_i zarlino_1588-zarlino_1588 :: Tuning-zarlino_1588 = Tuning (Left zarlino_1588_r) 2---- * 20th Century---- | Ratios for 'ben_johnston_mtp_1977'.------ > let c = [0,105,204,298,386,471,551,702,841,906,969,1088]--- > in map (round . ratio_to_cents) ben_johnston_mtp_1977_r == c-ben_johnston_mtp_1977_r :: [Rational]-ben_johnston_mtp_1977_r =-    [1,17/16-    ,9/8,19/16-    ,5/4-    ,21/16,11/8-    ,3/2,13/8-    ,27/16,7/4-    ,15/8]---- | Ben Johnston's \"Suite for Microtonal Piano\" (1977), see--- <http://www.kylegann.com/tuning.html>------ > cents_i ben_johnston_mtp_1977 == [0,105,204,298,386,471,551,702,841,906,969,1088]-ben_johnston_mtp_1977 :: Tuning-ben_johnston_mtp_1977 = Tuning (Left ben_johnston_mtp_1977_r) 2---- * Gann---- | Ratios for 'gann_arcana_xvi'.-gann_arcana_xvi_r :: [Rational]-gann_arcana_xvi_r =-    [1/1,21/20,16/15,9/8,7/6,6/5,11/9,5/4,21/16,4/3,27/20,7/5-    ,22/15,3/2,55/36,8/5,44/27,5/3,42/25,7/4,9/5,11/6,15/8,88/45]---- | Kyle Gann, _Arcana XVI_, see <http://www.kylegann.com/Arcana.html>.------ > let r = [0,84,112,204,267,316,347,386,471,498,520,583,663,702,734,814,845,884,898,969,1018,1049,1088,1161]--- > in cents_i gann_arcana_xvi == r-gann_arcana_xvi :: Tuning-gann_arcana_xvi = Tuning (Left gann_arcana_xvi_r) 2---- | Ratios for 'gann_superparticular'.-gann_superparticular_r :: [Rational]-gann_superparticular_r =-    [1/1,11/10,10/9,9/8,8/7,7/6,6/5,5/4,9/7,4/3-    ,11/8,7/5,10/7,3/2-    ,11/7,14/9,8/5,5/3,12/7,7/4,16/9,9/5]---- | Kyle Gann, _Superparticular_, see <http://www.kylegann.com/Super.html>.------ > divisions gann_superparticular == 22------ > let r = [0,165,182,204,231,267,316,386,435,498,551,583,617,702--- >         ,782,765,814,884,933,969,996,1018]--- > in cents_i gann_superparticular == r------ > scl <- scl_load "gann_super"--- > cents_i (scale_tuning 0.01 scl) == cents_i gann_superparticular-gann_superparticular :: Tuning-gann_superparticular = Tuning (Left gann_superparticular_r) 2
− Music/Theory/Tuning/DB/Microtonal_Synthesis.hs 
@@ -1,230 +0,0 @@--- | <http://www.microtonal-synthesis.com/scales.html>-module Music.Theory.Tuning.DB.Microtonal_Synthesis where--import Music.Theory.Tuning {- hmt -}---- | Ratios for 'pythagorean'.-pythagorean_12_r :: [Rational]-pythagorean_12_r =-    [1,2187/2048 {- 256/243 -}-    ,9/8,32/27-    ,81/64-    ,4/3,729/512-    ,3/2,6561/4096 {- 128/81 -}-    ,27/16,16/9-    ,243/128]---- | Pythagorean tuning, <http://www.microtonal-synthesis.com/scale_pythagorean.html>.------ > cents_i pythagorean_12 == [0,114,204,294,408,498,612,702,816,906,996,1110]------ > scl <- scl_load "pyth_12"--- > cents_i (scale_tuning 0.1 scl) == cents_i pythagorean_12-pythagorean_12 :: Tuning-pythagorean_12 = Tuning (Left pythagorean_12_r) 2---- | Ratios for 'five_limit_tuning'.------ > let c = [0,112,204,316,386,498,590,702,814,884,996,1088]--- > in map (round . ratio_to_cents) five_limit_tuning_r == c-five_limit_tuning_r :: [Rational]-five_limit_tuning_r =-    [1,16/15-    ,9/8,6/5-    ,5/4-    ,4/3,45/32 {- 64/45 -}-    ,3/2,8/5-    ,5/3,16/9 {- 9/5 -}-    ,15/8]---- | Five-limit tuning (five limit just intonation), Alexander Malcolm's Monochord (1721).------ > cents_i five_limit_tuning == [0,112,204,316,386,498,590,702,814,884,996,1088]------ > scl <- scl_load "malcolm"--- > cents_i (scale_tuning 0.1 scl) == cents_i five_limit_tuning-five_limit_tuning :: Tuning-five_limit_tuning = Tuning (Left five_limit_tuning_r) 2---- | Ratios for 'septimal_tritone_just_intonation'.------ > let c = [0,112,204,316,386,498,583,702,814,884,1018,1088]--- > in map (round . ratio_to_cents) septimal_tritone_just_intonation == c-septimal_tritone_just_intonation_r :: [Rational]-septimal_tritone_just_intonation_r =-    [1,16/15-    ,9/8,6/5-    ,5/4-    ,4/3,7/5-    ,3/2,8/5-    ,5/3,9/5-    ,15/8]---- | Septimal tritone Just Intonation, see--- <http://www.microtonal-synthesis.com/scale_just_intonation.html>------ > let c = [0,112,204,316,386,498,583,702,814,884,1018,1088]--- > in cents_i septimal_tritone_just_intonation == c------ > scl <- scl_load "ji_12"--- > cents_i (scale_tuning 0.1 scl) == cents_i septimal_tritone_just_intonation-septimal_tritone_just_intonation :: Tuning-septimal_tritone_just_intonation = Tuning (Left septimal_tritone_just_intonation_r) 2---- | Ratios for 'seven_limit_just_intonation'.------ > let c = [0,112,204,316,386,498,583,702,814,884,969,1088]--- > in map (round . ratio_to_cents) seven_limit_just_intonation == c-seven_limit_just_intonation_r :: [Rational]-seven_limit_just_intonation_r =-    [1,16/15-    ,9/8,6/5-    ,5/4-    ,4/3,7/5-    ,3/2,8/5-    ,5/3,7/4-    ,15/8]---- | Seven limit Just Intonation.------ > cents_i seven_limit_just_intonation == [0,112,204,316,386,498,583,702,814,884,969,1088]-seven_limit_just_intonation :: Tuning-seven_limit_just_intonation = Tuning (Left seven_limit_just_intonation_r) 2---- | Approximate ratios for 'kirnberger_iii'.------ > let c = [0,90,193,294,386,498,590,697,792,890,996,1088]--- > in map (round.to_cents) kirnberger_iii_ar == c-kirnberger_iii_ar :: [Approximate_Ratio]-kirnberger_iii_ar =-    [1,256/243-    ,sqrt 5 / 2,32/27-    ,5/4-    ,4/3,45/32-    ,5 ** 0.25,128/81-    ,(5 ** 0.75)/2,16/9-    ,15/8]---- | <http://www.microtonal-synthesis.com/scale_kirnberger.html>.------ > cents_i kirnberger_iii == [0,90,193,294,386,498,590,697,792,890,996,1088]------ > scl <- scl_load "kirnberger"--- > cents_i (scale_tuning 0.1 scl) == cents_i kirnberger_iii-kirnberger_iii :: Tuning-kirnberger_iii = Tuning (Right (map approximate_ratio_to_cents kirnberger_iii_ar)) 2---- > let c = [0,94,196,298,392,502,592,698,796,894,1000,1090]--- > in map round vallotti_c == c-vallotti_c :: [Cents]-vallotti_c =-    [0.0,94.135-    ,196.09,298.045-    ,392.18-    ,501.955,592.18-    ,698.045,796.09-    ,894.135,1000.0-    ,1090.225]---- | Vallotti & Young scale (Vallotti version), see--- <http://www.microtonal-synthesis.com/scale_vallotti_young.html>.------ > cents_i vallotti == [0,94,196,298,392,502,592,698,796,894,1000,1090]------ > scl <- scl_load "vallotti"--- > cents_i (scale_tuning 0.1 scl) == cents_i vallotti-vallotti :: Tuning-vallotti = Tuning (Right vallotti_c) 2---- > let c = [0,128,139,359,454,563,637,746,841,911,1072,1183]--- > in map (round . ratio_to_cents) mayumi_tsuda == c-mayumi_tsuda_r :: [Rational]-mayumi_tsuda_r =-    [1,14/13-    ,13/12,16/13-    ,13/10-    ,18/13,13/9-    ,20/13,13/8-    ,22/13,13/7-    ,208/105]---- | Mayumi Tsuda 13-limit Just Intonation scale,--- <http://www.microtonal-synthesis.com/scale_reinhard.html>.------ > cents_i mayumi_tsuda == [0,128,139,359,454,563,637,746,841,911,1072,1183]------ > scl <- scl_load "tsuda13"--- > cents_i (scale_tuning 0.1 scl) == cents_i mayumi_tsuda-mayumi_tsuda :: Tuning-mayumi_tsuda = Tuning (Left mayumi_tsuda_r) 2---- | Ratios for 'lou_harrison_16'.------ > length lou_harrison_16_r == 16------ > let c = [0,112,182,231,267,316,386,498,603,702,814,884,933,969,1018,1088]--- > in map (round . ratio_to_cents) lou_harrison_16_r == c-lou_harrison_16_r :: [Rational]-lou_harrison_16_r =-    [1,16/15-    ,10/9,8/7-    ,7/6,6/5,5/4-    ,4/3-    ,17/12-    ,3/2-    ,8/5,5/3,12/7-    ,7/4,9/5,15/8]---- | Lou Harrison 16 tone Just Intonation scale, see--- <http://www.microtonal-synthesis.com/scale_harrison_16.html>------ > let r = [0,112,182,231,267,316,386,498,603,702,814,884,933,969,1018,1088]--- > in cents_i lou_harrison_16 == r------ > import Music.Theory.Tuning.Scala--- > scl <- scl_load "harrison_16"--- > cents_i (scale_tuning 0.1 scl) == cents_i lou_harrison_16-lou_harrison_16 :: Tuning-lou_harrison_16 = Tuning (Left lou_harrison_16_r) 2---- | Ratios for 'partch_43'.-partch_43_r :: [Rational]-partch_43_r =-    [1,81/80,33/32,21/20,16/15,12/11,11/10,10/9,9/8,8/7-    ,7/6,32/27,6/5,11/9,5/4,14/11,9/7-    ,21/16,4/3,27/20-    ,11/8,7/5,10/7,16/11-    ,40/27,3/2,32/21,14/9,11/7,8/5,18/11,5/3,27/16,12/7-    ,7/4,16/9,9/5,20/11,11/6,15/8,40/21,64/33,160/81]---- | Harry Partch 43 tone scale, see--- <http://www.microtonal-synthesis.com/scale_partch.html>------ > cents_i partch_43 == [0,22,53,84,112,151,165--- >                      ,182,204,231,267,294,316--- >                      ,347,386,418,435--- >                      ,471,498,520,551,583,617,649--- >                      ,680,702,729,765,782,814,853,884,906,933--- >                      ,969,996,1018,1035,1049,1088,1116,1147,1178]------ > scl <- scl_load "partch_43"--- > cents_i (scale_tuning 0.1 scl) == cents_i partch_43-partch_43 :: Tuning-partch_43 = Tuning (Left partch_43_r) 2---- | Ratios for 'ben_johnston_25'.-ben_johnston_25_r :: [Rational]-ben_johnston_25_r =-    [1/1,25/24,135/128,16/15,10/9-    ,9/8,75/64,6/5,5/4,81/64-    ,32/25,4/3,27/20,45/32,36/25-    ,3/2,25/16,8/5,5/3,27/16-    ,225/128,16/9,9/5,15/8,48/25]---- | Ben Johnston 25 note just enharmonic scale, see--- <http://www.microtonal-synthesis.com/scale_johnston_25.html>------ > scl <- scl_load "johnston_25"--- > cents_i (scale_tuning 0.1 scl) == cents_i ben_johnston_25-ben_johnston_25 :: Tuning-ben_johnston_25 = Tuning (Left ben_johnston_25_r) 2
− Music/Theory/Tuning/DB/Riley.hs 
@@ -1,22 +0,0 @@--- | Terry Riley.-module Music.Theory.Tuning.DB.Riley where--import Music.Theory.Tuning {- hmt -}---- | Ratios for 'riley_albion'.------ > let r = [0,112,204,316,386,498,610,702,814,884,996,1088]--- > in map (round . ratio_to_cents) riley_albion_r == r-riley_albion_r :: [Rational]-riley_albion_r = [1/1,16/15,9/8,6/5,5/4,4/3,64/45,3/2,8/5,5/3,16/9,15/8]---- | Riley's five-limit tuning as used in _The Harp of New Albion_,--- see <http://www.ex-tempore.org/Volx1/hudson/hudson.htm>.------ > cents_i riley_albion == [0,112,204,316,386,498,610,702,814,884,996,1088]------ > import Music.Theory.Tuning.Scala--- > scl <- scl_load "riley_albion"--- > cents_i (scale_tuning 0.01 scl) == cents_i riley_albion-riley_albion :: Tuning-riley_albion = Tuning (Left riley_albion_r) 2
− Music/Theory/Tuning/DB/Werckmeister.hs 
@@ -1,117 +0,0 @@--- | Andreas Werckmeister (1645-1706).-module Music.Theory.Tuning.DB.Werckmeister where--import Music.Theory.Tuning {- hmt -}---- | Approximate ratios for 'werckmeister_iii'.------ > let c = [0,90,192,294,390,498,588,696,792,888,996,1092]--- > in map (round . ratio_to_cents) werckmeister_iii_ar == c-werckmeister_iii_ar :: [Approximate_Ratio]-werckmeister_iii_ar =-    let c0 = 2 ** (1/2)-        c1 = 2 ** (1/4)-        c2 = 8 ** (1/4)-    in [1,256/243-       ,64/81 * c0,32/27-       ,256/243 * c1-       ,4/3,1024/729-       ,8/9 * c2,128/81-       ,1024/729 * c1,16/9-       ,128/81 * c1]---- | Cents for 'werckmeister_iii'.-werckmeister_iii_ar_c :: [Cents]-werckmeister_iii_ar_c = map approximate_ratio_to_cents werckmeister_iii_ar---- | Werckmeister III, Andreas Werckmeister (1645-1706)------ > cents_i werckmeister_iii == [0,90,192,294,390,498,588,696,792,888,996,1092]------ > import Music.Theory.Tuning.Scala--- > scl <- scl_load "werck3"--- > cents_i (scale_tuning 0.01 scl) == cents_i werckmeister_iii-werckmeister_iii :: Tuning-werckmeister_iii = Tuning (Right werckmeister_iii_ar_c) 2---- | Approximate ratios for 'werckmeister_iv'.------ > let c = [0,82,196,294,392,498,588,694,784,890,1004,1086]--- > in map (round . ratio_to_cents) werckmeister_iv_ar == c-werckmeister_iv_ar :: [Approximate_Ratio]-werckmeister_iv_ar =-    let c0 = 2 ** (1/3)-        c1 = 4 ** (1/3)-    in [1,16384/19683 * c0-       ,8/9 * c0,32/27-       ,64/81 * c1-       ,4/3,1024/729-       ,32/27 * c0,8192/6561 * c0-       ,256/243 * c1,9/(4*c0)-       ,4096/2187]---- | Cents for 'werckmeister_iv'.-werckmeister_iv_c :: [Cents]-werckmeister_iv_c = map approximate_ratio_to_cents werckmeister_iv_ar---- | Werckmeister IV, Andreas Werckmeister (1645-1706)------ > cents_i werckmeister_iv == [0,82,196,294,392,498,588,694,784,890,1004,1086]------ > scl <- scl_load "werck4"--- > cents_i (scale_tuning 0.01 scl) == cents_i werckmeister_iv-werckmeister_iv :: Tuning-werckmeister_iv = Tuning (Right werckmeister_iv_c) 2---- | Approximate ratios for 'werckmeister_v'.------ > let c = [0,96,204,300,396,504,600,702,792,900,1002,1098]--- > in map (round . ratio_to_cents) werckmeister_v_ar == c-werckmeister_v_ar :: [Approximate_Ratio]-werckmeister_v_ar =-    let c0 = 2 ** (1/4)-        c1 = 2 ** (1/2)-        c2 = 8 ** (1/4)-    in [1,8/9 * c0-       ,9/8,c0-       ,8/9 * c1-       ,9/8 * c0,c1-       ,3/2,128/81-       ,c2,3/c2-       ,4/3 * c1]---- | Cents for 'werckmeister_v'.-werckmeister_v_c :: [Cents]-werckmeister_v_c = map approximate_ratio_to_cents werckmeister_v_ar---- | Werckmeister V, Andreas Werckmeister (1645-1706)------ > cents_i werckmeister_v == [0,96,204,300,396,504,600,702,792,900,1002,1098]------ > scl <- scl_load "werck5"--- > cents_i (scale_tuning 0.01 scl) == cents_i werckmeister_v-werckmeister_v :: Tuning-werckmeister_v = Tuning (Right werckmeister_v_c) 2---- | Ratios for 'werckmeister_vi', with supposed correction of 28/25 to 49/44.------ > let c = [0,91,186,298,395,498,595,698,793,893,1000,1097]--- > in map (round . ratio_to_cents) werckmeister_vi_r == c-werckmeister_vi_r :: [Rational]-werckmeister_vi_r =-    [1,98/93-    ,49/44 {- 28/25 -},196/165-    ,49/39-    ,4/3,196/139-    ,196/131,49/31-    ,196/117,98/55-    ,49/26]---- | Werckmeister VI, Andreas Werckmeister (1645-1706)------ > cents_i werckmeister_vi == [0,91,186,298,395,498,595,698,793,893,1000,1097]------ > scl <- scl_load "werck6"--- > cents_i (scale_tuning 0.01 scl) == cents_i werckmeister_vi-werckmeister_vi :: Tuning-werckmeister_vi = Tuning (Left werckmeister_vi_r) 2
+ Music/Theory/Tuning/Db.hs view
@@ -0,0 +1,74 @@+-- | Db of locally defined tunings, but for ordinary use see "Music.Theory.Tuning.Scala".+module Music.Theory.Tuning.Db where++import Data.List {- base -}++import Music.Theory.Tuning.Type++import Music.Theory.Tuning.Alves_1997+import Music.Theory.Tuning.Gann_1993+import Music.Theory.Tuning.Polansky_1978+import Music.Theory.Tuning.Polansky_1985c++import Music.Theory.Tuning.Db.Alves+import Music.Theory.Tuning.Db.Gann+import Music.Theory.Tuning.Db.Microtonal_Synthesis+import Music.Theory.Tuning.Db.Riley+import Music.Theory.Tuning.Db.Werckmeister++-- | (last-name,first-name,title,year,hmt/tuning,scala/name)+type Named_Tuning = (String,String,String,String,Tuning,String)++named_tuning_t :: Named_Tuning -> Tuning+named_tuning_t (_,_,_,_,t,_) = t++tuning_db :: [Named_Tuning]+tuning_db =+    [("Aaron","Pietro","","1523",pietro_aaron_1523,"meanquar")+    ,("Alves","Bill","Slendro","",alves_slendro,"slendro_alves") -- slendro9+    ,("Alves","Bill","Pelog/Bem","",alves_pelog_bem,"") -- hirajoshi2 / pelog_jc+    ,("Alves","Bill","Pelog/Barang","",alves_pelog_barang,"") -- surupan_degung / degung3+    ,("Gann","Kyle","Superparticular","1992",gann_superparticular,"gann_super")+    ,("Harrison","Lou","Ditone","",harrison_ditone,"") -- pyth_12 / zwolle+    ,("Harrison","Lou","16-tone","",lou_harrison_16,"harrison_16")+    ,("Johnston","Ben","MTP","1977",ben_johnston_mtp_1977,"") -- carlos_harm+    ,("Johnston","Ben","25-tone","",ben_johnston_25,"johnston_25")+    ,("Kirnberger","Johann Philipp","III","",kirnberger_iii,"kirnberger")+    ,("Malcolm","Alexander","Monochord","1721",five_limit_tuning,"malcolm") -- wurschmidt+    ,("Partch","Harry","43-tone","",partch_43,"partch_43")+    ,("Polansky","Larry","Piano Study #5","1985",ps5_jpr,"polansky_ps") -- 56-any+    ,("Polansky","Larry","Psaltery","1978",psaltery_o,"") -- dconv9marv+    ,("Riley","Terry","Harp of New Albion","",riley_albion,"riley_albion")+    ,("Tsuda","Mayumi","13-limit","",mayumi_tsuda,"tsuda13")+    ,("Vallotti","","","1754",vallotti,"vallotti") -- bemetzrieder2+    ,("Werckmeister","Andreas","Werckmeister III","",werckmeister_iii,"werck3")+    ,("Werckmeister","Andreas","Werckmeister IV","",werckmeister_iv,"werck4")+    ,("Werckmeister","Andreas","Werckmeister V","",werckmeister_v,"werck5") -- ammerbach1+    ,("Werckmeister","Andreas","Werckmeister VI","",werckmeister_vi,"werck6")+    ,("Young","La Monte","The Well-Tuned Piano","",lmy_wtp,"young-lm_piano")+    ,("Young","Thomas","","1799",thomas_young_1799,"young1") -- young2+    ,("Zarlino","Gioseffo","","1588",zarlino_1588,"zarlino2") -- mersen_s3+    ,("","","JI/12 7-limit","",septimal_tritone_just_intonation,"ji_12")+    ,("","","ET/12","",tn_equal_temperament_12,"et12")+    ,("","","ET/19","",tn_equal_temperament_19,"et19")+    ,("","","ET/31","",tn_equal_temperament_31,"et13")+    ,("","","ET/53","",tn_equal_temperament_53,"et53")+    ,("","","ET/72","",tn_equal_temperament_72,"et72")+    ,("","","ET/96","",tn_equal_temperament_96,"et96")+    ,("","","Pythagorean/12","",pythagorean_12,"pyth_12") -- zwolle+    ]++tuning_db_lookup_scl :: String -> Maybe Tuning+tuning_db_lookup_scl nm = fmap named_tuning_t (find (\(_,_,_,_,_,scl) -> scl == nm) tuning_db)++{-++import Music.Theory.Tuning.Scala+db <- scl_load_db+f n = take n . scl_db_query_cdiff_asc round db . sort . tn_cents_octave+f 2 pietro_aaron_1523+pp = mapM_ (putStrLn . unlines . scale_stat . snd)+mapM_ pp (map (f 2 . named_tuning_t) tuning_db)++-}+
+ Music/Theory/Tuning/Db/Alves.hs view
@@ -0,0 +1,30 @@+-- | Bill Alves.+module Music.Theory.Tuning.Db.Alves where++import Music.Theory.Tuning.Type {- hmt -}++{- | Ratios for 'harrison_ditone' (SCALA=pyth_12)++> import Music.Theory.Tuning {- hmt -}+> let c = [0,114,204,294,408,498,612,702,816,906,996,1110]+> map (round . ratio_to_cents) harrison_ditone_r == c++> import Music.Theory.Tuning.Scala {- hmt -}+> scl_find_ji (harrison_ditone_r ++ [2])+-}+harrison_ditone_r :: [Rational]+harrison_ditone_r =+    [1,2187/2048 {- 256/243 -}+    ,9/8,32/27+    ,81/64+    ,4/3,729/512+    ,3/2,6561/4096 {- 128/81 -}+    ,27/16,16/9+    ,243/128]++-- | Ditone/pythagorean tuning, <http://www.billalves.com/porgitaro/ditonesettuning.html>+--+-- > tn_divisions harrison_ditone == 12+-- > tn_cents_i harrison_ditone == [0,114,204,294,408,498,612,702,816,906,996,1110]+harrison_ditone :: Tuning+harrison_ditone = Tuning (Left harrison_ditone_r) Nothing
+ Music/Theory/Tuning/Db/Gann.hs view
@@ -0,0 +1,130 @@+-- | Kyle Gann.+module Music.Theory.Tuning.Db.Gann where++import Music.Theory.Tuning {- hmt -}+import Music.Theory.Tuning.Type {- hmt -}++-- * Historical++-- | Cents for 'pietro_aaron_1523'.+--+-- > let c = [0,76,193,310,386,503,580,697,773,890,1007,1083]+-- > map round pietro_aaron_1523_c == c+--+-- > map ((+ 60) . (/ 100)) pietro_aaron_1523_c+pietro_aaron_1523_c :: [Cents]+pietro_aaron_1523_c =+    [0,76.0+    ,193.2,310.3+    ,386.3 -- 5/4+    ,503.4,579.5+    ,696.8,772.6 -- 25/16+    ,889.7,1006.8+    ,1082.9]++-- | Pietro Aaron (1523) meantone temperament, see+-- <http://www.kylegann.com/histune.html>+--+-- > tn_cents_i pietro_aaron_1523 == [0,76,193,310,386,503,580,697,773,890,1007,1083]+--+-- > import Music.Theory.Tuning.Scala+-- > scl <- scl_load "meanquar"+-- > tn_cents_i (scale_to_tuning 0.01 scl) == [0,76,193,310,386,503,579,697,773,890,1007,1083]+pietro_aaron_1523 :: Tuning+pietro_aaron_1523 = Tuning (Right pietro_aaron_1523_c) Nothing++-- | Cents for 'thomas_young_1799'.+--+-- > let c = [0,94,196,298,392,500,592,698,796,894,1000,1092]+-- > map round thomas_young_1799_c == c+thomas_young_1799_c :: [Cents]+thomas_young_1799_c =+    [0,93.9+    ,195.8,297.8+    ,391.7+    ,499.9,591.9+    ,697.9,795.8+    ,893.8,999.8+    ,1091.8]++-- | Thomas Young (1799), Well Temperament, <http://www.kylegann.com/histune.html>.+--+-- > tn_cents_i thomas_young_1799 == [0,94,196,298,392,500,592,698,796,894,1000,1092]+--+-- > scl <- scl_load "young2"+-- > tn_cents_i (scale_to_tuning 0.01 scl) == tn_cents_i thomas_young_1799+thomas_young_1799 :: Tuning+thomas_young_1799 = Tuning (Right thomas_young_1799_c) Nothing++-- | Ratios for 'zarlino'.+--+-- > length zarlino_1588_r == 16+zarlino_1588_r :: [Rational]+zarlino_1588_r = [1,25/24,10/9,9/8,32/27,6/5,5/4,4/3,25/18,45/32,3/2,25/16,5/3,16/9,9/5,15/8]++-- | Gioseffo Zarlino, 1588, see <http://www.kylegann.com/tuning.html>.+--+-- > tn_divisions zarlino_1588 == 16+-- > tn_cents_i zarlino_1588 == [0,71,182,204,294,316,386,498,569,590,702,773,884,996,1018,1088]+--+-- > scl <- scl_load "zarlino2"+-- > tn_cents_i (scale_to_tuning 0.01 scl) == tn_cents_i zarlino_1588+zarlino_1588 :: Tuning+zarlino_1588 = Tuning (Left zarlino_1588_r) Nothing++-- * 20th Century++-- | Ratios for 'ben_johnston_mtp_1977'.+--+-- > let c = [0,105,204,298,386,471,551,702,841,906,969,1088]+-- > map (round . ratio_to_cents) ben_johnston_mtp_1977_r == c+ben_johnston_mtp_1977_r :: [Rational]+ben_johnston_mtp_1977_r =+    [1,17/16+    ,9/8,19/16+    ,5/4+    ,216,11/8+    ,3/2,13/8+    ,27/16,7/4+    ,15/8]++-- | Ben Johnston's \"Suite for Microtonal Piano\" (1977), see+-- <http://www.kylegann.com/tuning.html>+--+-- > tn_cents_i ben_johnston_mtp_1977 == [0,105,204,298,386,471,551,702,841,906,969,1088]+ben_johnston_mtp_1977 :: Tuning+ben_johnston_mtp_1977 = Tuning (Left ben_johnston_mtp_1977_r) Nothing++-- * Gann++-- | Ratios for 'gann_arcana_xvi'.+gann_arcana_xvi_r :: [Rational]+gann_arcana_xvi_r =+    [1,21/20,16/15,9/8,7/6,6/5,11/9,5/4,216,4/3,27/20,7/5+    ,22/15,3/2,55/36,8/5,44/27,5/3,42/25,7/4,9/5,11/6,15/8,88/45]++-- | Kyle Gann, _Arcana XVI_, see <http://www.kylegann.com/Arcana.html>.+--+-- > let r = [0,84,112,204,267,316,347,386,471,498,520,583,663,702,734,814,845,884,898,969,1018,1049,1088,1161]+-- > tn_cents_i gann_arcana_xvi == r+gann_arcana_xvi :: Tuning+gann_arcana_xvi = Tuning (Left gann_arcana_xvi_r) Nothing++-- | Ratios for 'gann_superparticular'.+gann_superparticular_r :: [Rational]+gann_superparticular_r =+    [1,110,10/9,9/8,8/7,7/6,6/5,5/4,9/7,4/3+    ,11/8,7/5,10/7,3/2+    ,11/7,14/9,8/5,5/3,12/7,7/4,16/9,9/5]++-- | Kyle Gann, _Superparticular_, see <http://www.kylegann.com/Super.html>.+--+-- > tn_divisions gann_superparticular == 22+--+-- > let r = [0,165,182,204,231,267,316,386,435,498,551,583,617,702,782,765,814,884,933,969,996,1018]+-- > tn_cents_i gann_superparticular == r+--+-- > scl <- scl_load "gann_super"+-- > tn_cents_i (scale_to_tuning 0.01 scl) == tn_cents_i gann_superparticular+gann_superparticular :: Tuning+gann_superparticular = Tuning (Left gann_superparticular_r) Nothing
+ Music/Theory/Tuning/Db/Microtonal_Synthesis.hs view
@@ -0,0 +1,231 @@+-- | <http://www.microtonal-synthesis.com/scales.html>+module Music.Theory.Tuning.Db.Microtonal_Synthesis where++import Music.Theory.Tuning {- hmt -}+import Music.Theory.Tuning.Type {- hmt -}++-- | Ratios for 'pythagorean'.+pythagorean_12_r :: [Rational]+pythagorean_12_r =+    [1,2187/2048 {- 256/243 -}+    ,9/8,32/27+    ,81/64+    ,4/3,729/512+    ,3/2,6561/4096 {- 128/81 -}+    ,27/16,16/9+    ,243/128]++-- | Pythagorean tuning, <http://www.microtonal-synthesis.com/scale_pythagorean.html>.+--+-- > cents_i pythagorean_12 == [0,114,204,294,408,498,612,702,816,906,996,1110]+--+-- > scl <- scl_load "pyth_12"+-- > cents_i (scale_tuning 0.1 scl) == cents_i pythagorean_12+pythagorean_12 :: Tuning+pythagorean_12 = Tuning (Left pythagorean_12_r) Nothing++-- | Ratios for 'five_limit_tuning'.+--+-- > let c = [0,112,204,316,386,498,590,702,814,884,996,1088]+-- > in map (round . ratio_to_cents) five_limit_tuning_r == c+five_limit_tuning_r :: [Rational]+five_limit_tuning_r =+    [1,16/15+    ,9/8,6/5+    ,5/4+    ,4/3,45/32 {- 64/45 -}+    ,3/2,8/5+    ,5/3,16/9 {- 9/5 -}+    ,15/8]++-- | Five-limit tuning (five limit just intonation), Alexander Malcolm's Monochord (1721).+--+-- > cents_i five_limit_tuning == [0,112,204,316,386,498,590,702,814,884,996,1088]+--+-- > scl <- scl_load "malcolm"+-- > cents_i (scale_tuning 0.1 scl) == cents_i five_limit_tuning+five_limit_tuning :: Tuning+five_limit_tuning = Tuning (Left five_limit_tuning_r) Nothing++-- | Ratios for 'septimal_tritone_just_intonation'.+--+-- > let c = [0,112,204,316,386,498,583,702,814,884,1018,1088]+-- > in map (round . ratio_to_cents) septimal_tritone_just_intonation == c+septimal_tritone_just_intonation_r :: [Rational]+septimal_tritone_just_intonation_r =+    [1,16/15+    ,9/8,6/5+    ,5/4+    ,4/3,7/5+    ,3/2,8/5+    ,5/3,9/5+    ,15/8]++-- | Septimal tritone Just Intonation, see+-- <http://www.microtonal-synthesis.com/scale_just_intonation.html>+--+-- > let c = [0,112,204,316,386,498,583,702,814,884,1018,1088]+-- > in cents_i septimal_tritone_just_intonation == c+--+-- > scl <- scl_load "ji_12"+-- > cents_i (scale_tuning 0.1 scl) == cents_i septimal_tritone_just_intonation+septimal_tritone_just_intonation :: Tuning+septimal_tritone_just_intonation = Tuning (Left septimal_tritone_just_intonation_r) Nothing++-- | Ratios for 'seven_limit_just_intonation'.+--+-- > let c = [0,112,204,316,386,498,583,702,814,884,969,1088]+-- > in map (round . ratio_to_cents) seven_limit_just_intonation == c+seven_limit_just_intonation_r :: [Rational]+seven_limit_just_intonation_r =+    [1,16/15+    ,9/8,6/5+    ,5/4+    ,4/3,7/5+    ,3/2,8/5+    ,5/3,7/4+    ,15/8]++-- | Seven limit Just Intonation.+--+-- > cents_i seven_limit_just_intonation == [0,112,204,316,386,498,583,702,814,884,969,1088]+seven_limit_just_intonation :: Tuning+seven_limit_just_intonation = Tuning (Left seven_limit_just_intonation_r) Nothing++-- | Approximate ratios for 'kirnberger_iii'.+--+-- > let c = [0,90,193,294,386,498,590,697,792,890,996,1088]+-- > in map (round.to_cents) kirnberger_iii_ar == c+kirnberger_iii_ar :: [Approximate_Ratio]+kirnberger_iii_ar =+    [1,256/243+    ,sqrt 5 / 2,32/27+    ,5/4+    ,4/3,45/32+    ,5 ** 0.25,128/81+    ,(5 ** 0.75)/2,16/9+    ,15/8]++-- | <http://www.microtonal-synthesis.com/scale_kirnberger.html>.+--+-- > cents_i kirnberger_iii == [0,90,193,294,386,498,590,697,792,890,996,1088]+--+-- > scl <- scl_load "kirnberger"+-- > cents_i (scale_tuning 0.1 scl) == cents_i kirnberger_iii+kirnberger_iii :: Tuning+kirnberger_iii = Tuning (Right (map approximate_ratio_to_cents kirnberger_iii_ar)) Nothing++-- > let c = [0,94,196,298,392,502,592,698,796,894,1000,1090]+-- > in map round vallotti_c == c+vallotti_c :: [Cents]+vallotti_c =+    [0.0,94.135+    ,196.09,298.045+    ,392.18+    ,501.955,592.18+    ,698.045,796.09+    ,894.135,1000.0+    ,1090.225]++-- | Vallotti & Young scale (Vallotti version), see+-- <http://www.microtonal-synthesis.com/scale_vallotti_young.html>.+--+-- > cents_i vallotti == [0,94,196,298,392,502,592,698,796,894,1000,1090]+--+-- > scl <- scl_load "vallotti"+-- > cents_i (scale_tuning 0.1 scl) == cents_i vallotti+vallotti :: Tuning+vallotti = Tuning (Right vallotti_c) Nothing++-- > let c = [0,128,139,359,454,563,637,746,841,911,1072,1183]+-- > in map (round . ratio_to_cents) mayumi_tsuda == c+mayumi_tsuda_r :: [Rational]+mayumi_tsuda_r =+    [1,14/13+    ,13/12,16/13+    ,13/10+    ,18/13,13/9+    ,20/13,13/8+    ,22/13,13/7+    ,208/105]++-- | Mayumi Tsuda 13-limit Just Intonation scale,+-- <http://www.microtonal-synthesis.com/scale_reinhard.html>.+--+-- > cents_i mayumi_tsuda == [0,128,139,359,454,563,637,746,841,911,1072,1183]+--+-- > scl <- scl_load "tsuda13"+-- > cents_i (scale_tuning 0.1 scl) == cents_i mayumi_tsuda+mayumi_tsuda :: Tuning+mayumi_tsuda = Tuning (Left mayumi_tsuda_r) Nothing++-- | Ratios for 'lou_harrison_16'.+--+-- > length lou_harrison_16_r == 16+--+-- > let c = [0,112,182,231,267,316,386,498,603,702,814,884,933,969,1018,1088]+-- > in map (round . ratio_to_cents) lou_harrison_16_r == c+lou_harrison_16_r :: [Rational]+lou_harrison_16_r =+    [1,16/15+    ,10/9,8/7+    ,7/6,6/5,5/4+    ,4/3+    ,17/12+    ,3/2+    ,8/5,5/3,12/7+    ,7/4,9/5,15/8]++-- | Lou Harrison 16 tone Just Intonation scale, see+-- <http://www.microtonal-synthesis.com/scale_harrison_16.html>+--+-- > let r = [0,112,182,231,267,316,386,498,603,702,814,884,933,969,1018,1088]+-- > in cents_i lou_harrison_16 == r+--+-- > import Music.Theory.Tuning.Scala+-- > scl <- scl_load "harrison_16"+-- > cents_i (scale_tuning 0.1 scl) == cents_i lou_harrison_16+lou_harrison_16 :: Tuning+lou_harrison_16 = Tuning (Left lou_harrison_16_r) Nothing++-- | Ratios for 'partch_43'.+partch_43_r :: [Rational]+partch_43_r =+    [1,81/80,33/32,21/20,16/15,12/11,110,10/9,9/8,8/7+    ,7/6,32/27,6/5,11/9,5/4,14/11,9/7+    ,216,4/3,27/20+    ,11/8,7/5,10/7,16/11+    ,40/27,3/2,32/21,14/9,11/7,8/5,18/11,5/3,27/16,12/7+    ,7/4,16/9,9/5,20/11,11/6,15/8,40/21,64/33,160/81]++-- | Harry Partch 43 tone scale, see+-- <http://www.microtonal-synthesis.com/scale_partch.html>+--+-- > cents_i partch_43 == [0,22,53,84,112,151,165+-- >                      ,182,204,231,267,294,316+-- >                      ,347,386,418,435+-- >                      ,471,498,520,551,583,617,649+-- >                      ,680,702,729,765,782,814,853,884,906,933+-- >                      ,969,996,1018,1035,1049,1088,1116,1147,1178]+--+-- > scl <- scl_load "partch_43"+-- > cents_i (scale_tuning 0.1 scl) == cents_i partch_43+partch_43 :: Tuning+partch_43 = Tuning (Left partch_43_r) Nothing++-- | Ratios for 'ben_johnston_25'.+ben_johnston_25_r :: [Rational]+ben_johnston_25_r =+    [1,25/24,135/128,16/15,10/9+    ,9/8,75/64,6/5,5/4,81/64+    ,32/25,4/3,27/20,45/32,36/25+    ,3/2,25/16,8/5,5/3,27/16+    ,225/128,16/9,9/5,15/8,48/25]++-- | Ben Johnston 25 note just enharmonic scale, see+-- <http://www.microtonal-synthesis.com/scale_johnston_25.html>+--+-- > scl <- scl_load "johnston_25"+-- > cents_i (scale_tuning 0.1 scl) == cents_i ben_johnston_25+ben_johnston_25 :: Tuning+ben_johnston_25 = Tuning (Left ben_johnston_25_r) Nothing
+ Music/Theory/Tuning/Db/Riley.hs view
@@ -0,0 +1,22 @@+-- | Terry Riley.+module Music.Theory.Tuning.Db.Riley where++import Music.Theory.Tuning.Type {- hmt -}++-- | Ratios for 'riley_albion'.+--+-- > let r = [0,112,204,316,386,498,610,702,814,884,996,1088]+-- > in map (round . ratio_to_cents) riley_albion_r == r+riley_albion_r :: [Rational]+riley_albion_r = [1,16/15,9/8,6/5,5/4,4/3,64/45,3/2,8/5,5/3,16/9,15/8]++-- | Riley's five-limit tuning as used in _The Harp of New Albion_,+-- see <http://www.ex-tempore.org/Volx1/hudson/hudson.htm>.+--+-- > cents_i riley_albion == [0,112,204,316,386,498,610,702,814,884,996,1088]+--+-- > import Music.Theory.Tuning.Scala+-- > scl <- scl_load "riley_albion"+-- > cents_i (scale_tuning 0.01 scl) == cents_i riley_albion+riley_albion :: Tuning+riley_albion = Tuning (Left riley_albion_r) Nothing
+ Music/Theory/Tuning/Db/Werckmeister.hs view
@@ -0,0 +1,118 @@+-- | Andreas Werckmeister (1645-1706).+module Music.Theory.Tuning.Db.Werckmeister where++import Music.Theory.Tuning {- hmt -}+import Music.Theory.Tuning.Type {- hmt -}++-- | Approximate ratios for 'werckmeister_iii'.+--+-- > let c = [0,90,192,294,390,498,588,696,792,888,996,1092]+-- > in map (round . ratio_to_cents) werckmeister_iii_ar == c+werckmeister_iii_ar :: [Approximate_Ratio]+werckmeister_iii_ar =+    let c0 = 2 ** (1/2)+        c1 = 2 ** (1/4)+        c2 = 8 ** (1/4)+    in [1,256/243+       ,64/81 * c0,32/27+       ,256/243 * c1+       ,4/3,1024/729+       ,8/9 * c2,128/81+       ,1024/729 * c1,16/9+       ,128/81 * c1]++-- | Cents for 'werckmeister_iii'.+werckmeister_iii_ar_c :: [Cents]+werckmeister_iii_ar_c = map approximate_ratio_to_cents werckmeister_iii_ar++-- | Werckmeister III, Andreas Werckmeister (1645-1706)+--+-- > cents_i werckmeister_iii == [0,90,192,294,390,498,588,696,792,888,996,1092]+--+-- > import Music.Theory.Tuning.Scala+-- > scl <- scl_load "werck3"+-- > cents_i (scale_tuning 0.01 scl) == cents_i werckmeister_iii+werckmeister_iii :: Tuning+werckmeister_iii = Tuning (Right werckmeister_iii_ar_c) Nothing++-- | Approximate ratios for 'werckmeister_iv'.+--+-- > let c = [0,82,196,294,392,498,588,694,784,890,1004,1086]+-- > in map (round . ratio_to_cents) werckmeister_iv_ar == c+werckmeister_iv_ar :: [Approximate_Ratio]+werckmeister_iv_ar =+    let c0 = 2 ** (1/3)+        c1 = 4 ** (1/3)+    in [1,16384/19683 * c0+       ,8/9 * c0,32/27+       ,64/81 * c1+       ,4/3,1024/729+       ,32/27 * c0,8192/6561 * c0+       ,256/243 * c1,9/(4*c0)+       ,4096/2187]++-- | Cents for 'werckmeister_iv'.+werckmeister_iv_c :: [Cents]+werckmeister_iv_c = map approximate_ratio_to_cents werckmeister_iv_ar++-- | Werckmeister IV, Andreas Werckmeister (1645-1706)+--+-- > cents_i werckmeister_iv == [0,82,196,294,392,498,588,694,784,890,1004,1086]+--+-- > scl <- scl_load "werck4"+-- > cents_i (scale_tuning 0.01 scl) == cents_i werckmeister_iv+werckmeister_iv :: Tuning+werckmeister_iv = Tuning (Right werckmeister_iv_c) Nothing++-- | Approximate ratios for 'werckmeister_v'.+--+-- > let c = [0,96,204,300,396,504,600,702,792,900,1002,1098]+-- > in map (round . ratio_to_cents) werckmeister_v_ar == c+werckmeister_v_ar :: [Approximate_Ratio]+werckmeister_v_ar =+    let c0 = 2 ** (1/4)+        c1 = 2 ** (1/2)+        c2 = 8 ** (1/4)+    in [1,8/9 * c0+       ,9/8,c0+       ,8/9 * c1+       ,9/8 * c0,c1+       ,3/2,128/81+       ,c2,3/c2+       ,4/3 * c1]++-- | Cents for 'werckmeister_v'.+werckmeister_v_c :: [Cents]+werckmeister_v_c = map approximate_ratio_to_cents werckmeister_v_ar++-- | Werckmeister V, Andreas Werckmeister (1645-1706)+--+-- > cents_i werckmeister_v == [0,96,204,300,396,504,600,702,792,900,1002,1098]+--+-- > scl <- scl_load "werck5"+-- > cents_i (scale_tuning 0.01 scl) == cents_i werckmeister_v+werckmeister_v :: Tuning+werckmeister_v = Tuning (Right werckmeister_v_c) Nothing++-- | Ratios for 'werckmeister_vi', with supposed correction of 28/25 to 49/44.+--+-- > let c = [0,91,186,298,395,498,595,698,793,893,1000,1097]+-- > in map (round . ratio_to_cents) werckmeister_vi_r == c+werckmeister_vi_r :: [Rational]+werckmeister_vi_r =+    [1,98/93+    ,49/44 {- 28/25 -},196/165+    ,49/39+    ,4/3,196/139+    ,196/131,49/31+    ,196/117,98/55+    ,49/26]++-- | Werckmeister VI, Andreas Werckmeister (1645-1706)+--+-- > cents_i werckmeister_vi == [0,91,186,298,395,498,595,698,793,893,1000,1097]+--+-- > scl <- scl_load "werck6"+-- > cents_i (scale_tuning 0.01 scl) == cents_i werckmeister_vi+werckmeister_vi :: Tuning+werckmeister_vi = Tuning (Left werckmeister_vi_r) Nothing
− Music/Theory/Tuning/ET.hs 
@@ -1,259 +0,0 @@--- | Equal temperament tuning tables.-module Music.Theory.Tuning.ET where--import Data.List {- base -}-import Data.List.Split {- split -}-import Data.Ratio {- base -}-import Text.Printf {- base -}--import qualified Music.Theory.List as T {- hmt -}-import Music.Theory.Pitch {- hmt -}-import Music.Theory.Pitch.Note {- hmt -}-import Music.Theory.Pitch.Spelling.Table {- hmt -}-import Music.Theory.Tuning {- hmt -}---- | 'octpc_to_pitch' and 'octpc_to_cps'.-octpc_to_pitch_cps_f0 :: (Floating n) => n -> OctPC -> (Pitch,n)-octpc_to_pitch_cps_f0 f0 x = (octpc_to_pitch pc_spell_ks x,octpc_to_cps_f0 f0 x)---- | 'octpc_to_pitch' and 'octpc_to_cps'.-octpc_to_pitch_cps :: (Floating n) => OctPC -> (Pitch,n)-octpc_to_pitch_cps = octpc_to_pitch_cps_f0 440---- | 12-tone equal temperament table equating 'Pitch' and frequency--- over range of human hearing, where @A4@ has given frequency.------ > tbl_12et_f0 415-tbl_12et_f0 :: Double -> [(Pitch,Double)]-tbl_12et_f0 f0 =-    let z = [(o,pc) | o <- [0..10], pc <- [0..11]]-    in map (octpc_to_pitch_cps_f0 f0) z---- | 'tbl_12et_f0' @440@hz.------ > length tbl_12et == 132--- > minmax (map (round . snd) tbl_12et) == (16,31609)-tbl_12et :: [(Pitch,Double)]-tbl_12et = tbl_12et_f0 440---- | 24-tone equal temperament variant of 'tbl_12et_f0'.-tbl_24et_f0 :: Double -> [(Pitch,Double)]-tbl_24et_f0 f0 =-    let f x = let p = fmidi_to_pitch_err pc_spell_ks x-                  p' = pitch_rewrite_threequarter_alteration p-              in (p',fmidi_to_cps_f0 f0 x)-    in map f [12,12.5 .. 143.5]---- | 'tbl_24et_f0' @440@.------ > length tbl_24et == 264--- > minmax (map (round . snd) tbl_24et) == (16,32535)-tbl_24et :: [(Pitch,Double)]-tbl_24et = tbl_24et_f0 440---- | Given an @ET@ table (or like) find bounds of frequency.------ import qualified Music.Theory.Tuple as T------ > let r = Just (T.t2_map octpc_to_pitch_cps ((3,11),(4,0)))--- > in bounds_et_table tbl_12et 256 == r-bounds_et_table :: Ord s => [(t,s)] -> s -> Maybe ((t,s),(t,s))-bounds_et_table = T.find_bounds True (compare . snd)---- | 'bounds_et_table' of 'tbl_12et'.------ > map bounds_12et_tone (hsn 17 55)-bounds_12et_tone :: Double -> Maybe ((Pitch,Double),(Pitch,Double))-bounds_12et_tone = bounds_et_table tbl_12et---- | Tuple indicating nearest 'Pitch' to /frequency/ with @ET@--- frequency, and deviation in hertz and 'Cents'.------ (cps,nearest-pitch,cps-of-nearest-pitch,cps-deviation,cents-deviation)-type HS_R p = (Double,p,Double,Double,Cents)---- | /n/-decimal places.------ > ndp 3 (1/3) == "0.333"-ndp :: Int -> Double -> String-ndp = printf "%.*f"---- | Pretty print 'HS_R'.-hs_r_pp :: (p -> String) -> Int -> HS_R p -> [String]-hs_r_pp pp n (f,p,pf,fd,c) =-    let dp = ndp n-    in [dp f-       ,pp p-       ,dp pf-       ,dp fd-       ,dp c]--hs_r_pitch_pp :: Int -> HS_R Pitch -> [String]-hs_r_pitch_pp = hs_r_pp pitch_pp--{- | Form 'HS_R' for /frequency/ by consulting table.--> let {f = 256->     ;f' = octpc_to_cps (4,0)->     ;r = (f,Pitch C Natural 4,f',f-f',fratio_to_cents (f/f'))}-> in nearest_et_table_tone tbl_12et 256 == r---}-nearest_et_table_tone :: [(p,Double)] -> Double -> HS_R p-nearest_et_table_tone tbl f =-    case bounds_et_table tbl f of-      Nothing -> error "nearest_et_table_tone: no bounds?"-      Just ((lp,lf),(rp,rf)) ->-          let ld = f - lf-              rd = f - rf-          in if abs ld < abs rd-             then (f,lp,lf,ld,fratio_to_cents (f/lf))-             else (f,rp,rf,rd,fratio_to_cents (f/rf))---- | 'nearest_et_table_tone' for 'tbl_12et'.-nearest_12et_tone :: Double -> HS_R Pitch-nearest_12et_tone = nearest_et_table_tone tbl_12et---- | 'nearest_et_table_tone' for 'tbl_24et'.------ > let r = "55.0 A1 55.0 0.0 0.0"--- > in unwords (hs_r_pitch_pp 1 (nearest_24et_tone 55)) == r-nearest_24et_tone :: Double -> HS_R Pitch-nearest_24et_tone = nearest_et_table_tone tbl_24et---- * 72ET---- | Monzo 72-edo HEWM notation.  The domain is (-9,9).--- <http://www.tonalsoft.com/enc/number/72edo.aspx>------ > let r = ["+",">","^","#<","#-","#","#+","#>","#^"]--- > in map alteration_72et_monzo [1 .. 9] == r------ > let r = ["-","<","v","b>","b+","b","b-","b<","bv"]--- > in map alteration_72et_monzo [-1,-2 .. -9] == r-alteration_72et_monzo :: Integral n => n -> String-alteration_72et_monzo n =-    let spl = splitOn ","-        asc = spl ",+,>,^,#<,#-,#,#+,#>,#^"-        dsc = spl ",-,<,v,b>,b+,b,b-,b<,bv"-    in case compare n 0 of-         LT -> genericIndex dsc (- n)-         EQ -> ""-         GT -> genericIndex asc n---- | Given a midi note number and @1/6@ deviation determine 'Pitch''--- and frequency.------ > let {f = pitch'_pp . fst . pitch_72et--- >     ;r = "C4 C+4 C>4 C^4 C#<4 C#-4 C#4 C#+4 C#>4 C#^4"}--- > in unwords (map f (zip (repeat 60) [0..9])) == r------ > let {f = pitch'_pp . fst . pitch_72et--- >     ;r = "A4 A+4 A>4 A^4 Bb<4 Bb-4 Bb4 Bb+4 Bb>4 Bv4"}--- > in unwords (map f (zip (repeat 69) [0..9]))------ > let {f = pitch'_pp . fst . pitch_72et--- >     ;r = "Bb4 Bb+4 Bb>4 Bv4 B<4 B-4 B4 B+4 B>4 B^4"}--- > in unwords (map f (zip (repeat 70) [0..9])) == r-pitch_72et :: (Int,Int) -> (Pitch_R,Double)-pitch_72et (x,n) =-    let p = midi_to_pitch pc_spell_ks x-        t = note p-        a = alteration p-        (t',n') = case a of-                    Flat -> if n < (-3) then (pred t,n + 6) else (t,n - 6)-                    Natural -> (t,n)-                    Sharp -> if n > 3 then (succ t,n - 6) else (t,n + 6)-                    _ -> error "pitch_72et: alteration?"-        a' = alteration_72et_monzo n'-        x' = fromIntegral x + (fromIntegral n / 6)-        r = (Pitch_R t' (fromIntegral n' % 12,a') (octave p),fmidi_to_cps x')-        r' = if n > 3-             then pitch_72et (x + 1,n - 6)-             else if n < (-3)-                  then pitch_72et (x - 1,n + 6)-                  else r-    in case a of-         Natural -> r'-         _ -> r---- | 72-tone equal temperament table equating 'Pitch'' and frequency--- over range of human hearing, where @A4@ = @440@hz.------ > length tbl_72et == 792--- > min_max (map (round . snd) tbl_72et) == (16,33167)-tbl_72et :: [(Pitch_R,Double)]-tbl_72et =-    let f n = map pitch_72et (zip (replicate 6 n) [0..5])-    in concatMap f [12 .. 143]---- | 'nearest_et_table_tone' for 'tbl_72et'.------ > let r = "324.0 E<4 323.3 0.7 3.5"--- > in unwords (hs_r_pp pitch'_pp 1 (nearest_72et_tone 324))------ > let {f = take 2 . hs_r_pp pitch'_pp 1 . nearest_72et_tone . snd}--- > in mapM_ (print . unwords . f) tbl_72et-nearest_72et_tone :: Double -> HS_R Pitch_R-nearest_72et_tone = nearest_et_table_tone tbl_72et---- * Detune---- | 'Pitch' with 12-ET/24-ET tuning deviation given in 'Cents'.-type Pitch_Detune = (Pitch,Cents)---- | Extract 'Pitch_Detune' from 'HS_R'.-hsr_to_pitch_detune :: HS_R Pitch -> Pitch_Detune-hsr_to_pitch_detune (_,p,_,_,c) = (p,c)---- | Nearest 12-ET 'Pitch_Detune' to indicated frequency (hz).------ > nearest_pitch_detune_12et 452.8929841231365-nearest_pitch_detune_12et :: Double -> Pitch_Detune-nearest_pitch_detune_12et = hsr_to_pitch_detune . nearest_12et_tone---- | Nearest 24-ET 'Pitch_Detune' to indicated frequency (hz).------ > nearest_pitch_detune_24et 452.8929841231365-nearest_pitch_detune_24et :: Double -> Pitch_Detune-nearest_pitch_detune_24et = hsr_to_pitch_detune . nearest_24et_tone---- | Given /near/ function, /f0/ and ratio derive 'Pitch_Detune'.-ratio_to_pitch_detune :: (Double -> HS_R Pitch) -> OctPC -> Rational -> Pitch_Detune-ratio_to_pitch_detune near_f f0 r =-    let f = octpc_to_cps f0 * realToFrac r-        (_,p,_,_,c) = near_f f-    in (p,c)---- | Frequency (hz) of 'Pitch_Detune'.------ > pitch_detune_to_cps (octpc_to_pitch pc_spell_ks (4,9),50)-pitch_detune_to_cps :: Floating n => Pitch_Detune -> n-pitch_detune_to_cps (p,d) = cps_shift_cents (pitch_to_cps p) (realToFrac d)---- | 'ratio_to_pitch_detune' of 'nearest_12et_tone'-ratio_to_pitch_detune_12et :: OctPC -> Rational -> Pitch_Detune-ratio_to_pitch_detune_12et = ratio_to_pitch_detune nearest_12et_tone---- | 'ratio_to_pitch_detune' of 'nearest_24et_tone'-ratio_to_pitch_detune_24et :: OctPC -> Rational -> Pitch_Detune-ratio_to_pitch_detune_24et = ratio_to_pitch_detune nearest_24et_tone--pitch_detune_in_octave_nearest  :: Pitch -> Pitch_Detune -> Pitch_Detune-pitch_detune_in_octave_nearest p1 (p2,d2) = (pitch_in_octave_nearest p1 p2,d2)---- | Markdown pretty-printer for 'Pitch_Detune'.-pitch_detune_md :: Pitch_Detune -> String-pitch_detune_md (p,c) = pitch_pp p ++ cents_diff_md (round c :: Integer)---- | HTML pretty-printer for 'Pitch_Detune'.-pitch_detune_html :: Pitch_Detune -> String-pitch_detune_html (p,c) = pitch_pp p ++ cents_diff_html (round c :: Integer)---- | No-octave variant of 'pitch_detune_md'.-pitch_class_detune_md :: Pitch_Detune -> String-pitch_class_detune_md (p,c) = pitch_class_pp p ++ cents_diff_md (round c :: Integer)---- | No-octave variant of 'pitch_detune_html'.-pitch_class_detune_html :: Pitch_Detune -> String-pitch_class_detune_html (p,c) = pitch_class_pp p ++ cents_diff_html (round c :: Integer)
+ Music/Theory/Tuning/Efg.hs view
@@ -0,0 +1,111 @@+-- | Euler-Fokker genus <http://www.huygens-fokker.org/microtonality/efg.html>+module Music.Theory.Tuning.Efg where++import Data.List {- base -}++import qualified Music.Theory.List as T {- hmt -}+import qualified Music.Theory.Set.List as T {- hmt -}++import Music.Theory.Tuning {- hmt -}++-- | Normal form, value with occurences count (ie. exponent in notation above).+type Efg i = [(i,Int)]++-- | Degree of Efg, ie. sum of exponents.+--+-- > efg_degree [(3,3),(7,2)] == 3 + 2+efg_degree :: Efg i -> Int+efg_degree = sum . map snd++-- | Number of tones of Efg, ie. product of increment of exponents.+--+-- > efg_tones [(3,3),(7,2)] == (3 + 1) * (2 + 1)+efg_tones :: Efg i -> Int+efg_tones = product . map ((+ 1) . snd)++-- | Collate a genus given as a multiset into standard form, ie. histogram.+--+-- > efg_collate [3,3,3,7,7] == [(3,3),(7,2)]+efg_collate :: Ord i => [i] -> Efg i+efg_collate = T.histogram . sort++{- | Factors of Efg given with co-ordinate of grid location.++> efg_factors [(3,3)]++> let r = [([0,0],[]),([0,1],[7]),([0,2],[7,7])+>         ,([1,0],[3]),([1,1],[3,7]),([1,2],[3,7,7])+>         ,([2,0],[3,3]),([2,1],[3,3,7]),([2,2],[3,3,7,7])+>         ,([3,0],[3,3,3]),([3,1],[3,3,3,7]),([3,2],[3,3,3,7,7])]++> efg_factors [(3,3),(7,2)] == r++-}+efg_factors :: Efg i -> [([Int],[i])]+efg_factors efg =+    let k = map (\(_,n) -> [0 .. n]) efg+        k' = if length efg == 1+             then concatMap (map return) k+             else T.nfold_cartesian_product k+        z = map fst efg+        f ix = (ix,concat (zipWith (\n m -> replicate n (z !! m)) ix [0..]))+    in map f k'++{- | Ratios of Efg, taking /n/ as the 1:1 ratio, with indices, folded into one octave.++> import Data.List+> let r = sort $ map snd $ efg_ratios 7 [(3,3),(7,2)]+> r == [1/1,9/8,8/7,9/7,21/16,189/128,3/2,27/16,12/7,7/4,27/14,63/32]+> map (round . ratio_to_cents) r == [0,204,231,435,471,675,702,906,933,969,1137,1173]++      0:         1/1          C          0.000 cents+      1:         9/8          D        203.910 cents+      2:         8/7          D+       231.174 cents+      3:         9/7          E+       435.084 cents+      4:        21/16         F-       470.781 cents+      5:       189/128        G-       674.691 cents+      6:         3/2          G        701.955 cents+      7:        27/16         A        905.865 cents+      8:        12/7          A+       933.129 cents+      9:         7/4          Bb-      968.826 cents+     10:        27/14         B+      1137.039 cents+     11:        63/32         C-      1172.736 cents+     12:         2/1          C       1200.000 cents++> let r' = sort $ map snd $ efg_ratios 5 [(5,2),(7,3)]+> r' == [1/1,343/320,35/32,49/40,5/4,343/256,7/5,49/32,8/5,1715/1024,7/4,245/128]+> map (round . ratio_to_cents) r' == [0,120,155,351,386,506,583,738,814,893,969,1124]++> let r'' = sort $ map snd $ efg_ratios 3 [(3,1),(5,1),(7,1)]+> r'' == [1/1,35/32,7/6,5/4,4/3,35/24,5/3,7/4]+> map (round . ratio_to_cents) r'' == [0,155,267,386,498,653,884,969]++> let c0 = [0,204,231,435,471,675,702,906,933,969,1137,1173,1200]+> let c1 = [0,120,155,351,386,506,583,738,814,893,969,1124,1200]+> let c2 = [0,155,267,386,498,653,884,969,1200]+> let f (c',y) = map (\x -> (x,y,x,y + 10)) c'+> map f (zip [c0,c1,c2] [0,20,40])++-}+efg_ratios :: Real r => Rational -> Efg r -> [([Int],Rational)]+efg_ratios n =+    let to_r = fold_ratio_to_octave_err . (/ n) . toRational . product+        f (ix,i) = (ix,to_r i)+    in map f . efg_factors++{- | Generate a line drawing, as a set of (x0,y0,x1,y1) 4-tuples.+     h=row height, m=distance of vertical mark from row edge, k=distance between rows++> let e = [[3,3,3],[3,3,5],[3,5,5],[3,5,7],[3,7,7],[5,5,5],[5,5,7],[3,3,7],[5,7,7],[7,7,7]]+> let e = [[3,3,3],[5,5,5],[7,7,7],[3,3,5],[3,5,5],[5,5,7],[5,7,7],[3,7,7],[3,3,7],[3,5,7]]+> let e' = map efg_collate e+> efg_diagram_set (round,25,4,75) e'++-}+efg_diagram_set :: (Enum n,Real n) => (Cents -> n,n,n,n) -> [Efg n] -> [(n,n,n,n)]+efg_diagram_set (to_f,h,m,k) e =+    let f = (++ [1200]) . sort . map (to_f . ratio_to_cents . snd) . efg_ratios 1+        g (c,y) = let y' = y + h+                      b = [(0,y,1200,y),(0,y',1200,y')]+                  in b ++ map (\x -> (x,y + m,x,y' - m)) c+    in concatMap g (zip (map f e) [0,k ..])
+ Music/Theory/Tuning/Et.hs view
@@ -0,0 +1,253 @@+-- | Equal temperament tuning tables.+module Music.Theory.Tuning.Et where++import Data.List {- base -}+import Data.List.Split {- split -}+import Data.Ratio {- base -}+import Text.Printf {- base -}++import qualified Music.Theory.List as T {- hmt -}+import Music.Theory.Pitch {- hmt -}+import Music.Theory.Pitch.Note {- hmt -}+import Music.Theory.Pitch.Spelling.Table {- hmt -}+import Music.Theory.Tuning {- hmt -}++-- | 'octpc_to_pitch' and 'octpc_to_cps_k0'.+octpc_to_pitch_cps_k0 :: (Floating n) => (n,n) -> OctPc -> (Pitch,n)+octpc_to_pitch_cps_k0 zero x = (octpc_to_pitch pc_spell_ks x,octpc_to_cps_k0 zero x)++-- | 'octpc_to_pitch_cps_k0' of (69,440)+octpc_to_pitch_cps :: (Floating n) => OctPc -> (Pitch,n)+octpc_to_pitch_cps = octpc_to_pitch_cps_k0 (69,440)++-- | 12-tone equal temperament table equating 'Pitch' and frequency+-- over range of human hearing, where @A4@ has given frequency.+--+-- > tbl_12et_k0 (69,440)+tbl_12et_k0 :: (Double,Double) -> [(Pitch,Double)]+tbl_12et_k0 zero =+    let z = [(o,pc) | o <- [-5 .. 10], pc <- [0 .. 11]]+    in map (octpc_to_pitch_cps_k0 zero) z++-- | 'tbl_12et_k0' @(69,440)@.+--+-- > length tbl_12et == 192+-- > T.minmax (map (round . snd) tbl_12et) == (1,31609)+tbl_12et :: [(Pitch,Double)]+tbl_12et = tbl_12et_k0 (69,440)++-- | 24-tone equal temperament variant of 'tbl_12et_k0'.+tbl_24et_k0 :: (Double,Double) -> [(Pitch,Double)]+tbl_24et_k0 zero =+    let f x = let p = fmidi_to_pitch_err pc_spell_ks x+                  p' = pitch_rewrite_threequarter_alteration p+              in (p',fmidi_to_cps_k0 zero x)+        k0 = -36+    in map f [k0,k0 + 0.5 .. 143.5]++-- | 'tbl_24et_k0' @(69,440)@.+--+-- > length tbl_24et == 360+-- > T.minmax (map (round . snd) tbl_24et) == (1,32535)+tbl_24et :: [(Pitch,Double)]+tbl_24et = tbl_24et_k0 (69,440)++-- | Given an @Et@ table (or like) find bounds of frequency.+--+-- > import qualified Music.Theory.Tuple as T+-- > let r = Just (T.t2_map octpc_to_pitch_cps ((3,11),(4,0)))+-- > bounds_et_table tbl_12et 256 == r+bounds_et_table :: Ord s => [(t,s)] -> s -> Maybe ((t,s),(t,s))+bounds_et_table = T.find_bounds True (compare . snd)++-- | 'bounds_et_table' of 'tbl_12et'.+--+-- > import qualified Music.Theory.Tuning.Hs as T+-- > map bounds_12et_tone (T.harmonic_series_cps_n 17 55)+bounds_12et_tone :: Double -> Maybe ((Pitch,Double),(Pitch,Double))+bounds_12et_tone = bounds_et_table tbl_12et++-- | Tuple indicating nearest 'Pitch' to /frequency/ with @Et@+-- frequency, and deviation in hertz and 'Cents'.+--+-- (cps,nearest-pitch,cps-of-nearest-pitch,cps-deviation,cents-deviation)+type HS_R p = (Double,p,Double,Double,Cents)++-- | /n/-decimal places.+--+-- > ndp 3 (1/3) == "0.333"+ndp :: Int -> Double -> String+ndp = printf "%.*f"++-- | Pretty print 'HS_R'.  This discards the /cps-deviation/ field, ie. it has only four fields.+hs_r_pp :: (p -> String) -> Int -> HS_R p -> [String]+hs_r_pp pp n (f,p,pf,_,c) = let dp = ndp n in [dp f,pp p,dp pf,dp c]++-- | 'hs_r_pp' of 'pitch_pp'+hs_r_pitch_pp :: Int -> HS_R Pitch -> [String]+hs_r_pitch_pp = hs_r_pp pitch_pp++{- | Form 'HS_R' for /frequency/ by consulting table.++> let f = 256+> let f' = octpc_to_cps (4,0)+> let r = (f,Pitch C Natural 4,f',f-f',fratio_to_cents (f/f'))+> nearest_et_table_tone tbl_12et 256 == r++-}+nearest_et_table_tone :: [(p,Double)] -> Double -> HS_R p+nearest_et_table_tone tbl f =+    case bounds_et_table tbl f of+      Nothing -> error "nearest_et_table_tone: no bounds?"+      Just ((lp,lf),(rp,rf)) ->+          let ld = f - lf+              rd = f - rf+          in if abs ld < abs rd+             then (f,lp,lf,ld,fratio_to_cents (f/lf))+             else (f,rp,rf,rd,fratio_to_cents (f/rf))++-- | 'nearest_et_table_tone' for 'tbl_12et_k0'.+nearest_12et_tone_k0 :: (Double,Double) -> Double -> HS_R Pitch+nearest_12et_tone_k0 zero = nearest_et_table_tone (tbl_12et_k0 zero)++-- | 'nearest_et_table_tone' for 'tbl_24et'.+--+-- > let r = "55.0 A1 55.0 0.0"+-- > unwords (hs_r_pitch_pp 1 (nearest_24et_tone_k0 (69,440) 55)) == r+nearest_24et_tone_k0 :: (Double,Double) -> Double -> HS_R Pitch+nearest_24et_tone_k0 zero = nearest_et_table_tone (tbl_24et_k0 zero)++-- * 72Et++-- | Monzo 72-edo HEWM notation.  The domain is (-9,9).+-- <http://www.tonalsoft.com/enc/number/72edo.aspx>+--+-- > let r = ["+",">","^","#<","#-","#","#+","#>","#^"]+-- > map alteration_72et_monzo [1 .. 9] == r+--+-- > let r = ["-","<","v","b>","b+","b","b-","b<","bv"]+-- > map alteration_72et_monzo [-1,-2 .. -9] == r+alteration_72et_monzo :: Integral n => n -> String+alteration_72et_monzo n =+    let spl = splitOn ","+        asc = spl ",+,>,^,#<,#-,#,#+,#>,#^"+        dsc = spl ",-,<,v,b>,b+,b,b-,b<,bv"+    in case compare n 0 of+         LT -> genericIndex dsc (- n)+         EQ -> ""+         GT -> genericIndex asc n++-- | Given a midi note number and @1/6@ deviation determine 'Pitch''+-- and frequency.+--+-- > let f = pitch_r_pp . fst . pitch_72et_k0 (69,440)+-- > let r = "C4 C+4 C>4 C^4 C#<4 C#-4 C#4 C#+4 C#>4 C#^4"+-- > unwords (map f (zip (repeat 60) [0..9])) == r+--+-- > let r = "A4 A+4 A>4 A^4 Bb<4 Bb-4 Bb4 Bb+4 Bb>4 Bv4"+-- > unwords (map f (zip (repeat 69) [0..9])) == r+--+-- > let r = "Bb4 Bb+4 Bb>4 Bv4 B<4 B-4 B4 B+4 B>4 B^4"+-- > unwords (map f (zip (repeat 70) [0..9])) == r+pitch_72et_k0 :: (Double,Double) -> (Midi,Int) -> (Pitch_R,Double)+pitch_72et_k0 zero (x,n) =+    let p = midi_to_pitch_ks x+        t = note p+        a = alteration p+        (t',n') = case a of+                    Flat -> if n < (-3) then (pred t,n + 6) else (t,n - 6)+                    Natural -> (t,n)+                    Sharp -> if n > 3 then (succ t,n - 6) else (t,n + 6)+                    _ -> error "pitch_72et: alteration?"+        a' = alteration_72et_monzo n'+        x' = fromIntegral x + (fromIntegral n / 6)+        r = (Pitch_R t' (fromIntegral n' % 12,a') (octave p),fmidi_to_cps_k0 zero x')+        r' = if n > 3+             then pitch_72et_k0 zero (x + 1,n - 6)+             else if n < (-3)+                  then pitch_72et_k0 zero (x - 1,n + 6)+                  else r+    in case a of+         Natural -> r'+         _ -> r++-- | 72-tone equal temperament table equating 'Pitch'' and frequency+-- over range of human hearing, where @A4@ = @440@hz.+--+-- > length (tbl_72et_k0 (69,440)) == 792+-- > T.minmax (map (round . snd) (tbl_72et_k0 (69,440))) == (16,33167)+tbl_72et_k0 :: (Double, Double) -> [(Pitch_R,Double)]+tbl_72et_k0 zero =+    let f n = zipWith (curry (pitch_72et_k0 zero)) (replicate 6 n) [0..5]+    in concatMap f [12 .. 143]++-- | 'nearest_et_table_tone' for 'tbl_72et'.+--+-- > let r = "324.0 E<4 323.3 0.7 3.5"+-- > unwords (hs_r_pp pitch_r_pp 1 (nearest_72et_tone_k0 (69,440) 324))+--+-- > let f = take 2 . hs_r_pp pitch_r_pp 1 . nearest_72et_tone_k0 (69,440) . snd+-- > mapM_ (print . unwords . f) (tbl_72et_k0 (69,440))+nearest_72et_tone_k0 :: (Double,Double) -> Double -> HS_R Pitch_R+nearest_72et_tone_k0 zero = nearest_et_table_tone (tbl_72et_k0 zero)++-- * Detune++-- | 'Pitch' with 12-Et/24-Et tuning deviation given in 'Cents'.+type Pitch_Detune = (Pitch,Cents)++-- | Extract 'Pitch_Detune' from 'HS_R'.+hsr_to_pitch_detune :: HS_R Pitch -> Pitch_Detune+hsr_to_pitch_detune (_,p,_,_,c) = (p,c)++-- | Nearest 12-Et 'Pitch_Detune' to indicated frequency (hz).+--+-- > nearest_pitch_detune_12et_k0 (69,440) 452.8929841231365+nearest_pitch_detune_12et_k0 :: (Double, Double) -> Double -> Pitch_Detune+nearest_pitch_detune_12et_k0 zero = hsr_to_pitch_detune . nearest_12et_tone_k0 zero++-- | Nearest 24-Et 'Pitch_Detune' to indicated frequency (hz).+--+-- > nearest_pitch_detune_24et_k0 (69,440) 452.8929841231365+nearest_pitch_detune_24et_k0 :: (Double, Double) -> Double -> Pitch_Detune+nearest_pitch_detune_24et_k0 zero = hsr_to_pitch_detune . nearest_24et_tone_k0 zero++-- | Given /near/ function, /f0/ and ratio derive 'Pitch_Detune'.+ratio_to_pitch_detune :: (Double -> HS_R Pitch) -> OctPc -> Rational -> Pitch_Detune+ratio_to_pitch_detune near_f f0 r =+    let f = octpc_to_cps f0 * realToFrac r+        (_,p,_,_,c) = near_f f+    in (p,c)++-- | Frequency (hz) of 'Pitch_Detune'.+--+-- > pitch_detune_to_cps (octpc_to_pitch pc_spell_ks (4,9),50)+pitch_detune_to_cps :: Floating n => Pitch_Detune -> n+pitch_detune_to_cps (p,d) = cps_shift_cents (pitch_to_cps p) (realToFrac d)++-- | 'ratio_to_pitch_detune' of 'nearest_12et_tone'+ratio_to_pitch_detune_12et_k0 :: (Double, Double) -> OctPc -> Rational -> Pitch_Detune+ratio_to_pitch_detune_12et_k0 zero = ratio_to_pitch_detune (nearest_12et_tone_k0 zero)++-- | 'ratio_to_pitch_detune' of 'nearest_24et_tone'+ratio_to_pitch_detune_24et_k0 :: (Double, Double) -> OctPc -> Rational -> Pitch_Detune+ratio_to_pitch_detune_24et_k0 zero = ratio_to_pitch_detune (nearest_24et_tone_k0 zero)++pitch_detune_in_octave_nearest  :: Pitch -> Pitch_Detune -> Pitch_Detune+pitch_detune_in_octave_nearest p1 (p2,d2) = (pitch_in_octave_nearest p1 p2,d2)++-- | Markdown pretty-printer for 'Pitch_Detune'.+pitch_detune_md :: Pitch_Detune -> String+pitch_detune_md (p,c) = pitch_pp p ++ cents_diff_md (round c :: Integer)++-- | HTML pretty-printer for 'Pitch_Detune'.+pitch_detune_html :: Pitch_Detune -> String+pitch_detune_html (p,c) = pitch_pp p ++ cents_diff_html (round c :: Integer)++-- | No-octave variant of 'pitch_detune_md'.+pitch_class_detune_md :: Pitch_Detune -> String+pitch_class_detune_md (p,c) = pitch_class_pp p ++ cents_diff_md (round c :: Integer)++-- | No-octave variant of 'pitch_detune_html'.+pitch_class_detune_html :: Pitch_Detune -> String+pitch_class_detune_html (p,c) = pitch_class_pp p ++ cents_diff_html (round c :: Integer)
− Music/Theory/Tuning/Euler.hs 
@@ -1,138 +0,0 @@--- | Euler plane diagrams as /dot/ language graph.-module Music.Theory.Tuning.Euler where--import Data.List {- base -}-import Data.Ratio {- base -}--import qualified Music.Theory.List as T {- hmt -}-import qualified Music.Theory.Math as T {- hmt -}-import qualified Music.Theory.Pitch.Note as T {- hmt -}-import qualified Music.Theory.Tuning as T {- hmt -}-import qualified Music.Theory.Tuple as T {- hmt -}---- | 'T.fold_ratio_to_octave' of '*'.-rat_mul :: Rational -> Rational -> Rational-rat_mul r = T.fold_ratio_to_octave_err . (* r)---- | 'T.fold_ratio_to_octave' of '/'.-rat_div :: Rational -> Rational -> Rational-rat_div p q = T.fold_ratio_to_octave_err (p / q)---- | /n/ = length, /m/ equals multiplier, /r/ = initial ratio.------ > tun_seq 5 (3/2) 1 == [1/1,3/2,9/8,27/16,81/64]-tun_seq :: Int -> Rational -> Rational -> [Rational]-tun_seq n m = take n . iterate (rat_mul m)--mod12 :: Integral a => a -> a-mod12 n = n `mod` 12---- | 'T.ratio_to_cents' rounded to nearest multiple of 100, modulo 12.------ > map (ratio_to_pc 0) [1,4/3,3/2,2] == [0,5,7,0]-ratio_to_pc :: Int -> Rational -> Int-ratio_to_pc n = mod12 . (+ n) . round . (/ 100) . T.ratio_to_cents--all_pairs :: [t] -> [u] -> [(t,u)]-all_pairs p q = [(x,y) | x <- p, y <- q]---- | Give all pairs from (l2,l1) and (l3,l2) that are at interval ratios r1 and r2 respectively.-euler_align_rat :: T.T2 Rational -> T.T3 [Rational] -> T.T2 [T.T2 Rational]-euler_align_rat (r1,r2) (l1,l2,l3) =-    let f r (p,q) = rat_mul p r == q-    in (filter (f r1) (all_pairs l2 l1)-       ,filter (f r2) (all_pairs l3 l2))---- | Pretty printer for pitch class.------ > unwords (map pc_pp [0..11]) == "C♮ C♯ D♮ E♭ E♮ F♮ F♯ G♮ A♭ A♮ B♭ B♮"-pc_pp :: (Integral i,Show i) => i -> String-pc_pp x =-    case T.pc_to_note_alteration_ks x of-      Just (n,a) -> [T.note_pp n,T.alteration_symbol a]-      Nothing -> error (show ("pc_pp",x))--cents_pp :: Rational -> String-cents_pp = show . (round :: Double -> Integer) . T.ratio_to_cents---- > rat_label (0,False) 1 == "C♮\\n1:1"--- > rat_label (3,True) (7/4) == "C♯=969\\n7:4"-rat_label :: (Int,Bool) -> Rational -> String-rat_label (k,with_cents) r =-    if r < 1 || r >= 2-    then error (show ("rat_label",r))-    else concat [pc_pp (ratio_to_pc k r)-                ,if with_cents-                 then '=' : cents_pp r-                 else ""-                ,"\\n",T.ratio_pp r]---- > rat_id (5/4) == "R_5_4"-rat_id :: Rational-> String-rat_id r = "R_" ++ show (numerator r) ++ "_" ++ show (denominator r)--rat_edge_label :: (Rational, Rational) -> String-rat_edge_label (p,q) = concat ["   (",T.ratio_pp (rat_div p q),")"]---- | Zip start-middle-end.------ > zip_sme (0,1,2) "abcd" == [(0,'a'),(1,'b'),(1,'c'),(2,'d')]-zip_sme :: (t,t,t) -> [u] -> [(t,u)]-zip_sme (s,m,e) xs =-    case xs of-      x0:x1:xs' -> (s,x0) : (m,x1) : T.at_last (\x -> (m,x)) (\x -> (e,x)) xs'-      _ -> error "zip_sme: not SME list"--type Euler_Plane t = ([[t]],[(t,t)])--euler_plane_to_dot :: (t -> String,t -> String,(t,t) -> String) -> Euler_Plane t -> [String]-euler_plane_to_dot (n_id,n_pp,e_pp) (h,v) =-    let mk_lab_term x =concat [" [label=\"",x,"\"];"]-        node_to_dot x = concat [n_id x,mk_lab_term (n_pp x)]-        subgraph_edges x = intercalate " -- " (map n_id x) ++ ";"-        edge_to_dot (lhs,rhs) = concat [n_id lhs," -- ",n_id rhs,mk_lab_term (e_pp (lhs,rhs))]-        subgraphs_to_dot (ty,x) = concat ["{rank=",ty,"; ",unwords (map n_id x),"}"]-    in ["graph g {"-       ,"graph [layout=\"dot\",rankdir=\"TB\",nodesep=0.5];"-       ,"edge [fontsize=\"8\",fontname=\"century schoolbook\"];"-       ,"node [shape=\"plaintext\",fontsize=\"10\",fontname=\"century schoolbook\"];"] ++-       map node_to_dot (concat h) ++-       map subgraph_edges h ++-       map edge_to_dot v ++-       map subgraphs_to_dot (zip_sme ("min","same","max") h) ++-       ["}"]--euler_plane_to_dot_rat :: (Int, Bool) -> Euler_Plane Rational -> [String]-euler_plane_to_dot_rat opt = euler_plane_to_dot (rat_id,rat_label opt,rat_edge_label)--{---let j5 =-    let {l1 = tun_seq 3 (3%2) (5%3)-        ;l2 = tun_seq 5 (3%2) (16%9)-        ;l3 = tun_seq 4 (3%2) (64%45)-        ;(c1,c2) = euler_align_rat (5%8,5%4) (l1,l2,l3)}-    in ([l1,l2,l3],c1 ++ c2)--let j5' =-    let {f = T.fold_ratio_to_octave_err-        ;l1 = tun_seq 4 (3/2) (f (1 * 2/3 * 5/4))-        ;l2 = tun_seq 5 (3/2) (f (1 * 2/3 * 2/3))-        ;l3 = tun_seq 3 (3/2) (f (1 * 2/3 * 4/5))-        ;(c1,c2) = euler_align_rat (5/4,5/4) (l1,l2,l3)}-    in ([l1,l2,l3],c1 ++ c2)--let j7 =-    let {l1 = tun_seq 4 (3%2) (5%4)-        ;l2 = tun_seq 5 (3%2) (4%3)-        ;l3 = tun_seq 3 (3%2) (14%9)-        ;(c1,c2) = euler_align_rat (5%4,4%7) (l1,l2,l3)}-    in ([l1,l2,l3],c1 ++ c2)--let dir = "/home/rohan/sw/hmt/data/dot/"-let f = unlines . euler_plane_to_dot_rat (0,False)-writeFile (dir ++ "euler-j5-a.dot") (f j5)-writeFile (dir ++ "euler-j5-b.dot") (f j5')-writeFile (dir ++ "euler-j7.dot") (f j7)---}
Music/Theory/Tuning/Gann_1993.hs view
@@ -6,9 +6,11 @@ import Data.Maybe {- base -}  import qualified Music.Theory.List as T {- hmt -}+import qualified Music.Theory.Math as T {- hmt -} import qualified Music.Theory.Pitch as T {- hmt -} import qualified Music.Theory.Tuning as T {- hmt -}-import qualified Music.Theory.Tuning.Euler as T {- hmt -}+import qualified Music.Theory.Tuning.Graph.Euler as T {- hmt -}+import qualified Music.Theory.Tuning.Type as T {- hmt -}  {- | Ratios for 'lmy_wtp'. lmy = La Monte Young. wtp = Well-Tuned Piano. @@ -82,7 +84,7 @@  -} lmy_wtp_uniq :: [(Rational,[(T.PitchClass,T.PitchClass)])]-lmy_wtp_uniq = sortOn (T.ratio_nd_sum . fst) $ T.collate_on fst snd $ lmy_wtp_univ+lmy_wtp_uniq = sortOn (T.ratio_nd_sum . fst) (T.collate_on fst snd lmy_wtp_univ)  {- | Gann, 1993, p.137. @@ -101,7 +103,7 @@  -} lmy_wtp :: T.Tuning-lmy_wtp = T.Tuning (Left lmy_wtp_r) 2+lmy_wtp = T.Tuning (Left lmy_wtp_r) Nothing  -- | Ratios for 'lmy_wtp_1964. lmy_wtp_1964_r :: [Rational]@@ -121,7 +123,7 @@  -} lmy_wtp_1964 :: T.Tuning-lmy_wtp_1964 = T.Tuning (Left lmy_wtp_1964_r) 2+lmy_wtp_1964 = T.Tuning (Left lmy_wtp_1964_r) Nothing  {- | Euler diagram for 'lmy_wtp'. @@ -134,6 +136,6 @@ lmy_wtp_euler =     let {l1 = T.tun_seq 4 (3/2) (49/32)         ;l2 = T.tun_seq 5 (3/2) (7/4)-        ;l3 = T.tun_seq 3 (3/2) (1/1)+        ;l3 = T.tun_seq 3 (3/2) 1         ;(c1,c2) = T.euler_align_rat (7/4,7/4) (l1,l2,l3)}     in ([l1,l2,l3],c1 ++ c2)
+ Music/Theory/Tuning/Graph/Euler.hs view
@@ -0,0 +1,124 @@+-- | Euler plane diagrams as /dot/ language graphs.+--+-- <http://rohandrape.net/?t=hmt-texts&e=md/euler.md>+module Music.Theory.Tuning.Graph.Euler where++import Data.List {- base -}+import Data.Ratio {- base -}++import qualified Music.Theory.Function as T {- hmt -}+import qualified Music.Theory.List as T {- hmt -}+import qualified Music.Theory.Pitch.Note as T {- hmt -}+import qualified Music.Theory.Show as T {- hmt -}+import qualified Music.Theory.Tuning as T {- hmt -}+import qualified Music.Theory.Tuple as T {- hmt -}++-- | 'T.fold_ratio_to_octave_err' of '*'.+rat_mul :: Rational -> Rational -> Rational+rat_mul r = T.fold_ratio_to_octave_err . (* r)++-- | 'T.fold_ratio_to_octave_err' of '/'.+rat_div :: Rational -> Rational -> Rational+rat_div p q = T.fold_ratio_to_octave_err (p / q)++-- | /n/ = length, /m/ = multiplier, /r/ = initial ratio.+--+-- > tun_seq 5 (3/2) 1 == [1/1,3/2,9/8,27/16,81/64]+tun_seq :: Int -> Rational -> Rational -> [Rational]+tun_seq n m = take n . iterate (rat_mul m)++-- | All possible pairs of elements (/x/,/y/) where /x/ is from /p/ and /y/ from /q/.+--+-- > all_pairs "ab" "cde" == [('a','c'),('a','d'),('a','e'),('b','c'),('b','d'),('b','e')]+all_pairs :: [t] -> [u] -> [(t,u)]+all_pairs p q = [(x,y) | x <- p, y <- q]++-- | Give all pairs from (l2,l1) and (l3,l2) that are at interval ratios r1 and r2 respectively.+euler_align_rat :: T.T2 Rational -> T.T3 [Rational] -> T.T2 [T.T2 Rational]+euler_align_rat (r1,r2) (l1,l2,l3) =+    let f r (p,q) = rat_mul p r == q+    in (filter (f r1) (all_pairs l2 l1)+       ,filter (f r2) (all_pairs l3 l2))++-- | Pretty printer for pitch class (UNICODE).+--+-- > unwords (map pc_pp [0..11]) == "C♮ C♯ D♮ E♭ E♮ F♮ F♯ G♮ A♭ A♮ B♭ B♮"+pc_pp :: (Integral i,Show i) => i -> String+pc_pp x =+    case T.pc_to_note_alteration_ks x of+      Just (n,a) -> [T.note_pp n,T.alteration_symbol a]+      Nothing -> error (show ("pc_pp",x))++-- | Show ratio as intergral ('round') cents value.+cents_pp :: Rational -> String+cents_pp = show . (round :: Double -> Integer) . T.ratio_to_cents++-- | (unit-pitch-class,print-cents)+type RAT_LABEL_OPT = (Int,Bool)++-- | Dot label for ratio, /k/ is the pitch-class of the unit ratio.+--+-- > rat_label (0,False) 1 == "C♮\\n1:1"+-- > rat_label (3,True) (7/4) == "C♯=969\\n7:4"+rat_label :: RAT_LABEL_OPT -> Rational -> String+rat_label (k,with_cents) r =+    if r < 1 || r >= 2+    then error (show ("rat_label",r))+    else concat [pc_pp (T.ratio_to_pc k r)+                ,if with_cents+                 then '=' : cents_pp r+                 else ""+                ,"\\n",T.ratio_pp r]++-- | Generate value /dot/ node identifier for ratio.+--+-- > rat_id (5/4) == "R_5_4"+rat_id :: Rational-> String+rat_id r = "R_" ++ show (numerator r) ++ "_" ++ show (denominator r)++-- | Printer for edge label between given ratio nodes.+rat_edge_label :: (Rational, Rational) -> String+rat_edge_label (p,q) = concat ["   (",T.ratio_pp (rat_div p q),")"]++-- | Zip start-middle-end.+--+-- > zip_sme (0,1,2) "abcd" == [(0,'a'),(1,'b'),(1,'c'),(2,'d')]+zip_sme :: (t,t,t) -> [u] -> [(t,u)]+zip_sme (s,m,e) xs =+    case xs of+      x0:x1:xs' -> (s,x0) : (m,x1) : T.at_last (\x -> (m,x)) (\x -> (e,x)) xs'+      _ -> error "zip_sme: not SME list"++-- | Euler diagram given as (/h/,/v/) duple,+-- where /h/ are the horizontal sequences and /v/ are the vertical edges.+type Euler_Plane t = ([[t]],[(t,t)])++-- | Ratios at plane, sorted.+euler_plane_r :: Ord t => Euler_Plane t -> [t]+euler_plane_r = sort . concat . fst++-- | Apply /f/ at all nodes of the plane.+euler_plane_map :: (t -> u) -> Euler_Plane t -> Euler_Plane u+euler_plane_map f (p,q) = (map (map f) p,map (T.bimap1 f) q)++-- | Generate /dot/ graph given printer functions and an /Euler_Plane/.+euler_plane_to_dot :: (t -> String,t -> String,(t,t) -> String) -> Euler_Plane t -> [String]+euler_plane_to_dot (n_id,n_pp,e_pp) (h,v) =+    let mk_lab_term x = concat [" [label=\"",x,"\"];"]+        node_to_dot x = concat [n_id x,mk_lab_term (n_pp x)]+        subgraph_edges x = intercalate " -- " (map n_id x) ++ ";"+        edge_to_dot (lhs,rhs) = concat [n_id lhs," -- ",n_id rhs,mk_lab_term (e_pp (lhs,rhs))]+        subgraphs_to_dot (ty,x) = concat ["{rank=",ty,"; ",unwords (map n_id x),"}"]+    in ["graph g {"+       ,"graph [layout=\"dot\",rankdir=\"TB\",nodesep=0.5];"+       ,"edge [fontsize=\"8\",fontname=\"century schoolbook\"];"+       ,"node [shape=\"plaintext\",fontsize=\"10\",fontname=\"century schoolbook\"];"] +++       map node_to_dot (concat h) +++       map subgraph_edges h +++       map edge_to_dot v +++       map subgraphs_to_dot (zip_sme ("min","same","max") h) +++       ["}"]++-- | Variant with default printers and fixed node type.+euler_plane_to_dot_rat :: RAT_LABEL_OPT -> Euler_Plane Rational -> [String]+euler_plane_to_dot_rat opt = euler_plane_to_dot (rat_id,rat_label opt,rat_edge_label)
+ Music/Theory/Tuning/Graph/Iset.hs view
@@ -0,0 +1,127 @@+-- | Tuning graph with edges determined by interval set.+module Music.Theory.Tuning.Graph.Iset where++import Data.List {- base -}+import Data.Maybe {- base -}++import qualified Data.Graph.Inductive.Graph as Fgl {- fgl -}+import qualified Data.Graph.Inductive.PatriciaTree as Fgl {- fgl -}++import qualified Music.Theory.Graph.Type as T {- hmt-base -}+import qualified Music.Theory.List as T {- hmt-base -}+import qualified Music.Theory.Show as T {- hmt-base -}++import qualified Music.Theory.Graph.Dot as T {- hmt -}+import qualified Music.Theory.Graph.Fgl as T {- hmt -}+import qualified Music.Theory.Tuning as T {- hmt -}+import qualified Music.Theory.Tuning.Graph.Euler as Euler {- hmt -}+import qualified Music.Theory.Tuning.Scala as Scala {- hmt -}++-- * R++-- | R = Rational+type R = Rational++-- | Flip a ratio in (1,2) and multiply by 2.+--+-- > import Data.Ratio {- base -}+-- > map r_flip [5%4,3%2,7%4] == [8%5,4%3,8%7]+-- > map r_flip [3/2,5/4,7/4] == [4/3,8/5,8/7]+r_flip :: R -> R+r_flip n = if n < 1 || n > 2 then error "r_flip" else 1 / n * 2++-- | r = ratio, nrm = normalise+r_nrm :: R -> R+r_nrm = T.ratio_interval_class_by id++-- | The folded interval from p to q.+--+-- > r_rel (1,3/2) == 4/3+r_rel :: (R,R) -> R+r_rel (p,q) = T.fold_ratio_to_octave_err (p / q)++-- | The interval set /i/ and it's 'r_flip'.+iset_sym :: [R] -> [R]+iset_sym l = l ++ map r_flip l++-- | Require r to have a perfect octave as last element, and remove it.+rem_oct :: [R] -> [R]+rem_oct r = if last r /= 2 then error "rem_oct" else T.drop_last r++r_pcset :: [R] -> [Int]+r_pcset = sort . map (T.ratio_to_pc 0)++r_pcset_univ :: [R] -> [Int]+r_pcset_univ = nub . r_pcset++-- | Does [R] construct indicated /pcset/.+r_is_pcset :: [Int] -> [R] -> Bool+r_is_pcset pcset = (==) pcset . r_pcset++-- * G++-- | Edges are (v1,v2) where v1 < v2+type G = T.Gr R++edj_r :: (R, R) -> R+edj_r = r_nrm . r_rel++-- | The graph with vertices /scl_r/ and all edges where the interval (i,j) is in /iset/.+mk_graph :: [R] -> [R] -> G+mk_graph iset scl_r =+  (scl_r+  ,filter+    (\e -> edj_r e `elem` iset_sym iset)+    [(p,q) |+     p <- scl_r,+     q <- scl_r,+     p < q])++gen_graph :: Ord v => [T.Dot_Meta_Attr] -> T.Graph_Pp v e -> [T.Edge_Lbl v e] -> [String]+gen_graph opt pp es = T.fgl_to_udot opt pp (T.g_from_edges_l es)++g_to_dot :: Int -> [(String,String)] -> (R -> [(String,String)]) -> G -> [String]+g_to_dot k attr v_attr (_,e_set) =+  let opt =+        [("graph:layout","neato")+        ,("node:shape","plaintext")+        ,("node:fontsize","10")+        ,("node:fontname","century schoolbook")+        ,("edge:fontsize","9")]+  in gen_graph+     (opt ++ attr)+     (\(_,v) -> ("label",Euler.rat_label (k,True) v) : v_attr v+     ,\(_,e) -> [("label",T.rational_pp e)])+     (map (\e -> (e,edj_r e)) e_set)++-- * SCALA++mk_graph_scl :: [R] -> Scala.Scale -> G+mk_graph_scl iset = mk_graph iset . rem_oct . Scala.scale_ratios_req++scl_to_dot :: ([R], Int, [(String, String)], R -> [(String, String)]) -> String -> IO [String]+scl_to_dot (iset,k,attr,v_attr) nm = do+  sc <- Scala.scl_load nm+  let gr = mk_graph_scl iset sc+  return (g_to_dot k attr v_attr gr)++-- * Fgl++graph_to_fgl :: G -> Fgl.Gr R R+graph_to_fgl (v,e) =+  let fgl_v = zip [0..] v+      r_to_v :: R -> Int+      r_to_v x = fromJust (T.reverse_lookup x fgl_v)+      fgl_e = map (\(p,q) -> (r_to_v p,r_to_v q,edj_r (p,q))) e+  in Fgl.mkGraph fgl_v fgl_e++mk_graph_fgl :: [R] -> [R] -> Fgl.Gr R R+mk_graph_fgl iset = graph_to_fgl . mk_graph iset++{-+-- | List of nodes at /g/ connected to node /r/.+g_edge_list :: G -> R -> [R]+g_edge_list (_,e) r =+  let f (p,q) = if r == p then Just q else if r == q then Just p else Nothing+  in mapMaybe f e+-}
+ Music/Theory/Tuning/Hs.hs view
@@ -0,0 +1,81 @@+-- | Harmonic series+module Music.Theory.Tuning.Hs where++import Data.List {- base -}+import Data.Ratio {- base -}+import qualified Safe {- safe -}++import qualified Music.Theory.Pitch as T {- hmt -}+import Music.Theory.Tuning {- hmt -}+import Music.Theory.Tuning.Type {- hmt -}+++-- | Harmonic series to /n/th partial, with indicated octave.+--+-- > harmonic_series 17 2+harmonic_series :: Integer -> Maybe Rational -> Tuning+harmonic_series n o = Tuning (Left [1 .. n%1]) (fmap Left o)++-- | Harmonic series on /n/.+harmonic_series_cps :: (Num t, Enum t) => t -> [t]+harmonic_series_cps n = [n,n * 2 ..]++-- | /n/ elements of 'harmonic_series_cps'.+--+-- > let r = [55,110,165,220,275,330,385,440,495,550,605,660,715,770,825,880,935]+-- > harmonic_series_cps_n 17 55 == r+harmonic_series_cps_n :: (Num a, Enum a) => Int -> a -> [a]+harmonic_series_cps_n n = take n . harmonic_series_cps++-- | Sub-harmonic series on /n/.+subharmonic_series_cps :: (Fractional t,Enum t) => t -> [t]+subharmonic_series_cps n = map ((* n) . recip) [1..]++-- | /n/ elements of 'harmonic_series_cps'.+--+-- > let r = [1760,880,587,440,352,293,251,220,196,176,160,147,135,126,117,110,104]+-- > map round (subharmonic_series_cps_n 17 1760) == r+subharmonic_series_cps_n :: (Fractional t,Enum t) => Int -> t -> [t]+subharmonic_series_cps_n n = take n . subharmonic_series_cps++-- | /n/th partial of /f1/, ie. one indexed.+--+-- > map (partial 55) [1,5,3] == [55,275,165]+partial :: (Num a, Enum a) => a -> Int -> a+partial f1 k = harmonic_series_cps f1 `Safe.at` (k - 1)++-- | Derivative harmonic series, based on /k/th partial of /f1/.+--+-- > import Music.Theory.Pitch+--+-- > let r = [52,103,155,206,258,309,361,412,464,515,567,618,670,721,773]+-- > let d = harmonic_series_cps_derived 5 (T.octpc_to_cps (1,4))+-- > map round (take 15 d) == r+harmonic_series_cps_derived :: (RealFrac a, Floating a, Enum a) => Int -> a -> [a]+harmonic_series_cps_derived k f1 =+    let f0 = T.cps_in_octave_above f1 (partial f1 k)+    in harmonic_series_cps f0++-- | Harmonic series to /n/th harmonic (folded, duplicated removed).+--+-- > harmonic_series_folded_r 17 == [1,17/16,9/8,5/4,11/8,3/2,13/8,7/4,15/8]+--+-- > let r = [0,105,204,386,551,702,841,969,1088]+-- > map (round . ratio_to_cents) (harmonic_series_folded_r 17) == r+harmonic_series_folded_r :: Integer -> [Rational]+harmonic_series_folded_r n = nub (sort (map fold_ratio_to_octave_err [1 .. n%1]))++-- | 'ratio_to_cents' variant of 'harmonic_series_folded'.+harmonic_series_folded_c :: Integer -> [Cents]+harmonic_series_folded_c = map ratio_to_cents . harmonic_series_folded_r++harmonic_series_folded :: Integer -> Tuning+harmonic_series_folded n = Tuning (Left (harmonic_series_folded_r n)) Nothing++-- | @12@-tone tuning of first @21@ elements of the harmonic series.+--+-- > tn_cents_i harmonic_series_folded_21 == [0,105,204,298,386,471,551,702,841,969,1088]+-- > tn_divisions harmonic_series_folded_21 == 11+harmonic_series_folded_21 :: Tuning+harmonic_series_folded_21 = harmonic_series_folded 21+
Music/Theory/Tuning/Load.hs view
@@ -3,16 +3,19 @@  import System.Random {- random -} -import qualified Music.Theory.Array.CSV as T-import qualified Music.Theory.Pitch as T+import qualified Music.Theory.Array.Csv as T {- hmt-base -}++import qualified Music.Theory.Pitch as T {- hmt -} import qualified Music.Theory.Tuning as T+import qualified Music.Theory.Tuning.Midi as T import qualified Music.Theory.Tuning.Scala as T+import qualified Music.Theory.Tuning.Type as T  -- | Load possibly sparse and possibly one-to-many--- (midi-note-number,cps-frequency) table from CSV file.+-- (midi-note-number,cps-frequency) table from Csv file. -- -- > load_cps_tbl "/home/rohan/dr.csv"-load_cps_tbl :: FilePath -> IO [(Int,Double)]+load_cps_tbl :: FilePath -> IO [(T.Midi,Double)] load_cps_tbl nm = do   tbl <- T.csv_table_read_def id nm   let f e = case e of@@ -22,22 +25,26 @@  -- | Load scala scl file as 'T.Tuning'. load_tuning_scl :: String -> IO T.Tuning-load_tuning_scl = fmap (T.scale_to_tuning 0.01) . T.scl_load+load_tuning_scl = fmap T.scale_to_tuning . T.scl_load +-- | cps = (tuning-name,frequency-zero,midi-note-number-of-f0)+--   d12 = (tuning-name,cents-deviation,midi-note-offset)+type Load_Tuning_Opt = (String,Double,T.Midi)+ -- | Load scala file and apply 'T.cps_midi_tuning_f'.-load_tuning_cps :: (String,Double,Int) -> IO T.Sparse_Midi_Tuning_F+load_tuning_cps :: Load_Tuning_Opt -> IO T.Sparse_Midi_Tuning_f load_tuning_cps (nm,f0,k) =-    let f tn = T.cps_midi_tuning_f (tn,f0,k,128-k)+    let f tn = T.cps_midi_tuning_f (tn,f0,k,128 - T.midi_to_int k)     in fmap f (load_tuning_scl nm)  -- | Load scala file and apply 'T.d12_midi_tuning_f'.-load_tuning_d12 :: (String,Double,Int) -> IO T.Sparse_Midi_Tuning_F+load_tuning_d12 :: Load_Tuning_Opt -> IO T.Sparse_Midi_Tuning_f load_tuning_d12 (nm,dt,k) =     let f tn = T.lift_tuning_f (T.d12_midi_tuning_f (tn,dt,k))     in fmap f (load_tuning_scl nm)  -- | Lookup first matching element in table.-load_tuning_tbl :: (String,Double,Int) -> IO T.Sparse_Midi_Tuning_F+load_tuning_tbl :: Load_Tuning_Opt -> IO T.Sparse_Midi_Tuning_f load_tuning_tbl (nm,dt,k) =     let from_cps = T.cps_to_midi_detune . flip T.cps_shift_cents dt         f tbl mnn = fmap from_cps (lookup (mnn + k) tbl)@@ -52,7 +59,7 @@     in (l !! i,g')  -- | Load tuning table with stateful selection function for one-to-many entries.-load_tuning_tbl_st :: Choose_f st (Int,Double) -> (String,Double,Int) -> IO (T.Sparse_Midi_Tuning_ST_F st)+load_tuning_tbl_st :: Choose_f st (T.Midi,Double) -> Load_Tuning_Opt -> IO (T.Sparse_Midi_Tuning_St_f st) load_tuning_tbl_st choose_f (nm,dt,k) =     let from_cps = T.cps_to_midi_detune . flip T.cps_shift_cents dt         f tbl g mnn = case filter ((== (mnn + k)) . fst) tbl of@@ -61,7 +68,7 @@                              in (g',Just (from_cps e))     in fmap f (load_cps_tbl nm) -load_tuning_ty :: String -> (String,Double,Int) -> IO T.Sparse_Midi_Tuning_F+load_tuning_ty :: String -> Load_Tuning_Opt -> IO T.Sparse_Midi_Tuning_f load_tuning_ty ty opt =     case ty of       "cps" -> load_tuning_cps opt@@ -69,7 +76,7 @@       "tbl" -> load_tuning_tbl opt       _ -> error "cps|d12|tbl" -load_tuning_st_ty :: String -> (String,Double,Int) -> IO (T.Sparse_Midi_Tuning_ST_F StdGen)+load_tuning_st_ty :: String -> Load_Tuning_Opt -> IO (T.Sparse_Midi_Tuning_St_f StdGen) load_tuning_st_ty ty opt =     case ty of       "cps" -> fmap T.lift_sparse_tuning_f (load_tuning_cps opt)
Music/Theory/Tuning/Meyer_1929.hs view
@@ -95,13 +95,17 @@ degree :: Integral i => i -> i degree = genericLength . elements --- | <http://en.wikipedia.org/wiki/Farey_sequence>------ > let r = [[0,1/2,1]--- >         ,[0,1/3,1/2,2/3,1]--- >         ,[0,1/4,1/3,1/2,2/3,3/4,1]--- >         ,[0,1/5,1/4,1/3,2/5,1/2,3/5,2/3,3/4,4/5,1]--- >         ,[0,1/6,1/5,1/4,1/3,2/5,1/2,3/5,2/3,3/4,4/5,5/6,1]]--- > in map farey_sequence [2..6] == r+{- | <http://en.wikipedia.org/wiki/Farey_sequence>++> r = [[0                                              ]+>     ,[0                                            ,1]+>     ,[0                    ,1/2                    ,1]+>     ,[0            ,1/3    ,1/2    ,2/3            ,1]+>     ,[0        ,1/4,1/3    ,1/2    ,2/3,3/4        ,1]+>     ,[0    ,1/5,1/4,1/3,2/5,1/2,3/5,2/3,3/4,4/5    ,1]+>     ,[0,1/6,1/5,1/4,1/3,2/5,1/2,3/5,2/3,3/4,4/5,5/6,1]]++> map farey_sequence [0..6]+-} farey_sequence :: Integral a => a -> [Ratio a] farey_sequence k = 0 : nub (sort [n%d | d <- [1..k], n <- [1..d]])
+ Music/Theory/Tuning/Midi.hs view
@@ -0,0 +1,128 @@+-- | Midi + Tuning+module Music.Theory.Tuning.Midi where++import Data.List {- base -}+import qualified Data.Map as M {- containers -}+import Data.Maybe {- base -}+import qualified Safe {- safe -}++import qualified Music.Theory.List as T {- hmt -}+import qualified Music.Theory.Map as T {- hmt -}+import qualified Music.Theory.Pitch as T {- hmt -}+import qualified Music.Theory.Tuple as T {- hmt -}++import Music.Theory.Tuning {- hmt -}+import Music.Theory.Tuning.Type {- hmt -}++-- | (/n/ -> /dt/).  Function from midi note number /n/ to+-- 'Midi_Detune' /dt/.  The incoming note number is the key pressed,+-- which may be distant from the note sounded.+type Midi_Tuning_f = T.Midi -> T.Midi_Detune++-- | Variant for tunings that are incomplete.+type Sparse_Midi_Tuning_f = T.Midi -> Maybe T.Midi_Detune++-- | Variant for sparse tunings that require state.+type Sparse_Midi_Tuning_St_f st = st -> T.Midi -> (st,Maybe T.Midi_Detune)++-- | Lift 'Midi_Tuning_f' to 'Sparse_Midi_Tuning_f'.+lift_tuning_f :: Midi_Tuning_f -> Sparse_Midi_Tuning_f+lift_tuning_f tn_f = Just . tn_f++-- | Lift 'Sparse_Midi_Tuning_f' to 'Sparse_Midi_Tuning_St_f'.+lift_sparse_tuning_f :: Sparse_Midi_Tuning_f -> Sparse_Midi_Tuning_St_f st+lift_sparse_tuning_f tn_f st k = (st,tn_f k)++-- | (t,c,k) where+--   t=tuning (must have 12 divisions of octave),+--   c=cents deviation (ie. constant detune offset),+--   k=midi offset (ie. value to be added to incoming midi note number).+type D12_Midi_Tuning = (Tuning,Cents,T.Midi)++-- | 'Midi_Tuning_f' for 'D12_Midi_Tuning'.+--+-- > let f = d12_midi_tuning_f (equal_temperament 12,0,0)+-- > map f [0..127] == zip [0..127] (repeat 0)+d12_midi_tuning_f :: D12_Midi_Tuning -> Midi_Tuning_f+d12_midi_tuning_f (t,c_diff,k) n =+    let (_,pc) = T.midi_to_octpc (n + k)+        dt = zipWith (-) (tn_cents t) [0,100 .. 1200]+    in if tn_divisions t /= 12+       then error "d12_midi_tuning_f: not d12"+       else case dt `Safe.atMay` pc of+              Nothing -> error "d12_midi_tuning_f: pc?"+              Just c -> (n,c + c_diff)++-- | (t,f0,k,g) where+--   t=tuning, f0=fundamental-frequency, k=midi-note-number (for f0), g=gamut+type Cps_Midi_Tuning = (Tuning,Double,T.Midi,Int)++-- | 'Midi_Tuning_f' for 'Cps_Midi_Tuning'.  The function is sparse, it is only+-- valid for /g/ values from /k/.+--+-- > import qualified Music.Theory.Pitch as T+-- > let f = cps_midi_tuning_f (equal_temperament 72,T.midi_to_cps 59,59,72 * 4)+-- > map f [59 .. 59 + 72]+cps_midi_tuning_f :: Cps_Midi_Tuning -> Sparse_Midi_Tuning_f+cps_midi_tuning_f (t,f0,k,g) n =+    let r = tn_approximate_ratios_cyclic t+        m = take g (map (T.cps_to_midi_detune . (* f0)) r)+    in m `Safe.atMay` T.midi_to_int (n - k)++-- * Midi tuning tables.++-- | midi-note-number -> fractional-midi-note-number table, possibly sparse.+type Mnn_Fmnn_Table = [(Int,Double)]++-- | Load 'Mnn_Fmnn_Table' from two-column Csv file.+mnn_fmnn_table_load_csv :: FilePath -> IO Mnn_Fmnn_Table+mnn_fmnn_table_load_csv fn = do+  s <- readFile fn+  let f x = case break (== ',') x of+              (lhs,_:rhs) -> (read lhs,read rhs)+              _ -> error "mnn_fmidi_table_load_csv?"+  return (map f (lines s))++-- | Midi-note-number -> Cps table, possibly sparse.+type Mnn_Cps_Table = [(T.Midi,Double)]++-- | Generates 'Mnn_Cps_Table' given 'Midi_Tuning_f' with keys for all valid @Mnn@.+--+-- > import Sound.SC3.Plot+-- > let f = cps_midi_tuning_f (equal_temperament 12,T.midi_to_cps 0,0,127)+-- > plot_p2_ln [map (fmap round) (gen_cps_tuning_tbl f)]+gen_cps_tuning_tbl :: Sparse_Midi_Tuning_f -> Mnn_Cps_Table+gen_cps_tuning_tbl tn_f =+    let f n = case tn_f n of+                Just r -> Just (n,T.midi_detune_to_cps r)+                Nothing -> Nothing+    in mapMaybe f [0 .. 127]++-- * Derived (secondary) tuning table (DTT) lookup.++-- | Given an 'Mnn_Cps_Table' /tbl/, a list of @Cps@ /c/, and a @Mnn@ /m/+-- find the @Cps@ in /c/ that is nearest to the @Cps@ in /t/ for /m/.+-- In equal distance cases bias left.+dtt_lookup :: (Eq k, Num v, Ord v) => [(k,v)] -> [v] -> k -> (Maybe v,Maybe v)+dtt_lookup tbl cps n =+    let f = lookup n tbl+    in (f,fmap (T.find_nearest_err True cps) f)++-- | Require table be non-sparse.+dtt_lookup_err :: (Eq k, Num v, Ord v) => [(k,v)] -> [v] -> k -> (k,v,v)+dtt_lookup_err tbl cps n =+    case dtt_lookup tbl cps n of+      (Just f,Just g) -> (n,f,g)+      _ -> error "dtt_lookup"++-- | Given two tuning tables generate the @dtt@ table.+gen_dtt_lookup_tbl :: Mnn_Cps_Table -> Mnn_Cps_Table -> Mnn_Cps_Table+gen_dtt_lookup_tbl t0 t1 =+    let ix = [0..127]+        cps = sort (map (T.p3_third . dtt_lookup_err t0 (map snd t1)) ix)+    in zip ix cps++gen_dtt_lookup_f :: Mnn_Cps_Table -> Mnn_Cps_Table -> Midi_Tuning_f+gen_dtt_lookup_f t0 t1 =+    let m = M.fromList (gen_dtt_lookup_tbl t0 t1)+    in T.cps_to_midi_detune . T.map_ix_err m
+ Music/Theory/Tuning/Partch.hs view
@@ -0,0 +1,68 @@+-- | Tuning, Harry Partch+module Music.Theory.Tuning.Partch where++import qualified Data.Map.Strict as M {- containers -}+import Data.Ratio {- base -}++import qualified Music.Theory.Tuning as T++orelate :: Integral i => Ratio i -> i -> Ratio i+orelate r m = T.fold_ratio_to_octave_err (r * (m % 1))++urelate :: Integral i => Ratio i -> i -> Ratio i+urelate r m = T.fold_ratio_to_octave_err (r * (1 % m))++-- | Incipient Tonality Diamond+--+-- > itd_map [4 .. 6]+itd_map :: [Integer] -> M.Map (Int,Int) Rational+itd_map relation =+  let limit = length relation+      z = map (orelate 1) relation+      c0 = zip (map (\n -> (n,0)) [0 .. limit - 1]) z+      cN = [((i,k),urelate (z !! i) (relation !! k)) |+            i <- [0 .. limit - 1],+            k <- [1 .. limit - 1]]+  in M.fromList (c0 ++ cN)++map_to_table :: t -> (Int,Int) -> M.Map (Int,Int) t -> [[t]]+map_to_table k (nr,nc) m =+  [[M.findWithDefault k (i,j) m | j <- [0 .. nc - 1]] | i <- [0 .. nr - 1]]++-- | 'map_to_table' of 'itd_map'.+--+-- > itd_tbl [4 .. 13]+itd_tbl :: [Integer] -> [[Rational]]+itd_tbl r =+  let err = error "itd_tbl"+      n = length r+  in map_to_table err (n,n) (itd_map r)++{-++import Data.List {- base -}+import qualified Music.Theory.Array.Text as T {- hmt -}+import qualified Music.Theory.Show as T {- hmt -}++pp tbl = putStrLn $ unlines $ T.table_pp T.table_opt_plain (map (map T.rational_pp) tbl)+pp (itd_tbl [4 .. 6])+pp (itd_tbl [4 .. 13])++$ itd 4 5 6+  1/1     8/5     4/3+  5/4     1/1     5/3+  3/2     6/5     1/1+$ itd 4 5 6 7 8 9 10 11 12 13+  1/1     8/5     4/3     8/7     1/1    16/9     8/5    16/11    4/3    16/13+  5/4     1/1     5/3    10/7     5/4    10/9     1/1    20/11    5/3    20/13+  3/2     6/5     1/1    12/7     3/2     4/3     6/5    12/11    1/1    24/13+  7/4     7/5     7/6     1/1     7/4    14/9     7/5    14/11    7/6    14/13+  1/1     8/5     4/3     8/7     1/1    16/9     8/5    16/11    4/3    16/13+  9/8     9/5     3/2     9/7     9/8     1/1     9/5    18/11    3/2    18/13+  5/4     1/1     5/3    10/7     5/4    10/9     1/1    20/11    5/3    20/13+ 11/8    11/10   11/6    11/7    11/8    11/9    11/10    1/1    11/6    22/13+  3/2     6/5     1/1    12/7     3/2     4/3     6/5    12/11    1/1    24/13+ 13/8    13/10   13/12   13/7    13/8    13/9    13/10   13/11   13/12    1/1+$++-}
Music/Theory/Tuning/Polansky_1978.hs view
@@ -4,7 +4,8 @@  import Data.List {- base -} -import qualified Music.Theory.Tuning as T+import qualified Music.Theory.Tuning as T {- hmt -}+import qualified Music.Theory.Tuning.Type as T {- hmt -}  {- | Three interlocking harmonic series on 1:5:3, by Larry Polansky in \"Psaltery\". @@ -43,4 +44,4 @@  -} psaltery_o :: T.Tuning-psaltery_o = T.Tuning (Left psaltery_o_r) 2+psaltery_o = T.Tuning (Left psaltery_o_r) Nothing
Music/Theory/Tuning/Polansky_1985c.hs view
@@ -1,16 +1,16 @@ -- | Larry Polansky. "Notes on Piano Study #5".--- _1/1, The Journal of the Just Intonation Newtork_, 1(4), Autumn 1985.+-- _1, The Journal of the Just Intonation Newtork_, 1(4), Autumn 1985. module Music.Theory.Tuning.Polansky_1985c where -import Music.Theory.Tuning {- hmt -}+import Music.Theory.Tuning.Type {- hmt -}  -- | The tuning has four octaves, these ratios are per-octave. ps5_jpr_r :: [[Rational]] ps5_jpr_r =-    [[1/1, 21/20, 9/8, 6/5, 5/4,  4/3,   7/5, 3/2, 8/5,  5/3,  7/4, 15/8]-    ,[1/1, 21/20, 9/8, 6/5, 5/4,  4/3,   7/5, 3/2, 8/5,  5/3,  7/4, 15/8]-    ,[1/1, 33/32, 9/8, 6/5, 5/4, 21/16, 11/8, 3/2, 8/5, 13/8,  7/4, 15/8]-    ,[1/1, 21/20, 9/8, 7/6, 5/4,  4/3,  11/8, 3/2, 8/5, 27/16, 7/4, 15/8]]+    [[1, 21/20, 9/8, 6/5, 5/4,  4/3,   7/5, 3/2, 8/5,  5/3,  7/4, 15/8]+    ,[1, 21/20, 9/8, 6/5, 5/4,  4/3,   7/5, 3/2, 8/5,  5/3,  7/4, 15/8]+    ,[1, 33/32, 9/8, 6/5, 5/4, 21/16, 11/8, 3/2, 8/5, 13/8,  7/4, 15/8]+    ,[1, 21/20, 9/8, 7/6, 5/4,  4/3,  11/8, 3/2, 8/5, 27/16, 7/4, 15/8]]  {- | Four-octave tuning. @@ -30,6 +30,6 @@ -} ps5_jpr :: Tuning ps5_jpr =-    let f (m,n) = map (* m) n-        r = concat (map f (zip [1,2,4,8] ps5_jpr_r))-    in Tuning (Left r) 16+    let f m n = map (* m) n+        r = concat (zipWith f [1,2,4,8] ps5_jpr_r)+    in Tuning (Left r) (Just (Left 4))
Music/Theory/Tuning/Rosenboom_1979.hs view
@@ -7,10 +7,11 @@ import Data.List {- base -} import Data.Ratio {- base -} +import qualified Music.Theory.Function as T import qualified Music.Theory.List as T import qualified Music.Theory.Pitch as T import qualified Music.Theory.Pitch.Name as T-import qualified Music.Theory.Tuning.ET as T+import qualified Music.Theory.Tuning.Et as T import qualified Music.Theory.Tuning.Scala as Scala import qualified Music.Theory.Tuple as T @@ -35,7 +36,7 @@ -- | Actual scale, in CPS. -- -- > let r = [52,69,76,83,92,104,119,138,156,166,185,208,234,260,277,286,311,332,363]--- > in map round dr_scale == r+-- > map round dr_scale == r dr_scale :: [Double] dr_scale =     let f0 = T.octpc_to_cps (1::Int,8)@@ -45,38 +46,14 @@ -- > putStrLn (unlines (map (unwords . T.hs_r_pitch_pp 1)  dr_scale_tbl_12et)) -- > map (\(f,p,_,_,_) -> (T.pitch_to_midi p,f)) dr_scale_tbl_12et dr_scale_tbl_12et :: [T.HS_R T.Pitch]-dr_scale_tbl_12et = map T.nearest_12et_tone dr_scale--{---51.9 A♭1 51.9 0.0 0.0-69.2 C♯2 69.3 -0.1 -2.0-75.5 D2 73.4 2.1 48.7-83.1 E2 82.4 0.7 13.7-92.3 F♯2 92.5 -0.2 -3.9-103.8 A♭2 103.8 0.0 0.0-118.7 B♭2 116.5 2.1 31.2-138.4 C♯3 138.6 -0.2 -2.0-155.7 E♭3 155.6 0.2 2.0-166.1 E3 164.8 1.3 13.7-184.6 F♯3 185.0 -0.4 -3.9-207.7 A♭3 207.7 0.0 0.0-233.6 B♭3 233.1 0.5 3.9-259.6 C4 261.6 -2.1 -13.7-276.9 C♯4 277.2 -0.3 -2.0-285.5 D4 293.7 -8.1 -48.7-311.5 E♭4 311.1 0.4 2.0-332.2 E4 329.6 2.6 13.7-363.4 F♯4 370.0 -6.6 -31.2---}+dr_scale_tbl_12et = map (T.nearest_12et_tone_k0 (69,440)) dr_scale  -- > Scala.scale_verify dr_scale_scala -- > putStrLn $ unlines $ Scala.scale_pp dr_scale_scala-dr_scale_scala :: Scala.Scale Integer+dr_scale_scala :: Scala.Scale dr_scale_scala =-    let f (r,(_,p,_,_,_)) = (T.pitch_to_midi p :: Int,r)-        sq = map f (zip dr_tuning dr_scale_tbl_12et)+    let f r (_,p,_,_,_) = (T.pitch_to_midi p :: Int,r)+        sq = zipWith f dr_tuning dr_scale_tbl_12et         g z k = case lookup k sq of                   Nothing -> (z,(k,z))                   Just r -> (r,(k,r))@@ -85,31 +62,7 @@  -- > putStrLn (unlines (map (unwords . T.hs_r_pitch_pp 1)  dr_scale_tbl_24et)) dr_scale_tbl_24et :: [T.HS_R T.Pitch]-dr_scale_tbl_24et = map T.nearest_24et_tone dr_scale--{---51.9 A♭1 51.9 0.0 0.0-69.2 C♯2 69.3 -0.1 -2.0-75.5 D𝄲2 75.6 -0.1 -1.3-83.1 E2 82.4 0.7 13.7-92.3 F♯2 92.5 -0.2 -3.9-103.8 A♭2 103.8 0.0 0.0-118.7 B𝄳2 120.0 -1.3 -18.8-138.4 C♯3 138.6 -0.2 -2.0-155.7 E♭3 155.6 0.2 2.0-166.1 E3 164.8 1.3 13.7-184.6 F♯3 185.0 -0.4 -3.9-207.7 A♭3 207.7 0.0 0.0-233.6 B♭3 233.1 0.5 3.9-259.6 C4 261.6 -2.1 -13.7-276.9 C♯4 277.2 -0.3 -2.0-285.5 D𝄳4 285.3 0.2 1.3-311.5 E♭4 311.1 0.4 2.0-332.2 E4 329.6 2.6 13.7-363.4 F𝄲4 359.5 3.9 18.8---}+dr_scale_tbl_24et = map (T.nearest_24et_tone_k0 (69,440)) dr_scale  dr_chords :: [[T.Pitch]] dr_chords =@@ -160,8 +113,8 @@     ,[(8,1),(1,10)]     ] --- > import Data.Function--- > import Data.List+-- > import Data.Function {- base -}+-- > import Data.List {- base -} -- > reverse (sortBy (compare `on` snd) dr_ratio_seq_hist) dr_ratio_seq_hist :: (Ord n,Num n) => [((n,n),Int)] dr_ratio_seq_hist = T.histogram (concat dr_ratio_seq)
Music/Theory/Tuning/Scala.hs view
@@ -1,7 +1,10 @@--- | Parser for the Scala scale file format.  See--- <http://www.huygens-fokker.org/scala/scl_format.html> for details.--- This module succesfully parses all 4671 scales in v.85 of the scale--- library.+{- | Parser for the Scala scale file format.++See <http://www.huygens-fokker.org/scala/scl_format.html> for details.++This module succesfully parses all scales in v.91 of the scale library.++-} module Music.Theory.Tuning.Scala where  import Control.Monad {- base -}@@ -13,20 +16,23 @@ import System.Environment {- base -} import System.FilePath {- filepath -} -import qualified Music.Theory.Directory as T {- hmt -}-import qualified Music.Theory.Either as T {- hmt -}-import qualified Music.Theory.Function as T {- hmt -}-import qualified Music.Theory.IO as T {- hmt -}-import qualified Music.Theory.List as T {- hmt -}-import qualified Music.Theory.Math as T {- hmt -}+import qualified Music.Theory.Array.Csv as Csv {- hmt -}+import qualified Music.Theory.Directory as Directory {- hmt -}+import qualified Music.Theory.Either as Either {- hmt -}+import qualified Music.Theory.Function as Function {- hmt -}+import qualified Music.Theory.Io as Io {- hmt -}+import qualified Music.Theory.List as List {- hmt -}+import qualified Music.Theory.Math.Prime as Prime {- hmt -} import qualified Music.Theory.Read as T {- hmt -}+import qualified Music.Theory.Show as T {- hmt -} import qualified Music.Theory.String as T {- hmt -} import qualified Music.Theory.Tuning as T {- hmt -}+import qualified Music.Theory.Tuning.Type as T {- hmt -}  -- * Pitch  -- | A @.scl@ pitch is either in 'Cents' or is a 'Ratio'.-type Pitch i = Either T.Cents (Ratio i)+type Pitch = Either T.Cents Rational  -- | An enumeration type for @.scl@ pitch classification. data Pitch_Type = Pitch_Cents | Pitch_Ratio deriving (Eq,Show)@@ -35,11 +41,11 @@ type Epsilon = Double  -- | Derive 'Pitch_Type' from 'Pitch'.-pitch_type :: Pitch i -> Pitch_Type+pitch_type :: Pitch -> Pitch_Type pitch_type = either (const Pitch_Cents) (const Pitch_Ratio)  -- | Pitch as 'T.Cents', conversion by 'T.ratio_to_cents' if necessary.-pitch_cents :: Integral i => Pitch i -> T.Cents+pitch_cents :: Pitch -> T.Cents pitch_cents p =     case p of       Left c -> c@@ -47,14 +53,14 @@  -- | Pitch as 'Rational', conversion by 'T.reconstructed_ratio' if -- necessary, hence /epsilon/.-pitch_ratio :: Epsilon -> Pitch Integer -> Rational+pitch_ratio :: Epsilon -> Pitch -> Rational pitch_ratio epsilon p =     case p of       Left c -> T.reconstructed_ratio epsilon c       Right r -> r  -- | A pair giving the number of 'Cents' and number of 'Ratio' pitches.-pitch_representations :: Integral t => [Pitch i] -> (t,t)+pitch_representations :: [Pitch] -> (Int,Int) pitch_representations =     let f (l,r) p = case p of                       Left _ -> (l + 1,r)@@ -62,132 +68,148 @@     in foldl f (0,0)  -- | If scale is uniform, give type.-uniform_pitch_type :: [Pitch i] -> Maybe Pitch_Type+uniform_pitch_type :: [Pitch] -> Maybe Pitch_Type uniform_pitch_type p =-    case pitch_representations p :: (Int,Int) of+    case pitch_representations p of       (0,_) -> Just Pitch_Ratio       (_,0) -> Just Pitch_Cents       _ -> Nothing  -- | The predominant type of the pitches for 'Scale'.-pitch_type_predominant :: [Pitch i] -> Pitch_Type+pitch_type_predominant :: [Pitch] -> Pitch_Type pitch_type_predominant p =-    let (c,r) = pitch_representations p :: (Int,Int)+    let (c,r) = pitch_representations p     in if c >= r then Pitch_Cents else Pitch_Ratio  -- * Scale --- | A scale has a name, a description, a degree, and a list of 'Pitch'es.-type Scale i = (String,String,Int,[Pitch i])+-- | A scale has a name, a description, a degree, and a sequence of pitches.+--   The /name/ is the the file-name without the /.scl/ suffix.+--   By convention the first comment line gives the file name (with suffix).+--   The pitches do NOT include 1:1 or 0c and do include the octave.+type Scale = (String,String,Int,[Pitch])  -- | The name of a scale.-scale_name :: Scale i -> String+scale_name :: Scale -> String scale_name (nm,_,_,_) = nm  -- | Text description of a scale.-scale_description :: Scale i -> String+scale_description :: Scale -> String scale_description (_,d,_,_) = d  -- | The degree of the scale (number of 'Pitch'es).-scale_degree :: Scale i -> Int+scale_degree :: Scale -> Int scale_degree (_,_,n,_) = n  -- | The 'Pitch'es at 'Scale'.-scale_pitches :: Scale i -> [Pitch i]+scale_pitches :: Scale -> [Pitch] scale_pitches (_,_,_,p) = p +-- | Is 'Pitch' outside of the standard octave (ie. cents 0-1200 and ratios 1-2)+pitch_non_oct :: Pitch -> Bool+pitch_non_oct p =+  case p of+    Left c -> c < 0 || c > 1200+    Right r -> r < 1 || r > 2+ -- | Ensure degree and number of pitches align.-scale_verify :: Scale i -> Bool+scale_verify :: Scale -> Bool scale_verify (_,_,n,p) = n == length p  -- | Raise error if scale doesn't verify, else 'id'.-scale_verify_err :: Scale i -> Scale i-scale_verify_err scl = if scale_verify scl then scl else error "invalid scale"+scale_verify_err :: Scale -> Scale+scale_verify_err scl = if scale_verify scl then scl else error ("invalid scale: " ++ scale_name scl) --- | The last 'Pitch' element of the scale (ie. the /ocatve/).-scale_octave :: Scale i -> Maybe (Pitch i)+-- | The last 'Pitch' element of the scale (ie. the /octave/).  For empty scales give 'Nothing'.+scale_octave :: Scale -> Maybe Pitch scale_octave (_,_,_,s) =     case s of       [] -> Nothing       _ -> Just (last s) --- | Is 'scale_octave' perfect, ie. 'Ratio' of @2@ or 'Cents' of--- @1200@.-perfect_octave :: Integral i => Scale i -> Bool-perfect_octave s = scale_octave s `elem` [Just (Right 2),Just (Left 1200)]+-- | Error variant.+scale_octave_err :: Scale -> Pitch+scale_octave_err = fromMaybe (error "scale_octave?") . scale_octave +-- | Is 'scale_octave' perfect, ie. 'Ratio' of @2@ or 'Cents' of @1200@.+perfect_octave :: Scale -> Bool+perfect_octave s =+  case scale_octave s of+    Just (Right 2) -> True+    Just (Left 1200.0) -> True+    _ -> False+ -- | Are all pitches of the same type.-is_scale_uniform :: Scale i -> Bool+is_scale_uniform :: Scale -> Bool is_scale_uniform = isJust . uniform_pitch_type . scale_pitches --- | Make scale pitches uniform, conforming to the most promininent--- pitch type.-scale_uniform :: Epsilon -> Scale Integer -> Scale Integer+-- | Are the pitches in ascending sequence.+is_scale_ascending :: Scale -> Bool+is_scale_ascending = List.is_ascending . map pitch_cents . scale_pitches++-- | Make scale pitches uniform, conforming to the most predominant pitch type.+scale_uniform :: Epsilon -> Scale -> Scale scale_uniform epsilon (nm,d,n,p) =     case pitch_type_predominant p of       Pitch_Cents -> (nm,d,n,map (Left . pitch_cents) p)       Pitch_Ratio -> (nm,d,n,map (Right . pitch_ratio epsilon) p)  -- | Scale as list of 'T.Cents' (ie. 'pitch_cents') with @0@ prefix.-scale_cents :: Integral i => Scale i -> [T.Cents]+scale_cents :: Scale -> [T.Cents] scale_cents s = 0 : map pitch_cents (scale_pitches s)  -- | 'map' 'round' of 'scale_cents'.-scale_cents_i :: Integral i => Scale i -> [i]+scale_cents_i :: Scale -> [T.Cents_I] scale_cents_i = map round . scale_cents  -- | Scale as list of 'Rational' (ie. 'pitch_ratio') with @1@ prefix.-scale_ratios :: Epsilon -> Scale Integer -> [Rational]+scale_ratios :: Epsilon -> Scale -> [Rational] scale_ratios epsilon s = 1 : map (pitch_ratio epsilon) (scale_pitches s) --- | Require that 'Scale' be uniformlay of 'Ratio's.-scale_ratios_req :: Integral i => Scale i -> [Ratio i]-scale_ratios_req =-    let err = error "scale_ratios_req"-    in (1 :) . map (fromMaybe err . T.fromRight) . scale_pitches---- | Translate 'Scale' to 'T.Tuning'.  If 'Scale' is uniformly--- rational, 'T.Tuning' is rational, else 'T.Tuning' is in 'T.Cents'.--- 'Epsilon' is used to recover the 'Rational' octave if required.-scale_to_tuning :: Epsilon -> Scale Integer -> T.Tuning-scale_to_tuning epsilon (_,_,_,p) =-    case partitionEithers p of-      ([],r) -> let (r',o) = T.separate_last r-                in T.Tuning (Left (1 : r')) o-      _ -> let (c,o) = T.separate_last p-               c' = 0 : map pitch_cents c-               o' = either (T.reconstructed_ratio epsilon) id o-           in T.Tuning (Right c') o'+-- | Require that 'Scale' be uniformly of 'Ratio's.+scale_ratios_u :: Scale -> Maybe [Rational]+scale_ratios_u scl =+  let err = error "scale_ratios_u?"+      p = scale_pitches scl+  in case uniform_pitch_type p of+       Just Pitch_Ratio -> Just (1 : map (fromMaybe err . Either.from_right) p)+       _ -> Nothing --- | Convert 'T.Tuning' to 'Scale'.------ > tuning_to_scale ("et12","12 tone equal temperament") (T.equal_temperament 12)-tuning_to_scale :: (String,String) -> T.Tuning -> Scale Integer-tuning_to_scale (nm,dsc) (T.Tuning p o) =-    let n = either length length p-        p' = either (map Right . tail) (map Left . tail) p ++ [Right o]-    in (nm,dsc,n,p')+-- | Erroring variant of 'scale_ratios_u.+scale_ratios_req :: Scale -> [Rational]+scale_ratios_req = fromMaybe (error "scale_ratios_req") . scale_ratios_u  {- | Are scales equal ('==') at degree and tuning data.  > db <- scl_load_db > let r = [2187/2048,9/8,32/27,81/64,4/3,729/512,3/2,6561/4096,27/16,16/9,243/128,2/1]-> let Just py = find (scale_eq ("","",12,map Right r)) db+> let Just py = find (scale_eq ("","",length r,map Right r)) db > scale_name py == "pyth_12" +'scale_eqv' provides an approximate equality function.+ > let c = map T.ratio_to_cents r-> let Just py' = find (scale_eqv ("","",12,map Left c)) db+> let Just py' = find (scale_eqv 0.00001 ("","",length c,map Left c)) db > scale_name py' == "pyth_12"+ -}-scale_eq :: Eq n => Scale n -> Scale n -> Bool+scale_eq :: Scale -> Scale -> Bool scale_eq (_,_,d0,p0) (_,_,d1,p1) = d0 == d1 && p0 == p1 --- | Are scales equal ('==') at degree and tuning data after 'pitch_cents'.-scale_eqv :: Integral n => Scale n -> Scale n -> Bool-scale_eqv (_,_,d0,p0) (_,_,d1,p1) =-    let f = map pitch_cents-    in d0 == d1 && f p0 == f p1+-- | Are scales equal at degree and 'intersect' to at least /k/ places of tuning data.+scale_eq_n :: Int -> Scale -> Scale -> Bool+scale_eq_n k (_,_,d0,p0) (_,_,d1,p1) = d0 == d1 && length (p0 `intersect` p1) >= k +-- | Is `s1` a proper subset of `s2`.+scale_sub :: Scale -> Scale -> Bool+scale_sub (_,_,d0,p0) (_,_,d1,p1) = d0 < d1 && intersect p0 p1 == p0++-- | Are scales equal at degree and equivalent to within /epsilon/ at 'pitch_cents'.+scale_eqv :: Epsilon -> Scale -> Scale -> Bool+scale_eqv epsilon (_,_,d0,p0) (_,_,d1,p1) =+    let (~=) p q = abs (pitch_cents p - pitch_cents q) < epsilon+    in d0 == d1 && and (zipWith (~=) p0 p1)+ -- * Parser  -- | Comment lines begin with @!@.@@ -203,45 +225,48 @@ remove_eol_comments :: String -> String remove_eol_comments = takeWhile (/= '!') --- | Remove comments and null lines and trailing comments.+-- | Remove comments and trailing comments (the description may be empty, keep nulls) ----- > filter_comments ["!a","b","","c","d!e"] == ["b","c","d"]+-- > filter_comments ["!a","b","","c","d!e"] == ["b","","c","d"] filter_comments :: [String] -> [String] filter_comments =     map remove_eol_comments .-    filter (not . T.predicate_any [is_comment,null])+    filter (not . Function.predicate_any [is_comment])  -- | Pitches are either cents (with decimal point, possibly trailing) or ratios (with @/@). ----- > map parse_pitch ["700.0","350.","3/2","2"] == [Left 700,Left 350,Right (3/2),Right 2]-parse_pitch :: (Read i,Integral i) => String -> Pitch i+-- > map parse_pitch ["70.0","350.","3/2","2","2/1"] == [Left 70,Left 350,Right (3/2),Right 2,Right 2]+parse_pitch :: String -> Pitch parse_pitch p =     if '.' `elem` p     then Left (T.read_fractional_allow_trailing_point_err p)     else Right (T.read_ratio_with_div_err p)  -- | Pitch lines may contain commentary.-parse_pitch_ln :: (Read i, Integral i) => String -> Pitch i+parse_pitch_ln :: String -> Pitch parse_pitch_ln x =     case words x of       p:_ -> parse_pitch p       _ -> error (show ("parse_pitch_ln",words x))  -- | Parse @.scl@ file.-parse_scl :: (Read i, Integral i) => String -> String -> Scale i+parse_scl :: String -> String -> Scale parse_scl nm s =     case filter_comments (lines (T.filter_cr s)) of-      t:n:p -> let scl = (nm,T.delete_trailing_whitespace t,T.read_err n,map parse_pitch_ln p)+      t:n:p -> let scl = (nm+                         ,T.delete_trailing_whitespace t+                         ,T.read_err_msg "degree" n+                         ,map parse_pitch_ln p)                in scale_verify_err scl       _ -> error "parse" --- * IO+-- * Io  -- | Read the environment variable @SCALA_SCL_DIR@, which is a -- sequence of directories used to locate scala files on. ----- > setEnv "SCALA_DIST_DIR" "/home/rohan/data/scala/85/scl"-scl_get_dir :: IO [String]+-- > setEnv "SCALA_SCL_DIR" "/home/rohan/data/scala/90/scl"+scl_get_dir :: IO [FilePath] scl_get_dir = fmap splitSearchPath (getEnv "SCALA_SCL_DIR")  -- | Lookup the @SCALA_SCL_DIR@ environment variable, which must exist, and derive the filepath.@@ -253,14 +278,14 @@   dir <- scl_get_dir   when (null dir) (error "scl_derive_filename: SCALA_SCL_DIR: nil")   when (hasExtension nm) (error "scl_derive_filename: name has extension")-  T.path_scan_err dir (nm <.> "scl")+  Directory.path_scan_err dir (nm <.> "scl")  -- | If the name is an absolute file path and has a @.scl@ extension, -- then return it, else run 'scl_derive_filename'. -- -- > scl_resolve_name "young-lm_piano"--- > scl_resolve_name "/home/rohan/data/scala/85/scl/young-lm_piano.scl"--- > scl_resolve_name "/home/rohan/data/scala/85/scl/unknown-tuning.scl"+-- > scl_resolve_name "/home/rohan/data/scala/90/scl/young-lm_piano.scl"+-- > scl_resolve_name "/home/rohan/data/scala/90/scl/unknown-tuning.scl" scl_resolve_name :: String -> IO FilePath scl_resolve_name nm =     let ex_f x = if x then return nm else error "scl_resolve_name: file does not exist"@@ -273,81 +298,76 @@ -- > s <- scl_load "xenakis_chrom" -- > pitch_representations (scale_pitches s) == (6,1) -- > scale_ratios 1e-3 s == [1,21/20,29/23,179/134,280/187,11/7,100/53,2]-scl_load :: (Read i, Integral i) => String -> IO (Scale i)+scl_load :: String -> IO Scale scl_load nm = do   fn <- scl_resolve_name nm-  s <- T.read_file_iso_8859_1 fn+  s <- Io.read_file_iso_8859_1 fn   return (parse_scl (takeBaseName nm) s) --- | 'scale_to_tuning' of 'scl_load'.-scl_load_tuning :: Epsilon -> String -> IO T.Tuning-scl_load_tuning epsilon = fmap (scale_to_tuning epsilon) . scl_load--{- | Load all @.scl@ files at /dir/.--> dir <- scl_get_dir-> dir == ["/home/rohan/data/scala/85/scl","/home/rohan/sw/hmt/data/scl"]-> let [scl_85_dir,ext_dir] = dir-> db <- scl_load_dir scl_85_dir-> length db == 4671-> length (filter ((== 0) . scale_degree) db) == 0-> length (filter ((/= 1) . head . scale_ratios 1e-3) db) == 0-> length (filter ((/= 0) . head . scale_cents) db) == 0-> length (filter (== Just (Right 2)) (map scale_octave db)) == 4003-> length (filter is_scale_uniform db) == 2816--> let na = filter (not . T.is_ascending . scale_cents) db-> length na == 121-> mapM_ (putStrLn . unlines . scale_stat) na--> import qualified Music.Theory.List as T-> import Sound.SC3.Plot-> plot_p2_stp [T.histogram (map scale_degree db)]--> import Data.List--> let r = ["Xenakis's Byzantine Liturgical mode, 5 + 19 + 6 parts"->         ,"Xenakis's Byzantine Liturgical mode, 12 + 11 + 7 parts"->         ,"Xenakis's Byzantine Liturgical mode, 7 + 16 + 7 parts"]-> in filter (isInfixOf "Xenakis") (map scale_description db) == r--> let r = ["LaMonte Young, tuning of For Guitar '58. 1/1 March '92, inv.of Mersenne lute 1"->         ,"LaMonte Young's Well-Tuned Piano"]-> in filter (isInfixOf "LaMonte Young") (map scale_description db) == r--> length (filter (not . perfect_octave) db) == 663+{- | Load all @.scl@ files at /dir/, associate with file-name. +> db <- scl_load_dir_fn "/home/rohan/data/scala/91/scl"+> length db == 5176 -- v.91+> map (\(fn,s) -> (takeFileName fn,scale_name s)) db -}-scl_load_dir :: (Read i, Integral i) => FilePath -> IO [Scale i]-scl_load_dir d = T.dir_subset [".scl"] d >>= mapM scl_load+scl_load_dir_fn :: FilePath -> IO [(FilePath,Scale)]+scl_load_dir_fn d = do+  fn <- Directory.dir_subset [".scl"] d+  scl <- mapM scl_load fn+  return (zip fn scl) +-- | 'snd' of 'scl_load_dir_fn'+scl_load_dir :: FilePath -> IO [Scale]+scl_load_dir = fmap (map snd) . scl_load_dir_fn+ -- | Load Scala data base at 'scl_get_dir'. -- -- > db <- scl_load_db--- > mapM_ (putStrLn.unlines.scale_stat) (filter (not . perfect_octave) db)-scl_load_db :: (Read i, Integral i) => IO [Scale i]+-- > mapM_ (putStrLn . unlines . scale_stat) (filter (not . perfect_octave) db)+scl_load_db :: IO [Scale] scl_load_db = do   dir <- scl_get_dir   r <- mapM scl_load_dir dir   return (concat r) --- * PP+-- * Pp -scale_stat :: (Integral i,Show i) => Scale i -> [String]+-- | <http://www.huygens-fokker.org/docs/scalesdir.txt>+scales_dir_txt_tbl :: [Scale] -> [[String]]+scales_dir_txt_tbl =+  let f s = [scale_name s,show (scale_degree s),scale_description s]+  in map f++-- | Format as CSV file.+--+-- > db <- scl_load_db+-- > writeFile "/tmp/scl.csv" (scales_dir_txt_csv db)+scales_dir_txt_csv :: [Scale] -> String+scales_dir_txt_csv db = Csv.csv_table_pp id Csv.def_csv_opt (Nothing,scales_dir_txt_tbl db)++-- | Simple plain-text display of scale data.+--+-- > db <- scl_load_db+-- > writeFile "/tmp/scl.txt" (unlines (intercalate [""] (map scale_stat db)))+scale_stat :: Scale -> [String] scale_stat s =-    let ty = uniform_pitch_type (scale_pitches s)-    in ["scale-name        : " ++ scale_name s-       ,"scale-description : " ++ scale_description s-       ,"scale-degree      : " ++ show (scale_degree s)-       ,"scale-type        : " ++ maybe "non-uniform" show ty-       ,"perfect-octave    : " ++ show (perfect_octave s)-       ,"scale-cents-i     : " ++ show (scale_cents_i s)-       ,if ty == Just Pitch_Ratio-        then "scale-ratios      : " ++ intercalate "," (map T.rational_pp (scale_ratios_req s))+    let p = scale_pitches s+        u_ty = uniform_pitch_type p+        n_ty = let p_ty = pitch_type_predominant p+                   (p_i,p_j) = pitch_representations p+               in concat ["non-uniform (",show p_ty,",",show p_i,":",show p_j,")"]+    in ["name        : " ++ scale_name s+       ,"description : " ++ scale_description s+       ,"degree      : " ++ show (scale_degree s)+       ,"type        : " ++ maybe n_ty show u_ty+       ,"perfect-oct : " ++ show (perfect_octave s)+       ,"cents-i     : " ++ show (scale_cents_i s)+       ,if u_ty == Just Pitch_Ratio+        then "ratios      : " ++ intercalate "," (map T.rational_pp (scale_ratios_req s))         else ""]  -- | Pretty print 'Pitch' in @Scala@ format.-pitch_pp :: Show i => Pitch i -> String+pitch_pp :: Pitch -> String pitch_pp p =     case p of       Left c -> show c@@ -355,10 +375,10 @@  -- | Pretty print 'Scale' in @Scala@ format. ----- > s <- scl_load "et19"--- > s <- scl_load "young-lm_piano"--- > putStr $ unlines $ scale_pp s-scale_pp :: Show i => Scale i -> [String]+-- > scl <- scl_load "et19"+-- > scl <- scl_load "young-lm_piano"+-- > putStr $ unlines $ scale_pp scl+scale_pp :: Scale -> [String] scale_pp (nm,dsc,k,p) =     ["! " ++ nm ++ ".scl"     ,"!"@@ -366,19 +386,119 @@     ,show k     ,"!"] ++ map pitch_pp p --- * DIST+scale_wr :: FilePath -> Scale -> IO ()+scale_wr fn = writeFile fn . unlines . scale_pp +-- | Write /scl/ to /dir/ with the file-name 'scale_name'.scl+scale_wr_dir :: FilePath -> Scale -> IO ()+scale_wr_dir dir scl = scale_wr (dir </> scale_name scl <.> "scl") scl++-- * Dist+ -- | @scala@ distribution directory, given at @SCALA_DIST_DIR@. ----- > fmap (== "/home/rohan/opt/build/scala-22-pc64-linux") dist_get_dir+-- > setEnv "SCALA_DIST_DIR" "/home/rohan/opt/build/scala-22" dist_get_dir :: IO String dist_get_dir = getEnv "SCALA_DIST_DIR"  -- | Load file from 'dist_get_dir'.------ > s <- load_dist_file "intnam.par"--- > length s == 473-load_dist_file :: FilePath -> IO [String]+load_dist_file :: FilePath -> IO String load_dist_file nm = do   d <- dist_get_dir-  fmap lines (readFile (d </> nm))+  readFile (d </> nm)++{- | 'fmap' 'lines' 'load_dist_file'++> s <- load_dist_file_ln "intnam.par"+> length s == 565 -- Scala 2.46d+-}+load_dist_file_ln :: FilePath -> IO [String]+load_dist_file_ln = fmap lines . load_dist_file++-- * Query++-- | Is scale just-intonation (ie. are all pitches ratios)+scl_is_ji :: Scale -> Bool+scl_is_ji = (==) (Just Pitch_Ratio) . uniform_pitch_type . scale_pitches++-- | Calculate limit for JI scale (ie. largest prime factor)+scl_ji_limit :: Scale -> Integer+scl_ji_limit = maximum . map fst . concatMap Prime.rational_prime_factors_m . scale_ratios_req++-- | Sum of absolute differences to scale given in cents, sorted, with rotation.+scl_cdiff_abs_sum :: [T.Cents] -> Scale -> [(Double,[T.Cents],Int)]+scl_cdiff_abs_sum c scl =+  let r = map (List.dx_d 0) (List.rotations (List.d_dx (sort (scale_cents scl))))+      ndiff x i = let d = zipWith (-) c x in (sum (map abs d),d,i)+  in sort (zipWith ndiff r [0..])++{- | Variant selecting only nearest and with post-processing function.++> scl <- scl_load "holder"+> scale_cents_i scl+> c = [0,83,193,308,388,502,584,695,778,890,1004,1085,1200]+> (_,r,_) = scl_cdiff_abs_sum_1 round c scl+> r == [0,2,-1,1,0,-1,0,-1,0,0,0,0,0]+-}+scl_cdiff_abs_sum_1 :: (Double -> n) -> [T.Cents] -> Scale -> (Double,[n],Int)+scl_cdiff_abs_sum_1 pp c scl =+  case scl_cdiff_abs_sum c scl of+    [] -> error "scl_cdiff_abs_sum_1"+    (n,d,r):_ -> (n,map pp d,r)++{- | Sort DB into ascending order of sum of absolute of differences to scale given in cents.+     Scales are sorted and all rotations are considered.++> db <- scl_load_db+> c = [0,83,193,308,388,502,584,695,778,890,1004,1085,1200]+> r = scl_db_query_cdiff_asc round db c+> ((_,dx,_),_):_ = r+> dx == [0,2,-1,1,0,-1,0,-1,0,0,0,0,0]+> mapM_ (putStrLn . unlines . scale_stat . snd) (take 10 r)+-}+scl_db_query_cdiff_asc :: Ord n => (Double -> n) -> [Scale] -> [T.Cents] -> [((Double,[n],Int),Scale)]+scl_db_query_cdiff_asc pp db c =+  let n = length c - 1+      db_n = filter ((== n) . scale_degree) db+  in sort (map (\scl -> (scl_cdiff_abs_sum_1 pp c scl,scl)) db_n)++-- | Is /x/ the same scale as /scl/ under /cmp/.+scale_cmp_ji :: ([Rational] -> [Rational] -> Bool) -> [Rational] -> Scale -> Bool+scale_cmp_ji cmp x scl =+  case scale_ratios_u scl of+    Nothing -> False+    Just r -> cmp x r++-- | Find scale(s) that are 'scale_cmp_ji' to /x/.+--   Usual /cmp/ are (==) and 'is_subset'.+scl_find_ji :: ([Rational] -> [Rational] -> Bool) -> [Rational] -> [Scale] -> [Scale]+scl_find_ji cmp x = filter (scale_cmp_ji cmp x)++-- * Tuning++-- | Translate 'Scale' to 'T.Tuning'.  If 'Scale' is uniformly+-- rational, 'T.Tuning' is rational, else it is in 'T.Cents'.+scale_to_tuning :: Scale -> T.Tuning+scale_to_tuning (_,_,_,p) =+    case partitionEithers p of+      ([],r) -> let (r',o) = List.separate_last r+                in T.Tuning (Left (1 : r')) (if o == 2 then Nothing else Just (Left o))+      _ -> let (c,o) = List.separate_last p+               c' = 0 : map pitch_cents c+               o' = if o == Left 1200 || o == Right 2 then Nothing else Just (Either.either_swap o)+           in T.Tuning (Right c') o'++-- | Convert 'T.Tuning' to 'Scale'.+--+-- > tuning_to_scale ("et12","12 tone equal temperament") (T.tn_equal_temperament 12)+tuning_to_scale :: (String,String) -> T.Tuning -> Scale+tuning_to_scale (nm,dsc) tn@(T.Tuning p _) =+    let n = either length length p+        p' = either (map Right . tail) (map Left . tail) p ++ [Either.either_swap (T.tn_octave_def tn)]+    in (nm,dsc,n,p')++-- | 'scale_to_tuning' of 'scl_load'.+--+-- > fmap T.tn_limit (scl_load_tuning "pyra") -- Just 59+scl_load_tuning :: String -> IO T.Tuning+scl_load_tuning = fmap scale_to_tuning . scl_load
+ Music/Theory/Tuning/Scala/Cli.hs view
@@ -0,0 +1,271 @@+-- | Command line interface to hmt/scala.+module Music.Theory.Tuning.Scala.Cli where++import Data.Char {- base -}+import Data.List {- base -}+import System.Environment {- base -}+import Text.Printf {- base -}++import qualified Music.Theory.Array.Text as T {- hmt-base -}+import qualified Music.Theory.Function as T {- hmt-base -}+import qualified Music.Theory.List as T {- hmt-base -}+import qualified Music.Theory.Read as T {- hmt-base -}+import qualified Music.Theory.Show as T {- hmt-base -}++import qualified Music.Theory.Array.Csv.Midi.Mnd as T {- hmt -}+import qualified Music.Theory.Pitch as T {- hmt -}+import qualified Music.Theory.Pitch.Spelling.Table as T {- hmt -}+import qualified Music.Theory.Time.Seq as T {- hmt -}+import qualified Music.Theory.Tuning as T {- hmt -}+import qualified Music.Theory.Tuning.Et as T {- hmt -}+import qualified Music.Theory.Tuning.Midi as T {- hmt -}+import qualified Music.Theory.Tuning.Scala as Scala {- hmt -}+import qualified Music.Theory.Tuning.Scala.Kbm as Kbm {- hmt -}+import qualified Music.Theory.Tuning.Scala.Functions as Functions {- hmt -}+import qualified Music.Theory.Tuning.Scala.Interval as Interval {- hmt -}+import qualified Music.Theory.Tuning.Scala.Mode as Mode {- hmt -}+import qualified Music.Theory.Tuning.Type as T {- hmt -}++type R = Double++db_stat :: IO ()+db_stat = do+  db <- Scala.scl_load_db+  let po = filter (== Just (Right 2)) (map Scala.scale_octave db)+      uf = filter Scala.is_scale_uniform db+      r = ["# entries        : " ++ show (length db)+          ,"# perfect-octave : " ++ show (length po)+          ,"# scale-uniform  : " ++ show (length uf)]+  putStrLn (unlines r)++-- > db_summarise (Just 15) (Just 65)+db_summarise :: Maybe Int -> Maybe Int -> IO ()+db_summarise nm_lim dsc_lim = do+  db <- Scala.scl_load_db+  let nm_seq = map Scala.scale_name db+      nm_max = maybe (maximum (map length nm_seq)) id nm_lim+      dsc_seq = map Scala.scale_description db+      fmt (nm,dsc) = printf "%-*s : %s" nm_max (take nm_max nm) (maybe dsc (flip take dsc) dsc_lim)+      tbl = map fmt (zip nm_seq dsc_seq)+  putStrLn (unlines tbl)++env :: IO ()+env = do+  scl_dir <- Scala.scl_get_dir+  dist_dir <- getEnv "SCALA_DIST_DIR"+  putStrLn ("SCALA_SCL_DIR = " ++ if null scl_dir then "NOT SET" else intercalate ":" scl_dir)+  putStrLn ("SCALA_DIST_DIR = " ++ if null dist_dir then "NOT SET" else dist_dir)++cut :: Maybe Int -> [a] -> [a]+cut lm s = maybe s (\n -> take n s) lm++search :: (IO [a], a -> String, a -> [String]) -> (Bool, Maybe Int) -> [String] -> IO ()+search (load_f,descr_f,stat_f) (ci,lm) txt = do+  db <- load_f+  let modify = if ci then map toLower else id+      txt' = map modify txt+      db' = filter (T.predicate_all (map isInfixOf txt') . modify . descr_f) db+  mapM_ (putStrLn . unlines . map (cut lm) . stat_f) db'++-- > search_scale (True,Nothing) ["xenakis"]+-- > search_scale (True,Just 75) ["lamonte","young"]+search_scale :: (Bool,Maybe Int) -> [String] -> IO ()+search_scale = search (Scala.scl_load_db,Scala.scale_description,Scala.scale_stat)++-- > search_mode (True,Nothing) ["xenakis"]+search_mode :: (Bool,Maybe Int) -> [String] -> IO ()+search_mode = search (fmap Mode.modenam_modes Mode.load_modenam,Mode.mode_description,Mode.mode_stat)++-- > stat_all Nothing+stat_all :: Maybe Int -> IO ()+stat_all character_limit = do+  db <- Scala.scl_load_db+  mapM_ (putStrLn . unlines . map (cut character_limit) . Scala.scale_stat) db++-- > stat_by_name Nothing "young-lm_piano"+stat_by_name :: Maybe Int -> FilePath -> IO ()+stat_by_name lm nm = do+  sc <- Scala.scl_load nm+  putStrLn (unlines (map (cut lm) (Scala.scale_stat sc)))++-- > rng_enum (60,72) == [60 .. 72]+rng_enum :: Enum t => (t,t) -> [t]+rng_enum (l,r) = [l .. r]++cps_tbl :: String -> T.Mnn_Cps_Table -> (T.Midi,T.Midi) -> IO ()+cps_tbl fmt tbl mnn_rng = do+  let cps_pp = T.double_pp 2+      cents_pp = T.double_pp 1+      gen_t i = (i,T.midi_to_pitch_ks i,T.lookup_err i tbl)+      t_pp (i,p,cps) =+          let ref = T.midi_to_cps i+              (_,nr,nr_cps,_,_) = T.nearest_12et_tone_k0 (69,440) cps+          in [show i+             ,cps_pp cps,T.pitch_pp_iso nr,cents_pp (T.cps_difference_cents nr_cps cps)+             ,cps_pp ref,T.pitch_pp_iso p,cents_pp (T.cps_difference_cents ref cps)]+      hdr = ["MNN"+            ,"CPS","ET12","CENTS-/+"+            ,"REF CPS","REF ET12","CENTS-/+"]+      dat = map (t_pp . gen_t) (rng_enum mnn_rng)+      ln = case fmt of+             "md" -> T.table_pp T.table_opt_simple (hdr : dat)+             "csv" -> map (intercalate ",") dat+             _ -> error "cps_tbl: fmt?"+  putStr (unlines ln)++-- > cps_tbl_d12 "md" ("young-lm_piano",-74.7,-3) (60,72)+cps_tbl_d12 :: String -> (String,T.Cents,T.Midi) -> (T.Midi,T.Midi) -> IO ()+cps_tbl_d12 fmt (nm,c,k) mnn_rng = do+  t <- Scala.scl_load_tuning nm :: IO T.Tuning+  let tbl = T.gen_cps_tuning_tbl (T.lift_tuning_f (T.d12_midi_tuning_f (t,c,k)))+  cps_tbl fmt tbl mnn_rng++-- > cps_tbl_cps "md" ("cet111",27.5,9,127-9) (69,69+25)+cps_tbl_cps :: String -> (String,R,T.Midi,Int) -> (T.Midi,T.Midi) -> IO ()+cps_tbl_cps fmt (nm,f0,k,n) mnn_rng = do+  t <- Scala.scl_load_tuning nm+  let tbl = T.gen_cps_tuning_tbl (T.cps_midi_tuning_f (t,f0,k,n))+  cps_tbl fmt tbl mnn_rng++csv_mnd_retune_d12 :: (String,T.Cents,T.Midi) -> FilePath -> FilePath -> IO ()+csv_mnd_retune_d12 (nm,c,k) in_fn out_fn = do+  t <- Scala.scl_load_tuning nm+  let retune_f = T.midi_detune_to_fmidi . T.d12_midi_tuning_f (t,c,k)+  m <- T.csv_midi_read_wseq in_fn :: IO (T.Wseq R (R,R,T.Channel,T.Param))+  let f (tm,(mnn,vel,ch,pm)) = (tm,(retune_f (floor mnn),vel,ch,pm))+  T.csv_mndd_write_wseq 4 out_fn (map f m)++-- > fluidsynth_tuning_d12 ("young-lm_piano",0,0) ("young-lm_piano",-74.7,-3)+fluidsynth_tuning_d12 :: (String,Int,Int) -> (String,T.Cents,T.Midi) -> IO ()+fluidsynth_tuning_d12 (fs_name,fs_bank,fs_prog) (nm,c,k) = do+  t <- Scala.scl_load_tuning nm :: IO T.Tuning+  let tun_f = T.d12_midi_tuning_f (t,c,k)+      pp_f n = let (mnn,dt) = tun_f n+                   cents = fromIntegral mnn * 100 + dt+                   cents_non_neg = if cents < 0 then 0 else cents+               in printf "tune %d %d %d %.2f" fs_bank fs_prog n cents_non_neg+      l = printf "tuning \"%s\" %d %d" fs_name fs_bank fs_prog : map pp_f [0 .. 127]+  putStrLn (unlines l)++{-+import Data.Int {- base -}+import Data.Word {- base -}++int_to_int8 :: Int -> Int8+int_to_int8 = fromIntegral++int8_to_word8 :: Int8 -> Word8+int8_to_word8 = fromIntegral++midi_tbl_binary_mnn_cents_tuning_d12 :: FilePath -> (String,T.Cents,Int) -> IO ()+midi_tbl_binary_mnn_cents_tuning_d12 fn (nm,c,k) = do+  t <- Scala.scl_load_tuning nm :: IO T.Tuning+  let tun_f = T.d12_midi_tuning_f (t,c,k)+      pp_f n = let (mnn,dt) = T.midi_detune_normalise (tun_f n)+               in [int_to_int8 mnn,int_to_int8 (round dt)]+  B.writeFile fn (B.pack (map int8_to_word8 (concatMap pp_f [0 .. 127])))+-}++{-+> midi_tbl_tuning_d12 "freq" ("meanquar",0,0)+> midi_tbl_tuning_d12 "fmidi" ("meanquar",0,0)+> midi_tbl_tuning_d12 "mts" ("young-lm_piano",-74.7,-3)+-}+midi_tbl_tuning_d12 :: String -> (String,T.Cents,T.Midi) -> IO ()+midi_tbl_tuning_d12 typ (nm,c,k) = do+  t <- Scala.scl_load_tuning nm :: IO T.Tuning+  let tun_f = T.d12_midi_tuning_f (t,c,k)+      pp_f n =+        case typ of+          "fmidi" -> printf "%3d,%10.6f" n (T.midi_detune_to_fmidi (tun_f n))+          "freq" -> printf "%3d,%10.4f" n (T.midi_detune_to_cps (tun_f n))+          "mts" ->+            let (mnn,dt) = T.midi_detune_normalise_positive (tun_f n)+            in printf "%3d,%3d,%7.4f" n (mnn `mod` 0x80) dt+          _ -> error "midi_tbl_tuning_d12"+  putStr (unlines (map pp_f [0 .. 127]))++ratio_cents_pp :: Rational -> String+ratio_cents_pp = show . (round :: Double -> Int) . T.ratio_to_cents++-- > intnam_lookup [7/4,7/6,9/8,13/8]+intnam_lookup :: [Rational] -> IO ()+intnam_lookup r_sq = do+  let f db r = let nm = maybe "*Unknown*" snd (Interval.intnam_search_ratio db r)+               in concat [T.ratio_pp r," = ",nm," = ",ratio_cents_pp r]+  db <- Interval.load_intnam+  mapM_ (putStrLn . f db) r_sq++-- > intnam_search "didymus"+intnam_search :: String -> IO ()+intnam_search txt = do+  db <- Interval.load_intnam+  let f (r,nm) = concat [T.ratio_pp r," = ",nm," = ",ratio_cents_pp r]+  mapM_ (putStrLn . f) (Interval.intnam_search_description_ci db txt)++kbm_tbl :: String -> String -> String -> IO ()+kbm_tbl ty scl_nm kbm_nm = do+  scl <- Scala.scl_load scl_nm+  kbm <- Kbm.kbm_load kbm_nm+  let tbl = case ty of+        "cps" -> Kbm.kbm_cps_tbl kbm scl+        "fmidi" -> Kbm.kbm_fmidi_tbl kbm scl+        _ -> error "kbm_tbl: unknown type"+      fmt (i,j) = printf "%d,%.4f" i j+      txt = unlines (map fmt tbl)+  putStrLn txt++-- * Main++help :: [String]+help =+    ["cps-tbl md|csv cps name:string f0:real mnn0:int gamut:int mnn-l:int mnn-r:int"+    ,"cps-tbl md|csv d12 name:string cents:real mnn:int mnn-l:int mnn-r:int"+    ,"csv-mnd-retune d12 name:string cents:real mnn:int input-file output-file"+    ,"db stat"+    ,"db summarise nm-lm|nil dsc-lm|nil"+    ,"env"+    ,"fluidsynth d12 scl-name:string cents:real mnn:int fs-name:string fs-bank:int fs-prog:int"+    ,"intervals {half-matrix|list|matrix} {cents|ratios} scale-name:string"+    ,"intname lookup interval:rational..."+    ,"intname search text:string"+    ,"kbm table {cps | fmidi} scala-name:string kbm-name:string"+    ,"midi-table fmidi|freq|mts d12 name:string cents:real mnn:int"+    ,"search scale|mode ci|cs lm|nil text:string..."+    ,"stat all lm|nil"+    ,"stat scale lm|nil name:string|file-path"+    ,""+    ,"  lm:int = line character limit"]++nil_or_read :: Read a => String -> Maybe a+nil_or_read s = if s == "nil" then Nothing else Just (T.read_err s)++scala_cli :: [String] -> IO ()+scala_cli arg = do+  let usage = putStrLn (unlines help)+  case arg of+    ["cps-tbl",fmt,"cps",nm,f0,k,n,l,r] -> cps_tbl_cps fmt (nm,read f0,read k,read n) (read l,read r)+    ["cps-tbl",fmt,"d12",nm,c,k,l,r] -> cps_tbl_d12 fmt (nm,read c,read k) (read l,read r)+    ["csv-mnd-retune","d12",nm,c,k,in_fn,out_fn] -> csv_mnd_retune_d12 (nm,read c,read k) in_fn out_fn+    ["db","stat"] -> db_stat+    ["db","summarise",nm_lim,dsc_lim] -> db_summarise (nil_or_read nm_lim) (nil_or_read dsc_lim)+    ["env"] -> env+    ["fluidsynth","d12",scl_nm,c,k,fs_nm,fs_bank,fs_prog] ->+        fluidsynth_tuning_d12 (fs_nm,read fs_bank,read fs_prog) (scl_nm,read c,read k)+    ["intervals","half-matrix",'c':_,k,nm] -> Functions.intervals_half_matrix_cents (read k) nm+    ["intervals","half-matrix",'r':_,nm] -> Functions.intervals_half_matrix_ratios nm+    ["intervals","list",'r':_,nm] -> Functions.intervals_list_ratios nm+    ["intervals","matrix",'c':_,k,nm] -> Functions.intervals_matrix_cents (read k) nm+    ["intervals","matrix",'r':_,nm] -> Functions.intervals_matrix_ratios nm+    "intnam":"lookup":r_sq -> intnam_lookup (map T.read_ratio_with_div_err r_sq)+    ["intnam","search",txt] -> intnam_search txt+    ["kbm","table",ty,scl_nm,kbm_nm] -> kbm_tbl ty scl_nm kbm_nm+    ["midi-table",typ,"d12",scl_nm,c,k] -> midi_tbl_tuning_d12 typ (scl_nm,read c,read k)+    "search":ty:ci:lm:txt ->+        case ty of+          "scale" -> search_scale (ci == "ci",nil_or_read lm) txt+          "mode" -> search_mode (ci == "ci",nil_or_read lm) txt+          _ -> usage+    ["stat","all",lm] -> stat_all (nil_or_read lm)+    ["stat","scale",lm,nm] -> stat_by_name (nil_or_read lm) nm+    _ -> usage
+ Music/Theory/Tuning/Scala/Functions.hs view
@@ -0,0 +1,123 @@+-- | Scala functions, <http://www.huygens-fokker.org/scala/help.htm>+module Music.Theory.Tuning.Scala.Functions where++import Data.List {- base -}++import qualified Music.Theory.Array.Text as Text {- hmt -}+import qualified Music.Theory.List as List {- hmt -}+import qualified Music.Theory.Math as Math {- hmt -}+import qualified Music.Theory.Show as Show {- hmt -}+import qualified Music.Theory.Tuning as Tuning {- hmt -}+import qualified Music.Theory.Tuning.Scala as Scala {- hmt -}+import qualified Music.Theory.Tuning.Scala.Interval as Interval {- hmt -}++{- | <http://www.huygens-fokker.org/scala/help.htm#EQUALTEMP>++> map round (equaltemp 12 2 13) == [0,100,200,300,400,500,600,700,800,900,1000,1100,1200]+> map round (equaltemp 13 3 14) == [0,146,293,439,585,732,878,1024,1170,1317,1463,1609,1756,1902]+> map round (equaltemp 12.5 3 14) == [0,152,304,456,609,761,913,1065,1217,1369,1522,1674,1826,1978]+-}+equaltemp :: Double -> Double -> Int -> [Double]+equaltemp division octave scale_size =+  let step = Tuning.fratio_to_cents octave / division+  in take scale_size [0,step ..]++{- | <http://www.huygens-fokker.org/scala/help.htm#LINEARTEMP>++> let py = lineartemp 12 2 () (3/2 :: Rational) 3+> py == [1/1,2187/2048,9/8,32/27,81/64,4/3,729/512,3/2,6561/4096,27/16,16/9,243/128,2/1]+-}+lineartemp :: (Fractional n, Ord n) => Int -> n -> () -> n -> Int -> [n]+lineartemp scale_size octave _degree_of_fifth fifth down =+  let geom i m = i : geom (i * m) m+      geom_oct i = map Tuning.fold_ratio_to_octave_err . geom i+      lhs = take (down + 1) (geom_oct 1 (1 / fifth))+      rhs = tail (take (scale_size - down) (geom_oct 1 fifth))+  in sort (lhs ++ rhs) ++ [octave]++-- * INTERVALS++interval_hist_ratios :: (Fractional t,Ord t) => [t] -> [(t,Int)]+interval_hist_ratios x = List.histogram [(if p < q then p * 2 else p) / q | p <- x, q <- x, p /= q]++intervals_list_ratios_r :: Interval.INTNAM -> [Rational] -> IO ()+intervals_list_ratios_r nam_db rat = do+  let hst = interval_hist_ratios rat+      ln (r,n) = let nm = maybe "" snd (Interval.intnam_search_ratio nam_db r)+                     c = Tuning.ratio_to_cents r+                     i = Math.real_round_int (c / 100)+                 in [show i,show n,Show.ratio_pp r,Show.real_pp 1 c,nm]+      tbl = map ln hst+      pp = Text.table_pp Text.table_opt_plain+  putStrLn (unlines (pp tbl))++{- | <http://www.huygens-fokker.org/scala/help.htm#SHOW_INTERVALS>++> mapM_ intervals_list_ratios (words "pyth_12 kepler1")+-}+intervals_list_ratios :: String -> IO ()+intervals_list_ratios scl_nm = do+  nam_db <- Interval.load_intnam+  scl <- Scala.scl_load scl_nm+  intervals_list_ratios_r nam_db (tail (Scala.scale_ratios_req scl))++-- * INTERVALS++-- | Given interval function (ie. '-' or '/') and scale generate interval half-matrix.+interval_half_matrix :: (t -> t -> u) -> [t] -> [[u]]+interval_half_matrix interval_f =+  let tails' = filter ((>= 2) . length) . tails+      f l = case l of+              [] -> []+              i : l' -> map (`interval_f` i) l'+  in map f . tails'++interval_half_matrix_tbl :: (t -> String) -> (t -> t -> t) -> [t] -> [[String]]+interval_half_matrix_tbl show_f interval_f scl =+    let f n l = replicate n "" ++ map show_f l+    in zipWith f [1..] (interval_half_matrix interval_f scl)++intervals_half_matrix :: (Scala.Scale -> [t]) -> (t -> t -> t) -> (t -> String) -> String -> IO ()+intervals_half_matrix scl_f interval_f show_f nm = do+  scl <- Scala.scl_load nm+  let txt = interval_half_matrix_tbl show_f interval_f (scl_f scl)+      pp = Text.table_pp Text.table_opt_plain+  putStrLn (unlines (pp txt))++-- > mapM_ (intervals_half_matrix_cents 0) (words "pyth_12 kepler1")+intervals_half_matrix_cents :: Int -> String -> IO ()+intervals_half_matrix_cents k = intervals_half_matrix Scala.scale_cents (-) (Show.real_pp k)++-- > mapM_ (intervals_half_matrix_ratios) (words "pyth_12 kepler1")+intervals_half_matrix_ratios :: String -> IO ()+intervals_half_matrix_ratios = intervals_half_matrix Scala.scale_ratios_req (/) Show.ratio_pp++{-+> r = [3*5,3*7,3*11,5*7,5*11,7*11]+> r = let u = [1,3,5,7,9,11] in [i*j*k | i <- u, j <- u, k <- u, i < j, j < k]+> intervals_matrix_wr Show.ratio_pp (interval_matrix_ratio r)+-}+interval_matrix_ratio :: [Rational] -> [[Rational]]+interval_matrix_ratio x = let f i = map (\j -> if j < i then j * 2 / i else j / i) x in map f x++interval_matrix_cents :: [Tuning.Cents] -> [[Tuning.Cents]]+interval_matrix_cents x = let f i = map (\j -> if j < i then j + 1200 - i else j - i) x in map f x++intervals_matrix_wr :: (t -> String) -> [[t]] -> IO ()+intervals_matrix_wr pp_f x = do+  let txt = map (map pp_f) x+      pp = Text.table_pp Text.table_opt_plain+  putStrLn (unlines (pp txt))++intervals_matrix :: (Scala.Scale -> [t]) -> ([t] -> [[t]]) -> (t -> String) -> String -> IO ()+intervals_matrix scl_f tbl_f pp_f nm = do+  scl <- Scala.scl_load nm+  intervals_matrix_wr pp_f (tbl_f (scl_f scl))++-- > mapM_ (intervals_matrix_cents 0) (words "pyth_12 kepler1")+intervals_matrix_cents :: Int -> String -> IO ()+intervals_matrix_cents k = intervals_matrix Scala.scale_cents interval_matrix_cents (Show.real_pp k)++-- > mapM_ intervals_matrix_ratios (words "pyth_12 kepler1")+intervals_matrix_ratios :: String -> IO ()+intervals_matrix_ratios = intervals_matrix Scala.scale_ratios_req interval_matrix_ratio Show.ratio_pp
Music/Theory/Tuning/Scala/Interval.hs view
@@ -1,11 +1,12 @@--- | Parser for the @intnam.par@ file.+-- | Parser for the SCALA @intnam.par@ file. module Music.Theory.Tuning.Scala.Interval where  import Data.Char {- base -} import Data.List {- base -}+import Data.Maybe {- base -} -import qualified Music.Theory.Read as T {- hmt -}-import qualified Music.Theory.Tuning.Scala as T+import qualified Music.Theory.Read as Read {- hmt -}+import qualified Music.Theory.Tuning.Scala as Scala {- hmt -}  -- | Interval and name, ie. (3/2,"perfect fifth") type INTERVAL = (Rational,String)@@ -13,21 +14,39 @@ -- | Length prefixed list of 'INTERVAL'. type INTNAM = (Int,[INTERVAL]) --- | Lookup ratio in 'INTNAM'.------ > db <- load_intnam--- > intnam_search_ratio db (3/2) == Just (3/2,"perfect fifth")--- > intnam_search_ratio db (2/3) == Nothing--- > intnam_search_ratio db (4/3) == Just (4/3,"perfect fourth")--- > map (intnam_search_ratio db) [3/2,4/3,7/4,7/6,9/7,12/7,14/9]--- > intnam_search_ratio db (31/16) == Just (31/16,"31st harmonic")+{- | Lookup ratio in 'INTNAM'.++> db <- load_intnam+> intnam_search_ratio db (3/2) == Just (3/2,"perfect fifth")+> intnam_search_ratio db (2/3) == Nothing+> intnam_search_ratio db (4/3) == Just (4/3,"perfect fourth")+> intnam_search_ratio db (31/16) == Just (31/16,"=31st harmonic")+> intnam_search_ratio db (64/49) == Just (64 % 49,"=2 septatones or septatonic major third")+> map (intnam_search_ratio db) [3/2,4/3,7/4,7/6,9/7,9/8,12/7,14/9]+> import Data.Maybe {- base -}+> mapMaybe (intnam_search_ratio db) [567/512,147/128,21/16,1323/1024,189/128,49/32,441/256,63/32]+-} intnam_search_ratio :: INTNAM -> Rational -> Maybe INTERVAL intnam_search_ratio (_,i) x = find ((== x) . fst) i +{- | Lookup approximate ratio in 'INTNAM' given espilon.++> r = [Just (3/2,"perfect fifth"),Just (64/49,"=2 septatones or septatonic major third")]+> map (intnam_search_fratio 0.0001 db) [1.5,1.3061] == r+-}+intnam_search_fratio :: (Fractional n,Ord n) => n -> INTNAM -> n -> Maybe INTERVAL+intnam_search_fratio epsilon (_,i) x =+  let near p q = abs (p - q) < epsilon+  in find (near x . fromRational . fst) i++-- | Lookup name of interval, or error.+intnam_search_ratio_name_err :: INTNAM -> Rational -> String+intnam_search_ratio_name_err db = snd . fromJust . intnam_search_ratio db+ -- | Lookup interval name in 'INTNAM', ci = case-insensitive. -- -- > db <- load_intnam--- > intnam_search_description_ci db "didymus"+-- > intnam_search_description_ci db "didymus" == [(81/80,"syntonic comma, Didymus comma")] intnam_search_description_ci :: INTNAM -> String -> [INTERVAL] intnam_search_description_ci (_,i) x =     let downcase = map toLower@@ -36,27 +55,32 @@  -- * Parser -parse_intnam_entry :: [String] -> INTERVAL-parse_intnam_entry w =-    case w of-      r:w' -> (T.read_ratio_with_div_err r,unwords w')+-- | Parse line from intnam.par+parse_intnam_entry :: String -> INTERVAL+parse_intnam_entry str =+    case words str of+      r:w -> (Read.read_ratio_with_div_err r,unwords w)       _ -> error "parse_intnam_entry" +-- | Parse non-comment lines from intnam.par parse_intnam :: [String] -> INTNAM parse_intnam l =     case l of       _:n:i -> let n' = read n :: Int-                   i' = map (parse_intnam_entry . words) i+                   i' = map parse_intnam_entry i                in if n' == length i' then (n',i') else error "parse_intnam"       _ -> error "parse_intnam"  -- * IO --- | 'parse_intnam' of 'T.load_dist_file' of "intnam.par".------ > intnam <- load_intnam--- > fst intnam == length (snd intnam)+{- | 'parse_intnam' of 'Scala.load_dist_file_ln' of "intnam.par".++> intnam <- load_intnam+> fst intnam == 516 -- Scala 2.42p+> fst intnam == length (snd intnam)+> lookup (129140163/128000000) (snd intnam) == Just "gravity comma"+-} load_intnam :: IO INTNAM load_intnam = do-  l <- T.load_dist_file "intnam.par"-  return (parse_intnam (T.filter_comments l))+  l <- Scala.load_dist_file_ln "intnam.par"+  return (parse_intnam (Scala.filter_comments l))
+ Music/Theory/Tuning/Scala/Kbm.hs view
@@ -0,0 +1,217 @@+{- | Scala "keyboard mapping" files (.kbm) and related data structure.++<http://www.huygens-fokker.org/scala/help.htm#mappings>+-}+module Music.Theory.Tuning.Scala.Kbm where++import Data.List {- base -}+import Data.Maybe {- base -}+import System.FilePath {- filepath -}+import Text.Printf {- base -}++import qualified Music.Theory.Directory as Directory {- hmt -}+import qualified Music.Theory.List as List {- hmt -}+import qualified Music.Theory.Pitch as Pitch {- hmt -}+import qualified Music.Theory.Tuning as Tuning {- hmt -}+import qualified Music.Theory.Tuning.Scala as Scala {- hmt -}++{- | Scala keyboard mapping++(sz,(m0,mN),mC,(mF,f),o,m)++- sz      = size of map, the pattern repeats every so many keys+- (m0,mN) = the first and last midi note numbers to retune+- mC      = the middle note where the first entry of the mapping is mapped to+- (mF,f)  = the reference midi-note for which a frequency is given, ie. (69,440)+- o       = scale degree to consider as formal octave+- m       = mapping, numbers represent scale degrees mapped to keys, Nothing indicates no mapping++-}+type Kbm = (Int,(Int,Int),Int,(Int,Double),Int,[Maybe Int])++-- | Pretty-printer for scala .kbm file.+kbm_pp :: Kbm -> String+kbm_pp (sz,(m0,mN),mC,(mF,f),o,m) =+  unlines+  [printf "size = %d" sz+  ,printf "note-range = (%d,%d)" m0 mN+  ,printf "note-center = %d" mC+  ,printf "note-reference = (%d,%f)" mF f+  ,printf "formal-octave = %d" o+  ,printf "map = [%s] #%d" (intercalate "," (map (maybe "x" show) m)) (length m)]++-- | Is /mnn/ in range?+kbm_in_rng :: Kbm -> Int -> Bool+kbm_in_rng (_,(m0,mN),_,_,_,_) mnn = mnn >= m0 && mnn <= mN++-- | Is /kbm/ linear?, ie. is size zero? (formal-octave may or may not be zero)+kbm_is_linear :: Kbm -> Bool+kbm_is_linear (sz,_,_,_,_o,_) = sz == 0 -- && o == 0++{- | Given kbm and midi-note-number lookup (octave,scale-degree).++> k <- kbm_load_dist "example.kbm" -- 12-tone scale+> k <- kbm_load_dist "a440.kbm" -- linear+> k <- kbm_load_dist "white.kbm" -- 7-tone scale on white notes+> k <- kbm_load_dist "black.kbm" -- 5-tone scale on black notes+> k <- kbm_load_dist "128.kbm"++> map (kbm_lookup k) [48 .. 72]++-}+kbm_lookup :: Kbm -> Int -> Maybe (Int,Int)+kbm_lookup kbm mnn =+  if not (kbm_in_rng kbm mnn)+  then Nothing+  else if kbm_is_linear kbm+       then Just (0,mnn)+       else let (sz,(_m0,_mN),mC,(_mF,_f),_o,m) = kbm+                (oct,ix) = ((mnn - mC) `divMod` sz)+            in fmap (\dgr -> (oct,dgr)) (m !! ix)++-- | Return the triple (mF,kbm_lookup k mF,f).  The lookup for mF is not-nil by definition.+--+-- > kbm_lookup_mF k+kbm_lookup_mF :: Kbm -> (Int,(Int,Int),Double)+kbm_lookup_mF k@(_,_,_,(mF,f),_,_) =+  case kbm_lookup k mF of+    Nothing -> error "kbm_lookup_mF?"+    Just r -> (mF,r,f)++-- | Parser for scala .kbm file.+kbm_parse :: String -> Kbm+kbm_parse s =+  let f x = case x of+              "x" -> Nothing+              _ -> Just (read x)+      to_m sz = List.pad_right_no_truncate Nothing sz . map f -- _err -- some scala .kbm have |m| > sz?+  in case Scala.filter_comments (lines s) of+       i1:i2:i3:i4:i5:d1:i6:m ->+         let sz = read i1+         in (sz,(read i2,read i3),read i4,(read i5,read d1),read i6,to_m sz m)+       _ -> error "kbm_parse?"++-- | 'kbm_parse' of 'readFile'+kbm_load_file :: FilePath -> IO Kbm+kbm_load_file = fmap kbm_parse . readFile++{- | 'kbm_parse' of 'Scala.load_dist_file'++> pp nm = kbm_load_dist nm >>= \x -> putStrLn (kbm_pp x)+> pp "example"+> pp "bp"+> pp "7" -- error -- 12/#13+> pp "8" -- error -- 12/#13+> pp "white" -- error -- 12/#13+> pp "black" -- error -- 12/#13+> pp "128"+> pp "a440"+> pp "61"+-}+kbm_load_dist :: String -> IO Kbm+kbm_load_dist nm = fmap kbm_parse (Scala.load_dist_file (nm <.> "kbm"))++-- | If /nm/ is a file name (has a .kbm) extension run 'kbm_load_file' else run 'kbm_load_dist'.+kbm_load :: String -> IO Kbm+kbm_load nm = if hasExtension nm then kbm_load_file nm else kbm_load_dist nm++-- | Load all .kbm files at directory.+kbm_load_dir_fn :: FilePath -> IO [(FilePath, Kbm)]+kbm_load_dir_fn d = do+  fn <- Directory.dir_subset [".kbm"] d+  kbm <- mapM kbm_load fn+  return (zip fn kbm)++{- | Load all .kbm files at scala dist dir.++> db <- kbm_load_dist_dir_fn+> length db == 41+> x = map (\(fn,(sz,_,_,_,o,m)) -> (System.FilePath.takeFileName fn,sz,length m,o)) db+> filter (\(_,i,j,_) -> i < j) x -- size < map-length+> filter (\(_,i,_,k) -> i == 0 && k == 0) x -- size and formal octave both zero++> map (\(fn,k) -> (System.FilePath.takeFileName fn,kbm_lookup_mF k)) db+-}+kbm_load_dist_dir_fn :: IO [(FilePath, Kbm)]+kbm_load_dist_dir_fn = Scala.dist_get_dir >>= kbm_load_dir_fn++{- | Pretty-printer for scala .kbm file.++> m <- kbm_load_dist "7.kbm"+> kbm_parse (kbm_format m) == m+> putStrLn $ kbm_pp m+-}+kbm_format :: Kbm -> String+kbm_format (i1,(i2,i3),i4,(i5,d1),i6,m) =+  let from_m = map (maybe "x" show)+  in unlines ([show i1,show i2,show i3,show i4,show i5,show d1,show i6] ++ from_m m)++-- | 'writeFile' of 'kbm_format'+kbm_wr :: FilePath -> Kbm -> IO ()+kbm_wr fn = writeFile fn . kbm_format++{- | Standard 12-tone mapping with A=440hz (ie. example.kbm)++> fmap (== kbm_d12_a440) (kbm_load_dist "example.kbm")+> putStrLn $ kbm_pp kbm_d12_a440+-}+kbm_d12_a440 :: Kbm+kbm_d12_a440 = (12,(0,127),60,(69,440.0),12,map Just [0 .. 11])++kbm_d12_c256 :: Kbm+kbm_d12_c256 = (12,(0,127),60,(60,256.0),12,map Just [0 .. 11])++-- | Given size and note-center calculate relative octave and key+--   number (not scale degree) of the zero entry.+--+-- > map (kbm_k0 12) [59,60,61] == [(-4,1),(-5,0),(-5,11)]+kbm_k0 :: Int -> Int -> (Int,Int)+kbm_k0 sz mC = let (o,r) = mC `quotRem` sz in (negate o,negate r `mod` sz)++-- | Given size and note-center calculate complete octave and key+-- number sequence (ie. for entries 0 - 127).+--+-- > map (zip [0..] . kbm_oct_key_seq 12) [59,60,61]+kbm_oct_key_seq :: Kbm -> [(Int,(Int,Int))]+kbm_oct_key_seq (sz,(m0,mN),mC,(_mF,_f),_o,_m) =+  let (o0,k0) = kbm_k0 sz mC+      dgr = map (`mod` sz) (take 128 [k0 ..])+      upd o j = if j == 0 then (o + 1,(o + 1,j)) else (o,(o,j))+      key_seq = snd (mapAccumL upd (o0 - 1) dgr)+  in zip [m0 .. ] (take (mN - m0 + 1) (drop m0 key_seq))++-- | Given Kbm and SCL calculate frequency of note-center.+kbm_mC_freq :: Kbm -> Scala.Scale -> Double+kbm_mC_freq (sz,(_m0,_mN),mC,(mF,f),_o,m) scl =+  let dist_k = (mF - mC) `mod` sz+      dgr = fromMaybe (error "kbm_mC_freq") (m !! dist_k)+      c = Scala.scale_cents scl !! dgr+  in Tuning.cps_shift_cents f (- c)++-- | Given Kbm and SCL calculate fractional midi note-numbers for each key.+kbm_fmidi_tbl :: Kbm -> Scala.Scale -> [(Int, Double)]+kbm_fmidi_tbl kbm scl =+  let (_sz,(_m0,_mN),_mC,(_mF,_f),o,m) = kbm+      mC_freq = kbm_mC_freq kbm scl+      mC_fmidi = Pitch.cps_to_fmidi mC_freq+      key_seq = kbm_oct_key_seq kbm+      c = Scala.scale_cents scl+      oct_cents = c !! o+      oct_key_to_cents (oct,key) = maybe 0 (c !!) (m !! key) + (fromIntegral oct * oct_cents)+  in map (\(mnn,oct_key) -> (mnn,mC_fmidi + (oct_key_to_cents oct_key / 100.0))) key_seq++-- | Given Kbm and SCL calculate frequencies for each key.+kbm_cps_tbl :: Kbm -> Scala.Scale -> [(Int, Double)]+kbm_cps_tbl kbm = let f (k,n) = (k,Tuning.fmidi_to_cps n) in map f . kbm_fmidi_tbl kbm++{-++scl <- Scala.scl_load "young-lm_piano"+scl <- Scala.scl_load "meanquar"+scl <- Scala.scl_load "et12"+kbm <- kbm_load "example" -- d12_a440 -- kbm_d12_a440 kbm_d12_c256++kbm_fmidi_tbl kbm scl+kbm_cps_tbl kbm scl++-}
+ Music/Theory/Tuning/Scala/Meta.hs view
@@ -0,0 +1,196 @@+-- | Scala DB meta-data.+module Music.Theory.Tuning.Scala.Meta where++-- | Just-intonation (ie. all rational) scales, collected by author.+scl_ji_au :: [(String,[String])]+scl_ji_au =+  [("Alves, Bill",words "alves_12 alves_22 alves_pelog alves alves_slendro")+  ,("Archytas"+   ,["arch_chrom","arch_chromc2" -- "archchro" NON-JI+    ,"arch_dor"+    ,"arch_enh","arch_enh2","arch_enh3","arch_enhp"+    ,"arch_enht","arch_enht2","arch_enht3","arch_enht4","arch_enht5","arch_enht6","arch_enht7"+    ,"arch_mult"+    ,"arch_ptol","arch_ptol2"+    ,"arch_sept"+    -- "archytas7" "archytas12","archytas12sync" NON-JI+    ])+  ,("Barlow, Clarence",words "barlow_13 barlow_17")+  ,("Boethius",words "boeth_chrom boeth_enh")+  ,("Burt, Warren",+     concat [map (\n -> "burt" ++ show n) [1::Int .. 20]+            ,words "burt_fibo burt_fibo23 burt_forks burt_primes"])+  ,("Chalmers, John"+   ,["chalmers"+    ,"chalmers_17"+    ,"chalmers_19"+    ,"chalmers_ji1"+    ,"chalmers_ji2"+    ,"chalmers_ji3"+    ,"chalmers_ji4"+    ,"corner7"+    ,"corner11"+    ,"corner13"+    ,"corners7"+    ,"corners11"+    ,"corners13"+    ,"finnamore_jc"+    ,"hamilton_jc"+    ,"major_clus"+    ,"major_wing"+    ,"minor_clus"+    ,"minor_wing"+    ,"pelog_jc"+    ,"prod7d"+    ,"prodq13"+    ,"slen_pel_jc"])+  ,("Didymus", words "didy_chrom didy_chrom1 didy_chrom2 didy_chrom3 didy_diat didy_enh didy_enh2")+  ,("Eratosthenes",words "eratos_chrom eratos_diat eratos_enh")+  ,("Euler, Leonhard",words "euler euler_diat euler_enh euler_gm")+  ,("Gann, Kyle",words "gann_arcana gann_charingcross gann_cinderella gann_custer gann_fractured gann_fugitive gann_ghost gann_love gann_new_aunts gann_revisited gann_sitting gann_solitaire gann_suntune gann_super gann_things gann_wolfe hulen_33")+  ,("Grady, Kraig"+   ,["dekany-cs"+    ,"grady11"+    ,"grady_14"+    ,"grady_centaur"+    ,"grady_centaur17"+    ,"grady_centaur19"])+  ,("Hahn, Paul",words "duohex hahn_7 hahn9 hahnmaxr indian-hahn") -- hahn_g mean14a+  ,("Harrison, Lou"+   ,["dudon_slendro_matrix" -- NON-UNIQ+    ,"harrison_5"+    ,"harrison_5_1"+    ,"harrison_5_3" -- NON-STEP+    ,"harrison_5_4" -- NON-STEP+    ,"harrison_8" -- NON-STEP+    ,"harrison_15"+    ,"harrison_16"+    ,"harrison_bill"+    ,"harrison_cinna"+    ,"harrison_diat"+    ,"harrison_handel"+    ,"harrison_kyai" -- NON-STEP+    ,"harrison_mid"+    ,"harrison_mid2"+    ,"harrison_mix2"+    ,"harrison_mix3" -- NON-STEP+    ,"harrison_mix4"+    ,"harrison_slye"+    ,"harrison_songs"+    ,"hexany10"+    ,"hirajoshi2"+    ,"korea_5"+    ,"olympos"+    ,"pelog_jc" -- STRICT SONGS+    ,"pelog_laras" -- NON-STEP+    ,"prime_5"+    ,"slendro5_1","slendro5_2"+    ,"slendro_7_1","slendro_7_2","slendro_7_3","slendro_7_4"+    -- "slendro_laras" -- NON-OCT+    ,"tranh"])+  ,("Johnston, Ben"+   ,["johnston"+    ,"johnston_21"+    ,"johnston_22"+    ,"johnston_25"+    ,"johnston_81"+    ,"johnston_6-qt"+    ,"johnston_6-qt_row"])+  ,("Kepler, Johannes",words "kepler1 kepler2 kepler3")+  ,("Partch, Harry"+   ,["kring1"+    ,"diamond7"+    ,"diamond9"+    ,"diamond17b"+    ,"novaro15"+    ,"partch_29-av"+    ,"partch_29"+    ,"partch_37"+    ,"partch_39"+    ,"partch_41"+    ,"partch_43"+    ,"partch-barstow"])+  ,("Ptolemy"+   ,["ptolemy_chrom"+    ,"ptolemy_ddiat"+    ,"ptolemy_diat","ptolemy_diat2","ptolemy_diat3","ptolemy_diat4","ptolemy_diat5"+    ,"ptolemy_diff"+    ,"ptolemy_enh"+    ,"ptolemy_exp"+    ,"ptolemy_ext"+    ,"ptolemy_hominv","ptolemy_hominv2"+    ,"ptolemy_hom"+    ,"ptolemy_iastaiol","ptolemy_iast"+    ,"ptolemy_ichrom"+    ,"ptolemy_idiat"+    ,"ptolemy_imix"+    ,"ptolemy_malak","ptolemy_malak2"+    ,"ptolemy_mdiat","ptolemy_mdiat2","ptolemy_mdiat3"+    ,"ptolemy_meta"+    ,"ptolemy_mix"+    ,"ptolemy_perm"+    ,"ptolemy_prod"+    ,"ptolemy"+    ,"ptolemy_tree"])+  ,("Pythagoras"+   ,["pyth_7a","pyth_12","pyth_12s","pyth_17","pyth_17s","pyth_22","pyth_27","pyth_chrom"+    -- "pyth_31" "pyth_sev" "pyth_third" NOT-JI+    ])+  ,("Riley, Terry",words "riley_albion riley_rosary")+  ,("Smith, Gene Ward",["smithgw_15highschool1","smithgw_15highschool2","smithgw_18","smithgw_19highschool1","smithgw_19highschool2","smithgw_21","smithgw_22highschool","smithgw_58","smithgw_9","smithgw_ball","smithgw_ball2","smithgw_circu","smithgw_decab","smithgw_decac","smithgw_decad","smithgw_diff13","smithgw_dwarf6_7","smithgw_ennon13","smithgw_ennon15","smithgw_ennon28","smithgw_ennon43","smithgw_euclid3","smithgw_glamma","smithgw_glumma","smithgw_gm","smithgw_hahn12","smithgw_hahn15","smithgw_hahn16","smithgw_hahn19","smithgw_hahn22","smithgw_indianred","smithgw_majraj1","smithgw_majraj2","smithgw_majraj3","smithgw_majsyn1","smithgw_majsyn2","smithgw_majsyn3","smithgw_meandin","smithgw_meanred","smithgw_mir22","smithgw_monzoblock37","smithgw_orw18r","smithgw_pel1","smithgw_pel3","smithgw_pris","smithgw_prisa","smithgw_ragasyn1","smithgw_ratwell","smithgw_rectoo","smithgw_red72_11geo","smithgw_red72_11pro","smithgw_sc19","smithgw_scj22a","smithgw_scj22b","smithgw_scj22c","smithgw_smalldi11","smithgw_smalldi19a","smithgw_smalldi19b","smithgw_smalldi19c","smithgw_star","smithgw_star2","smithgw_syndia2","smithgw_syndia3","smithgw_syndia4","smithgw_syndia6","smithgw_well1","smithgw_wiz28","smithgw_wiz34","smithgw_wiz38"])+  ,("Tenney, James",words "mund45 tenney_8 tenney_11 tenn41a tenn41b tenn41c")+  ,("Wilson, Erv"+   ,["chin_7"+    ,"ckring9"+    ,"diamond7-13"+    ,"dodeceny","dorian_diat2inv","hypol_diatinv"+    ,"dkring3"+    ,"efg33357","efg3335711","efg35711"+    ,"eikosany"+    ,"erlich9"+    ,"harm6","harm8","harm9","harm14","harm15"+    ,"hexany_union"+    ,"indian-magrama"+    ,"malkauns"+    ,"malcolme"+    ,"novaro15"+    ,"partch_29"+    ,"ptolemy","ptolemy_diat2","ptolemy_idiat"+    ,"slendro5_1","slendro5_2","slendro_7_4"+    ,"steldek1","steldek1s","steldek2","steldek2s"+    ,"steldia"+    ,"steleik1","steleik1s","steleik2","steleik2s"+    ,"stelhex1","stelhex2","stelhex5","stelhex6" -- stelhex3 stelhex4+    ,"stelpd1","stelpd1s"+    ,"stelpent1","stelpent1s"+    ,"steltet1","steltet1s","steltet2"+    ,"steltri1","steltri2"+    ,"tritriad14"+    ,"wilson1","wilson2","wilson3","wilson5","wilson7","wilson11"+    ,"wilson7_2","wilson7_3","wilson7_4"+    ,"wilson_17","wilson_31","wilson_41"+    ,"wilcent17"+    ,"wilson_alessandro"+    ,"wilson_bag"+    ,"wilson_class"+    ,"wilson_dia1","wilson_dia2","wilson_dia3","wilson_dia4"+    ,"wilson_duo"+    ,"wilson_enh","wilson_enh2"+    ,"wilson_facet"+    -- ,"wilson_gh1","wilson_gh2","wilson_gh11","wilson_gh50" -- NON-JI+    ,"wilson_hebdome1"+    ,"wilson_hexflank"+    ,"wilson_hypenh"+    ,"wilson-rastbayyati24"+    ,"wilson_l1","wilson_l2","wilson_l3","wilson_l4","wilson_l5","wilson_l6"])+  ,("Young, La Monte",["young-lm_guitar","young-lm_piano"])+  ]++{-+import Music.Theory.Tuning.Scala+db <- scl_load_db+nm = concatMap snd scl_ji_au+scl = filter (\x -> scale_name x `elem` nm) db+non_ji = filter (not . scl_is_ji) scl+map scale_name non_ji+-}
Music/Theory/Tuning/Scala/Mode.hs view
@@ -1,37 +1,69 @@--- | Parser for the @modename.par@ file.+{- | Parser for the @modename.par@ file.++The terminology here is:++- a mode is a subset of the notes of a tuning system (which in scala is called a scale)++- the length (or degree) of the mode is the number of tones in the mode++- the universe (or scale) of the mode is the number of tones in the+  tuning system (or scale) the mode is a subset of++-} module Music.Theory.Tuning.Scala.Mode where  import Data.Char {- base -} import Data.List {- base -} import Data.Maybe {- base -} -import qualified Music.Theory.Function as T-import qualified Music.Theory.List as T-import qualified Music.Theory.Tuning.Scala as T+import qualified Music.Theory.Function as Function {- hmt -}+import qualified Music.Theory.List as List {- hmt -}+import qualified Music.Theory.Tuning.Scala as Scala {- hmt -} --- | (start-degree,intervals,description)-type MODE = (Int,[Int],String)+-- | (mode-start-degree,mode-intervals,mode-description)+type Mode = (Int,[Int],String) -mode_starting_degree :: MODE -> Int+-- | Starting degree of mode in underlying scale.  If non-zero the+-- mode will not lie within an ordinary octave of the tuning.+mode_starting_degree :: Mode -> Int mode_starting_degree (d,_,_) = d -mode_intervals :: MODE -> [Int]+-- | Intervals (in steps) between adjacent elements of the mode.+mode_intervals :: Mode -> [Int] mode_intervals (_,i,_) = i -mode_description :: MODE -> String+-- | Interval set of mode (ie. 'nub' of 'sort' of 'mode_intervals')+mode_iset :: Mode -> [Int]+mode_iset = nub . sort . mode_intervals++-- | Histogram ('List.histogram') of 'mode_intervals'+mode_histogram :: Mode -> [(Int, Int)]+mode_histogram = List.histogram . mode_intervals++-- | The text description of the mode, ordinarily a comma separated list of names.+mode_description :: Mode -> String mode_description (_,_,d) = d -mode_degree :: MODE -> Int-mode_degree = sum . mode_intervals+-- | 'length' (or degree) of 'mode_intervals' (ie. number of notes in mode)+mode_length :: Mode -> Int+mode_length = length . mode_intervals --- | (mode-count,_,mode-list)-type MODENAM = (Int,Int,[MODE])+-- | 'sum' of 'mode_intervals' (ie. number of notes in tuning system)+mode_univ :: Mode -> Int+mode_univ = sum . mode_intervals -modenam_modes :: MODENAM -> [MODE]+-- | 'List.dx_d' of 'mode_intervals'.  This seqence includes the octave.+mode_degree_seq :: Mode -> [Int]+mode_degree_seq = List.dx_d 0 . mode_intervals++-- | (mode-count,mode-length-maxima,mode-list)+type ModeNam = (Int,Int,[Mode])++modenam_modes :: ModeNam -> [Mode] modenam_modes (_,_,m) = m  -- | Search for mode by interval list.-modenam_search_seq :: MODENAM -> [Int] -> [MODE]+modenam_search_seq :: ModeNam -> [Int] -> [Mode] modenam_search_seq (_,_,m) x = filter ((== x) . mode_intervals) m  -- | Expect /one/ result.@@ -45,23 +77,49 @@ -- > sq [1,2,1,2,1,2,1,2] -- > sq [2,1,2,1,2,1,2,1] -- > sq (replicate 12 1)-modenam_search_seq1 :: MODENAM -> [Int] -> Maybe MODE-modenam_search_seq1 mn = T.unlist1 . modenam_search_seq mn+modenam_search_seq1 :: ModeNam -> [Int] -> Maybe Mode+modenam_search_seq1 mn = List.unlist1 . modenam_search_seq mn  -- | Search for mode by description text. -- -- > map (modenam_search_description mn) ["Messiaen","Xenakis","Raga"]-modenam_search_description :: MODENAM -> String -> [MODE]+modenam_search_description :: ModeNam -> String -> [Mode] modenam_search_description (_,_,m) x = filter (isInfixOf x . mode_description) m --- | Pretty printer.-mode_stat :: MODE -> [String]-mode_stat (d,i,s) =-    ["mode-start-degree : " ++ show d-    ,"mode-intervals    : " ++ intercalate "," (map show i)-    ,"mode-degree       : " ++ show (sum i)-    ,"mode-description  : " ++ s]+-- | Is /p/ an element of the set of rotations of /q/.+mode_rot_eqv :: Mode -> Mode -> Bool+mode_rot_eqv p q =+  (mode_length p == mode_length q) &&+  (mode_univ p == mode_univ q) &&+  (mode_intervals p `elem` List.rotations (mode_intervals q)) +{- | Pretty printer.++> mn <- load_modenam++> let r = filter ((/=) 0 . mode_starting_degree) (modenam_modes mn) -- non-zero starting degrees+> let r = filter ((== [(1,2),(2,5)]) . mode_histogram) (modenam_modes mn) -- 2×1 and 5×2+> let r = filter ((== 22) . mode_univ) (modenam_search_description mn "Raga") -- raga of 22 shruti univ++> [(p,q) | p <- r, q <- r, p < q, mode_rot_eqv p q] -- rotationally equivalent elements of r++> length r+> putStrLn $ unlines $ intercalate ["\n"] $ map mode_stat r+-}+mode_stat :: Mode -> [String]+mode_stat m =+  let hst = mode_histogram m+      comma_map f = intercalate "," . map f+  in ["mode-start-degree : " ++ show (mode_starting_degree m)+     ,"mode-intervals    : " ++ comma_map show (mode_intervals m)+     ,"mode-description  : " ++ mode_description m+     ,"mode-length       : " ++ show (mode_length m)+     ,"mode-univ         : " ++ show (mode_univ m)+     ,"mode-interval-set : " ++ intercalate "," (map show (mode_iset m))+     ,"mode-histogram    : " ++ intercalate "," (map (\(e,n) -> concat [show n,"×",show e]) hst)+     ,"mode-degree-seq   : " ++ comma_map show (mode_degree_seq m)+     ]+ -- * Parser  -- | Bracketed integers are a non-implicit starting degree.@@ -69,49 +127,53 @@ -- > map non_implicit_degree ["4","[4]"] == [Nothing,Just 4] non_implicit_degree :: String -> Maybe Int non_implicit_degree s =-    case T.unbracket s of-      Just ('[',s',']') -> Just (read s')+    case List.unbracket s of+      Just ('[',x,']') -> Just (read x)       _ -> Nothing +-- | Predicate form is_non_implicit_degree :: String -> Bool is_non_implicit_degree = isJust . non_implicit_degree  is_integer :: String -> Bool is_integer = all isDigit -parse_modenam_entry :: [String] -> MODE+parse_modenam_entry :: [String] -> Mode parse_modenam_entry w =-    let (n0:n,c) = span (T.predicate_or is_non_implicit_degree is_integer) w-    in case non_implicit_degree n0 of-         Nothing -> (0,map read (n0:n),unwords c)-         Just d -> (d,map read n,unwords c)+    let (n,c) = span (Function.predicate_or is_non_implicit_degree is_integer) w+    in case non_implicit_degree (n !! 0) of+         Nothing -> (0,map read n,unwords c)+         Just d -> (d,map read (tail n),unwords c)  -- | Lines ending with @\@ continue to next line. join_long_lines :: [String] -> [String] join_long_lines l =     case l of-      p:q:l' -> case T.separate_last' p of+      p:q:l' -> case List.separate_last' p of                   (p',Just '\\') -> join_long_lines ((p' ++ q) : l')                   _ -> p : join_long_lines (q : l')       _ -> l -parse_modenam :: [String] -> MODENAM+-- | Parse joined non-comment lines of modenam file.+parse_modenam :: [String] -> ModeNam parse_modenam l =     case l of-      n:x:m -> let n' = read n :: Int-                   x' = read x :: Int-                   m' = map (parse_modenam_entry . words) m-               in if n' == length m' then (n',x',m') else error "parse_modenam"+      n_str:x_str:m_str ->+        let n = read n_str :: Int+            x = read x_str :: Int+            m = map (parse_modenam_entry . words) m_str+        in if n == length m then (n,x,m) else error "parse_modenam"       _ -> error "parse_modenam" --- * IO+-- * Io --- | 'parse_modenam' of 'T.load_dist_file' of @modenam.par@.------ > mn <- load_modenam--- > let (n,x,m) = mn--- > n == 2125 && x == 15 && length m == n-load_modenam :: IO MODENAM+{- | 'parse_modenam' of 'Scala.load_dist_file' of @modenam.par@.++> mn <- load_modenam+> let (n,x,m) = mn+> (n, x, length m) == (3087,15,3087) -- Scala 2.64p+-}+load_modenam :: IO ModeNam load_modenam = do-  l <- T.load_dist_file "modenam.par"-  return (parse_modenam (T.filter_comments (join_long_lines l)))+  l <- Scala.load_dist_file_ln "modenam.par"+  return (parse_modenam (Scala.filter_comments (join_long_lines l)))
Music/Theory/Tuning/Sethares_1994.hs view
@@ -1,16 +1,26 @@ -- | William A. Sethares. -- "Adaptive Tunings for Musical Scales". -- /Journal of the Acoustical Society of America/, 96(1), July 1994.------ <http://sethares.engr.wisc.edu/consemi.html> module Music.Theory.Tuning.Sethares_1994 where -import qualified Music.Theory.Tuning as T+import Data.Maybe {- base -} --- > import Sound.SC3.Plot--- > plotTable1 (map (\f -> d (220,1) (f,1)) [220 .. 440])-d :: (Floating n, Ord n) => (n,n) -> (n,n) -> n-d (f1,v1) (f2,v2) =+import qualified Music.Theory.Tuning as T {- hmt -}++{- | Plomp-Levelt consonance curve.++R. Plomp and W. J. M. Levelt,+"Tonal Consonance and Critical Bandwidth,"+Journal of the Acoustical Society of America.38, 548-560 (1965).++"Relating Tuning and Timbre" <http://sethares.engr.wisc.edu/consemi.html>+MATLAB: <https://sethares.engr.wisc.edu/comprog.html>++> import Sound.SC3.Plot {- hsc3-plot -}+> plot_p1_ln [map (\f -> pl_dissonance (220,1) (f,1)) [220 .. 440]]+-}+pl_dissonance :: (Floating n, Ord n) => (n,n) -> (n,n) -> n+pl_dissonance (f1,v1) (f2,v2) =     let d_star = 0.24         s1 = 0.0207         s2 = 18.96@@ -24,16 +34,52 @@         e2 = c2 * exp (a2 * s * f_dif)     in v1 * v2 * (e1 + e2) --- > plotTable fig_1-fig_1 :: (Floating n,Enum n,Ord n) => [[n]]-fig_1 =+-- | Sum of 'pl_dissonance' for all p in s1 and all q in s2.+pl_dissonance_h :: (Floating n, Ord n) => [(n,n)] -> [(n,n)] -> n+pl_dissonance_h s1 s2 = sum [pl_dissonance p q | p <- s1, q <- s2]++-- | Return local minima of sequence with index.+local_minima :: Ord t => [t] -> [(Int,t)]+local_minima =+  let f (ix,i,j,k) = if j <= i && j <= k then Just (ix,j) else Nothing+      triples ix l = case l of+                       i:j:k:_ -> (ix,i,j,k) : triples (ix + 1) (tail l)+                       _ -> []+  in mapMaybe f . triples 1++-- | William A. Sethares "Adaptive Tunings for Musical Scales".+--+-- > plot_p1_ln atms_fig_1+atms_fig_1 :: (Floating n,Enum n,Ord n) => [[n]]+atms_fig_1 =     let f0 = [125,250,500,1000,2000]-        r_seq = map T.cents_to_ratio [0 .. 1200]-    in map (\f -> map (\r -> d (f,1) (f * r,1)) r_seq) f0+        r_seq = map T.cents_to_fratio [0 .. 1200]+    in map (\f -> map (\r -> pl_dissonance (f,1) (f * r,1)) r_seq) f0 --- > let a_seq = take 7 (iterate (* 0.88) 1.0)--- > let gen f0 = zipWith (\r a -> (f0 * r,a)) [1 .. 7] a_seq--- > let r_seq = map T.cents_to_ratio [0,1 .. 1200]--- > plotTable1 (let f0 = 880 in map (\r -> d_h (gen f0) (gen (f0 * r))) r_seq)-d_h :: (Floating n, Ord n) => [(n,n)] -> [(n,n)] -> n-d_h s1 s2 = sum [d p q | p <- s1, q <- s2]+-- > plot_p1_ln [atms_fig_2 880]+-- > map fst (local_minima (atms_fig_2 880)) == [204,231,267,316,386,435,498,583,702,814,884,969,1018]+atms_fig_2 :: (Ord t, Floating t, Enum t) => t -> [t]+atms_fig_2 f0 =+  let gen fq = map (\r -> (fq * r,1)) [1 .. 9]+      r_seq = map T.cents_to_fratio [0,1 .. 1200]+  in map (\r -> pl_dissonance_h (gen f0) (gen (f0 * r))) r_seq++-- > Sound.SC3.Plot.plot_p1_ln [atms_fig_3 880]+-- > map fst (local_minima (atms_fig_3 880)) == [267,400,533,667,800,933,1043]+atms_fig_3 :: (Ord t, Floating t, Enum t) => t -> [t]+atms_fig_3 f0 =+  let b = 2 ** (1/9)+      gen fq = map (\r -> (fq * r,1)) (1 : map (b **) [9,14,18,21,25,27,30])+      r_seq = map T.cents_to_fratio [0,1 .. 1200]+  in map (\r -> pl_dissonance_h (gen f0) (gen (f0 * r))) r_seq++-- | "Relating Tuning and Timbre" <http://sethares.engr.wisc.edu/consemi.html>+--+-- > plot_p1_ln [rtt_fig_2 880]+-- > map fst (local_minima (rtt_fig_2 880)) == [267,316,386,498,582,702,884,969]+rtt_fig_2 :: (Ord t, Floating t, Enum t) => t -> [t]+rtt_fig_2 f0 =+  let a_seq = take 7 (iterate (* 0.88) 1.0)+      gen fq = zipWith (\r a -> (fq * r,a)) [1 .. 7] a_seq+      r_seq = map T.cents_to_fratio [0,1 .. 1200]+  in map (\r -> pl_dissonance_h (gen f0) (gen (f0 * r))) r_seq
Music/Theory/Tuning/Syntonic.hs view
@@ -3,10 +3,18 @@  import Data.List {- base -} -import Music.Theory.Tuning {- hmt -}+import qualified Music.Theory.Tuning as T {- hmt -}+import qualified Music.Theory.Tuning.Type as T {- hmt -} --- | Construct an isomorphic layout of /r/ rows and /c/ columns with--- an upper left value of /(i,j)/.+{- | Construct an isomorphic layout of /r/ rows and /c/ columns with an upper left value of /(i,j)/.++> r = [[(0,0),(-1,2),(-2,4)],[(-1,1),(-2,3),(-3,5)],[(-2,2),(-3,4),(-4,6)]]+> mk_isomorphic_layout 3 3 (0,0) == r+> map (map fst) r == [[0,-1,-2],[-1,-2,-3],[-2,-3,-4]]+> map (map snd) r == [[0,2,4],[1,3,5],[2,4,6]]+> map (map fst) r == map (map fst) (transpose r)+> map (map snd) (transpose r) == [[0,1,2],[2,3,4],[4,5,6]]+-} mk_isomorphic_layout :: Integral a => a -> a -> (a,a) -> [[(a,a)]] mk_isomorphic_layout n_row n_col top_left =     let (a,b) `plus` (c,d) = (a+c,b+d)@@ -18,12 +26,12 @@ -- | A minimal isomorphic note layout. -- -- > let [i,j,k] = mk_isomorphic_layout 3 5 (3,-4)--- > in [i,take 4 j,(2,-4):take 4 k] == minimal_isomorphic_note_layout+-- > [i,take 4 j,(2,-4):take 4 k] == minimal_isomorphic_note_layout minimal_isomorphic_note_layout :: [[(Int,Int)]] minimal_isomorphic_note_layout =-    [[(3,-4),(2,-2),(1,0),(0,2),(-1,4)]-       ,[(2,-3),(1,-1),(0,1),(-1,3)]-    ,[(2,-4),(1,-2),(0,0),(-1,2),(-2,4)]]+  [[(3,-4),(2,-2),(1,0),(0,2),(-1,4)]+  ,[(2,-3),(1,-1),(0,1),(-1,3)]+  ,[(2,-4),(1,-2),(0,0),(-1,2),(-2,4)]]  -- | Make a rank two regular temperament from a list of /(i,j)/ -- positions by applying the scalars /a/ and /b/.@@ -34,27 +42,27 @@ -- rows and @7@ columns starting at @(3,-4)@ and a -- 'rank_two_regular_temperament' with /a/ of @1200@ and indicated -- /b/.-mk_syntonic_tuning :: Int -> [Cents]+mk_syntonic_tuning :: Int -> [T.Cents] mk_syntonic_tuning b =   let l = mk_isomorphic_layout 5 7 (3,-4)       t = map (rank_two_regular_temperament 1200 b) l   in nub (sort (map (\x -> fromIntegral (x `mod` 1200)) (concat t))) --- | 'mk_syntonic_tuning' of @697@.------ > divisions syntonic_697 == 17------ > let c = [0,79,194,273,309,388,467,503,582,697,776,812,891,970,1006,1085,1164]--- > in cents_i syntonic_697 == c-syntonic_697 :: Tuning-syntonic_697 = Tuning (Right (mk_syntonic_tuning 697)) 2+{- | 'mk_syntonic_tuning' of @697@. +> tn_divisions syntonic_697 == 17++> let c = [0,79,194,273,309,388,467,503,582,697,776,812,891,970,1006,1085,1164]+> tn_cents_i syntonic_697 == c+-}+syntonic_697 :: T.Tuning+syntonic_697 = T.Tuning (Right (mk_syntonic_tuning 697)) Nothing+ -- | 'mk_syntonic_tuning' of @702@. ----- > divisions syntonic_702 == 17+-- > tn_divisions syntonic_702 == 17 -- -- > let c = [0,24,114,204,294,318,408,498,522,612,702,792,816,906,996,1020,1110]--- > in cents_i syntonic_702 == c-syntonic_702 :: Tuning-syntonic_702 = Tuning (Right (mk_syntonic_tuning 702)) 2-+-- > tn_cents_i syntonic_702 == c+syntonic_702 :: T.Tuning+syntonic_702 = T.Tuning (Right (mk_syntonic_tuning 702)) Nothing
+ Music/Theory/Tuning/Type.hs view
@@ -0,0 +1,166 @@+-- | Tuning type+module Music.Theory.Tuning.Type where++import Data.List {- base -}+import Data.Maybe {- base -}++import qualified Music.Theory.Either as T {- hmt -}+import qualified Music.Theory.Math.Prime as T {- hmt -}+import qualified Music.Theory.Tuning as T {- hmt -}++-- * Tuning++-- | A tuning specified 'Either' as a sequence of exact ratios, or as+-- a sequence of possibly inexact 'Cents', and an octave if not 2:1 or 1200.+--+-- In both cases, the values are given in relation to the first degree+-- of the scale, which for ratios is 1 and for cents 0.+data Tuning = Tuning {tn_ratios_or_cents :: Either [Rational] [T.Cents]+                     ,tn_octave :: Maybe (Either Rational T.Cents)}+              deriving (Eq,Show)++-- | Default epsilon for recovering ratios from cents.+tn_epsilon :: Double+tn_epsilon = 0.001++-- | Tuning value as rational, reconstructed if required.+tn_as_ratio :: Double -> Either Rational T.Cents -> Rational+tn_as_ratio epsilon = either id (T.reconstructed_ratio epsilon)++-- | Tuning value as cents.+tn_as_cents :: Either Rational T.Cents -> T.Cents+tn_as_cents = either T.ratio_to_cents id++-- | Tuning octave, defaulting to 2:1.+tn_octave_def :: Tuning -> Either Rational T.Cents+tn_octave_def = fromMaybe (Left 2) . tn_octave++-- | Tuning octave in cents.+tn_octave_cents :: Tuning -> T.Cents+tn_octave_cents = tn_as_cents . tn_octave_def++-- | Tuning octave as ratio cents.+tn_octave_ratio :: Double -> Tuning -> Rational+tn_octave_ratio epsilon = tn_as_ratio epsilon . tn_octave_def++-- | Divisions of octave.+--+-- > tn_divisions (tn_equal_temperament 12) == 12+tn_divisions :: Tuning -> Int+tn_divisions = either length length . tn_ratios_or_cents++-- | 'Maybe' exact ratios of 'Tuning', NOT including the octave.+tn_ratios :: Tuning -> Maybe [Rational]+tn_ratios = T.from_left . tn_ratios_or_cents++-- | Limit of JI tuning.+tn_limit :: Tuning -> Maybe Integer+tn_limit = fmap (maximum . map T.rational_prime_limit) . tn_ratios++-- | 'error'ing variant.+tn_ratios_err :: Tuning -> [Rational]+tn_ratios_err = fromMaybe (error "ratios") . tn_ratios++-- | Possibly inexact 'Cents' of tuning, NOT including the octave.+tn_cents :: Tuning -> [T.Cents]+tn_cents = either (map T.ratio_to_cents) id . tn_ratios_or_cents++-- | 'map' 'round' '.' 'cents'.+tn_cents_i :: Integral i => Tuning -> [i]+tn_cents_i = map round . tn_cents++-- | Variant of 'tn_cents' that includes octave at right.+tn_cents_octave :: Tuning -> [T.Cents]+tn_cents_octave t = tn_cents t ++ [tn_octave_cents t]++-- | 'tn_cents' / 100+tn_fmidi :: Tuning -> [Double]+tn_fmidi = map (* 0.01) . tn_cents++-- | Possibly inexact 'Approximate_Ratio's of tuning.+tn_approximate_ratios :: Tuning -> [T.Approximate_Ratio]+tn_approximate_ratios =+    either (map T.approximate_ratio) (map T.cents_to_fratio) .+    tn_ratios_or_cents++-- | Cyclic form, taking into consideration 'octave_ratio'.+tn_approximate_ratios_cyclic :: Tuning -> [T.Approximate_Ratio]+tn_approximate_ratios_cyclic t =+    let r = tn_approximate_ratios t+        m = T.cents_to_fratio (tn_octave_cents t)+        g = iterate (* m) 1+        f n = map (* n) r+    in concatMap f g++-- | Lookup function that allows both negative & multiple octave indices.+--+-- > :l Music.Theory.Tuning.DB.Werckmeister+-- > let map_zip f l = zip l (map f l)+-- > map_zip (tn_ratios_lookup werckmeister_vi) [-24 .. 24]+tn_ratios_lookup :: Tuning -> Int -> Maybe Rational+tn_ratios_lookup t n =+    let (o,pc) = n `divMod` tn_divisions t+        o_ratio = T.oct_diff_to_ratio (tn_octave_ratio tn_epsilon t) o+    in fmap (\r -> o_ratio * (r !! pc)) (tn_ratios t)++-- | Lookup function that allows both negative & multiple octave indices.+--+-- > map_zip (tn_approximate_ratios_lookup werckmeister_v) [-24 .. 24]+tn_approximate_ratios_lookup :: Tuning -> Int -> T.Approximate_Ratio+tn_approximate_ratios_lookup t n =+    let (o,pc) = n `divMod` tn_divisions t+        o_ratio = fromRational (T.oct_diff_to_ratio (tn_octave_ratio tn_epsilon t) o)+    in o_ratio * (tn_approximate_ratios t !! pc)++-- | 'Maybe' exact ratios reconstructed from possibly inexact 'Cents'+-- of 'Tuning'.+--+-- > :l Music.Theory.Tuning.DB.Werckmeister+-- > let r = [1,17/16,9/8,13/11,5/4,4/3,7/5,3/2,11/7,5/3,16/9,15/8]+-- > tn_reconstructed_ratios 1e-2 werckmeister_iii == Just r+tn_reconstructed_ratios :: Double -> Tuning -> Maybe [Rational]+tn_reconstructed_ratios epsilon =+    fmap (map (T.reconstructed_ratio epsilon)) .+    T.from_right .+    tn_ratios_or_cents++-- * Equal temperaments++-- | Make /n/ division equal temperament.+tn_equal_temperament :: Integral n => n -> Tuning+tn_equal_temperament n =+    let c = genericTake n [0,1200 / fromIntegral n ..]+    in Tuning (Right c) Nothing++-- | 12-tone equal temperament.+--+-- > tn_cents tn_equal_temperament_12 == [0,100..1100]+tn_equal_temperament_12 :: Tuning+tn_equal_temperament_12 = tn_equal_temperament (12::Int)++-- | 19-tone equal temperament.+--+-- > let c = [0,63,126,189,253,316,379,442,505,568,632,695,758,821,884,947,1011,1074,1137]+-- > tn_cents_i tn_equal_temperament_19 == c+tn_equal_temperament_19 :: Tuning+tn_equal_temperament_19 = tn_equal_temperament (19::Int)++-- | 31-tone equal temperament.+tn_equal_temperament_31 :: Tuning+tn_equal_temperament_31 = tn_equal_temperament (31::Int)++-- | 53-tone equal temperament.+tn_equal_temperament_53 :: Tuning+tn_equal_temperament_53 = tn_equal_temperament (53::Int)++-- | 72-tone equal temperament.+--+-- > let r = [0,17,33,50,67,83,100]+-- > take 7 (map round (tn_cents tn_equal_temperament_72)) == r+tn_equal_temperament_72 :: Tuning+tn_equal_temperament_72 = tn_equal_temperament (72::Int)++-- | 96-tone equal temperament.+tn_equal_temperament_96 :: Tuning+tn_equal_temperament_96 = tn_equal_temperament (96::Int)+
+ Music/Theory/Tuning/Wilson.hs view
@@ -0,0 +1,936 @@+-- | Erv Wilson, archives <http://anaphoria.com/wilson.html>+module Music.Theory.Tuning.Wilson where++import Control.Monad {- base -}+import Data.List {- base -}+import Data.Maybe {- base -}+import Data.Ord {- base -}+import Data.Ratio {- base -}+import Text.Printf {- base -}++import qualified Safe {- safe -}++import qualified Music.Theory.Array.Text as Text {- hmt-base -}+import qualified Music.Theory.Function as Function {- hmt-base -}+import qualified Music.Theory.Graph.Type as Graph {- hmt-base -}+import qualified Music.Theory.List as List {- hmt-base -}+import qualified Music.Theory.Math as Math {- hmt-base -}+import qualified Music.Theory.Math.Convert as Convert {- hmt-base -}+import qualified Music.Theory.Show as Show {- hmt-base -}+import qualified Music.Theory.Tuple as Tuple {- hmt-base -}++import qualified Music.Theory.Graph.Dot as Dot {- hmt -}+import qualified Music.Theory.Interval.Barlow_1987 as Barlow {- hmt -}+import qualified Music.Theory.Math.Oeis as OEIS {- hmt -}+import qualified Music.Theory.Math.Prime as Prime {- hmt -}+import qualified Music.Theory.Set.List as Set {- hmt -}+import qualified Music.Theory.Tuning as Tuning {- hmt -}+import qualified Music.Theory.Tuning.Scala as Scala {- hmt -}++-- * Geom (see "Data.CG.Minus.Plain")++type V2 n = (n,n)+v2_map :: (t -> u) -> V2 t -> V2 u+v2_map f (a,b) = (f a,f b)+v2_zip :: (a -> b -> c) -> V2 a -> V2 b -> V2 c+v2_zip f (i,j) (p,q) = (f i p,f j q)+v2_add :: Num n => V2 n -> V2 n -> V2 n+v2_add = v2_zip (+)+v2_sum :: Num n => [V2 n] -> V2 n+v2_sum = foldl v2_add (0,0)+v2_scale :: Num n => n -> V2 n -> V2 n+v2_scale n = v2_map (* n)++-- * Pt Set++{- | Normalise set of points to lie in (-1,-1) - (1,1), scaling symetrically about (0,0)++> pt_set_normalise_sym [(40,0),(0,40),(13,11),(-8,4)] == [(1,0),(0,1),(0.325,0.275),(-0.2,0.1)]+> pt_set_normalise_sym [(-10,0),(1,10)] == [(-1,0),(0.1,1)]+-}+pt_set_normalise_sym :: (Fractional n,Ord n) => [V2 n] -> [V2 n]+pt_set_normalise_sym x =+  let z = maximum (map (uncurry max . Function.bimap1 abs) x)+  in map (v2_scale (recip z)) x++-- * Lattice Design++-- | /k/-unit co-ordinates for /k/-lattice.+type Lattice_Design n = (Int,[V2 n])++-- | Erv Wilson standard lattice, unit co-ordinates for 5-dimensions, ie. [3,5,7,11,13]+--+-- <http://anaphoria.com/wilsontreasure.html>+ew_lc_std :: Num n => Lattice_Design n+ew_lc_std = (5,[(20,0),(0,20),(4,3),(-3,4),(-1,2)])++-- | Kraig Grady standard lattice, unit co-ordinates for 5-dimensions, ie. [3,5,7,11,13]+--+-- <http://anaphoria.com/wilsontreasure.html>+kg_lc_std :: Num n => Lattice_Design n+kg_lc_std = (5,[(40,0),(0,40),(13,11),(-14,18),(-8,4)])++-- | Erv Wilson tetradic lattice (3-lattice), used especially when working with hexanies or 7 limit tunings+--+-- <http://anaphoria.com/wilsontreasure.html>+ew_lc_tetradic :: Num n => Lattice_Design n+ew_lc_tetradic = (3,[(-4,-2),(6,1),(5,-2)])++-- * Lattice_Factors++-- | A discrete /k/-lattice is described by a sequence of /k/-factors.+--   Values are ordinarily though not necessarily primes beginning at three.+type Lattice_Factors i = (Int,[i])++-- | Positions in a /k/-lattice are given as a /k/-list of steps.+type Lattice_Position = (Int,[Int])++-- | Delete entry at index.+lc_pos_del :: Int -> Lattice_Position -> Lattice_Position+lc_pos_del ix (k,x) = (k - 1,List.remove_ix ix x)++-- | Resolve Lattice_Position against Lattice_Design to V2+lc_pos_to_pt :: (Fractional n, Ord n) => Lattice_Design n -> Lattice_Position -> V2 n+lc_pos_to_pt (_,lc) (_,x) = v2_sum (zipWith (v2_scale . fromIntegral) x (pt_set_normalise_sym lc))++-- | White-space pretty printer for Lattice_Position.+--+-- > pos_pp_ws (3,[0,-2,1]) == "  0 -2  1"+pos_pp_ws :: Lattice_Position -> String+pos_pp_ws = let f x = printf "%3d" x in concatMap f . snd++-- | Given Lattice_Factors [X,Y,Z..] and Lattice_Position [x,y,z..], calculate the indicated ratio.+--+-- > lat_res (2,[3,5]) (2,[-5,2]) == (5 * 5) / (3 * 3 * 3 * 3 * 3)+lat_res :: Integral i => Lattice_Factors i -> Lattice_Position -> Ratio i+lat_res (_,p) (_,q) =+  let f i j = case compare j 0 of+                GT -> (i ^ Convert.int_to_integer j) % 1+                EQ -> 1+                LT -> 1 % (i ^ abs (Convert.int_to_integer j))+  in product (zipWith f p q)++-- * Rat (n,d)++-- | Ratio given as (/n/,/d/)+type Rat = (Integer,Integer)++-- | Remove all octaves from /n/ and /d/.+rat_rem_oct :: Rat -> Rat+rat_rem_oct = Function.bimap1 (product . filter (/= 2)) . Prime.rat_prime_factors++-- | Lift 'Rat' function to 'Rational'.+rat_lift_1 :: (Rat -> Rat) -> Rational -> Rational+rat_lift_1 f = uncurry (%) . f . Math.rational_nd++-- | Convert 'Rat' to 'Rational'+rat_to_ratio :: Rat -> Rational+rat_to_ratio (n,d) = n % d++-- | Mediant, ie. n1+n2/d1+d2+--+-- > rat_mediant (0,1) (1,2) == (1,3)+rat_mediant :: Rat -> Rat -> Rat+rat_mediant (n1,d1) (n2,d2) = (n1 + n2,d1 + d2)++-- | Rat written as n/d+rat_pp :: Rat -> String+rat_pp (n,d) = concat [show n,"/",show d]++-- * Rational++-- | Lifted 'rat_rem_oct'.+--+-- > map ew_r_rem_oct [256/243,7/5,1/7] == [1/243,7/5,1/7]+r_rem_oct :: Rational -> Rational+r_rem_oct = rat_lift_1 rat_rem_oct++-- | Assert that /n/ is in [1,2).+r_verify_oct :: Rational -> Rational+r_verify_oct i = if i >= 1 && i < 2 then i else error (show ("r_verify_oct?",i))++-- | Find limit of set of ratios, ie. largest factor in either numerator or denominator.+--+-- > r_seq_limit [1] == 1+r_seq_limit :: [Rational] -> Integer+r_seq_limit = maximum . map Prime.rational_prime_limit++-- | Find factors of set of ratios, ie. the union of all factor in both numerator & denominator.+--+-- > r_seq_factors [1/3,5/7,9/8,13,27,31] == [2,3,5,7,13,31]+r_seq_factors :: [Rational] -> [Integer]+r_seq_factors = nub . sort . concatMap (uncurry (++) . Prime.rational_prime_factors)++-- * Table++-- | Vector of prime-factors up to /limit/.+--+-- > map (rat_fact_lm 11) [3,5,7,2/11] == [(5,[0,1,0,0,0]),(5,[0,0,1,0,0]),(5,[0,0,0,1,0]),(5,[1,0,0,0,-1])]+rat_fact_lm :: Integer -> Rational -> Lattice_Position+rat_fact_lm lm =+  let k = fromMaybe 1 (Prime.prime_k lm) + 1+  in (\c -> (k,c)) .+     Prime.rat_prime_factors_t k .+     Math.rational_nd++tbl_txt :: Bool -> Integer -> [Rational] -> [[String]]+tbl_txt del lm_z rs =+  let lm = r_seq_limit rs+      scl = map ((if del then lc_pos_del 0 else id) . rat_fact_lm lm) rs+      cs = map (Tuning.ratio_to_cents . Tuning.fold_ratio_to_octave_err) rs+      hs = map (Barlow.harmonicity_r Barlow.barlow) rs :: [Double]+      f (k,x,r,c,h) = [show k+                      ,if lm <= lm_z then pos_pp_ws x else "..."+                      ,Show.ratio_pp r+                      ,Show.real_pp 2 c+                      ,Show.real_pp_unicode 2 h]+  in map (intersperse "=" . f) (zip5 [0::Int ..] scl rs cs hs)++-- > tbl_wr False [1,7/6,5/4,4/3,3/2]+-- > tbl_wr True [1,3,1/5,15/31]+tbl_wr :: Bool -> [Rational] -> IO ()+tbl_wr del = putStr . unlines . Text.table_pp (False,True,False," ",False) . tbl_txt del 31++-- * Graph++-- | (maybe (maybe lattice-design, maybe primes),gr-attr,vertex-pp)+type Ew_Gr_Opt = (Maybe (Lattice_Design Rational,Maybe [Integer]),[Dot.Dot_Meta_Attr],Rational -> String)++ew_gr_opt_pos :: Ew_Gr_Opt -> Bool+ew_gr_opt_pos (lc_m,_,_) = isJust lc_m++-- > map (ew_gr_r_pos ew_lc_std (Just [3,5,31])) [3,5,31]+ew_gr_r_pos :: Lattice_Design Rational -> Maybe [Integer] -> Rational -> Dot.Dot_Attr+ew_gr_r_pos (k,lc) primes_l =+  let f m (x,y) = (m * x,m * y)+  in Dot.node_pos_attr .+     f 160 .+     lc_pos_to_pt (k,lc) .+     (\c -> (k,c)) .+     -- this is a little subtle, tail removes the '2' slot from rational_prime_factors_t+     maybe (tail . Prime.rational_prime_factors_t (k + 1)) Prime.rational_prime_factors_c primes_l++-- | 'Dot.lbl_to_udot' add position attribute if a 'Lattice_Design' is given.+ew_gr_udot :: Ew_Gr_Opt -> Graph.Lbl Rational () -> [String]+ew_gr_udot (lc_m,attr,v_pp) =+  let (e,p_f) = case lc_m of+                  Nothing -> ("sfdp",const Nothing)+                  Just (lc,primes_l) -> ("neato",Just . ew_gr_r_pos lc primes_l)+  in Dot.lbl_to_udot+     ([("graph:layout",e),("node:shape","plain")] ++ attr) -- ("graph:K","0.6") ("edge:len","1.0")+     (\(_,v) -> List.mcons (p_f v) [("label",v_pp v)]+     ,const [])++-- | 'writeFile' of 'ew_gr_udot'+ew_gr_udot_wr :: Ew_Gr_Opt -> FilePath -> Graph.Lbl Rational () -> IO ()+ew_gr_udot_wr opt fn = writeFile fn . unlines . ew_gr_udot opt++ew_gr_udot_wr_svg :: Ew_Gr_Opt -> FilePath -> Graph.Lbl Rational () -> IO ()+ew_gr_udot_wr_svg opt fn gr = do+  ew_gr_udot_wr opt fn gr+  void (Dot.dot_to_svg (if ew_gr_opt_pos opt then ["-n"] else []) fn)++-- * Zig-Zag++zz_seq_1 :: (Eq n,Num n) => Int -> (n,n) -> (n,n) -> [(n,n)]+zz_seq_1 k (p,q) (n,d) = if k == 0 then [(n,d)] else (n,d) : zz_seq_1 (k - 1) (p,q) (n+p,d+q)++-- > zz_next 3 [(0,1),(1,1)] == [(1,1),(1,2),(1,3),(1,4)]+zz_next :: (Eq n, Num n) => Int -> [(n,n)] -> [(n,n)]+zz_next k p =+  case reverse p of+    i:j:_ -> zz_seq_1 k j i+    _ -> error "zz_next?"++zz_recur :: (Eq n, Num n) => [Int] -> [(n,n)] -> [[(n,n)]]+zz_recur k_seq p =+  case k_seq of+    [] -> []+    k:k_rem -> let r = zz_next k p in r : zz_recur k_rem r++-- > zz_seq [3,9,2,2,4,6,2,1,1,3]+-- > zz_seq [2,4,2,158]+-- > zz_seq [1,1,4,2,1,3,1,6,2]+zz_seq :: (Eq n, Num n) => [Int] -> [[(n, n)]]+zz_seq k_seq = zz_recur k_seq [(0,1),(1,1)]++-- * Mos++-- > gen_coprime 12 == [1,5]+-- > gen_coprime 49 == [1..24] \\ [7,14,21]+gen_coprime :: Integral a => a -> [a]+gen_coprime x = filter (\y -> gcd y x == 1) [1 .. (x `div` 2)]++-- > mos_2 12 5 == (5,7)+mos_2 :: Num n => n -> n -> (n,n)+mos_2 p g = (g,p - g)++-- | Divide MOS, keeps retained value on same side+--+-- > mos_step (5,7) == (5,2)+-- > mos_step (5,2) == (3,2)+-- > mos_step (3,2) == (1,2)+mos_step :: (Ord a, Num a) => (a, a) -> (a, a)+mos_step (i,j) = if i < j then (i,j - i) else (i - j,j)++-- > mos_unfold (5,7)  == [(5,7),(5,2),(3,2),(1,2)]+-- > mos_unfold (41,17) == [(41,17),(24,17),(7,17),(7,10),(7,3),(4,3),(1,3),(1,2)]+mos_unfold :: (Ord b, Num b) => (b, b) -> [(b, b)]+mos_unfold x =+  let y = mos_step x+  in if Tuple.t2_sum y == 3 then [x,y] else x : mos_unfold y++mos_verify :: Integral a => a -> a -> Bool+mos_verify p g =+  let x = if g > (p `div` 2) then p `mod` g else g+  in x `elem` gen_coprime p++-- > mos 12 5 == [(5,7),(5,2),(3,2),(1,2)]+mos :: (Ord b, Integral b) => b -> b -> [(b, b)]+mos p g = if mos_verify p g then mos_unfold (mos_2 p g) else error "mos?"++-- > mos_seq 12 5 == [[5,7],[5,5,2],[3,2,3,2,2],[1,2,2,1,2,2,2]]+-- > mos_seq 41 17 !! 4 == [3,3,4,3,4,3,3,4,3,4,3,4]+-- > map length (mos_seq 49 27) == [2,3,5,7,9,11,20,29]+mos_seq :: (Ord b, Integral b) => b -> b -> [[b]]+mos_seq p g =+  let step_f (i,j) = concatMap (\x -> if x == i + j then [i,j] else [x])+      recur_f x l = if null x then [l] else l : recur_f (tail x) (step_f (head x) l)+      ((i0,j0), r) = List.headTail (mos p g)+  in recur_f r [i0,j0]++mos_cell_pp :: (Integral i,Show i) => i -> String+mos_cell_pp x = let s = show x in s ++ genericReplicate (x - genericLength s) '-'++mos_row_pp :: (Integral i,Show i) => [i] -> String+mos_row_pp = concatMap mos_cell_pp++mos_tbl_pp :: (Integral i,Show i) => [[i]] -> [String]+mos_tbl_pp = map mos_row_pp++-- > mos_tbl_wr (mos_seq 49 27)+mos_tbl_wr :: (Integral i,Show i) => [[i]] -> IO ()+mos_tbl_wr = putStrLn . unlines . mos_tbl_pp++-- * Mos/Log++mos_recip_seq :: Double -> [(Int,Double)]+mos_recip_seq x = let y = truncate x in (y,x) : mos_recip_seq (recip (x - fromIntegral y))++-- > take 3 (mos_log (5/4)) == [(3,3.10628371950539),(9,9.408778735385603),(2,2.4463112031908785)]+mos_log :: Double -> [(Int,Double)]+mos_log r = mos_recip_seq (recip (logBase 2 r))++-- > take 9 (mos_log_kseq 1.465571232) == [1,1,4,2,1,3,1,6,2]+mos_log_kseq :: Double -> [Int]+mos_log_kseq = map fst . mos_log++-- * Stern-Brocot Tree++data SBT_DIV = NIL | LHS | RHS deriving (Show)+type Sbt_Node = (SBT_DIV,Rat,Rat,Rat)++sbt_step :: Sbt_Node -> [Sbt_Node]+sbt_step (_,l,m,r) = [(LHS,l,rat_mediant l m, m),(RHS,m,rat_mediant m r,r)]++-- sbt = stern-brocot tree+sbt_root :: Sbt_Node+sbt_root = (NIL,(0,1),(1,1),(1,0))++sbt_half :: Sbt_Node+sbt_half = (NIL,(0,1),(1,2),(1,1))++-- > sbt_from sbt_root+sbt_from :: Sbt_Node -> [[Sbt_Node]]+sbt_from = iterate (concatMap sbt_step) . return++sbt_k_from :: Int -> Sbt_Node -> [[Sbt_Node]]+sbt_k_from k = take k . sbt_from++sbt_node_to_edge :: Sbt_Node -> String+sbt_node_to_edge (dv,l,m,r) =+  let edge_pp p q = printf "\"%s\" -- \"%s\"" (rat_pp p) (rat_pp q)+  in case dv of+       NIL -> ""+       LHS -> edge_pp r m+       RHS -> edge_pp l m++sbt_node_elem :: Sbt_Node -> [Rat]+sbt_node_elem (dv,l,m,r) =+  case dv of+    NIL -> [l,m,r]+    _ -> [m]++sbt_dot :: [Sbt_Node] -> [String]+sbt_dot n =+  let e = map sbt_node_to_edge n+  in concat [["graph {","node [shape=plain]"],e,["}"]]++-- * M-Gen++(^.) :: Rational -> Int -> Rational+(^.) = (^)++r_normalise :: [Rational] -> [Rational]+r_normalise = nub . sortOn Tuning.fold_ratio_to_octave_err++-- | (ratio,multiplier,steps)+type M_Gen = (Rational,Rational,Int)++m_gen_unfold :: M_Gen -> [Rational]+m_gen_unfold (r,m,n) = take n (iterate (* m) r)++m_gen_to_r :: [M_Gen] -> [Rational]+m_gen_to_r = r_normalise . concatMap m_gen_unfold++-- * M3-Gen++-- | (ratio,M3-steps)+type M3_Gen = (Rational,Int)++m3_to_m :: M3_Gen -> M_Gen+m3_to_m (r,n) = (r,3,n)++-- > map m3_gen_unfold [(3,4),(21/9,4),(15/9,4),(35/9,3),(21/5,4),(27/5,3)]+m3_gen_unfold :: M3_Gen -> [Rational]+m3_gen_unfold = m_gen_unfold . m3_to_m++m3_gen_to_r :: [M3_Gen] -> [Rational]+m3_gen_to_r = r_normalise . concatMap m3_gen_unfold++-- * Scala++r_to_scale :: String -> String -> [Rational] -> Scala.Scale+r_to_scale nm dsc r =+  let r' = map Tuning.fold_ratio_to_octave_err (tail r) ++ [2]+  in if r !! 0 /= 1 || not (List.is_ascending r')+     then error "r_to_scale?"+     else (nm,dsc,length r,map Right r')++ew_scl_find_r :: [Rational] -> [Scala.Scale] -> [String]+ew_scl_find_r r =+  let set_eq x y = sort x == sort y+      r' = map Tuning.fold_ratio_to_octave_err r+  in if head r' /= 1+     then error "ew_scl_find_r?: r'0 /= 1"+     else map Scala.scale_name . Scala.scl_find_ji set_eq (r' ++ [2])++-- * <http://anaphoria.com/1-3-5-7-9Genus.pdf>++ew_1357_3_gen :: [M3_Gen]+ew_1357_3_gen = [(3,4),(21/9,4),(15/9,4),(35/9,3),(21/5,4),(27/5,3)]++{- | P.3 7-limit {Scala=nil}++> db <- Scala.scl_load_db+> ew_scl_find_r (1 : ew_1357_3_r) db+-}+ew_1357_3_r :: [Rational]+ew_1357_3_r = r_normalise (concatMap m3_gen_unfold ew_1357_3_gen)++ew_1357_3_scl :: Scala.Scale+ew_1357_3_scl = r_to_scale "ew_1357_3" "EW, 1-3-5-7-9Genus.pdf, P.3" (1 : ew_1357_3_r)++-- * <http://anaphoria.com/earlylattices12.pdf>++{- | P.7 11-limit {Scala=nil}++> ew_scl_find_r ew_el12_7_r db+-}+ew_el12_7_r :: [Rational]+ew_el12_7_r = [1,5/(7*11),1/7,7*11,7*11*11/5,11,5/7,1/11,7*11*11,1/(7*11),11*11,7*11/5]++ew_el12_7_scl :: Scala.Scale+ew_el12_7_scl = r_to_scale "ew_el12_7" "EW, earlylattices12.pdf, P.7" ew_el12_7_r++{- | P.9 7-limit {Scala=wilson_class}++> ew_scl_find_r ew_el12_9_r db+-}+ew_el12_9_r :: [Rational]+ew_el12_9_r = [1,5*5/3,7/(5*5),7/3,5,1/3,7/5,5*7/3,1/5,5/3,7,7/(3*5)]++--ew_el12_9_scl :: Scala.Scale+--ew_el12_9_scl = r_to_scale "ew_el12_9" "EW, earlylattices12.pdf, P.9" ew_el12_9_r++{- | P.12 11-limit {Scala=nil}++> ew_scl_find_r ew_el12_12_r db+-}+ew_el12_12_r :: [Rational]+ew_el12_12_r = [1,3*3*5/11,3/11,7/3,5,7/11,3*5/11,5*7/3,7/(3*3),5*7/11,7/(3*11),3*5]++ew_el12_12_scl :: Scala.Scale+ew_el12_12_scl = r_to_scale "ew_el12_12" "EW, earlylattices12.pdf, P.12" ew_el12_12_r++-- * <http://anaphoria.com/earlylattices22.pdf>++{- | P.2 11-limit {Scala=wilson_l4}++> ew_scl_find_r ew_el22_2_r db+-}+ew_el22_2_r :: [Rational]+ew_el22_2_r =+  [1,7*7/3,3*7/5,5/(3*3),1/7,7/3,3/5,5,5*7/(3*3*3),1/3,7*7/(3*3)+  ,7/5,5*7/3,3,7/(3*3),1/5,5/3,3/7,7,3*3/5,7/(3*5),5*7/(3*3)]++{- | P.3 11-limit {Scala=wilson_l5}++> ew_scl_find_r ew_el22_3_r db+-}+ew_el22_3_r :: [Rational]+ew_el22_3_r =+  [1,7*7/3,7*11/(3*3),3/11,1/7,7/3,3/5,5,7/11,1/3,7*7/(3*3)+  ,7/5,5*7/3,3,7/(3*3),1/5,5/3,3/7,7,11/3,7/(3*5),5*7/(3*3)]++{- | P.4 11-limit {Scala=wilson_l3}++> ew_scl_find_r ew_el22_4_r db+-}+ew_el22_4_r :: [Rational]+ew_el22_4_r =+  [1,3*11,3*7/5,5*7,3*3,7/3,3/5,5,7/11,3*7,11+  ,7/5,5*7/3,3,7/(3*3),1/5,3*5*7,3*3*3,7,3*3/5,3*5,3*7/11]++{- | P.5 11-limit {Scala=wilson_l1}++> ew_scl_find_r ew_el22_5_r db+-}+ew_el22_5_r :: [Rational]+ew_el22_5_r =+  [1,3*11,3*7/5,5*7,3*3,7/3,7*11,5,3*5*11,3*7,11+  ,7/5,3*7*11/5,3,3*3*11,7*11/3,3*11/5,5*11,7,3*7*11,3*5,7*11/5]++{- | P.6 11-limit {Scala=wilson_l2}++> ew_scl_find_r ew_el22_6_r db+-}+ew_el22_6_r :: [Rational]+ew_el22_6_r =+  [1,7*7/3,7*11/(3*3),11/5,3*3,7/3,7*11,5,7*11/(3*5),1/3,11+  ,7*11/(3*3*3),5*7/3,3,11/7,7*11/3,5/3,7*11/(3*3*5),7,11/3,3*5,7*11/5]++-- * <http://anaphoria.com/diamond.pdf>++ew_diamond_mk :: [Integer] -> [Rational]+ew_diamond_mk u = r_normalise [x % y | x <- u, y <- u]++-- > m3_gen_to_r ew_diamond_12_gen == ew_diamond_12_r+ew_diamond_12_gen :: [M3_Gen]+ew_diamond_12_gen =+  [(1/(3^.2),5),(5/(3^.2),3),(7/(3^.2),3),(11/(3^.2),3)+  ,(1/5,3),(1/7,3),(1/11,3)+  ,(5/7,1),(5/11,1),(7/5,1),(7/11,1),(11/5,1),(11/7,1)]++{- | P.7 & P.12 11-limit {Scala=partch_29}++1,3,5,7,9,11 diamond++> ew_scl_find_r ew_diamond_12_r db -- partch_29+-}+ew_diamond_12_r :: [Rational]+ew_diamond_12_r = ew_diamond_mk [1,3,5,7,9,11]++{- | P.10 & P.13 13-limit {Scala=novaro15}++1,3,5,7,9,11,13,15 diamond++> ew_scl_find_r ew_diamond_13_r db -- novaro15+-}+ew_diamond_13_r :: [Rational]+ew_diamond_13_r = ew_diamond_mk [1,3,5,7,9,11,13,15]++-- * <http://anaphoria.com/hel.pdf>++hel_r_asc :: (Integer,Integer) -> [Rational]+hel_r_asc (n,d) = n%d : hel_r_asc (n+1,d+1)++type HEL = ([Rational],[Rational])++-- | P.6+hel_1_i :: HEL+hel_1_i =+  let i = take 6 (hel_r_asc (7,6))+  in (take 5 i,take 5 (List.rotate_left 2 i))++-- | P.6+hel_2_i :: HEL+hel_2_i =+  let i = take 10 (hel_r_asc (9,8))+  in (take 8 (List.rotate_left 3 (tail i))+     ,take 7 i)++-- | P.10+hel_3_i :: HEL+hel_3_i =+  let i = take 16 (hel_r_asc (15,14))+  in (take 13 (List.rotate_left 6 (take 14 i)),take 14 (tail i))++hel_r :: HEL -> [[Rational]]+hel_r (p,q) =+  let i_to_r = scanl (*) 1+  in [i_to_r p,i_to_r q,r_normalise (concat [i_to_r p,i_to_r q])]++{- | P.12 {Scala=nil}++22-tone 23-limit Evangalina tuning (2001)++> ew_scl_find_r ew_hel_12_r db+-}+ew_hel_12_r :: [Rational]+ew_hel_12_r =+  [1,3*3*3*5,13/3,5/(3*3),3*3,7/3,11/(3*3),5,3*3*3*3,1/3,11+  ,3*3*5,17/3,3,3*3*3*3*5,13,5/3,3*3*3,7,11/3,3*5,23/3]++ew_hel_12_scl :: Scala.Scale+ew_hel_12_scl = r_to_scale "ew_hel_12" "EW, hel.pdf, P.12" ew_hel_12_r++-- * <http://anaphoria.com/HexanyStellatesExpansions.pdf>++-- > she_div "ABCD" == [["BCD","A"],["ACD","B"],["ABD","C"],["ABC","D"]]+she_div :: Eq a => [a] -> [[[a]]]+she_div x =+  let f = (== [1,length x - 1]) . sort . map length+  in map (sortOn (Down . length)) (filter f (Set.partitions x))++-- > she_div_r [1,3,5,7] == [105,35/3,21/5,15/7]+she_div_r :: [Rational] -> [Rational]+she_div_r =+  let f x =+        case x of+          [[a,b,c],[d]] -> (a * b * c) / d+          _ -> error "she_div?"+  in map f . she_div++-- > she_mul_r [1,3,5,7] == [1,3,5,7,9,15,21,25,35,49]+she_mul_r :: [Rational] -> [Rational]+she_mul_r r = [x * y | x <- r,y <- r,x <= y]++{- | she = Stellate Hexany Expansions, P.10 {Scala=stelhex1,stelhex2,stelhex5,stelhex6}++> she [1,3,5,7] == [1,21/20,15/14,35/32,9/8,5/4,21/16,35/24,3/2,49/32,25/16,105/64,7/4,15/8]+> mapM (flip ew_scl_find_r db . she) [[1,3,5,7],[1,3,5,9],[1,3,7,9],[1,3,5,11]]+> ew_scl_find_r (she [1,(5*7)/(3*3),1/(3 * 5),1/3]) db -- NIL+-}+she :: [Rational] -> [Rational]+she r = nub (sort (map Tuning.fold_ratio_to_octave_err (she_mul_r r ++ she_div_r r)))++-- * <http://anaphoria.com/meru.pdf>++-- > map (every_nth "abcdef") [1..3] == ["abcdef","ace","ad"]+every_nth :: [t] -> Int -> [t]+every_nth l k =+  case l of+    [] -> []+    x:_ -> x : every_nth (drop k l) k++meru :: Num n => [[n]]+meru =+  let f xs = zipWith (+) (0 : xs) (xs ++ [0])+  in iterate f [1]++-- > meru_k 13+meru_k :: Num n => Int -> [[n]]+meru_k k = take k meru++-- > map (sum . meru_1) [1 .. 13] == [1,1,2,3,5,8,13,21,34,55,89,144,233]+meru_1 :: Num n => Int -> [n]+meru_1 k = zipWith (flip (Safe.atDef 0)) [0..] (reverse (meru_k k))++-- > take 13 meru_1_direct == [1,1,2,3,5,8,13,21,34,55,89,144,233]+meru_1_direct :: Num n => [n]+meru_1_direct = tail OEIS.a000045++-- | Meru 2 = META-PELOG+--+-- > map (sum . meru_2) [1 .. 14] == [1,1,1,2,3,4,6,9,13,19,28,41,60,88]+meru_2 :: Num n => Int -> [n]+meru_2 k = zipWith (flip (Safe.atDef 0)) [0..] (every_nth (reverse (meru_k k)) 2)++-- > take 14 meru_2_direct == [1,1,1,2,3,4,6,9,13,19,28,41,60,88]+meru_2_direct :: Num n => [n]+meru_2_direct = OEIS.a000930++-- | meru_3 = META-SLENDRO+meru_3 :: Num n => Int -> [[n]]+meru_3 k =+  let f t = zipWith (flip (Safe.atDef 0)) [0,2..] t+      t0 = reverse (meru_k k)+      t1 = map tail t0+  in [f t0,f t1]++-- > map sum (meru_3_seq 13) == [1,0,1,1,1,2,2,3,4,5,7,9,12,16,21,28,37,49,65,86,114,151,200,265,351,465]+meru_3_seq :: Num n => Int -> [[n]]+meru_3_seq k = concatMap meru_3 [1 .. k]++-- > take 26 meru_3_direct == [1,0,1,1,1,2,2,3,4,5,7,9,12,16,21,28,37,49,65,86,114,151,200,265,351,465]+meru_3_direct :: Num n => [n]+meru_3_direct = drop 3 OEIS.a000931++-- > map (sum . meru_4) [1 .. 13] == [1,1,1,1,2,3,4,5,7,10,14,19,26]+meru_4 :: Num n => Int -> [n]+meru_4 k = zipWith (flip (Safe.atDef 0)) [0..] (every_nth (reverse (meru_k k)) 3)++-- > take 31 meru_4_direct == map (sum . meru_4) [1 .. 31]+meru_4_direct :: Num n => [n]+meru_4_direct = tail OEIS.a003269++-- > map meru_5 [1..4]+meru_5 :: Num n => Int -> [[n]]+meru_5 k =+  let f t = zipWith (flip (Safe.atDef 0)) [0,3..] t+      t0 = reverse (meru_k k)+  in map (\n -> f (map (drop n) t0)) [0 .. 2]++-- > map sum (meru_5_seq 13)+meru_5_seq :: Num n => Int -> [[n]]+meru_5_seq k = concatMap meru_5 [1 .. k]++-- > take 39 meru_5_direct == map sum (meru_5_seq 13)+meru_5_direct :: Num n => [n]+meru_5_direct = OEIS.a017817++-- > map (sum . meru_6) [1 .. 21] == [1,1,1,1,1,2,3,4,5,6,8,11,15,20,26,34,45,60,80,106,140]+meru_6 :: Num n => Int -> [n]+meru_6 k = zipWith (flip (Safe.atDef 0)) [0..] (every_nth (reverse (meru_k k)) 4)++-- > take 21 meru_6_direct == map (sum . meru_6) [1 .. 21]+meru_6_direct :: Num n => [n]+meru_6_direct = OEIS.a003520++-- > take 26 meru_7_direct == [0,1,0,1,0,1,1,1,2,1,3,2,4,4,5,7,7,11,11,16,18,23,29,34,45,52]+meru_7_direct :: Num n => [n]+meru_7_direct = OEIS.a001687++-- * <http://anaphoria.com/mos.pdf>++{- | P.13, tanabe {Scala=chin_7}++> ew_scl_find_r ew_mos_13_tanabe_r db+-}+ew_mos_13_tanabe_r :: [Rational]+ew_mos_13_tanabe_r = [1,9/8,81/64,4/3,3/2,27/16,243/128]++-- * <http://anaphoria.com/novavotreediamond.pdf> (Novaro)++ew_novarotreediamond_1 :: ([[Rational]],[[Rational]])+ew_novarotreediamond_1 =+  let rem_oct x = if last x /= 2 then error "rem_oct?" else List.drop_last x+      add_oct x = if last x >= 2 then error "add_oct?" else x ++ [2]+      r_to_i = List.d_dx_by (/) . add_oct+      i_to_r = rem_oct . scanl (*) 1+      r_0 = [1,5/4,4/3,3/2,5/3,7/4]+      i_0 = r_to_i r_0+      i = List.rotations i_0+  in (i,map i_to_r i)++{- | P.1 {Scala=nil}++23-tone 7-limit (2004)++> ew_scl_find_r ew_novarotreediamond_1_r db+-}+ew_novarotreediamond_1_r :: [Rational]+ew_novarotreediamond_1_r = r_normalise (concat (snd ew_novarotreediamond_1))++ew_novarotreediamond_1_scl :: Scala.Scale+ew_novarotreediamond_1_scl = r_to_scale "ew_novarotreediamond_1" "EW, novavotreediamond.pdf, P.1" ew_novarotreediamond_1_r++-- * <http://anaphoria.com/Pelogflute.pdf>++{- | P.2 {Scala=nil}++9-tone Pelog cycle (1988)++> ew_scl_find_r ew_Pelogflute_2_r db+-}+ew_Pelogflute_2_r :: Fractional n => [n]+ew_Pelogflute_2_r = [1,16/15,64/55,5/4,4/3,16/11,8/5,128/75,20/11]++ew_Pelogflute_2_scl :: Scala.Scale+ew_Pelogflute_2_scl = r_to_scale "ew_Pelogflute_2" "EW, Pelogflute.pdf, P.2" ew_Pelogflute_2_r+++-- * <http://anaphoria.com/xen1.pdf>++-- | P.9, Fig. 3+xen1_fig3 :: (Sbt_Node,Int)+xen1_fig3 = ((NIL,(1,3),(2,5),(1,2)),5)++-- | P.9, Fig. 4+xen1_fig4 :: (Sbt_Node,Int)+xen1_fig4 = ((NIL,(2,5),(5,12),(3,7)),5)++-- * <http://anaphoria.com/xen3b.pdf>++-- | P.3 Turkisk Baglama Scale {11-limit, Scala=nil}+ew_xen3b_3_gen :: [(Rational,Int)]+ew_xen3b_3_gen = [(1/(3^.6),12),(1/11,2),(5/3,3)]++ew_xen3b_3_r :: [Rational]+ew_xen3b_3_r = m3_gen_to_r ew_xen3b_3_gen++ew_xen3b_3_scl :: Scala.Scale+ew_xen3b_3_scl = r_to_scale "ew_xen3b_3" "EW, xen3b.pdf, P.3" ew_xen3b_3_r++-- > map length xen3b_9_i == [5,7,12,19,31]+xen3b_9_i :: [[Rational]]+xen3b_9_i =+  [[6/5,                                             10/9,                          9/8,                           6/5,                                             10/9]+  ,[16/15,9/8,                                       10/9,                          9/8,                           16/15,9/8,                                       10/9]+  ,[16/15,135/128,16/15,                             25/24,16/15,                   16/15,135/128,                 16/15,135/128,16/15,                             25/24,16/15]+  ,[28/27,36/35,135/128,28/27,36/35,                 25/24,28/27,36/35,             28/27,36/35,135/128,           28/27,36/35,135/128,28/27,36/35,                 25/24,28/27,36/35]+  ,[64/63,49/48,36/35,45/44,33/32,64/63,49/48,36/35, 45/44,55/54,64/63,49/48,36/35, 64/63,49/48,36/35,45/44,33/32, 64/63,49/48,36/35,45/44,33/32,64/63,49/48,36/35, 45/44,55/54,64/63,49/48,36/35]]++{- | P.9 {SCALA 5=nil 7=ptolemy_idiat 12=nil 19=wilson2 31=wilson_31}++> mapM ew_scl_find_r xen3b_9_r db+-}+xen3b_9_r :: [[Rational]]+xen3b_9_r = map (List.drop_last . scanl (*) 1) xen3b_9_i++-- > map length xen3b_13_i == [5,7,12,17,22]+xen3b_13_i :: [[Rational]]+xen3b_13_i =+  [[7/6,                           8/7,                     9/8,                     7/6,                           8/7]+  ,[28/27,9/8,                     8/7,                     9/8,                     28/27,9/8,                     8/7]+  ,[28/27,243/224,28/27,           10/9,36/35,              28/27,243/224,           28/27,243/224,28/27,           10/9,36/35]+  ,[28/27,36/35,135/128,28/27,     36/35,175/162,36/35,     28/27,36/35,135/128,     28/27,36/35,135/128,28/27,     36/35,175/162,36/35]+  ,[28/27,36/35,25/24,81/80,28/27, 36/35,25/24,28/27,36/35, 28/27,36/35,25/24,81/80, 28/27,36/35,25/24,81/80,28/27, 36/35,25/24,28/27,36/35]]++-- | P.13 {SCALA 5=slendro5_2 7=ptolemy_diat2 12=nil 17=nil 22=wilson7_4}+xen3b_13_r :: [[Rational]]+xen3b_13_r = map (List.drop_last . scanl (*) 1) xen3b_13_i++-- * <http://anaphoria.com/xen3bappendix.pdf>++{- | PP.1-2 {SCALA: 22=wilson7_4}++17,31,41 lattices from XEN3B (1975)+-}+ew_xen3b_apx_gen :: [(Int,[M3_Gen])]+ew_xen3b_apx_gen =+  [(17,[(1/729,12)+       ,(5/3,3)+       ,(11,2)])+  ,(31,[(1/3,5)+       ,(5,2),(1/(5*(3^.2)),5)+       ,(7/(3^.4),5),(1/(7*(3^.4)),5)+       ,(1/11,5)+       ,((1/3)*(1/7)*5,2)+       ,((1/(7*(3^.3))) * 5,2)])+  ,(41,[(1/(3^.6),12)+       ,(5/(3^.3),5),(1/(5*(3^.2)),5)+       ,(7/(3^.4),7),(1/(7*(3^.3)),7)+       ,(11,5)])+  ,(22,[(1/3,5)+       ,(5/(3^.3),5),(1/(5*(3^.2)),5)+       ,(7/(3^.4),5)+       ,(7/(3^.3)*5,2)])]++ew_xen3b_apx_r :: [(Int,[Rational])]+ew_xen3b_apx_r =+  let f (k,g) = (k,r_normalise (concatMap m3_gen_unfold g))+  in map f ew_xen3b_apx_gen++-- * <http://anaphoria.com/xen456.pdf>++ew_xen456_7_gen :: [M3_Gen]+ew_xen456_7_gen = [(25/24,4),(5/3,4),(4/3,4),(16/15,4),(32/25,3)]++{- P.7 {Scala=wilson1}++19-tone "A Scale for Scott" (1976)++> ew_scl_find_r ew_xen456_7_r db -- wilson1+-}+ew_xen456_7_r :: [Rational]+ew_xen456_7_r = m3_gen_to_r ew_xen456_7_gen++ew_xen456_9_gen :: [M3_Gen]+ew_xen456_9_gen =+  [(1/(3^.3),4)+  ,(1/(5*(3^.2)),3)+  ,(1/(7*3),3)+  ,(1/11,3)+  ,(5/(11*3),4)+  ,(7/11,2)]++{- | P.9 {Scala=nil ; Scala:Rot=wilson11}++19-tone scale for the Clavichord-19 (1976)++> ew_scl_find_r ew_xen456_9_r db++> import qualified Music.Theory.List as List {- hmt -}+> Scala.scl_find_ji List.is_subset ew_xen456_9_r db -- NIL+-}+ew_xen456_9_r :: [Rational]+ew_xen456_9_r = m3_gen_to_r ew_xen456_9_gen++ew_xen456_9_scl :: Scala.Scale+ew_xen456_9_scl = r_to_scale "ew_xen456_9" "EW, xen456.pdf, P.9" ew_xen456_9_r++-- * Gems++{- | <http://wilsonarchives.blogspot.com/2010/10/scale-for-rod-poole.html>++13-limit 22-tone scale {Scala=nil}++> ew_scl_find_r ew_poole_r db+-}+ew_poole_r :: [Rational]+ew_poole_r =+  [1,11*3,7*3/5,13/3,3*3,7/3,11/(3*3),5,7/11,1/3+  ,11,7/5,13/(3*3),3,7/(3*3),11/(3*3*3),5/3,3*3*3,7,11/3,5*3,7*3/11]++ew_poole_scl :: Scala.Scale+ew_poole_scl = r_to_scale "ew_poole" "EW, 2010/10/scale-for-rod-poole.html" ew_poole_r++{- | <http://wilsonarchives.blogspot.com/2014/05/an-11-limit-centaur-implied-in-wilson.html>++11-limit 17-tone scale {Scala=wilcent17}++> ew_scl_find_r ew_centaur17_r db+-}+ew_centaur17_r :: [Rational]+ew_centaur17_r = [1,11/(3*7),11/5,3*3,7/3,11/(3*3),5,1/3,11,11/(3*5),3,11/7,11/(3*3*3),5/3,7,11/3,3*5]++{- | <http://wilsonarchives.blogspot.com/2018/03/an-unusual-22-tone-7-limit-tuning.html>++7-limit 22-tone scale {Scala=nil}++> ew_scl_find_r ew_two_22_7_r db+-}+ew_two_22_7_r :: [Rational]+ew_two_22_7_r =+  [1,9/35,1/15,35,9,7/3,3/5,315,245/3,21,27/5+  ,7/5,735,189,49,63/5,5/3,3/7,1/9,1/35,15,35/9]++ew_two_22_7_scl :: Scala.Scale+ew_two_22_7_scl = r_to_scale "ew_two_22_7" "EW, 2018/03/an-unusual-22-tone-7-limit-tuning.html" ew_two_22_7_r++-- * Db++{- | Scales /not/ present in the standard scala file set.++> mapM_ (Scala.scale_wr_dir "/home/rohan/sw/hmt/data/scl/") ew_scl_db+> map Scala.scale_name ew_scl_db+-}+ew_scl_db :: [Scala.Scale]+ew_scl_db =+  [ew_1357_3_scl+  ,ew_el12_7_scl+  ,ew_el12_12_scl+  ,ew_hel_12_scl+  ,ew_novarotreediamond_1_scl+  ,ew_Pelogflute_2_scl+  ,ew_xen3b_3_scl+  ,ew_xen456_9_scl+  ,ew_poole_scl+  ,ew_two_22_7_scl+  ]++-- Local Variables:+-- truncate-lines:t+-- End:
− Music/Theory/Tuple.hs 
@@ -1,319 +0,0 @@--- | Tuple functions.------ Uniform tuples have types 'T2', 'T3' etc. and functions names are--- prefixed @t2_@ etc.------ Heterogenous tuples (products) are prefixed @p2_@ etc.-module Music.Theory.Tuple where---- * P2 (2-product)--p2_swap :: (s,t) -> (t,s)-p2_swap (i,j) = (j,i)---- * T2 (2-tuple, regular)---- | Uniform two-tuple.-type T2 a = (a,a)--t2_from_list :: [t] -> T2 t-t2_from_list l = case l of {[p,q] -> (p,q);_ -> error "t2_from_list"}--t2_to_list :: T2 a -> [a]-t2_to_list (i,j) = [i,j]--t2_swap :: T2 t -> T2 t-t2_swap = p2_swap--t2_map :: (p -> q) -> T2 p -> T2 q-t2_map f (p,q) = (f p,f q)--t2_zipWith :: (p -> q -> r) -> T2 p -> T2 q -> T2 r-t2_zipWith f (p,q) (p',q') = (f p p',f q q')--t2_infix :: (a -> a -> b) -> T2 a -> b-t2_infix f (i,j) = i `f` j---- | Infix 'mappend'.------ > t2_join ([1,2],[3,4]) == [1,2,3,4]-t2_join :: Monoid m => T2 m -> m-t2_join = t2_infix mappend--t2_concat :: [T2 [a]] -> T2 [a]-t2_concat = t2_map mconcat . unzip--t2_sort :: Ord t => (t,t) -> (t,t)-t2_sort (p,q) = (min p q,max p q)---- * P3 (3-product)---- | Left rotation.------ > p3_rotate_left (1,2,3) == (2,3,1)-p3_rotate_left :: (s,t,u) -> (t,u,s)-p3_rotate_left (i,j,k) = (j,k,i)--p3_fst :: (a,b,c) -> a-p3_fst (a,_,_) = a--p3_snd :: (a,b,c) -> b-p3_snd (_,b,_) = b--p3_third :: (a,b,c) -> c-p3_third (_,_,c) = c---- * T3 (3 triple, regular)--type T3 a = (a,a,a)--t3_from_list :: [t] -> T3 t-t3_from_list l = case l of {[p,q,r] -> (p,q,r);_ -> error "t3_from_list"}--t3_to_list :: T3 a -> [a]-t3_to_list (i,j,k) = [i,j,k]--t3_rotate_left :: T3 t -> T3 t-t3_rotate_left = p3_rotate_left--t3_fst :: T3 t -> t-t3_fst = p3_fst--t3_snd :: T3 t -> t-t3_snd = p3_snd--t3_third :: T3 t -> t-t3_third = p3_third--t3_map :: (p -> q) -> T3 p -> T3 q-t3_map f (p,q,r) = (f p,f q,f r)--t3_zipWith :: (p -> q -> r) -> T3 p -> T3 q -> T3 r-t3_zipWith f (p,q,r) (p',q',r') = (f p p',f q q',f r r')--t3_infix :: (a -> a -> a) -> T3 a -> a-t3_infix f (i,j,k) = (i `f` j) `f` k--t3_join :: T3 [a] -> [a]-t3_join = t3_infix (++)---- * P4 (4-product)--p4_fst :: (a,b,c,d) -> a-p4_fst (a,_,_,_) = a--p4_snd :: (a,b,c,d) -> b-p4_snd (_,b,_,_) = b--p4_third :: (a,b,c,d) -> c-p4_third (_,_,c,_) = c--p4_fourth :: (a,b,c,d) -> d-p4_fourth (_,_,_,d) = d---- * T4 (4-tuple, regular)--type T4 a = (a,a,a,a)--t4_from_list :: [t] -> T4 t-t4_from_list l = case l of {[p,q,r,s] -> (p,q,r,s); _ -> error "t4_from_list"}--t4_to_list :: T4 t -> [t]-t4_to_list (p,q,r,s) = [p,q,r,s]--t4_fst :: T4 t -> t-t4_fst = p4_fst--t4_snd :: T4 t -> t-t4_snd = p4_snd--t4_third :: T4 t -> t-t4_third = p4_third--t4_fourth :: T4 t -> t-t4_fourth = p4_fourth--t4_map :: (p -> q) -> T4 p -> T4 q-t4_map f (p,q,r,s) = (f p,f q,f r,f s)--t4_zipWith :: (p -> q -> r) -> T4 p -> T4 q -> T4 r-t4_zipWith f (p,q,r,s) (p',q',r',s') = (f p p',f q q',f r r',f s s')--t4_infix :: (a -> a -> a) -> T4 a -> a-t4_infix f (i,j,k,l) = ((i `f` j) `f` k) `f` l--t4_join :: T4 [a] -> [a]-t4_join = t4_infix (++)---- * P5 (5-product)--p5_fst :: (a,b,c,d,e) -> a-p5_fst (a,_,_,_,_) = a--p5_snd :: (a,b,c,d,e) -> b-p5_snd (_,b,_,_,_) = b--p5_third :: (a,b,c,d,e) -> c-p5_third (_,_,c,_,_) = c--p5_fourth :: (a,b,c,d,e) -> d-p5_fourth (_,_,_,d,_) = d--p5_fifth :: (a,b,c,d,e) -> e-p5_fifth (_,_,_,_,e) = e--p5_from_list :: (t -> t1, t -> t2, t -> t3, t -> t4, t -> t5) -> [t] -> (t1,t2,t3,t4,t5)-p5_from_list (f1,f2,f3,f4,f5) l =-  case l of-    [c1,c2,c3,c4,c5] -> (f1 c1,f2 c2,f3 c3,f4 c4,f5 c5)-    _ -> error "p5_from_list"---p5_to_list :: (t1 -> t, t2 -> t, t3 -> t, t4 -> t, t5 -> t) -> (t1, t2, t3, t4, t5) -> [t]-p5_to_list (f1,f2,f3,f4,f5) (c1,c2,c3,c4,c5) = [f1 c1,f2 c2,f3 c3,f4 c4,f5 c5]---- * T5 (5-tuple, regular)--type T5 a = (a,a,a,a,a)--t5_from_list :: [t] -> T5 t-t5_from_list l = case l of {[p,q,r,s,t] -> (p,q,r,s,t); _ -> error "t5_from_list"}--t5_to_list :: T5 t -> [t]-t5_to_list (p,q,r,s,t) = [p,q,r,s,t]--t5_map :: (p -> q) -> T5 p -> T5 q-t5_map f (p,q,r,s,t) = (f p,f q,f r,f s,f t)--t5_fst :: T5 t -> t-t5_fst (p,_,_,_,_) = p--t5_snd :: T5 t -> t-t5_snd (_,q,_,_,_) = q--t5_fourth :: T5 t -> t-t5_fourth (_,_,_,t,_) = t--t5_fifth :: T5 t -> t-t5_fifth (_,_,_,_,u) = u--t5_infix :: (a -> a -> a) -> T5 a -> a-t5_infix f (i,j,k,l,m) = (((i `f` j) `f` k) `f` l) `f` m--t5_join :: T5 [a] -> [a]-t5_join = t5_infix (++)---- * P6 (6-product)--p6_fst :: (a,b,c,d,e,f) -> a-p6_fst (a,_,_,_,_,_) = a--p6_snd :: (a,b,c,d,e,f) -> b-p6_snd (_,b,_,_,_,_) = b--p6_third :: (a,b,c,d,e,f) -> c-p6_third (_,_,c,_,_,_) = c--p6_fourth :: (a,b,c,d,e,f) -> d-p6_fourth (_,_,_,d,_,_) = d--p6_fifth :: (a,b,c,d,e,f) -> e-p6_fifth (_,_,_,_,e,_) = e--p6_sixth :: (a,b,c,d,e,f) -> f-p6_sixth (_,_,_,_,_,f) = f---- * T6 (6-tuple, regular)--type T6 a = (a,a,a,a,a,a)--t6_from_list :: [t] -> T6 t-t6_from_list l = case l of {[p,q,r,s,t,u] -> (p,q,r,s,t,u);_ -> error "t6_from_list"}--t6_to_list :: T6 t -> [t]-t6_to_list (p,q,r,s,t,u) = [p,q,r,s,t,u]--t6_map :: (p -> q) -> T6 p -> T6 q-t6_map f (p,q,r,s,t,u) = (f p,f q,f r,f s,f t,f u)---- * T7 (7-tuple, regular)--type T7 a = (a,a,a,a,a,a,a)--t7_to_list :: T7 t -> [t]-t7_to_list (p,q,r,s,t,u,v) = [p,q,r,s,t,u,v]--t7_map :: (p -> q) -> T7 p -> T7 q-t7_map f (p,q,r,s,t,u,v) = (f p,f q,f r,f s,f t,f u,f v)---- * T8 (8-tuple, regular)--type T8 a = (a,a,a,a,a,a,a,a)--t8_to_list :: T8 t -> [t]-t8_to_list (p,q,r,s,t,u,v,w) = [p,q,r,s,t,u,v,w]--t8_map :: (p -> q) -> T8 p -> T8 q-t8_map f (p,q,r,s,t,u,v,w) = (f p,f q,f r,f s,f t,f u,f v,f w)---- * P8 (8-product)--p8_third :: (a,b,c,d,e,f,g,h) -> c-p8_third (_,_,c,_,_,_,_,_) = c---- * T9 (9-tuple, regular)--type T9 a = (a,a,a,a,a,a,a,a,a)--t9_to_list :: T9 t -> [t]-t9_to_list (p,q,r,s,t,u,v,w,x) = [p,q,r,s,t,u,v,w,x]--t9_map :: (p -> q) -> T9 p -> T9 q-t9_map f (p,q,r,s,t,u,v,w,x) = (f p,f q,f r,f s,f t,f u,f v,f w,f x)---- * T10 (10-tuple, regular)--type T10 a = (a,a,a,a,a,a,a,a,a,a)--t10_to_list :: T10 t -> [t]-t10_to_list (p,q,r,s,t,u,v,w,x,y) = [p,q,r,s,t,u,v,w,x,y]--t10_map :: (p -> q) -> T10 p -> T10 q-t10_map f (p,q,r,s,t,u,v,w,x,y) = (f p,f q,f r,f s,f t,f u,f v,f w,f x,f y)---- * T11 (11-tuple, regular)--type T11 a = (a,a,a,a,a,a,a,a,a,a,a)--t11_to_list :: T11 t -> [t]-t11_to_list (p,q,r,s,t,u,v,w,x,y,z) = [p,q,r,s,t,u,v,w,x,y,z]--t11_map :: (p -> q) -> T11 p -> T11 q-t11_map f (p,q,r,s,t,u,v,w,x,y,z) = (f p,f q,f r,f s,f t,f u,f v,f w,f x,f y,f z)---- * T12 (12-tuple, regular)--type T12 t = (t,t,t,t,t,t,t,t,t,t,t,t)--t12_to_list :: T12 t -> [t]-t12_to_list (p,q,r,s,t,u,v,w,x,y,z,a) = [p,q,r,s,t,u,v,w,x,y,z,a]--t12_from_list :: [t] -> T12 t-t12_from_list l =-    case l of-      [p,q,r,s,t,u,v,w,x,y,z,a] -> (p,q,r,s,t,u,v,w,x,y,z,a)-      _ -> error "t12_from_list"---- | 'foldr1' of 't12_to_list'.------ > t12_foldr1 (+) (1,2,3,4,5,6,7,8,9,10,11,12) == 78-t12_foldr1 :: (t -> t -> t) -> T12 t -> t-t12_foldr1 f = foldr1 f . t12_to_list---- | 'sum' of 't12_to_list'.------ > t12_sum (1,2,3,4,5,6,7,8,9,10,11,12) == 78-t12_sum :: Num n => T12 n -> n-t12_sum t =-    let (n1,n2,n3,n4,n5,n6,n7,n8,n9,n10,n11,n12) = t-    in n1 + n2 + n3 + n4 + n5 + n6 + n7 + n8 + n9 + n10 + n11 + n12
− Music/Theory/Unicode.hs 
@@ -1,239 +0,0 @@--- | <http://www.unicode.org/charts/PDF/U1D100.pdf>------ These symbols are in <http://www.gnu.org/software/freefont/>,--- debian=ttf-freefont.-module Music.Theory.Unicode where--import Data.List {- base -}-import Numeric {- base -}--import qualified Text.CSV.Lazy.String as C {- lazy-csv -}--import qualified Music.Theory.IO as T {- hmt -}-import qualified Music.Theory.List as T {- hmt -}-import qualified Music.Theory.Read as T {- hmt -}---- * Non-music---- | Unicode non breaking hypen character.------ > non_breaking_hypen == '‑'-non_breaking_hypen :: Char-non_breaking_hypen = toEnum 0x2011---- | Unicode non breaking space character.------ > non_breaking_space == ' '-non_breaking_space :: Char-non_breaking_space = toEnum 0x00A0---- * Music--type Unicode_Index = Int-type Unicode_Range = (Unicode_Index,Unicode_Index)-type Unicode_Point = (Unicode_Index,String)-type Unicode_Table = [Unicode_Point]---- > putStrLn$ map (toEnum . fst) (concat unicode)-unicode :: [Unicode_Table]-unicode = [accidentals,notes,rests,clefs]---- > putStrLn$ concatMap (unicode_table_hs . flip unicode_table_block tbl) accidentals_rng_set-accidentals_rng_set :: [Unicode_Range]-accidentals_rng_set = [(0x266D,0x266F),(0x1D12A,0x1D133)]---- | UNICODE accidental symbols.------ > let r = "♭♮♯𝄪𝄫𝄬𝄭𝄮𝄯𝄰𝄱𝄲𝄳" in map (toEnum . fst) accidentals == r-accidentals :: Unicode_Table-accidentals =-    [(0x266D,"MUSIC FLAT SIGN")-    ,(0x266E,"MUSIC NATURAL SIGN")-    ,(0x266F,"MUSIC SHARP SIGN")-    ,(0x1D12A,"MUSICAL SYMBOL DOUBLE SHARP")-    ,(0x1D12B,"MUSICAL SYMBOL DOUBLE FLAT")-    ,(0x1D12C,"MUSICAL SYMBOL FLAT UP")-    ,(0x1D12D,"MUSICAL SYMBOL FLAT DOWN")-    ,(0x1D12E,"MUSICAL SYMBOL NATURAL UP")-    ,(0x1D12F,"MUSICAL SYMBOL NATURAL DOWN")-    ,(0x1D130,"MUSICAL SYMBOL SHARP UP")-    ,(0x1D131,"MUSICAL SYMBOL SHARP DOWN")-    ,(0x1D132,"MUSICAL SYMBOL QUARTER TONE SHARP")-    ,(0x1D133,"MUSICAL SYMBOL QUARTER TONE FLAT")]---- > putStrLn$ unicode_table_hs (unicode_table_block notes_rng tbl)-notes_rng :: Unicode_Range-notes_rng = (0x1D15C,0x1D164)---- | UNICODE note duration symbols.------ > let r = "𝅜𝅝𝅗𝅥𝅘𝅥𝅘𝅥𝅮𝅘𝅥𝅯𝅘𝅥𝅰𝅘𝅥𝅱𝅘𝅥𝅲" in map (toEnum . fst) notes == r-notes :: Unicode_Table-notes =-    [(0x1D15C,"MUSICAL SYMBOL BREVE")-    ,(0x1D15D,"MUSICAL SYMBOL WHOLE NOTE")-    ,(0x1D15E,"MUSICAL SYMBOL HALF NOTE")-    ,(0x1D15F,"MUSICAL SYMBOL QUARTER NOTE")-    ,(0x1D160,"MUSICAL SYMBOL EIGHTH NOTE")-    ,(0x1D161,"MUSICAL SYMBOL SIXTEENTH NOTE")-    ,(0x1D162,"MUSICAL SYMBOL THIRTY-SECOND NOTE")-    ,(0x1D163,"MUSICAL SYMBOL SIXTY-FOURTH NOTE")-    ,(0x1D164,"MUSICAL SYMBOL ONE HUNDRED TWENTY-EIGHTH NOTE")]---- > putStrLn$ unicode_table_hs (unicode_table_block rests_rng tbl)-rests_rng :: Unicode_Range-rests_rng = (0x1D13B,0x1D142)---- | UNICODE rest symbols.------ > let r = "𝄻𝄼𝄽𝄾𝄿𝅀𝅁𝅂" in map (toEnum . fst) rests == r-rests :: Unicode_Table-rests =-    [(0x1D13B,"MUSICAL SYMBOL WHOLE REST")-    ,(0x1D13C,"MUSICAL SYMBOL HALF REST")-    ,(0x1D13D,"MUSICAL SYMBOL QUARTER REST")-    ,(0x1D13E,"MUSICAL SYMBOL EIGHTH REST")-    ,(0x1D13F,"MUSICAL SYMBOL SIXTEENTH REST")-    ,(0x1D140,"MUSICAL SYMBOL THIRTY-SECOND REST")-    ,(0x1D141,"MUSICAL SYMBOL SIXTY-FOURTH REST")-    ,(0x1D142,"MUSICAL SYMBOL ONE HUNDRED TWENTY-EIGHTH REST")]---- > map toEnum [0x1D15E,0x1D16D,0x1D16D] == "𝅗𝅥𝅭𝅭"-augmentation_dot :: Unicode_Point-augmentation_dot = (0x1D16D, "MUSICAL SYMBOL COMBINING AUGMENTATION DOT")---- > putStrLn$ unicode_table_hs (unicode_table_block clefs_rng tbl)-clefs_rng :: Unicode_Range-clefs_rng = (0x1D11E,0x1D126)---- | UNICODE clef symbols.------ > let r = "𝄞𝄟𝄠𝄡𝄢𝄣𝄤𝄥𝄦" in map (toEnum . fst) clefs == r-clefs :: Unicode_Table-clefs =-    [(0x1D11E,"MUSICAL SYMBOL G CLEF")-    ,(0x1D11F,"MUSICAL SYMBOL G CLEF OTTAVA ALTA")-    ,(0x1D120,"MUSICAL SYMBOL G CLEF OTTAVA BASSA")-    ,(0x1D121,"MUSICAL SYMBOL C CLEF")-    ,(0x1D122,"MUSICAL SYMBOL F CLEF")-    ,(0x1D123,"MUSICAL SYMBOL F CLEF OTTAVA ALTA")-    ,(0x1D124,"MUSICAL SYMBOL F CLEF OTTAVA BASSA")-    ,(0x1D125,"MUSICAL SYMBOL DRUM CLEF-1")-    ,(0x1D126,"MUSICAL SYMBOL DRUM CLEF-2")]---- > putStrLn$ unicode_table_hs (unicode_table_block tbl notehead_rng)-notehead_rng :: Unicode_Range-notehead_rng = (0x1D143,0x1D15B)---- | UNICODE notehead symbols.------ > let r = "𝅃𝅄𝅅𝅆𝅇𝅈𝅉𝅊𝅋𝅌𝅍𝅎𝅏𝅐𝅑𝅒𝅓𝅔𝅕𝅖𝅗𝅘𝅙𝅚𝅛" in map (toEnum . fst) noteheads == r-noteheads :: Unicode_Table-noteheads =-    [(0x1d143,"MUSICAL SYMBOL X NOTEHEAD")-    ,(0x1d144,"MUSICAL SYMBOL PLUS NOTEHEAD")-    ,(0x1d145,"MUSICAL SYMBOL CIRCLE X NOTEHEAD")-    ,(0x1d146,"MUSICAL SYMBOL SQUARE NOTEHEAD WHITE")-    ,(0x1d147,"MUSICAL SYMBOL SQUARE NOTEHEAD BLACK")-    ,(0x1d148,"MUSICAL SYMBOL TRIANGLE NOTEHEAD UP WHITE")-    ,(0x1d149,"MUSICAL SYMBOL TRIANGLE NOTEHEAD UP BLACK")-    ,(0x1d14a,"MUSICAL SYMBOL TRIANGLE NOTEHEAD LEFT WHITE")-    ,(0x1d14b,"MUSICAL SYMBOL TRIANGLE NOTEHEAD LEFT BLACK")-    ,(0x1d14c,"MUSICAL SYMBOL TRIANGLE NOTEHEAD RIGHT WHITE")-    ,(0x1d14d,"MUSICAL SYMBOL TRIANGLE NOTEHEAD RIGHT BLACK")-    ,(0x1d14e,"MUSICAL SYMBOL TRIANGLE NOTEHEAD DOWN WHITE")-    ,(0x1d14f,"MUSICAL SYMBOL TRIANGLE NOTEHEAD DOWN BLACK")-    ,(0x1d150,"MUSICAL SYMBOL TRIANGLE NOTEHEAD UP RIGHT WHITE")-    ,(0x1d151,"MUSICAL SYMBOL TRIANGLE NOTEHEAD UP RIGHT BLACK")-    ,(0x1d152,"MUSICAL SYMBOL MOON NOTEHEAD WHITE")-    ,(0x1d153,"MUSICAL SYMBOL MOON NOTEHEAD BLACK")-    ,(0x1d154,"MUSICAL SYMBOL TRIANGLE-ROUND NOTEHEAD DOWN WHITE")-    ,(0x1d155,"MUSICAL SYMBOL TRIANGLE-ROUND NOTEHEAD DOWN BLACK")-    ,(0x1d156,"MUSICAL SYMBOL PARENTHESIS NOTEHEAD")-    ,(0x1d157,"MUSICAL SYMBOL VOID NOTEHEAD")-    ,(0x1d158,"MUSICAL SYMBOL NOTEHEAD BLACK")-    ,(0x1d159,"MUSICAL SYMBOL NULL NOTEHEAD")-    ,(0x1d15a,"MUSICAL SYMBOL CLUSTER NOTEHEAD WHITE")-    ,(0x1d15b,"MUSICAL SYMBOL CLUSTER NOTEHEAD BLACK")]---- > map toEnum [0x1D143,0x1D165] == "𝅃𝅥"-stem :: Unicode_Point-stem = (0x1D165, "MUSICAL SYMBOL COMBINING STEM")---- > putStrLn$ unicode_table_hs (unicode_table_block dynamics_rng tbl)-dynamics_rng :: Unicode_Range-dynamics_rng = (0x1D18C,0x1D193)---- > map (toEnum . fst) dynamics == "𝆌𝆍𝆎𝆏𝆐𝆑𝆒𝆓"-dynamics :: Unicode_Table-dynamics =-    [(0x1d18c,"MUSICAL SYMBOL RINFORZANDO")-    ,(0x1d18d,"MUSICAL SYMBOL SUBITO")-    ,(0x1d18e,"MUSICAL SYMBOL Z")-    ,(0x1d18f,"MUSICAL SYMBOL PIANO")-    ,(0x1d190,"MUSICAL SYMBOL MEZZO")-    ,(0x1d191,"MUSICAL SYMBOL FORTE")-    ,(0x1d192,"MUSICAL SYMBOL CRESCENDO")-    ,(0x1d193,"MUSICAL SYMBOL DECRESCENDO")]---- > putStrLn$ unicode_table_hs (unicode_table_block articulations_rng tbl)-articulations_rng :: Unicode_Range-articulations_rng = (0x1D17B,0x1D18B)---- > putStrLn (map (toEnum . fst) articulations :: String)-articulations :: Unicode_Table-articulations =-    [(0x1d17b,"MUSICAL SYMBOL COMBINING ACCENT")-    ,(0x1d17c,"MUSICAL SYMBOL COMBINING STACCATO")-    ,(0x1d17d,"MUSICAL SYMBOL COMBINING TENUTO")-    ,(0x1d17e,"MUSICAL SYMBOL COMBINING STACCATISSIMO")-    ,(0x1d17f,"MUSICAL SYMBOL COMBINING MARCATO")-    ,(0x1d180,"MUSICAL SYMBOL COMBINING MARCATO-STACCATO")-    ,(0x1d181,"MUSICAL SYMBOL COMBINING ACCENT-STACCATO")-    ,(0x1d182,"MUSICAL SYMBOL COMBINING LOURE")-    ,(0x1d183,"MUSICAL SYMBOL ARPEGGIATO UP")-    ,(0x1d184,"MUSICAL SYMBOL ARPEGGIATO DOWN")-    ,(0x1d185,"MUSICAL SYMBOL COMBINING DOIT")-    ,(0x1d186,"MUSICAL SYMBOL COMBINING RIP")-    ,(0x1d187,"MUSICAL SYMBOL COMBINING FLIP")-    ,(0x1d188,"MUSICAL SYMBOL COMBINING SMEAR")-    ,(0x1d189,"MUSICAL SYMBOL COMBINING BEND")-    ,(0x1d18a,"MUSICAL SYMBOL COMBINING DOUBLE TONGUE")-    ,(0x1d18b,"MUSICAL SYMBOL COMBINING TRIPLE TONGUE")]---- * Blocks--type Unicode_Block = (Unicode_Range,String)---- > putStrLn$ unicode_table_hs (concatMap (flip unicode_table_block tbl . fst) unicode_blocks)-unicode_blocks :: [Unicode_Block]-unicode_blocks =-    [((0x1B00,0x1B7F),"Balinese")-    ,((0x2200,0x22FF),"Mathematical Operators")-    ,((0x25A0,0x25FF),"Geometric Shapes")-    ,((0x1D000,0x1D0FF),"Byzantine Musical Symbols")-    ,((0x1D100,0x1D1FF),"Musical Symbols")-    ,((0x1D200,0x1D24F),"Ancient Greek Musical Notation")]---- * Table---- | <http://unicode.org/Public/8.0.0/ucd/UnicodeData.txt>------ > let fn = "/home/rohan/data/unicode.org/Public/8.0.0/ucd/UnicodeData.txt"--- > tbl <- unicode_data_table_read fn--- > length tbl == 29215-unicode_data_table_read :: FilePath -> IO Unicode_Table-unicode_data_table_read fn = do-  s <- T.read_file_utf8 fn-  let t = C.fromCSVTable (C.csvTable (C.parseDSV False ';' s))-      f x = (T.read_hex_err (x !! 0),x !! 1)-  return (map f t)--unicode_table_block :: (Int,Int) -> Unicode_Table -> Unicode_Table-unicode_table_block (l,r) = takeWhile ((<= r) . fst) . dropWhile ((< l) . fst)--unicode_point_hs :: Unicode_Point -> String-unicode_point_hs (n,s) = concat ["(0x",showHex n "",",\"",s,"\")"]--unicode_table_hs :: Unicode_Table -> String-unicode_table_hs = T.bracket ('[',']') . intercalate "," . map unicode_point_hs
Music/Theory/Wyschnegradsky.hs view
@@ -3,13 +3,14 @@  import Data.Char {- base -} import Data.List {- list -}-import Data.List.Split {- split -} import Data.Maybe {- base -} -import Music.Theory.List {- hmt -}-import Music.Theory.Pitch {- hmt -}-import Music.Theory.Pitch.Spelling.Table {- hmt -}+import qualified Data.List.Split as Split {- split -} +import qualified Music.Theory.List as List {- hmt -}+import qualified Music.Theory.Pitch as Pitch {- hmt -}+import qualified Music.Theory.Pitch.Spelling.Table as Spelling {- hmt -}+ -- | In a modulo /m/ system, normalise step increments to be either -1 -- or 1.  Non steps raise an error. --@@ -27,7 +28,7 @@ -- > map parse_num_sign ["2+","4-"] == [2,-4] parse_num_sign :: (Num n, Read n) => String -> n parse_num_sign s =-    case separate_last s of+    case List.separate_last s of       (n,'+') -> read n       (n,'-') -> negate (read n)       _ -> error "parse_num_sign"@@ -46,9 +47,9 @@ parse_vec :: Num n => Maybe Int -> n -> String -> [n] parse_vec n m =     let f = case n of-              Just i -> dx_d m . take i . cycle-              Nothing -> dx_d m-    in dropRight 1 . f . concatMap (vec_expand . parse_num_sign) . splitOn ","+              Just i -> List.dx_d m . take i . cycle+              Nothing -> List.dx_d m+    in List.dropRight 1 . f . concatMap (vec_expand . parse_num_sign) . Split.splitOn ","  -- | Modulo addition. add_m :: Integral a => a -> a -> a -> a@@ -82,13 +83,13 @@ seq_group :: Int -> Int -> Seq a -> [[a]] seq_group c_div r_div s =     case s of-      Circumferential c -> chunksOf c_div c-      Radial r -> transpose (chunksOf r_div r)+      Circumferential c -> Split.chunksOf c_div c+      Radial r -> transpose (Split.chunksOf r_div r)  -- | Printer for pitch-class segments. iw_pc_pp :: Integral n => String -> [[n]] -> IO () iw_pc_pp sep =-    let f = pitch_pp_opt (False,False) . octpc_to_pitch pc_spell_ks . (,) 4+    let f = Pitch.pitch_pp_opt (False,False) . Pitch.octpc_to_pitch Spelling.pc_spell_ks . (,) 4     in putStrLn . intercalate sep . map (unwords . map f)  -- * U3@@ -133,7 +134,7 @@ -- > let f = parse_vec Nothing 0 in map (\(p,q) -> (f p,f q)) u3_vec_text_rw -- -- > let f (c,r) = putStrLn (unlines ["C: " ++ c,"R: " ++ r])--- > in mapM_ f (interleave u3_vec_text_iw u3_vec_text_rw)+-- > mapM_ f (List.interleave u3_vec_text_iw u3_vec_text_rw) u3_vec_text_rw :: [(String, String)] u3_vec_text_rw =     [("4+,3-,5+,3-,3+"@@ -160,7 +161,7 @@ u3_vec_ix :: Num n => ([[n]],[[n]]) u3_vec_ix =     let f (p,q) = [parse_vec Nothing 0 p,parse_vec Nothing 0 q]-        [c,r] = transpose (map f u3_vec_text_rw)+        (c,r) = List.firstSecond (transpose (map f u3_vec_text_rw))     in (c,r)  -- | Radial indices (ie. each /ray/ as an index sequence).@@ -170,7 +171,7 @@ u3_ix_radial =     let (c,r) = u3_vec_ix         r' = zipWith replicate (map length c) r-    in zipWith (\p q -> map (add_m 6 p) q) (concat c) (concat r')+    in zipWith (map . add_m 6) (concat c) (concat r')  -- | Colour names in index sequence. u3_clr_nm :: [String]@@ -207,7 +208,7 @@     map length .     group .     map (normalise_step 6) .-    d_dx .+    List.d_dx .     map u3_ch_ix .     filter (not . isSpace) @@ -263,7 +264,7 @@             ,"#c2ba3d","#a2a367"             ,"#537a77","#203342"             ,"#84525e","#bc6460"]-        n = interleave [6,4,2,0,10,8] [5,3,1,11,9,7] :: [Int]+        n = List.interleave [6,4,2,0,10,8] [5,3,1,11,9,7] :: [Int]     in map snd (sort (zip n c))  -- | RGB form of colours.@@ -302,7 +303,7 @@  -- > iw_pc_pp "|" [u11_gen_seq 7 18 [5]] u11_gen_seq :: Integral i => i -> Int -> [i] -> [i]-u11_gen_seq z n = map (`mod` 12) . take n . dx_d z . cycle+u11_gen_seq z n = map (`mod` 12) . take n . List.dx_d z . cycle  u11_seq_rule :: Integral i => Maybe Int -> [i] u11_seq_rule n = u11_gen_seq 0 18 (maybe [-1] (\x -> replicate x (-1) ++ [5]) n)
Music/Theory/Xenakis/S4.hs view
@@ -5,8 +5,8 @@  import Data.List {- base -} import Data.Maybe {- base -}-import qualified Data.Permute as P {- permutation -} +import qualified Music.Theory.List as T import qualified Music.Theory.Permutations as T  -- * S4 notation@@ -76,30 +76,29 @@ > import qualified Music.Theory.List as T  > let r = [D,Q12,Q4, E,Q8,Q2, E2,Q7,Q4, D2,Q3,Q11, L2,Q7,Q2, L,Q8,Q11]-> in (take 18 (fib_proc l_on D Q12) == r,T.duplicates r == [Q2,Q4,Q7,Q8,Q11])+> (take 18 (fib_proc l_on D Q12) == r,T.duplicates r == [Q2,Q4,Q7,Q8,Q11])  Beginning E then G2 no Q nodes are visited.  > let r = [E,G2,L2,C,G,D,E,B,D2,L,G,C,L2,E2,D2,B]-> in (take 16 (fib_proc l_on E G2) == r,T.duplicates r == [B,C,D2,E,G,L2])+> (take 16 (fib_proc l_on E G2) == r,T.duplicates r == [B,C,D2,E,G,L2]) -> import Music.Theory.List-> let [a,b] = take 2 (segments 18 18 (fib_proc l_on D Q12)) in a == b+> let [a,b] = take 2 (T.segments 18 18 (fib_proc l_on D Q12)) in a == b  The prime numbers that are not factors of 18 are {1,5,7,11,13,17}. They form a closed group under modulo 18 multiplication. -> let {n = [5,7,11,13,17]->     ;r = [(5,7,17),(5,11,1),(5,13,11),(5,17,13)->          ,(7,11,5),(7,13,1),(7,17,11)->          ,(11,13,17),(11,17,7)->          ,(13,17,5)]}-> in [(p,q,(p * q) `mod` 18) | p <- n, q <- n, p < q] == r+> let n = [5,7,11,13,17]+> let r0 = [(5,7,17),(5,11,1),(5,13,11),(5,17,13)]+> let r1 = [(7,11,5),(7,13,1),(7,17,11)]+> let r2 = [(11,13,17),(11,17,7)]+> let r3 = [(13,17,5)]+> [(p,q,(p * q) `mod` 18) | p <- n, q <- n, p < q] == concat [r0,r1,r2,r3]  The article also omits the 5 after 5,1 in the sequence below.  > let r = [11,13,17,5,13,11,17,7,11,5,1,5,5,7,17,11,7,5,17,13,5,11,1,11]-> in take 24 (fib_proc (\p q -> (p * q) `mod` 18) 11 13) == r+> take 24 (fib_proc (\p q -> (p * q) `mod` 18) 11 13) == r  -} fib_proc :: (a -> a -> a) -> a -> a -> [a]@@ -123,15 +122,6 @@ half_seq :: Seq -> Half_Seq half_seq = take 4 --- | Reverse table 'lookup'.------ > reverse_lookup 'b' (zip [1..] ['a'..]) == Just 2--- > lookup 2 (zip [1..] ['a'..]) == Just 'b'-reverse_lookup :: (Eq a) => a -> [(b,a)] -> Maybe b-reverse_lookup i =-    let f (p,q) = (q,p)-    in lookup i . map f- -- | 'Label' of 'Seq', inverse of 'seq_of'. -- -- > label_of [8,7,5,6,4,3,1,2] == Q1@@ -139,7 +129,7 @@ label_of :: Seq -> Label label_of i =     let err = error ("label_of: " ++ show i)-    in fromMaybe err (reverse_lookup i viii_6b)+    in fromMaybe err (T.reverse_lookup i viii_6b)  -- | 'True' if two 'Half_Seq's are complementary, ie. form a 'Seq'. --@@ -153,12 +143,12 @@  -- | Relation between to 'Half_Seq' values as a -- /(complementary,permutation)/ pair.-type Rel = (Bool,P.Permute)+type Rel = (Bool,T.Permutation)  -- | Determine 'Rel' of 'Half_Seq's. ----- > relate [1,4,2,3] [1,3,4,2] == (False,P.listPermute 4 [0,3,1,2])--- > relate [1,4,2,3] [8,5,6,7] == (True,P.listPermute 4 [1,0,2,3])+-- > relate [1,4,2,3] [1,3,4,2] == (False,[0,3,1,2])+-- > relate [1,4,2,3] [8,5,6,7] == (True,[1,0,2,3]) relate :: Half_Seq -> Half_Seq -> Rel relate p q =     if complementary p q@@ -167,7 +157,7 @@  -- | 'Rel' from 'Label' /p/ to /q/. ----- > relate_l L L2 == (False,P.listPermute 4 [0,3,1,2])+-- > relate_l L L2 == (False,[0,3,1,2]) relate_l :: Label -> Label -> Rel relate_l p q = relate (half_seq_of p) (half_seq_of q) @@ -177,14 +167,13 @@  -- | 'relate' adjacent 'Label's. ----- > relations_l [L2,L,A] == [(False,P.listPermute 4 [0,2,3,1])--- >                         ,(False,P.listPermute 4 [2,0,1,3])]+-- > relations_l [L2,L,A] == [(False,[0,2,3,1]),(False,[2,0,1,3])] relations_l :: [Label] -> [Rel] relations_l p = zipWith relate_l p (tail p)  -- | Apply 'Rel' to 'Half_Seq'. ----- > apply_relation (False,P.listPermute 4 [0,3,1,2]) [1,4,2,3] == [1,3,4,2]+-- > apply_relation (False,[0,3,1,2]) [1,4,2,3] == [1,3,4,2] apply_relation :: Rel -> Half_Seq -> Half_Seq apply_relation (c,p) i =     let j = T.apply_permutation p i@@ -212,11 +201,10 @@ data Face = F_Back | F_Front | F_Right | F_Left | F_Bottom | F_Top           deriving (Eq,Enum,Bounded,Ord,Show) --- | Table indicating set of faces of cubes as drawn in Fig. VIII-6--- (p.220).+-- | Table indicating set of faces of cubes as drawn in Fig. VIII-6 (p.220). -- -- > lookup [1,4,6,7] faces == Just F_Left--- > reverse_lookup F_Right faces == Just [2,3,5,8]+-- > T.reverse_lookup F_Right faces == Just [2,3,5,8] faces :: [([Int],Face)] faces =     [([1,3,6,8],F_Back) -- (I in viii-6)
Music/Theory/Xenakis/Sieve.hs view
@@ -6,12 +6,9 @@ import qualified Data.List as L import Music.Theory.List --- | Synonym for 'Integer'-type I = Integer- -- | A Sieve. data Sieve = Empty -- ^ 'Empty' 'Sieve'-           | L (I,I) -- ^ Primitive 'Sieve' of /modulo/ and /index/+           | L (Integer, Integer) -- ^ Primitive 'Sieve' of /modulo/ and /index/            | Union Sieve Sieve -- ^ 'Union' of two 'Sieve's            | Intersection Sieve Sieve -- ^ 'Intersection' of two 'Sieve's            | Complement Sieve -- ^ 'Complement' of a 'Sieve'@@ -50,21 +47,22 @@ -- | Variant of 'L', ie. 'curry' 'L'. -- -- > l 15 19 == L (15,19)-l :: I -> I -> Sieve+l :: Integer -> Integer -> Sieve l = curry L  -- | unicode synonym for 'l'.-(⋄) :: I -> I -> Sieve+(⋄) :: Integer -> Integer -> Sieve (⋄) = l  infixl 3 ∪ infixl 4 ∩ infixl 5 ⋄ --- | In a /normal/ 'Sieve' /m/ is '>' /i/.------ > normalise (L (15,19)) == L (15,4)--- > normalise (L (11,13)) == L (11,2)+{- | In a /normal/ 'Sieve' /m/ is '>' /i/.++> normalise (L (15,19)) == L (15,4)+> normalise (L (11,13)) == L (11,2)+-} normalise :: Sieve -> Sieve normalise s =     case s of@@ -74,18 +72,20 @@       Intersection s0 s1 -> Intersection (normalise s0) (normalise s1)       Complement s' -> Complement (normalise s') --- | Predicate to test if a 'Sieve' is /normal/.------ > is_normal (L (15,4)) == True--- > is_normal (L (11,13)) == False+{- | Predicate to test if a 'Sieve' is /normal/.++> is_normal (L (15,4)) == True+> is_normal (L (11,13)) == False+-} is_normal :: Sieve -> Bool is_normal s = s == normalise s --- | Predicate to determine if an 'I' is an element of the 'Sieve'.------ > map (element (L (3,1))) [1..4] == [True,False,False,True]--- > map (element (L (15,4))) [4,19 .. 49] == [True,True,True,True]-element :: Sieve -> I -> Bool+{- | Predicate to determine if an 'I' is an element of the 'Sieve'.++> map (element (L (3,1))) [1..4] == [True,False,False,True]+> map (element (L (15,4))) [4,19 .. 49] == [True,True,True,True]+-}+element :: Sieve -> Integer -> Bool element s n =     case s of       Empty -> False@@ -94,8 +94,11 @@       Intersection s0 s1 -> element s0 n && element s1 n       Complement s' -> not (element s' n) --- > take 9 (i_complement [1,3..]) == [0,2..16]-i_complement :: [I] -> [I]+{- | 'I' not in set.++> take 9 (i_complement [1,3..]) == [0,2..16]+-}+i_complement :: [Integer] -> [Integer] i_complement =     let f x s = case s of                 [] -> [x ..]@@ -105,14 +108,15 @@                           GT -> error "i_complement"     in f 0 --- | Construct the sequence defined by a 'Sieve'.  Note that building--- a sieve that contains an intersection clause that has no elements--- gives @_|_@.------ > let {d = [0,2,4,5,7,9,11]--- >     ;r = d ++ map (+ 12) d}--- > in take 14 (build (union (map (l 12) d))) == r-build :: Sieve -> [I]+{- | Construct the sequence defined by a 'Sieve'.  Note that building+     a sieve that contains an intersection clause that has no elements+     gives @_|_@.++> let d = [0,2,4,5,7,9,11]+> let r = d ++ map (+ 12) d+> take 14 (build (union (map (l 12) d))) == r+-}+build :: Sieve -> [Integer] build s =     let u_f = map head . L.group         i_f = let g [x,_] = [x]@@ -125,8 +129,7 @@          Intersection s0 s1 -> i_f (merge (build s0) (build s1))          Complement s' -> i_complement (build s') -{- | Variant of 'build' that gives the first /n/ places of the-  'reduce' of 'Sieve'.+{- | Variant of 'build' that gives the first /n/ places of the 'reduce' of 'Sieve'.  > buildn 6 (union (map (l 8) [0,3,6])) == [0,3,6,8,11,14] > buildn 12 (L (3,2)) == [2,5,8,11,14,17,20,23,26,29,32,35]@@ -137,117 +140,105 @@ > buildn 6 (3⋄0 ∪ 4⋄0) == [0,3,4,6,8,9] > buildn 8 (5⋄2 ∩ 2⋄0 ∪ 7⋄3) == [2,3,10,12,17,22,24,31] > buildn 12 (5⋄1 ∪ 7⋄2) == [1,2,6,9,11,16,21,23,26,30,31,36]+> buildn 19 (L (3,2) ∪ L (7, 1)) == [1, 2, 5, 8, 11, 14, 15, 17, 20, 22, 23, 26, 29, 32, 35, 36, 38, 41, 43]+> buildn 19 (3⋄0 ∪ 7⋄0) == [0, 3, 6, 7, 9, 12, 14, 15, 18, 21, 24, 27, 28, 30, 33, 35, 36, 39, 42]  > buildn 10 (3⋄2 ∩ 4⋄7 ∪ 6⋄9 ∩ 15⋄18) == [3,11,23,33,35,47,59,63,71,83] -> let {s = 3⋄2∩4⋄7∩6⋄11∩8⋄7 ∪ 6⋄9∩15⋄18 ∪ 13⋄5∩8⋄6∩4⋄2 ∪ 6⋄9∩15⋄19->     ;s' = 24⋄23 ∪ 30⋄3 ∪ 104⋄70}-> in buildn 16 s == buildn 16 s'+> let s = 3⋄2∩4⋄7∩6⋄11∩8⋄7 ∪ 6⋄9∩15⋄18 ∪ 13⋄5∩8⋄6∩4⋄2 ∪ 6⋄9∩15⋄19+> let s' = 24⋄23 ∪ 30⋄3 ∪ 104⋄70+> buildn 16 s == buildn 16 s'  > buildn 10 (24⋄23 ∪ 30⋄3 ∪ 104⋄70) == [3,23,33,47,63,70,71,93,95,119]  > let r = [2,3,4,5,8,9,10,11,14,17,19,20,23,24,26,29,31]-> in buildn 17 (5⋄4 ∪ 3⋄2 ∪ 7⋄3) == r+> buildn 17 (5⋄4 ∪ 3⋄2 ∪ 7⋄3) == r  > let r = [0,1,3,6,9,10,11,12,15,16,17,18,21,24,26,27,30]-> in buildn 17 (5⋄1 ∪ 3⋄0 ∪ 7⋄3) == r+> buildn 17 (5⋄1 ∪ 3⋄0 ∪ 7⋄3) == r  > let r = [0,2,3,4,6,7,9,11,12,15,17,18,21,22,24,25,27,30,32]-> in buildn 19 (5⋄2 ∪ 3⋄0 ∪ 7⋄4) == r+> buildn 19 (5⋄2 ∪ 3⋄0 ∪ 7⋄4) == r  Agon et. al. p.155 -> let {a = c (13⋄3 ∪ 13⋄5 ∪ 13⋄7 ∪ 13⋄9)->     ;b = 11⋄2->     ;c' = c (11⋄4 ∪ 11⋄8)->     ;d = 13⋄9->     ;e = 13⋄0 ∪ 13⋄1 ∪ 13⋄6->     ;f = (a ∩ b) ∪ (c' ∩ d) ∪ e}-> in buildn 13 f == [0,1,2,6,9,13,14,19,22,24,26,27,32]+> let a = c (13⋄3 ∪ 13⋄5 ∪ 13⋄7 ∪ 13⋄9)+> let b = 11⋄2+> let c' = c (11⋄4 ∪ 11⋄8)+> let d = 13⋄9+> let e = 13⋄0 ∪ 13⋄1 ∪ 13⋄6+> let f = (a ∩ b) ∪ (c' ∩ d) ∪ e+> buildn 13 f == [0,1,2,6,9,13,14,19,22,24,26,27,32]  > differentiate [0,1,2,6,9,13,14,19,22,24,26,27,32] == [1,1,4,3,4,1,5,3,2,2,1,5] -> import Music.Theory.Pitch+> import Music.Theory.Pitch {- hmt -} -> let {n = [0,1,2,6,9,13,14,19,22,24,26,27,32]->     ;r = "C C𝄲 C♯ D♯ E𝄲 F𝄰 G A𝄲 B C C♯ C𝄰 E"}-> in unwords (map (pitch_class_pp . pc24et_to_pitch . (`mod` 24)) n) == r+> let n = [0,1,2,6,9,13,14,19,22,24,26,27,32]+> let r = "C C𝄲 C♯ D♯ E𝄲 F𝄰 G A𝄲 B C C♯ C𝄰 E"+> unwords (map (pitch_class_pp . pc24et_to_pitch . (`mod` 24)) n) == r  Jonchaies  > let s = map (17⋄) [0,1,4,5,7,11,12,16]-> in differentiate (buildn 25 (union s))+> let r = [1,3,1,2,4,1,4,1,1,3,1,2,4,1,4,1,1,3,1,2,4,1,4,1]+> differentiate (buildn 25 (union s)) == r+> let a2 = octpc_to_midi (2,9)+> let m = scanl (+) a2 r+> import Music.Theory.Pitch.Spelling.Table {- hmt -}+> let p = "A2 A#2 C#3 D3 E3 G#3 A3 C#4 D4 D#4 F#4 G4 A4 C#5 D5 F#5 G5 G#5 B5 C6 D6 F#6 G6 B6 C7"+> unwords (map (pitch_pp_iso . midi_to_pitch pc_spell_sharp) m) == p  Nekuïa -> let s = [24⋄0,14⋄2,22⋄3,31⋄4,28⋄7,29⋄9,19⋄10,25⋄13,24⋄14,26⋄17,23⋄21->         ,24⋄10,30⋄9,35⋄17,29⋄24,32⋄25,30⋄29,26⋄21,30⋄17,31⋄16]-> in differentiate (buildn 24 (union s))+> let s = [24⋄0,14⋄2,22⋄3,31⋄4,28⋄7,29⋄9,19⋄10,25⋄13,24⋄14,26⋄17,23⋄21,24⋄10,30⋄9,35⋄17,29⋄24,32⋄25,30⋄29,26⋄21,30⋄17,31⋄16]+> let r = [2,1,1,3,2,1,3,1,2,1,4,3,1,4,1,4,1,3,1,4,1,3,1,4,1,4,1,1,3,1,3,1,2,3,1,4,1,4,4,1]+> differentiate (buildn 41 (union s)) == r+> let a0 = octpc_to_midi (0,9)+> let m = scanl (+) a0 r+> import Music.Theory.Pitch.Spelling.Table {- hmt -}+> let p = "A0 B0 C1 C#1 E1 F#1 G1 A#1 B1 C#2 D2 F#2 A2 A#2 D3 D#3 G3 G#3 B3 C4 E4 F4 G#4 A4 C#5 D5 F#5 G5 G#5 B5 C6 D#6 E6 F#6 A6 A#6 D7 D#7 G7 B7 C8"+> unwords (map (pitch_pp_iso . midi_to_pitch pc_spell_sharp) m) == p +> let s = [8⋄0∩3⋄0,2⋄0∩7⋄2,2⋄1∩11⋄3,31⋄4,4⋄3∩7⋄0,29⋄9,19⋄10,25⋄13,8⋄6∩3⋄2,2⋄1∩13⋄4,23⋄21,8⋄2∩3⋄1,2⋄1∩3⋄0∩5⋄4,5⋄2∩7⋄3,29⋄24,32⋄25,2⋄1∩3⋄2∩5⋄4,2⋄1∩13⋄8,2⋄1∩3⋄2∩5⋄2,31⋄16]+> differentiate (buildn 41 (union s)) == r+ Major scale:  > let s = (c(3⋄2) ∩ 4⋄0) ∪ (c(3⋄1) ∩ 4⋄1) ∪ (3⋄2 ∩ 4⋄2) ∪ (c(3⋄0) ∩ 4⋄3)-> in buildn 7 s == [0,2,4,5,7,9,11]+> buildn 7 s == [0,2,4,5,7,9,11]  Nomos Alpha: -let {s = (c (13⋄3 ∪ 13⋄5 ∪ 13⋄7 ∪ 13⋄9) ∩ 11⋄2) ∪ (c (11⋄4 ∪ 11⋄8) ∩ 13⋄9) ∪ (13⋄0 ∪ 13⋄1 ∪ 13⋄6)-    ;r = [0,1,2,6,9,13,14,19,22,24,26,27,32,35,39,40,45,52,53,58,61,65,66,71,78,79,84,87,90,91,92,97]}-in buildn 32 s == r--/Psappha/ (Flint):--> let {s = union [(8⋄0∪8⋄1∪8⋄7)∩(5⋄1∪5⋄3)->                ,(8⋄0∪8⋄1∪8⋄2)∩5⋄0->                ,8⋄3∩(5⋄0∪5⋄1∪5⋄2∪5⋄3∪5⋄4)->                ,8⋄4∩(5⋄0∪5⋄1∪5⋄2∪5⋄3∪5⋄4)->                ,(8⋄5∪8⋄6)∩(5⋄2∪5⋄3∪5⋄4)->                ,8⋄1∩5⋄2->                ,8⋄6∩5⋄1]->     ;r = [0,1,3,4,6,8,10,11,12->          ,13,14,16,17,19,20,22,23,25->          ,27,28,29,31,33,35,36,37,38]}-> in buildn 27 s == r--À R. (Hommage à Maurice Ravel) (Squibbs, 1996)--> let {s = union [8⋄0∩(11⋄0∪11⋄4∪11⋄5∪11⋄6∪11⋄10)->                ,8⋄1∩(11⋄2∪11⋄3∪11⋄6∪11⋄7∪11⋄9)->                ,8⋄2∩(11⋄0∪11⋄1∪11⋄2∪11⋄3∪11⋄5∪11⋄10)->                ,8⋄3∩(11⋄1∪11⋄2∪11⋄3∪11⋄4∪11⋄10)->                ,8⋄4∩(11⋄0∪11⋄4∪11⋄8)->                ,8⋄5∩(11⋄0∪11⋄2∪11⋄3∪11⋄7∪11⋄9∪11⋄10)->                ,8⋄6∩(11⋄1∪11⋄3∪11⋄5∪11⋄7∪11⋄8∪11⋄9)->                ,8⋄7∩(11⋄1∪11⋄3∪11⋄6∪11⋄7∪11⋄8∪11⋄10)]->     ;r = [0,2,3,4,7,9,10,13,14,16->          ,17,21,23,25,29,30,32,34,35,38->          ,39,43,44,47,48,52,53,57,58,59->          ,62,63,66,67,69,72,73,77,78,82->          ,86,87]}-> in buildn 42 s == r+let s = (c (13⋄3 ∪ 13⋄5 ∪ 13⋄7 ∪ 13⋄9) ∩ 11⋄2) ∪ (c (11⋄4 ∪ 11⋄8) ∩ 13⋄9) ∪ (13⋄0 ∪ 13⋄1 ∪ 13⋄6)+let r = [0,1,2,6,9,13,14,19,22,24,26,27,32,35,39,40,45,52,53,58,61,65,66,71,78,79,84,87,90,91,92,97]+buildn 32 s == r  -}-buildn :: Int -> Sieve -> [I]+buildn :: Int -> Sieve -> [Integer] buildn n = take n . build . reduce --- | Standard differentiation function.------ > differentiate [1,3,6,10] == [2,3,4]--- > differentiate [0,2,4,5,7,9,11,12] == [2,2,1,2,2,2,1]+{- | Standard differentiation function.++> differentiate [1,3,6,10] == [2,3,4]+> differentiate [0,2,4,5,7,9,11,12] == [2,2,1,2,2,2,1]+-} differentiate :: (Num a) => [a] -> [a] differentiate x = zipWith (-) (tail x) x --- | Euclid's algorithm for computing the greatest common divisor.------ > euclid 1989 867 == 51+{- | Euclid's algorithm for computing the greatest common divisor.++> euclid 1989 867 == 51+-} euclid :: (Integral a) => a -> a -> a euclid i j =     let k = i `mod` j     in if k == 0 then j else euclid j k --- | Bachet De Méziriac's algorithm.------ > de_meziriac 15 4 == 3 && euclid 15 4 == 1+{- | Bachet De Méziriac's algorithm.++> de_meziriac 15 4 == 3 && euclid 15 4 == 1+-} de_meziriac :: (Integral a) => a -> a -> a de_meziriac i j =     let f t = if (t * i) `mod` j /= 1@@ -255,12 +246,12 @@               else t     in if j == 1 then 1 else f 1 --- | Attempt to reduce the 'Intersection' of two 'L' nodes to a--- singular 'L' node.------ > reduce_intersection (3,2) (4,7) == Just (12,11)--- > reduce_intersection (12,11) (6,11) == Just (12,11)--- > reduce_intersection (12,11) (8,7) == Just (24,23)+{- | Attempt to reduce the 'Intersection' of two 'L' nodes to a singular 'L' node.++> reduce_intersection (3,2) (4,7) == Just (12,11)+> reduce_intersection (12,11) (6,11) == Just (12,11)+> reduce_intersection (12,11) (8,7) == Just (24,23)+-} reduce_intersection :: (Integral t) => (t,t) -> (t,t) -> Maybe (t,t) reduce_intersection (m1,i1) (m2,i2) =     let d = euclid m1 m2@@ -275,20 +266,21 @@        then Nothing        else Just (m3,i3) --- | Reduce the number of nodes at a 'Sieve'.------ > reduce (L (3,2) ∪ Empty) == L (3,2)--- > reduce (L (3,2) ∩ Empty) == L (3,2)--- > reduce (L (3,2) ∩ L (4,7)) == L (12,11)--- > reduce (L (6,9) ∩ L (15,18)) == L (30,3)------ > let s = 3⋄2∩4⋄7∩6⋄11∩8⋄7 ∪ 6⋄9∩15⋄18 ∪ 13⋄5∩8⋄6∩4⋄2 ∪ 6⋄9∩15⋄19--- > in reduce s == (24⋄23 ∪ 30⋄3 ∪ 104⋄70)------ > putStrLn $ sieve_pp (reduce s)------ > let s = 3⋄2∩4⋄7∩6⋄11∩8⋄7 ∪ 6⋄9∩15⋄18 ∪ 13⋄5∩8⋄6∩4⋄2 ∪ 6⋄9∩15⋄19--- > in reduce s == (24⋄23 ∪ 30⋄3 ∪ 104⋄70)+{- | Reduce the number of nodes at a 'Sieve'.++> reduce (L (3,2) ∪ Empty) == L (3,2)+> reduce (L (3,2) ∩ Empty) == L (3,2)+> reduce (L (3,2) ∩ L (4,7)) == L (12,11)+> reduce (L (6,9) ∩ L (15,18)) == L (30,3)++> let s = 3⋄2∩4⋄7∩6⋄11∩8⋄7 ∪ 6⋄9∩15⋄18 ∪ 13⋄5∩8⋄6∩4⋄2 ∪ 6⋄9∩15⋄19+> reduce s == (24⋄23 ∪ 30⋄3 ∪ 104⋄70)++> putStrLn $ sieve_pp (reduce s)++> let s = 3⋄2∩4⋄7∩6⋄11∩8⋄7 ∪ 6⋄9∩15⋄18 ∪ 13⋄5∩8⋄6∩4⋄2 ∪ 6⋄9∩15⋄19+> reduce s == (24⋄23 ∪ 30⋄3 ∪ 104⋄70)+-} reduce :: Sieve -> Sieve reduce s =     let f g s1 s2 =@@ -307,3 +299,43 @@          Intersection (L p) (L q) -> maybe Empty L (reduce_intersection p q)          Intersection s1 s2 -> f Intersection s1 s2          Complement s' -> Complement (reduce s')++-- * Literature++psappha_flint_c :: [Sieve]+psappha_flint_c =+  let s0 = (8⋄0∪8⋄1∪8⋄7)∩(5⋄1∪5⋄3)+      s1 = (8⋄0∪8⋄1∪8⋄2)∩5⋄0+      s2 = 8⋄3∩(5⋄0∪5⋄1∪5⋄2∪5⋄3∪5⋄4)+      s3 = 8⋄4∩(5⋄0∪5⋄1∪5⋄2∪5⋄3∪5⋄4)+      s4 = (8⋄5∪8⋄6)∩(5⋄2∪5⋄3∪5⋄4)+      s5 = 8⋄1∩5⋄2+      s6 = 8⋄6∩5⋄1+  in [s0, s1, s2, s3, s4, s5, s6]++{- | /Psappha/ (Flint)++> let r = [0,1,3,4,6,8,10,11,12,13,14,16,17,19,20,22,23,25,27,28,29,31,33,35,36,37,38]+> buildn 27 psappha_flint == r+-}+psappha_flint :: Sieve+psappha_flint = union psappha_flint_c++a_r_squibbs_c :: [Sieve]+a_r_squibbs_c =+  [8⋄0∩(11⋄0∪11⋄4∪11⋄5∪11⋄6∪11⋄10)+  ,8⋄1∩(11⋄2∪11⋄3∪11⋄6∪11⋄7∪11⋄9)+  ,8⋄2∩(11⋄0∪11⋄1∪11⋄2∪11⋄3∪11⋄5∪11⋄10)+  ,8⋄3∩(11⋄1∪11⋄2∪11⋄3∪11⋄4∪11⋄10)+  ,8⋄4∩(11⋄0∪11⋄4∪11⋄8)+  ,8⋄5∩(11⋄0∪11⋄2∪11⋄3∪11⋄7∪11⋄9∪11⋄10)+  ,8⋄6∩(11⋄1∪11⋄3∪11⋄5∪11⋄7∪11⋄8∪11⋄9)+  ,8⋄7∩(11⋄1∪11⋄3∪11⋄6∪11⋄7∪11⋄8∪11⋄10)]++{- | À R. (Hommage à Maurice Ravel) (Squibbs, 1996)++let r = [0,2,3,4,7,9,10,13,14,16,17,21,23,25,29,30,32,34,35,38,39,43,44,47,48,52,53,57,58,59,62,63,66,67,69,72,73,77,78,82,86,87]+buildn 42 a_r_squibbs == r+-}+a_r_squibbs :: Sieve+a_r_squibbs = union a_r_squibbs_c
Music/Theory/Z.hs view
@@ -1,4 +1,4 @@--- | Z-/n/ functions with modulo function as parameter.+-- | Z-/n/ functions module Music.Theory.Z where  import Data.Char {- base -}@@ -6,65 +6,69 @@  import qualified Music.Theory.List as T {- hmt -} --- | The modulo function for Z.-type Z t = (t -> t)+-- | Z type.+--+-- > map z_modulus [z7,z12] == [7,12]+newtype Z i = Z {z_modulus :: i} +-- | 'mod' of 'Z'.+--+-- > map (z_mod z12) [-1,0,1,11,12,13] == [11,0,1,11,0,1]+z_mod :: Integral i => Z i -> i -> i+z_mod (Z i) n = mod n i++-- | Common moduli in music theory.+z5,z7,z12,z16 :: Num i => Z i+z5 = Z 5+z7 = Z 7+z12 = Z 12+z16 = Z 16+ -- | Is /n/ in (0,/m/-1). is_z_n :: (Num a, Ord a) => a -> a -> Bool is_z_n m n = n >= 0 && n < m -mod5 :: Integral i => Z i-mod5 n = n `mod` 5--mod7 :: Integral i => Z i-mod7 n = n `mod` 7--mod12 :: Integral i => Z i-mod12 n = n `mod` 12--lift_unary_Z :: Z i -> (t -> i) -> t -> i-lift_unary_Z z f n = z (f n)+lift_unary_Z :: Integral i => Z i -> (t -> i) -> t -> i+lift_unary_Z z f = z_mod z . f -lift_binary_Z :: Z i -> (s -> t -> i) -> s -> t -> i-lift_binary_Z z f n1 n2 = z (n1 `f` n2)+lift_binary_Z :: Integral i => Z i -> (s -> t -> i) -> s -> t -> i+lift_binary_Z z f n1 = z_mod z . f n1 --- > import Music.Theory.Z--- > import qualified Music.Theory.Z12 as Z12--- > z_add id (11::Z12.Z12) 5 == 4--- > (11::Z12.Z12) + 5 == 4--- > map (z_add mod12 4) [1,5,6] == [5,9,10]+-- | Add two Z.+--+-- > map (z_add z12 4) [1,5,6,11] == [5,9,10,3] z_add :: Integral i => Z i -> i -> i -> i z_add z = lift_binary_Z z (+)  -- | The underlying type /i/ is presumed to be signed... ----- > z_sub mod12 0 8 == 4+-- > z_sub z12 0 8 == 4 ----- > import Data.Word--- > z_sub mod12 (0::Word8) 8 == 8+-- > import Data.Word {- base -}+-- > z_sub z12 (0::Word8) 8 == 8 -- > ((0 - 8) :: Word8) == 248 -- > 248 `mod` 12 == 8 z_sub :: Integral i => Z i -> i -> i -> i z_sub z = lift_binary_Z z (-) -{- | Allowing unsigned /i/ is rather inefficient...-z_sub :: Integral i => Z i -> i -> i -> i-z_sub z p q =+-- | Allowing unsigned /i/ is rather inefficient...+--+-- > z_sub_unsigned z12 (0::Word8) 8 == 4+z_sub_unsigned :: (Integral i,Ord i) => Z i -> i -> i -> i+z_sub_unsigned z p q =     if p > q-    then z (p - q)-    else let m = z_modulus z-         in z (p + m - q)--}+    then z_mod z (p - q)+    else z_mod z (p + z_modulus z - q)  z_mul :: Integral i => Z i -> i -> i -> i z_mul z = lift_binary_Z z (*) --- > z_negate mod12 7 == 5+-- > z_negate z12 7 == 5 z_negate :: Integral i => Z i -> i -> i z_negate z = z_sub z 0 -- error "Z numbers are not signed"  z_fromInteger :: Integral i => Z i -> Integer -> i-z_fromInteger z i = z (fromInteger i)+z_fromInteger z i = z_mod z (fromInteger i)  z_signum :: t -> u -> v z_signum _ _ = error "Z numbers are not signed"@@ -72,29 +76,23 @@ z_abs :: t -> u -> v z_abs _ _ = error "Z numbers are not signed" --- > map (to_Z mod12) [-9,-3,0] == [3,9,0]+-- > map (to_Z z12) [-9,-3,0] == [3,9,0] to_Z :: Integral i => Z i -> i -> i to_Z z = z_fromInteger z . fromIntegral  from_Z :: (Integral i,Num n) => i -> n from_Z = fromIntegral --- | Modulus of /z/.------ > z_modulus mod12 == 12-z_modulus :: Integral i => Z i -> i-z_modulus z = maybe (error "z_modulus") (fromIntegral . (+ 1)) (findIndex ((== 0) . z) [1..])- -- | Universe of 'Z'. ----- > z_univ mod12 == [0..11]+-- > z_univ z12 == [0..11] z_univ :: Integral i => Z i -> [i]-z_univ z = 0 : takeWhile ((> 0) . z) [1..]+z_univ (Z z) = [0 .. z - 1]  -- | Z of 'z_univ' not in given set. ----- > z_complement mod5 [0,2,3] == [1,4]--- > z_complement mod12 [0,2,4,5,7,9,11] == [1,3,6,8,10]+-- > z_complement z5 [0,2,3] == [1,4]+-- > z_complement z12 [0,2,4,5,7,9,11] == [1,3,6,8,10] z_complement :: Integral i => Z i -> [i] -> [i] z_complement z = (\\) (z_univ z) @@ -110,38 +108,39 @@ z_div :: Integral i => Z i -> i -> i -> i z_div z p = to_Z z . div_err "z_div" p --- > z_mod mod12 6 12 == 6-z_mod :: Integral i => Z i -> i -> i -> i-z_mod z p = to_Z z . mod p- z_quotRem :: Integral i => Z i -> i -> i -> (i,i) z_quotRem z p q = (z_quot z p q,z_quot z p q)  z_divMod :: Integral i => Z i -> i -> i -> (i,i)-z_divMod z p q = (z_div z p q,z_mod z p q)+z_divMod z p q = (z_div z p q,z_mod z (mod p q))  z_toInteger :: Integral i => Z i -> i -> i-z_toInteger z = to_Z z+z_toInteger = to_Z  -- * Z16 -mod16 :: Integral i => Z i-mod16 n = n `mod` 16-+-- | Type generalised 'intToDigit'.+--+-- > map integral_to_digit [0 .. 15] == "0123456789abcdef" integral_to_digit :: Integral t => t -> Char integral_to_digit = intToDigit . fromIntegral +-- | 'is_z_n' 16. is_z16 :: Integral t => t -> Bool is_z16 = is_z_n 16 +-- | Alias for 'integral_to_digit'. z16_to_char :: Integral t => t -> Char z16_to_char = integral_to_digit +-- | 'z16_to_char' in braces, {1,2,3}. z16_set_pp :: Integral t => [t] -> String z16_set_pp = T.bracket ('{','}') . map z16_to_char +-- | 'z16_to_char' in arrows, <1,2,3>. z16_seq_pp :: Integral t => [t] -> String z16_seq_pp = T.bracket ('<','>') . map z16_to_char +-- | 'z16_to_char' in brackets, [1,2,3]. z16_vec_pp :: Integral t => [t] -> String z16_vec_pp = T.bracket ('[',']') . map z16_to_char
Music/Theory/Z/Boros_1990.hs view
@@ -12,18 +12,18 @@ import qualified Data.Graph.Inductive.PatriciaTree as G {- fgl -} import qualified Data.Graph.Inductive.Query.BFS as G {- fgl -} -import qualified Music.Theory.Array.MD as T+import qualified Music.Theory.Array.Text as T import qualified Music.Theory.Combinations as T import qualified Music.Theory.Graph.Dot as T-import qualified Music.Theory.Graph.FGL as T+import qualified Music.Theory.Graph.Fgl as T import qualified Music.Theory.List as T import qualified Music.Theory.Set.List as T import qualified Music.Theory.Tuple as T import qualified Music.Theory.Z as T import qualified Music.Theory.Z.Forte_1973 as T-import qualified Music.Theory.Z.TTO as T+import qualified Music.Theory.Z.Tto as T --- * UTIL+-- * Util  singular :: String -> [t] -> t singular err l =@@ -37,80 +37,81 @@ elem_by :: (t -> t -> Bool) -> t -> [t] -> Bool elem_by f e = any (f e) --- * TTO+-- * Tto -tto_tni_univ :: Integral i => [T.TTO i]-tto_tni_univ = filter (not . T.tto_M) (T.z_tto_univ T.mod12)+tto_tni_univ :: Integral i => [T.Tto i]+tto_tni_univ = filter ((== 1) . T.tto_M) (T.z_tto_univ 5 T.z12)  all_tn :: Integral i => [i] -> [[i]]-all_tn p = map (\n -> map (T.z_add T.mod12 n) p) [0..11]+all_tn p = map (\n -> map (T.z_add T.z12 n) p) [0..11]  all_tni :: Integral i => [i] -> [[i]]-all_tni p = map (\f -> T.z_tto_apply 5 T.mod12 f p) tto_tni_univ+all_tni p = map (\f -> T.z_tto_apply T.z12 f p) tto_tni_univ  uniq_tni :: Integral i => [i] -> [[i]] uniq_tni = nub . all_tni -type PC = Int-type PCSET = [PC]-type SC = PCSET+type Pc = Int+type Pcset = [Pc]+type Sc = Pcset -pcset_trs :: Int -> PCSET -> PCSET-pcset_trs n p = sort (map (T.mod12 . (+ n)) p)+-- > pcset_trs 3 [0,1,9] == [0,3,4]+pcset_trs :: Int -> Pcset -> Pcset+pcset_trs = T.z_tto_tn T.z12  -- | Forte prime forms of the twelve trichordal set classes. -- -- > length trichords == 12-trichords :: [PCSET]-trichords = filter ((== 3) . length) (T.sc_univ T.mod12)+trichords :: [Pcset]+trichords = filter ((== 3) . length) (T.z_sc_univ T.z12)  -- | Is a pcset self-inversional, ie. is the inversion of /p/ a transposition of /p/. -- -- > map (\p -> (p,self_inv p)) trichords-self_inv :: PCSET -> Bool-self_inv p = elem_by set_eq (map (T.z_negate T.mod12) p) (all_tn p)+self_inv :: Pcset -> Bool+self_inv p = elem_by set_eq (map (T.z_negate T.z12) p) (all_tn p)  -- | Pretty printer, comma separated. -- -- > pcset_pp [0,3,7,10] == "0,3,7,10"-pcset_pp :: PCSET -> String+pcset_pp :: Pcset -> String pcset_pp = intercalate "," . map show  -- | Pretty printer, hexadecimal, no separator. -- -- > pcset_pp_hex [0,3,7,10] == "037A"-pcset_pp_hex :: PCSET -> String-pcset_pp_hex = map toUpper . concat . map (flip showHex "")+pcset_pp_hex :: Pcset -> String+pcset_pp_hex = map toUpper . concatMap (`showHex` "") --- * ATH+-- * Ath  -- | Forte prime form of the all-trichord hexachord. ----- > T.sc_name T.mod12 ath == "6-Z17"+-- > T.sc_name ath == "6-Z17" -- > T.sc "6-Z17" == ath-ath :: PCSET+ath :: Pcset ath = [0,1,2,4,7,8]  -- | Is /p/ an instance of 'ath'.-is_ath :: PCSET -> Bool-is_ath p = T.forte_prime T.mod12 p == ath+is_ath :: Pcset -> Bool+is_ath p = T.z_forte_prime T.z12 p == ath  -- | Table 1, p.20 -- -- > length ath_univ == 24-ath_univ :: [PCSET]+ath_univ :: [Pcset] ath_univ = uniq_tni ath --- | Calculate 'T.TTO' of pcset, which must be an instance of 'ath'.+-- | Calculate 'T.Tto' of pcset, which must be an instance of 'ath'. ----- > ath_tni [1,2,3,7,8,11] == T.TTO 3 False True-ath_tni :: PCSET -> T.TTO PC-ath_tni = singular "ath_tni" . filter (not . T.tto_M) . T.z_tto_rel 5 T.mod12 ath+-- > ath_tni [1,2,3,7,8,11] == T.Tto 3 1 True+ath_tni :: Pcset -> T.Tto Pc+ath_tni = singular "ath_tni" . filter ((== 1) . T.tto_M) . T.z_tto_rel 5 T.z12 ath  -- | Give label for instance of 'ath', prime forms are written H and inversions h. -- -- > ath_pp [1,2,3,7,8,11] == "h3"-ath_pp :: PCSET -> String+ath_pp :: Pcset -> String ath_pp p =     let r = ath_tni p         h = if T.tto_I r then 'h' else 'H'@@ -119,60 +120,63 @@ -- | The twenty three-element subsets of 'ath'. -- -- > length ath_trichords == 20-ath_trichords :: [PCSET]+ath_trichords :: [Pcset] ath_trichords = T.combinations (3::Int) ath  -- | '\\' of 'ath' and /p/, ie. the pitch classes that are in 'ath' and not in /p/. -- -- > ath_complement [0,1,2] == [4,7,8]-ath_complement :: PCSET -> PCSET+ath_complement :: Pcset -> Pcset ath_complement p = ath \\ p  -- | /p/ is a pcset, /q/ a sc, calculate pcsets in /q/ that with /p/ form 'ath'. -- -- > ath_completions [0,1,2] (T.sc "3-3") == [[6,7,10],[4,7,8]] -- > ath_completions [6,7,10] (T.sc "3-5") == [[1,2,8]]-ath_completions :: PCSET -> SC -> [PCSET]+ath_completions :: Pcset -> Sc -> [Pcset] ath_completions p q =     let f z = is_ath (p ++ z)     in filter f (uniq_tni q) -realise_ath_seq :: [PCSET] -> [[PCSET]]+realise_ath_seq :: [Pcset] -> [[Pcset]] realise_ath_seq sq =     case sq of       p:q:sq' -> concatMap (\z -> map (p :) (realise_ath_seq (z : sq'))) (ath_completions p q)       _ -> [sq]  -- return edges that connect z to nodes at gr in an ATH relation-ath_gr_extend :: T.GRAPH PCSET -> PCSET -> [T.EDGE PCSET]+ath_gr_extend :: [T.Edge Pcset] -> Pcset -> [T.Edge Pcset] ath_gr_extend gr c =     let f x y = if is_ath (x ++ y) then Just (x,y) else Nothing         g (p,q) = mapMaybe (f c) [p,q]     in nub (map T.t2_sort (concatMap g gr)) -gr_trs :: Int -> T.GRAPH PCSET -> T.GRAPH PCSET+gr_trs :: Int -> [T.Edge Pcset] -> [T.Edge Pcset] gr_trs n = let f (p,q) = (pcset_trs n p,pcset_trs n q) in map f --- * TABLES+-- * Tables  -- > length table_3 == 20-table_3 :: [((PCSET,SC,T.SC_Name),(PCSET,SC,T.SC_Name))]+table_3 :: [((Pcset,Sc,T.SC_Name),(Pcset,Sc,T.SC_Name))] table_3 =     let f p = let q = ath_complement p-                  i x = (x,T.forte_prime T.mod12 x,T.sc_name T.mod12 x)+                  i x = (x,T.z_forte_prime T.z12 x,T.sc_name x)               in (i p,i q)     in map f ath_trichords +pp_tbl :: T.Text_Table -> [String]+pp_tbl = T.table_pp T.table_opt_simple+ -- > putStrLn $ unlines $ table_3_md table_3_md :: [String] table_3_md =     let pp = pcset_pp_hex         f ((p,q,r),(s,t,u)) = [pp p,pp q,r,pp s,pp t,u]         hdr = ["P","P/SC","P/F","Q=H0-P","Q/SC","Q/F"]-    in T.md_table' (Just hdr,map f table_3)+    in pp_tbl (hdr : map f table_3)  -- > length table_4 == 10-table_4 :: [((PCSET,PCSET,T.SC_Name),(PCSET,PCSET,T.SC_Name))]+table_4 :: [((Pcset,Pcset,T.SC_Name),(Pcset,Pcset,T.SC_Name))] table_4 = nub (map T.t2_sort table_3)  -- > putStrLn $ unlines $ table_4_md@@ -181,18 +185,18 @@     let pp = pcset_pp_hex         f ((p,q,r),(s,t,u)) = [pp p ++ "/" ++ pp s,pp q ++ "/" ++ pp t,r ++ "/" ++ u]         hdr = ["Trichords","Prime Forms","Forte Numbers"]-    in T.md_table' (Just hdr,map f table_4)+    in pp_tbl (hdr : map f table_4) -table_5 :: [(PCSET,Int)]-table_5 = T.histogram (map (T.forte_prime T.mod12) ath_trichords)+table_5 :: [(Pcset,Int)]+table_5 = T.histogram (map (T.z_forte_prime T.z12) ath_trichords)  -- > putStrLn $ unlines $ table_5_md table_5_md :: [String] table_5_md =     let f (p,q) = [pcset_pp_hex p,show q]-    in T.md_table' (Just ["SC","#ATH"],map f table_5)+    in pp_tbl (["SC","#ATH"] : map f table_5) -table_6 :: [(PCSET,Int,Int)]+table_6 :: [(Pcset,Int,Int)] table_6 =     let f (p,n) = (p,n,length (filter (\q -> p `T.is_subset` q) ath_univ))     in map f table_5@@ -201,40 +205,40 @@ table_6_md :: [String] table_6_md =     let f (p,q,r) = [pcset_pp_hex p,show q,show r]-    in T.md_table' (Just ["SC","#H0","#Hn"],map f table_6)+    in pp_tbl (["SC","#H0","#Hn"] : map f table_6) --- * FIGURES+-- * Figures -fig_1 :: T.GRAPH PCSET+fig_1 :: [T.Edge Pcset] fig_1 = map (T.t2_map T.p3_snd) table_4 -fig_1_gr :: G.Gr PCSET ()+fig_1_gr :: G.Gr Pcset () fig_1_gr = T.g_from_edges fig_1  -- > putStrLn $ unlines $ map (unwords . map pcset_pp) fig_2-fig_2 :: [[PCSET]]+fig_2 :: [[Pcset]] fig_2 =  let g = G.undir fig_1_gr      n = G.labNodes g      n' = filter ((== 2) . G.deg g . fst) n      c = T.combinations (2::Int) n'-     p = map (\[lhs,rhs] -> G.esp (fst lhs) (fst rhs) g) c-     p' = (filter (not . null) p)- in map (mapMaybe (\x -> lookup x n)) p'+     p = map (\l -> let (lhs,rhs) = T.firstSecond l in G.esp (fst lhs) (fst rhs) g) c+     p' = filter (not . null) p+ in map (mapMaybe (`lookup` n)) p' -fig_3 :: [T.GRAPH PCSET]+fig_3 :: [[T.Edge Pcset]] fig_3 = map (concatMap (T.adj2 1) . realise_ath_seq) fig_2 -fig_3_gr :: [G.Gr PCSET ()]+fig_3_gr :: [G.Gr Pcset ()] fig_3_gr = map T.g_from_edges fig_3 -fig_4 :: [T.GRAPH PCSET]+fig_4 :: [[T.Edge Pcset]] fig_4 =     let p = concatMap realise_ath_seq fig_2         q = filter ([0,1,2] `elem`) p     in map (T.adj2 1) q -fig_5 :: [T.GRAPH PCSET]+fig_5 :: [[T.Edge Pcset]] fig_5 =     let c = [0,4,8]         f gr = case ath_gr_extend gr c of@@ -245,52 +249,52 @@  -- * Drawing -uedge_set :: Ord v => [T.EDGE v] -> [T.EDGE v]+uedge_set :: Ord v => [T.Edge v] -> [T.Edge v] uedge_set = nub . map T.t2_sort  -- | Self-inversional pcsets are drawn in a double circle, other pcsets in a circle.-set_shape :: PCSET -> String-set_shape v = if self_inv v then "doublecircle" else "circle"+set_shape :: Pcset -> T.Dot_Attr+set_shape v = ("shape",if self_inv v then "doublecircle" else "circle") -type GR = G.Gr PCSET ()+type Gr = G.Gr Pcset () -gr_pp' :: (PCSET -> String) -> T.GR_PP PCSET ()-gr_pp' f = (Just . set_shape,Just . f,const Nothing)+gr_pp' :: (Pcset -> String) -> T.Graph_Pp Pcset ()+gr_pp' f = (\(_,v) -> [set_shape v,("label",f v)],const []) -gr_pp :: T.GR_PP PCSET ()+gr_pp :: T.Graph_Pp Pcset () gr_pp = gr_pp' pcset_pp  d_fig_1 :: [String]-d_fig_1 = T.g_to_udot [] gr_pp fig_1_gr+d_fig_1 = T.fgl_to_udot [] gr_pp fig_1_gr -d_fig_3_g :: GR+d_fig_3_g :: Gr d_fig_3_g = T.g_from_edges (uedge_set (concat fig_3))  d_fig_3 :: [String]-d_fig_3 = T.g_to_udot [] gr_pp d_fig_3_g+d_fig_3 = T.fgl_to_udot [] gr_pp d_fig_3_g  d_fig_3' :: [[String]]-d_fig_3' = map (T.g_to_udot [("node:shape","circle")] gr_pp) fig_3_gr+d_fig_3' = map (T.fgl_to_udot [("node:shape","circle")] gr_pp) fig_3_gr -d_fig_4_g :: GR+d_fig_4_g :: Gr d_fig_4_g = T.g_from_edges (uedge_set (concat fig_4))  d_fig_4 :: [String]-d_fig_4 = T.g_to_udot [] gr_pp d_fig_4_g+d_fig_4 = T.fgl_to_udot [] gr_pp d_fig_4_g -d_fig_5_g :: GR+d_fig_5_g :: Gr d_fig_5_g = T.g_from_edges (uedge_set (concat fig_5))  d_fig_5 :: [String]-d_fig_5 = T.g_to_udot [("edge:len","1.5")] (gr_pp' pcset_pp_hex) d_fig_5_g+d_fig_5 = T.fgl_to_udot [("edge:len","1.5")] (gr_pp' pcset_pp_hex) d_fig_5_g -d_fig_5_e :: [T.EDGE_L PCSET PCSET]+d_fig_5_e :: [T.Edge_Lbl Pcset Pcset] d_fig_5_e = map (\(p,q) -> ((p,q),p++q)) (uedge_set (concat fig_5)) -d_fig_5_g' :: G.Gr PCSET PCSET+d_fig_5_g' :: G.Gr Pcset Pcset d_fig_5_g' = T.g_from_edges_l d_fig_5_e  d_fig_5' :: [String] d_fig_5' =-    let pp = (const (Just ""),const Nothing,Just . ath_pp)-    in T.g_to_udot [("node:shape","point"),("edge:len","1.25")] pp d_fig_5_g'+    let pp = (const [("shape","")],\(_,e) -> [("label",ath_pp e)])+    in T.fgl_to_udot [("node:shape","point"),("edge:len","1.25")] pp d_fig_5_g'
+ Music/Theory/Z/Castren_1994.hs view
@@ -0,0 +1,153 @@+-- | Marcus Castrén.+--   /RECREL: A Similarity Measure for Set-Classes/.+--   PhD thesis, Sibelius Academy, Helsinki, 1994.+module Music.Theory.Z.Castren_1994 where++import Data.Int {- base -}+import Data.List {- base -}+import Data.Maybe {- base -}+import Data.Ratio {- base -}++import qualified Music.Theory.List as List+import Music.Theory.Z+import qualified Music.Theory.Z.Forte_1973 as Forte+import qualified Music.Theory.Z.Sro as Sro++type Z12 = Int8++-- | Is /p/ symmetrical under inversion.+--+-- > map inv_sym (Forte.scs_n 2) == [True,True,True,True,True,True]+-- > map (fromEnum.inv_sym) (Forte.scs_n 3) == [1,0,0,0,0,1,0,0,1,1,0,1]+inv_sym :: [Z12] -> Bool+inv_sym x = x `elem` map (\i -> sort (Sro.z_sro_tn z12 i (Sro.z_sro_invert z12 0 x))) [0..11]++-- | If /p/ is not 'inv_sym' then @(p,invert 0 p)@ else 'Nothing'.+--+-- > sc_t_ti [0,2,4] == Nothing+-- > sc_t_ti [0,1,3] == Just ([0,1,3],[0,2,3])+sc_t_ti :: [Z12] -> Maybe ([Z12], [Z12])+sc_t_ti p =+    if inv_sym p+    then Nothing+    else Just (p,Forte.z_t_prime z12 (Sro.z_sro_invert z12 0 p))++-- | Transpositional equivalence variant of Forte's 'sc_table'.  The+-- inversionally related classes are distinguished by labels @A@ and+-- @B@; the class providing the /best normal order/ (Forte 1973) is+-- always the @A@ class. If neither @A@ nor @B@ appears in the name of+-- a set-class, it is inversionally symmetrical.+--+-- > (length Forte.sc_table,length t_sc_table) == (224,352)+-- > lookup "5-Z18B" t_sc_table == Just [0,2,3,6,7]+t_sc_table :: [(Forte.SC_Name,[Z12])]+t_sc_table =+    let f x = let nm = Forte.sc_name x+              in case sc_t_ti x of+                   Nothing -> [(nm,x)]+                   Just (p,q) -> [(nm++"A",p),(nm++"B",q)]+    in concatMap f Forte.scs++-- | Lookup a set-class name.  The input set is subject to+-- 't_prime' before lookup.+--+-- > t_sc_name [0,2,3,6,7] == "5-Z18B"+-- > t_sc_name [0,1,4,6,7,8] == "6-Z17B"+t_sc_name :: [Z12] -> Forte.SC_Name+t_sc_name p =+    let n = find (\(_,q) -> Forte.z_t_prime z12 p == q) t_sc_table+    in fst (fromJust n)++-- | Lookup a set-class given a set-class name.+--+-- > t_sc "6-Z17A" == [0,1,2,4,7,8]+t_sc :: Forte.SC_Name -> [Z12]+t_sc n = snd (fromJust (find (\(m,_) -> n == m) t_sc_table))++-- | List of set classes.+t_scs :: [[Z12]]+t_scs = map snd t_sc_table++-- | Cardinality /n/ subset of 't_scs'.+--+-- > map (length . t_scs_n) [2..10] == [6,19,43,66,80,66,43,19,6]+t_scs_n :: Integral i => i -> [[Z12]]+t_scs_n n = filter ((== n) . genericLength) t_scs++-- | T-related /q/ that are subsets of /p/.+--+-- > t_subsets [0,1,2,3,4] [0,1]  == [[0,1],[1,2],[2,3],[3,4]]+-- > t_subsets [0,1,2,3,4] [0,1,4] == [[0,1,4]]+-- > t_subsets [0,2,3,6,7] [0,1,4] == [[2,3,6]]+t_subsets :: [Z12] -> [Z12] -> [[Z12]]+t_subsets x a = filter (`List.is_subset` x) (map sort (Sro.z_sro_t_related z12 a))++-- | T\/I-related /q/ that are subsets of /p/.+--+-- > ti_subsets [0,1,2,3,4] [0,1]  == [[0,1],[1,2],[2,3],[3,4]]+-- > ti_subsets [0,1,2,3,4] [0,1,4] == [[0,1,4],[0,3,4]]+-- > ti_subsets [0,2,3,6,7] [0,1,4] == [[2,3,6],[3,6,7]]+ti_subsets :: [Z12] -> [Z12] -> [[Z12]]+ti_subsets x a = filter (`List.is_subset` x) (nub (map sort (Sro.z_sro_ti_related z12 a)))++-- | Trivial run length encoder.+--+-- > rle "abbcccdde" == [(1,'a'),(2,'b'),(3,'c'),(2,'d'),(1,'e')]+rle :: (Eq a,Integral i) => [a] -> [(i,a)]+rle =+    let f x = (genericLength x,head x)+    in map f . group++-- | Inverse of 'rle'.+--+-- > rle_decode [(5,'a'),(4,'b')] == "aaaaabbbb"+rle_decode :: (Integral i) => [(i,a)] -> [a]+rle_decode =+    let f (i,j) = genericReplicate i j+    in concatMap f++-- | Length of /rle/ encoded sequence.+--+-- > rle_length [(5,'a'),(4,'b')] == 9+rle_length :: (Integral i) => [(i,a)] -> i+rle_length = sum . map fst++-- | T-equivalence /n/-class vector (subset-class vector, nCV).+--+-- > t_n_class_vector 2 [0..4] == [4,3,2,1,0,0]+-- > rle (t_n_class_vector 3 [0..4]) == [(1,3),(2,2),(2,1),(4,0),(1,1),(9,0)]+-- > rle (t_n_class_vector 4 [0..4]) == [(1,2),(3,1),(39,0)]+t_n_class_vector :: (Num a, Integral i) => i -> [Z12] -> [a]+t_n_class_vector n x =+    let a = t_scs_n n+    in map (genericLength . t_subsets x) a++-- | T\/I-equivalence /n/-class vector (subset-class vector, nCV).+--+-- > ti_n_class_vector 2 [0..4] == [4,3,2,1,0,0]+-- > ti_n_class_vector 3 [0,1,2,3,4] == [3,4,2,0,0,1,0,0,0,0,0,0]+-- > rle (ti_n_class_vector 4 [0,1,2,3,4]) == [(2,2),(1,1),(26,0)]+ti_n_class_vector :: (Num b, Integral i) => i -> [Z12] -> [b]+ti_n_class_vector n x =+    let a = Forte.scs_n n+    in map (genericLength . ti_subsets x) a++-- | 'icv' scaled by sum of /icv/.+--+-- > dyad_class_percentage_vector [0,1,2,3,4] == [40,30,20,10,0,0]+-- > dyad_class_percentage_vector [0,1,4,5,7] == [20,10,20,20,20,10]+dyad_class_percentage_vector :: Integral i => [Z12] -> [i]+dyad_class_percentage_vector p =+    let p' = Forte.z_icv z12 p+    in map (sum p' *) p'++-- | /rel/ metric.+--+-- > rel [0,1,2,3,4] [0,1,4,5,7] == 40+-- > rel [0,1,2,3,4] [0,2,4,6,8] == 60+-- > rel [0,1,4,5,7] [0,2,4,6,8] == 60+rel :: Integral i => [Z12] -> [Z12] -> Ratio i+rel x y =+    let x' = dyad_class_percentage_vector x+        y' = dyad_class_percentage_vector y+    in sum (map abs (zipWith (-) x' y')) % 2
Music/Theory/Z/Clough_1979.hs view
@@ -6,13 +6,14 @@  import qualified Music.Theory.List as T {- hmt -} --- type Z7 = Int-+-- | Shift sequence so the initial value is zero.+--+-- > transpose_to_zero [1,2,5] == [0,1,4] transpose_to_zero :: Num n => [n] -> [n] transpose_to_zero p =     case p of       [] -> []-      n:_ -> map (+ (negate n)) p+      n:_ -> map (subtract n) p  -- | Diatonic pitch class (Z7) set to /chord/. --@@ -33,8 +34,10 @@ dpcset_complement p = filter (`notElem` p) z7_univ  -- | Interval class predicate (ie. 'is_z4').+--+-- > map is_ic [-1 .. 4] == [False,True,True,True,True,False] is_ic :: Integral n => n -> Bool-is_ic n = n >= 0 && n < 4+is_ic = is_z4  -- | Interval to interval class. --@@ -48,7 +51,7 @@ is_chord :: Integral n => [n] -> Bool is_chord = (== 7) . sum --- | Interval vector.+-- | Interval vector, given list of intervals. -- -- > iv [2,2,3] == [0,2,1] iv :: Integral n => [n] -> [n]@@ -97,20 +100,28 @@  -- * Z +-- | Is /n/ in (0,/m/ - 1). is_z_n :: Integral n => n -> n -> Bool is_z_n m n = n >= 0 && n < m -is_z4 :: Integral n => n -> Bool-is_z4 = is_z_n 4-+-- | Z /m/ universe, ie [0 .. m-1]. z_n_univ :: Integral n => n -> [n] z_n_univ m = [0 .. m - 1] +-- | 'is_z_n' of 4.+is_z4 :: Integral n => n -> Bool+is_z4 = is_z_n 4++-- | 'z_n_univ' of 7.+--+-- > z7_univ == [0 .. 6] z7_univ :: Integral n => [n] z7_univ = z_n_univ 7 +-- | 'is_z_n' of 7. is_z7 :: Integral n => n -> Bool is_z7 = is_z_n 7 +-- | 'mod' 7. mod7 :: Integral n => n -> n mod7 n = n `mod` 7
Music/Theory/Z/Drape_1999.hs view
@@ -1,18 +1,367 @@+-- | Haskell implementations of @pct@ operations.+-- See <http://rd.slavepianos.org/?t=pct> module Music.Theory.Z.Drape_1999 where +import Data.Function {- base -}+import Data.List {- base -}+import Data.Maybe {- base -}++import qualified Music.Theory.List as T {- hmt -}+import qualified Music.Theory.Set.List as T {- hmt -}+import qualified Music.Theory.Tuple as T {- hmt -} import Music.Theory.Z-import Music.Theory.Z.SRO-import Music.Theory.Z.TTO+import Music.Theory.Z.Forte_1973+import Music.Theory.Z.Sro+import Music.Theory.Z.Tto -{- | Relate sets (TnMI).+-- | Cardinality filter+--+-- > cf [0,3] (cg [1..4]) == [[1,2,3],[1,2,4],[1,3,4],[2,3,4],[]]+cf :: (Integral n) => [n] -> [[a]] -> [[a]]+cf ns = filter (\p -> genericLength p `elem` ns) +-- | Combinatorial sets formed by considering each set as possible+-- values for slot.+--+-- > cgg [[0,1],[5,7],[3]] == [[0,5,3],[0,7,3],[1,5,3],[1,7,3]]+-- > let n = "01" in cgg [n,n,n] == ["000","001","010","011","100","101","110","111"]+cgg :: [[a]] -> [[a]]+cgg l =+    case l of+      x:xs -> [ y:z | y <- x, z <- cgg xs ]+      _ -> [[]]++-- | Combinations generator, ie. synonym for 'powerset'.+--+-- > sort (cg [0,1,3]) == [[],[0],[0,1],[0,1,3],[0,3],[1],[1,3],[3]]+cg :: [a] -> [[a]]+cg = T.powerset++-- | Powerset filtered by cardinality.+--+-- >>> pct cg -r3 0159+-- 015+-- 019+-- 059+-- 159+--+-- > cg_r 3 [0,1,5,9] == [[0,1,5],[0,1,9],[0,5,9],[1,5,9]]+cg_r :: (Integral n) => n -> [a] -> [[a]]+cg_r n = cf [n] . cg++{- | Chain pcsegs.++>>> echo 024579 | pct chn T0 3 | sort -u+579468 (RT8M)+579A02 (T5)++> chn_t0 z12 3 [0,2,4,5,7,9] == [[5,7,9,10,0,2],[5,7,9,4,6,8]]++>>> echo 02457t | pct chn T0 2+7A0135 (RT5I)+7A81B9 (RT9MI)++> chn_t0 z12 2 [0,2,4,5,7,10] == [[7,10,0,1,3,5],[7,10,8,1,11,9]]++-}+chn_t0 :: Integral i => Z i -> Int -> [i] -> [[i]]+chn_t0 z n p =+    let f q = T.take_right n p == take n q+    in filter f (z_sro_rtmi_related z p)++{- | Cyclic interval segment.++>>> echo 014295e38t76 | pct cisg+13A7864529B6++> ciseg z12 [0,1,4,2,9,5,11,3,8,10,7,6] == [1,3,10,7,8,6,4,5,2,9,11,6]++-}+ciseg :: Integral i => Z i -> [i] -> [i]+ciseg z = T.d_dx_by (z_sub z) . cyc++-- | Synonynm for 'z_complement'.+--+-- >>> pct cmpl 02468t+-- 13579B+--+-- > cmpl z12 [0,2,4,6,8,10] == [1,3,5,7,9,11]+cmpl :: Integral i => Z i -> [i] -> [i]+cmpl = z_complement++-- | Form cycle.+--+-- >>> echo 056 | pct cyc+-- 0560+--+-- > cyc [0,5,6] == [0,5,6,0]+cyc :: [a] -> [a]+cyc l =+    case l of+      [] -> []+      x:xs -> (x:xs) ++ [x]++-- | Diatonic set name. 'd' for diatonic set, 'm' for melodic minor+-- set, 'o' for octotonic set.+d_nm :: (Integral a) => [a] -> Maybe Char+d_nm x =+    case x of+      [0,2,4,5,7,9,11] -> Just 'd'+      [0,2,3,5,7,9,11] -> Just 'm'+      [0,1,3,4,6,7,9,10] -> Just 'o'+      _ -> Nothing++-- | Diatonic implications.+dim :: Integral i => [i] -> [(i,[i])]+dim p =+    let g (i,q) = T.is_subset p (z_tto_tn z12 i q)+        f = filter g . zip [0..11] . repeat+        d = [0,2,4,5,7,9,11]+        m = [0,2,3,5,7,9,11]+        o = [0,1,3,4,6,7,9,10]+    in f d ++ f m ++ f o++-- | Variant of 'dim' that is closer to the 'pct' form.+--+-- >>> pct dim 016+-- T1d+-- T1m+-- T0o+--+-- > dim_nm [0,1,6] == [(1,'d'),(1,'m'),(0,'o')]+dim_nm :: Integral i => [i] -> [(i,Char)]+dim_nm =+    let pk f (i,j) = (i,f j)+    in nubBy ((==) `on` snd) .+       map (pk (fromMaybe (error "dim_mn") . d_nm)) .+       dim++-- | Diatonic interval set to interval set.+--+-- >>> pct dis 24+-- 1256+--+-- > dis [2,4] == [1,2,5,6]+dis :: (Integral t) => [Int] -> [t]+dis =+    let is = [[], [], [1,2], [3,4], [5,6], [6,7], [8,9], [10,11]]+    in concatMap (is !!)++-- | Degree of intersection.+--+-- >>> echo 024579e | pct doi 6 | sort -u+-- 024579A+-- 024679B+--+-- > let p = [0,2,4,5,7,9,11]+-- > doi z12 6 p p == [[0,2,4,5,7,9,10],[0,2,4,6,7,9,11]]+--+-- >>> echo 01234 | pct doi 2 7-35 | sort -u+-- 13568AB+--+-- > doi z12 2 (sc "7-35") [0,1,2,3,4] == [[1,3,5,6,8,10,11]]+doi :: Integral i => Z i -> Int -> [i] -> [i] -> [[i]]+doi z n p q =+    let f j = [z_tto_tn z j p,z_tto_tni z j p]+        xs = concatMap f [0 .. z_modulus z - 1]+    in T.set (filter (\x -> length (x `intersect` q) == n) xs)++-- | Embedded segment search.+--+-- >>> echo 23A | pct ess 0164325+-- 2B013A9+-- 923507A+--+-- > ess z12 [0,1,6,4,3,2,5] [2,3,10] == [[9,2,3,5,0,7,10],[2,11,0,1,3,10,9]]+ess :: Integral i => Z i -> [i] -> [i] -> [[i]]+ess z p q = filter (`T.is_embedding` q) (z_sro_rtmi_related z p)++-- | Forte name (ie 'sc_name').+fn :: Integral i => [i] -> String+fn = sc_name++-- | Z-12 cycles.+frg_cyc :: Integral i => T.T6 [[i]]+frg_cyc =+    let add = z_add z12+        mul = z_mul z12+        c1 = [[0 .. 11]]+        c2 = map (\n -> map (add n) [0,2..10]) [0..1]+        c3 = map (\n -> map (add n) [0,3..9]) [0..2]+        c4 = map (\n -> map (add n) [0,4..8]) [0..3]+        c5 = map (map (mul 5)) c1+        c6 = map (\n -> map (add n) [0,6]) [0..5]+    in (c1,c2,c3,c4,c5,c6)++-- | Fragmentation of cycles.+frg :: Integral i =>  [i] -> T.T6 [String]+frg p =+    let f = map (\n -> if n `elem` p then z16_to_char n else '-')+    in T.t6_map (map f) frg_cyc++-- | Header sequence for 'frg_pp'.+frg_hdr :: [String]+frg_hdr = map (\n -> "Fragmentation of " ++ show n ++ "-cycle(s)") [1::Int .. 6]++{-| Fragmentation of cycles.++>>> pct frg 024579+Fragmentation of 1-cycle(s):  [0-2-45-7-9--]+Fragmentation of 2-cycle(s):  [024---] [--579-]+Fragmentation of 3-cycle(s):  [0--9] [-47-] [25--]+Fragmentation of 4-cycle(s):  [04-] [-59] [2--] [-7-]+Fragmentation of 5-cycle(s):  [05------4927]+Fragmentation of 6-cycle(s):  [0-] [-7] [2-] [-9] [4-] [5-]+IC cycle vector: <1> <22> <111> <1100> <5> <000000>++> putStrLn $ frg_pp [0,2,4,5,7,9]+-}+frg_pp :: Integral i => [i] -> String+frg_pp =+    let f = unwords . map (T.bracket ('[',']'))+        g x y = x ++ ": " ++ y+    in unlines . zipWith g frg_hdr . T.t6_to_list . T.t6_map f . frg++-- | Can the set-class q (under prime form algorithm pf) be drawn from the pcset p.+has_sc_pf :: (Integral a) => ([a] -> [a]) -> [a] -> [a] -> Bool+has_sc_pf pf p q =+    let n = length q+    in pf q `elem` map pf (cf [n] (cg p))++-- | 'has_sc_pf' of 'forte_prime'+--+-- > let d = [0,2,4,5,7,9,11]+-- > has_sc z12 d (z_complement z12 d) == True+--+-- > has_sc z12 [] [] == True+has_sc :: Integral i => Z i -> [i] -> [i] -> Bool+has_sc z = has_sc_pf (z_forte_prime z)++-- | Interval-class cycle vector.+ic_cycle_vector :: Integral i => [i] -> T.T6 [Int]+ic_cycle_vector p =+    let f str = let str' = if length str > 2 then T.close 1 str else str+                in length (filter (\(x,y) -> x /= '-' && y /= '-') (T.adj2 1 str'))+    in T.t6_map (map f) (frg p)++-- | Pretty printer for 'ic_cycle_vector'.+--+-- > let r = "IC cycle vector: <1> <22> <111> <1100> <5> <000000>"+-- > ic_cycle_vector_pp (ic_cycle_vector [0,2,4,5,7,9]) == r+ic_cycle_vector_pp :: T.T6 [Int] -> String+ic_cycle_vector_pp = ("IC cycle vector: " ++) . unwords . T.t6_to_list . T.t6_map z16_seq_pp++-- | Interval cycle filter.+--+-- >>> echo 22341 | pct icf+-- 22341+--+-- > icf [[2,2,3,4,1]] == [[2,2,3,4,1]]+icf :: (Num a,Eq a) => [[a]] -> [[a]]+icf = filter ((== 12) . sum)++-- | Interval class set to interval sets.+--+-- >>> pct ici -c 123+-- 123+-- 129+-- 1A3+-- 1A9+--+-- > ici_c [1,2,3] == [[1,2,3],[1,2,9],[1,10,3],[1,10,9]]+ici :: (Num t) => [Int] -> [[t]]+ici xs =+    let is j = [[0], [1,11], [2,10], [3,9], [4,8], [5,7], [6]] !! j+        ys = map is xs+    in cgg ys++-- | Interval class set to interval sets, concise variant.+--+-- > ici_c [1,2,3] == [[1,2,3],[1,2,9],[1,10,3],[1,10,9]]+ici_c :: [Int] -> [[Int]]+ici_c [] = []+ici_c (x:xs) = map (x:) (ici xs)++-- | Interval segment (INT).+iseg :: Integral i => Z i -> [i] -> [i]+iseg z = T.d_dx_by (z_sub z)++-- | Imbrications.+--+-- > let r = [[[0,2,4],[2,4,5],[4,5,7],[5,7,9]]+-- >         ,[[0,2,4,5],[2,4,5,7],[4,5,7,9]]]+-- > in imb [3,4] [0,2,4,5,7,9] == r+imb :: (Integral n) => [n] -> [a] -> [[[a]]]+imb cs p =+    let g n = (== n) . genericLength+        f ps n = filter (g n) (map (genericTake n) ps)+    in map (f (tails p)) cs++{- | 'issb' gives the set-classes that can append to 'p' to give 'q'.++>>> pct issb 3-7 6-32+3-7+3-2+3-11++> issb (sc "3-7") (sc "6-32") == ["3-2","3-7","3-11"]++-}+issb :: Integral i => [i] -> [i] -> [String]+issb p q =+    let k = length q - length p+        f = any (\x -> z_forte_prime z12 (nub (p ++ x)) == q) . z_tto_ti_related z12+    in map sc_name (filter f (cf [k] scs))++-- | Matrix search.+--+-- >>> pct mxs 024579 642 | sort -u+-- 6421B9+-- B97642+--+-- > set (mxs z12 [0,2,4,5,7,9] [6,4,2]) == [[6,4,2,1,11,9],[11,9,7,6,4,2]]+mxs :: Integral i => Z i -> [i] -> [i] -> [[i]]+mxs z p q = filter (q `isInfixOf`) (z_sro_rti_related z p)++-- | Normalize (synonym for 'set')+--+-- >>> pct nrm 0123456543210+-- 0123456+--+-- > nrm [0,1,2,3,4,5,6,5,4,3,2,1,0] == [0,1,2,3,4,5,6]+nrm :: (Ord a) => [a] -> [a]+nrm = T.set++-- | Normalize, retain duplicate elements.+nrm_r :: (Ord a) => [a] -> [a]+nrm_r = sort++{- | Pitch-class invariances (called @pi@ at @pct@).++>>> pct pi 0236 12+pcseg 0236+pcseg 6320+pcseg 532B+pcseg B235++> pci z12 [1,2] [0,2,3,6] == [[0,2,3,6],[5,3,2,11],[6,3,2,0],[11,2,3,5]]++-}+pci :: Integral i => Z i-> [Int] -> [i] -> [[i]]+pci z i p =+    let f q = T.set (map (q !!) i)+    in filter (\q -> f q == f p) (z_sro_rti_related z p)++{- | Relate sets (TnMI), ie 'z_tto_rel'+ >>> $ pct rs 0123 641B >>> T1M -> map tto_pp (rs 5 mod12 [0,1,2,3] [6,4,1,11]) == ["T1M","T4MI"]+> map tto_pp (rs 5 z12 [0,1,2,3] [6,4,1,11]) == ["T1M","T4MI"]+ -}-rs :: Integral t => t -> Z t -> [t] -> [t] -> [TTO t]-rs = z_tto_rel+rs :: Integral t => t -> Z t -> [t] -> [t] -> [Tto t]+rs m z p q = z_tto_rel m z (T.set p) (T.set q)  {- | Relate segments. @@ -25,12 +374,205 @@ >>> $ pct rsg 0123 B614 >>> r3RT1M -> let sros = map sro_parse . words-> rsg 5 mod12 [1,5,6] [3,11,10] == sros "T4I r1RT4MI"-> rsg 5 mod12 [0,1,2,3] [0,5,10,3] == sros "T0M RT3MI"-> rsg 5 mod12 [0,1,2,3] [4,11,6,1] == sros "T4MI RT1M"-> rsg 5 mod12 [0,1,2,3] [11,6,1,4] == sros "r1T4MI r1RT1M"+> let sros = map (sro_parse 5) . words+> rsg 5 z12 [1,5,6] [3,11,10] == sros "T4I r1RT4MI"+> rsg 5 z12 [0,1,2,3] [0,5,10,3] == sros "T0M RT3MI"+> rsg 5 z12 [0,1,2,3] [4,11,6,1] == sros "T4MI RT1M"+> rsg 5 z12 [0,1,2,3] [11,6,1,4] == sros "r1T4MI r1RT1M"  -}-rsg :: Integral i => i -> Z i -> [i] -> [i] -> [SRO i]-rsg m z x y = filter (\o -> z_sro_apply m z o x == y) (z_sro_univ (length x) z)+rsg :: Integral i => i -> Z i -> [i] -> [i] -> [Sro i]+rsg = z_sro_rel++-- | Subsets.+--+-- > cf [4] (sb z12 [sc "6-32",sc "6-8"]) == [[0,2,3,5],[0,1,3,5],[0,2,3,7],[0,2,4,7],[0,2,5,7]]+sb :: Integral i => Z i -> [[i]] -> [[i]]+sb z xs =+    let f p = all (\q -> has_sc z q p) xs+    in filter f scs++{- | scc = set class completion++>>> pct scc 6-32 168+35A+49B+3AB+34B++> scc z12 (sc "6-32") [1,6,8] == [[3,5,10],[4,9,11],[3,10,11],[3,4,11]]++-}+scc :: Integral i => Z i -> [i] -> [i] -> [[i]]+scc z r p = map (\\ p) (filter (T.is_subset p) (z_tto_ti_related z r))++-- | Header fields for 'si'.+si_hdr :: [String]+si_hdr =+    ["pitch-class-set"+    ,"set-class"+    ,"interval-class-vector"+    ,"tics"+    ,"complement"+    ,"multiplication-by-five-transform"]++-- | (Pcset,Tto,Forte-Prime)+type Si i = ([i],Tto i,[i])++-- | Calculator for si.+--+-- > si_calc [0,5,3,11]+si_calc :: Integral i => [i] -> (Si i,[i],[Int],Si i,Si i)+si_calc p =+    let n = length p+        p_icv = fromIntegral n : z_icv z12 p+        gen_si x = let x_f = z_forte_prime z12 x+                       x_o = head (rs 5 z12 x_f x)+                   in (nub (sort x),x_o,x_f)+    in (gen_si p,p_icv,tics z12 p,gen_si (z_complement z12 p),gen_si (map (z_mul z12 5) p))++-- | Pretty printer for RHS for si.+--+-- > si_rhs_pp [0,5,3,11]+si_rhs_pp :: (Integral i,Show i) => [i] -> [String]+si_rhs_pp p =+    let pf_pp concise (x_o,x_f) =+            concat [tto_pp x_o," ",sc_name x_f+                   ,if concise then "" else z16_vec_pp x_f]+        si_pp (x,x_o,x_f) = concat [z16_set_pp x," (",pf_pp True (x_o,x_f),")"]+        ((p',p_o,p_f),p_icv,p_tics,c,m) = si_calc p+    in [z16_set_pp p'+       ,pf_pp False (p_o,p_f)+       ,z16_vec_pp p_icv+       ,z16_vec_pp p_tics+       ,si_pp c+       ,si_pp m]++{- | Set information.++$ pct si 053b+pitch-class-set: {035B}+set-class: TB  4-Z15[0146]+interval-class-vector: [4111111]+tics: [102222102022]+complement: {1246789A} (TAI 8-Z15)+multiplication-by-five-transform: {0317} (T0  4-Z29)+$++> putStr $ unlines $ si [0,5,3,11]+-}+si :: (Integral i,Show i) => [i] -> [String]+si p = zipWith (\k v -> concat [k,": ",v]) si_hdr (si_rhs_pp p)++{- | Super set-class.++>>> pct spsc 4-11 4-12+5-26[02458]++> spsc z12 [sc "4-11",sc "4-12"] == [[0,2,4,5,8]]++>>> pct spsc 3-11 3-8+4-27[0258]+4-Z29[0137]++> spsc z12 [sc "3-11",sc "3-8"] == [[0,2,5,8],[0,1,3,7]]++>>> pct spsc `pct fl 3`+6-Z17[012478]++> spsc z12 (cf [3] scs) == [[0,1,2,4,7,8]]++-}+spsc :: Integral i => Z i -> [[i]] -> [[i]]+spsc z xs =+    let f y = all (has_sc z y) xs+        g = (==) `on` length+    in (head . groupBy g . filter f) scs++{- | sra = stravinsky rotational array++>>> echo 019BA7 | pct sra+019BA7+08A96B+021A34+0B812A+0923B1+056243++> let r = [[0,1,9,11,10,7],[0,8,10,9,6,11],[0,2,1,10,3,4],[0,11,8,1,2,10],[0,9,2,3,11,1],[0,5,6,2,4,3]]+> sra z12 [0,1,9,11,10,7] == r++-}+sra :: Integral i => Z i -> [i] -> [[i]]+sra z = map (z_sro_tn_to z 0) . T.rotations++{- | Serial operation.++>>> echo 156 | pct sro T4+59A++> sro (Z.sro_parse "T4") [1,5,6] == [5,9,10]++>>> echo 024579 | pct sro RT4I+79B024++> sro (Z.Sro 0 True 4 False True) [0,2,4,5,7,9] == [7,9,11,0,2,4]++>>> echo 156 | pct sro T4I+3BA++> sro (Z.sro_parse "T4I") [1,5,6] == [3,11,10]+> sro (Z.Sro 0 False 4 False True) [1,5,6] == [3,11,10]++>>> echo 156 | pct sro T4  | pct sro T0I+732++> (sro (Z.sro_parse "T0I") . sro (Z.sro_parse "T4")) [1,5,6] == [7,3,2]++>>> echo 024579 | pct sro RT4I+79B024++> sro (Z.sro_parse "RT4I") [0,2,4,5,7,9] == [7,9,11,0,2,4]++-}+sro :: Integral i => Z i -> Sro i -> [i] -> [i]+sro = z_sro_apply++{- | tmatrix++>>> pct tmatrix 1258++1258+0147+9A14+67A1++> tmatrix z12 [1,2,5,8] == [[1,2,5,8],[0,1,4,7],[9,10,1,4],[6,7,10,1]]++-}+tmatrix :: Integral i => Z i -> [i] -> [[i]]+tmatrix z p =+    let i = map (z_negate z) (T.d_dx_by (z_sub z) p)+    in map (\n -> map (z_add z n) p) (T.dx_d 0 i)+++{- | trs = transformations search.  Search all RTnMI of /p/ for /q/.++>>> echo 642 | pct trs 024579 | sort -u+531642+6421B9+642753+B97642++> let r = [[5,3,1,6,4,2],[6,4,2,1,11,9],[6,4,2,7,5,3],[11,9,7,6,4,2]]+> sort (trs z12 [0,2,4,5,7,9] [6,4,2]) == r++-}+trs :: Integral i => Z i -> [i] -> [i] -> [[i]]+trs z p q = filter (q `isInfixOf`) (z_sro_rtmi_related z p)++-- | Like 'trs', but of 'z_sro_rti_related'.+--+-- > trs_m z12 [0,2,4,5,7,9] [6,4,2] == [[6,4,2,1,11,9],[11,9,7,6,4,2]]+trs_m :: Integral i => Z i -> [i] -> [i] -> [[i]]+trs_m z p q = filter (q `isInfixOf`) (z_sro_rti_related z p)
+ Music/Theory/Z/Drape_1999/Cli.hs view
@@ -0,0 +1,111 @@+module Music.Theory.Z.Drape_1999.Cli where++import Data.Char {- base -}+import Data.Int {- base -}++import Music.Theory.Z {- hmt -}+import Music.Theory.Z.Drape_1999 {- hmt -}+import Music.Theory.Z.Forte_1973 {- hmt -}+import Music.Theory.Z.Sro {- hmt -}++type Z12 = Int8++help :: [String]+help =+    ["pct ess pcset"+    ,"pct fl -c cset"+    ,"pct frg pcset"+    ,"pct si [pcset]"+    ,"pct spsc set-class..."+    ,"pct sra"+    ,"pct sro sro"+    ,"pct tmatrix pcseg"+    ,"pct trs [-m] pcseg"]++z16_seq_parse :: String -> [Int]+z16_seq_parse = map digitToInt++pco_parse :: String -> [Z12]+pco_parse = map fromIntegral . z16_seq_parse++pco_pp :: [Z12] -> String+pco_pp = map (toUpper . integral_to_digit)++-- > cset_parse "34" == [3,4]+cset_parse :: String -> [Int]+cset_parse = map digitToInt++type CMD = String -> String++mk_cmd :: ([Z12] -> [Z12]) -> CMD+mk_cmd f = pco_pp . f . pco_parse++mk_cmd_many :: ([Z12] -> [[Z12]]) -> CMD+mk_cmd_many f = unlines . map pco_pp . f . pco_parse++-- > ess_cmd "0164325" "23A" == unlines ["923507A","2B013A9"]+ess_cmd :: String -> CMD+ess_cmd p = mk_cmd_many (ess z12 (pco_parse p))++z12_sc_name :: [Z12] -> SC_Name+z12_sc_name = sc_name++fl_c_cmd :: CMD+fl_c_cmd = unlines . map z12_sc_name . concatMap scs_n . cset_parse++frg_cmd :: CMD+frg_cmd p =+    let p' = pco_parse p+    in unlines [frg_pp p',ic_cycle_vector_pp (ic_cycle_vector p')]++pi_cmd :: String -> CMD+pi_cmd p = mk_cmd_many (pci z12 (z16_seq_parse p))++scc_cmd :: String -> CMD+scc_cmd p = mk_cmd_many (scc z12 (sc p))++si_cmd :: CMD+si_cmd = unlines . si . pco_parse++z12_sc_name_long :: [Z12] -> SC_Name+z12_sc_name_long = sc_name_long++-- > spsc_cmd ["4-11","4-12"] == "5-26[02458]\n"+spsc_cmd :: [String] -> String+spsc_cmd = unlines . map z12_sc_name_long . spsc z12 . map sc++sra_cmd :: CMD+sra_cmd = mk_cmd_many (sra z12)++sro_cmd :: String -> CMD+sro_cmd o = mk_cmd (sro z12 (sro_parse 5 o))++-- > putStrLn $ tmatrix_cmd "1258"+tmatrix_cmd :: CMD+tmatrix_cmd = mk_cmd_many (tmatrix z12)++-- > putStrLn $ trs_cmd (trs z12) "024579" "642"+trs_cmd :: ([Z12] -> [Z12] -> [[Z12]]) -> String -> CMD+trs_cmd f p = mk_cmd_many (f (pco_parse p))++interact_ln :: CMD -> IO ()+interact_ln f = interact (unlines . map f . lines)++pct_cli :: [String] -> IO ()+pct_cli arg = do+  case arg of+    ["ess",p] -> interact_ln (ess_cmd p)+    ["fl","-c",c] -> putStr (fl_c_cmd c)+    ["frg",p] -> putStr (frg_cmd p)+    ["pi",p,q] -> putStr (pi_cmd q p)+    ["scc",p] -> interact_ln (scc_cmd p)+    ["scc",p,q] -> putStr (scc_cmd p q)+    ["si"] -> interact_ln si_cmd+    ["si",p] -> putStr (si_cmd p)+    "spsc":p -> putStr (spsc_cmd p)+    ["sra"] -> interact_ln sra_cmd+    ["sro",o] -> interact_ln (sro_cmd o)+    ["tmatrix",p] -> putStr (tmatrix_cmd p)+    ["trs",p] -> interact_ln (trs_cmd (trs z12) p)+    ["trs","-m",p] -> interact_ln (trs_cmd (trs_m z12) p)+    _ -> putStrLn (unlines help)
Music/Theory/Z/Forte_1973.hs view
@@ -1,7 +1,8 @@--- | Allen Forte. /The Structure of Atonal Music/. Yale University--- Press, New Haven, 1973.+-- | Allen Forte. /The Structure of Atonal Music/.+--   Yale University Press, New Haven, 1973. module Music.Theory.Z.Forte_1973 where +import Data.Bifunctor {- base -} import Data.List {- base -} import Data.Maybe {- base -} @@ -10,39 +11,34 @@  import Music.Theory.Unicode {- hmt -} import Music.Theory.Z {- hmt -}-import Music.Theory.Z.SRO {- hmt -}+import Music.Theory.Z.Sro {- hmt -}  -- * Prime form --- | T-related rotations of /p/.+-- | T-related rotations of /p/, ie. all rotations tranposed to be at zero. ----- > t_rotations mod12 [0,1,3] == [[0,1,3],[0,2,11],[0,9,10]]-t_rotations :: Integral i => Z i -> [i] -> [[i]]-t_rotations z p =+-- > z_t_rotations z12 [1,2,4] == [[0,1,3],[0,2,11],[0,9,10]]+z_t_rotations :: Integral i => Z i -> [i] -> [[i]]+z_t_rotations z p =     let r = T.rotations (sort p)     in map (z_sro_tn_to z 0) r  -- | T\/I-related rotations of /p/. ----- > ti_rotations mod12 [0,1,3] == [[0,1,3],[0,2,11],[0,9,10]--- >                               ,[0,9,11],[0,2,3],[0,1,10]]-ti_rotations :: Integral i => Z i -> [i] -> [[i]]-ti_rotations z p =+-- > ti_rotations z12 [0,1,3] == [[0,1,3],[0,2,11],[0,9,10],[0,9,11],[0,2,3],[0,1,10]]+z_ti_rotations :: Integral i => Z i -> [i] -> [[i]]+z_ti_rotations z p =     let q = z_sro_invert z 0 p         r = T.rotations (sort p) ++ T.rotations (sort q)     in map (z_sro_tn_to z 0) r --- | Variant with default value for empty input list case.-minimumBy_or :: t -> (t -> t -> Ordering) -> [t] -> t-minimumBy_or p f q = if null q then p else minimumBy f q- -- | Prime form rule requiring comparator, considering 't_rotations'.-t_cmp_prime :: Integral i => Z i -> ([i] -> [i] -> Ordering) -> [i] -> [i]-t_cmp_prime z f = minimumBy_or [] f . t_rotations z+z_t_cmp_prime :: Integral i => Z i -> ([i] -> [i] -> Ordering) -> [i] -> [i]+z_t_cmp_prime z f = T.minimumBy_or [] f . z_t_rotations z  -- | Prime form rule requiring comparator, considering 'ti_rotations'.-ti_cmp_prime :: Integral i => Z i -> ([i] -> [i] -> Ordering) -> [i] -> [i]-ti_cmp_prime z f = minimumBy_or [] f . ti_rotations z+z_ti_cmp_prime :: Integral i => Z i -> ([i] -> [i] -> Ordering) -> [i] -> [i]+z_ti_cmp_prime z f = T.minimumBy_or [] f . z_ti_rotations z  -- | Forte comparison function (rightmost first then leftmost outwards). --@@ -56,44 +52,52 @@       _ -> let r = compare (last p) (last q)            in if r == EQ then compare p q else r --- | Forte prime form, ie. 'cmp_prime' of 'forte_cmp'.------ > forte_prime mod12 [0,1,3,6,8,9] == [0,1,3,6,8,9]--- > forte_prime mod5 [0,1,4] == [0,1,2]------ > S.set (map (forte_prime mod5) (S.powerset [0..4]))--- > S.set (map (forte_prime mod7) (S.powerset [0..6]))-forte_prime :: Integral i => Z i -> [i] -> [i]-forte_prime z = ti_cmp_prime z forte_cmp+{- | Forte prime form, ie. 'z_ti_cmp_prime' of 'forte_cmp'. --- | Transpositional equivalence prime form, ie. 't_cmp_prime' of--- 'forte_cmp'.+> z_forte_prime z12 [0,1,3,6,8,9] == [0,1,3,6,8,9]+> z_forte_prime z5 [0,1,4] == [0,1,2]+> z_forte_prime z5 [0,1,1] -- ERROR++> S.set (map (z_forte_prime z5) (S.powerset [0..4]))+> S.set (map (z_forte_prime z7) (S.powerset [0..6]))+-}+z_forte_prime :: Integral i => Z i -> [i] -> [i]+z_forte_prime z x =+  if nub x /= x || map (z_mod z) x /= x+  then error "z_forte_prime: invalid input"+  else z_ti_cmp_prime z forte_cmp x++-- | Transpositional equivalence prime form,+--   ie. 'z_t_cmp_prime' of 'forte_cmp'. ----- > (forte_prime mod12 [0,2,3],t_prime mod12 [0,2,3]) == ([0,1,3],[0,2,3])-t_prime :: Integral i => Z i -> [i] -> [i]-t_prime z = t_cmp_prime z forte_cmp+-- > (z_forte_prime z12 [0,2,3],z_t_prime z12 [0,2,3]) == ([0,1,3],[0,2,3])+z_t_prime :: Integral i => Z i -> [i] -> [i]+z_t_prime z = z_t_cmp_prime z forte_cmp  -- * ICV Metric  -- | Interval class of interval /i/. ----- > map (ic 12) [0..11] == [0,1,2,3,4,5,6,5,4,3,2,1]--- > map (ic 7) [0..6] == [0,1,2,3,3,2,1]--- > map (ic 5) [1,2,3,4] == [1,2,2,1]--- > map (ic 12) [5,6,7] == [5,6,5]--- > map (ic 12 . to_Z mod12) [-13,-1,0,1,13] == [1,1,0,1,1]-ic :: Integral i => i -> i -> i-ic z i = if i <= (z `div` 2) then i else z - i+-- > map (z_ic z12) [0..12] == [0,1,2,3,4,5,6,5,4,3,2,1,0]+-- > map (z_ic z7) [0..7] == [0,1,2,3,3,2,1,0]+-- > map (z_ic z5) [0..5] == [0,1,2,2,1,0]+-- > map (z_ic z12) [5,6,7] == [5,6,5]+-- > map (z_ic z12) [-13,-1,0,1,13] == [1,1,0,1,1]+z_ic :: Integral i => Z i -> i -> i+z_ic z i =+  let j = z_mod z i+      m = z_modulus z+  in if j <= (m `div` 2) then j else m - j  -- | Forte notation for interval class vector. ----- > icv 12 [0,1,2,4,7,8] == [3,2,2,3,3,2]-icv :: (Integral i, Num n) => i -> [i] -> [n]-icv z s =-    let i = map (ic z . flip mod z . uncurry (-)) (S.pairs s)+-- > z_icv z12 [0,1,2,4,7,8] == [3,2,2,3,3,2]+z_icv :: (Integral i, Num n) => Z i -> [i] -> [n]+z_icv z s =+    let i = map (z_ic z . z_mod z . uncurry (-)) (S.pairs s)         f l = (head l,genericLength l)         j = map f (group (sort i))-        k = map (`lookup` j) [1 .. z `div` 2]+        k = map (`lookup` j) [1 .. z_modulus z `div` 2]     in map (fromMaybe 0) k  -- * BIP Metric@@ -104,43 +108,36 @@ -- >>> bip 0t95728e3416 -- 11223344556 ----- > bip 12 [0,10,9,5,7,2,8,11,3,4,1,6] == [1,1,2,2,3,3,4,4,5,5,6]-bip :: Integral a => a -> [a] -> [a]-bip z = sort . map (ic z . flip mod z) . T.d_dx---- * Name+-- > z_bip z12 [0,10,9,5,7,2,8,11,3,4,1,6] == [1,1,2,2,3,3,4,4,5,5,6]+z_bip :: Integral i => Z i -> [i] -> [i]+z_bip z = sort . map (z_ic z . z_mod z) . T.d_dx  {- | Generate SC universe, though not in order of the Forte table. -> let r = [[]->         ,[0]->         ,[0,1],[0,2],[0,3]->         ,[0,1,2],[0,1,3],[0,1,4],[0,2,4]->         ,[0,1,2,3],[0,1,2,4],[0,1,3,4],[0,1,3,5]->         ,[0,1,2,3,4],[0,1,2,3,5],[0,1,2,4,5]->         ,[0,1,2,3,4,5]->         ,[0,1,2,3,4,5,6]]-> in sc_univ mod7 == r--> sort (sc_univ mod12) == sort (map snd sc_table)--> zipWith (\p q -> (p == q,p,q)) (sc_univ mod12) (map snd sc_table)+> length (z_sc_univ z7) == 18+> sort (z_sc_univ z12) == sort (map snd sc_table)+> zipWith (\p q -> (p == q,p,q)) (z_sc_univ z12) (map snd sc_table)  -}-sc_univ :: Integral i => Z i -> [[i]]-sc_univ z =-    T.sort_by_two_stage length id $+z_sc_univ :: Integral i => Z i -> [[i]]+z_sc_univ z =+    T.sort_by_two_stage_on length id $     nub $-    map (forte_prime z) $+    map (z_forte_prime z) $     S.powerset (z_univ z) +-- * Forte Names (Z12)+ -- | Synonym for 'String'. type SC_Name = String --- | The set-class table (Forte prime forms).+-- | Table of (SC-NAME,PCSET).+type SC_Table n = [(SC_Name,[n])]++-- | The Z12 set-class table (Forte prime forms). -- -- > length sc_table == 224-sc_table :: Num n => [(SC_Name,[n])]+sc_table :: Num n => SC_Table n sc_table =     [("0-1",[])     ,("1-1",[0])@@ -368,10 +365,10 @@     ,("12-1",[0,1,2,3,4,5,6,7,8,9,10,11])]  -- | Unicode (non-breaking hyphen) variant.-sc_table_unicode :: Num n => [(SC_Name,[n])]+sc_table_unicode :: Num n => SC_Table n sc_table_unicode =     let f = map (\c -> if c == '-' then non_breaking_hypen else c)-    in map (\(nm,pc) -> (f nm,pc)) sc_table+    in map (first f) sc_table  -- | Lookup name of prime form of set class.  It is an error for the -- input not to be a forte prime form.@@ -380,34 +377,37 @@ forte_prime_name :: (Num n,Eq n) => [n] -> (SC_Name,[n]) forte_prime_name p = fromMaybe (error "forte_prime_name") (find (\(_,q) -> p == q) sc_table) -sc_tbl_lookup :: Integral i => Z i -> [(SC_Name,[i])] -> [i] -> Maybe (SC_Name,[i])-sc_tbl_lookup z tbl p = find (\(_,q) -> forte_prime z p == q) tbl+-- | Lookup entry for set in table.+sc_tbl_lookup :: Integral i => SC_Table i -> [i] -> Maybe (SC_Name,[i])+sc_tbl_lookup tbl p = find (\(_,q) -> z_forte_prime z12 p == q) tbl -sc_tbl_lookup_err :: Integral i => Z i -> [(SC_Name,[i])] -> [i] -> (SC_Name,[i])-sc_tbl_lookup_err z tbl = fromMaybe (error "sc_tbl_lookup") . sc_tbl_lookup z tbl+-- | Erroring variant+sc_tbl_lookup_err :: Integral i => SC_Table i -> [i] -> (SC_Name,[i])+sc_tbl_lookup_err tbl = fromMaybe (error "sc_tbl_lookup") . sc_tbl_lookup tbl -sc_name' :: Integral i => Z i -> [(SC_Name,[i])] -> [i] -> SC_Name-sc_name' z tbl = fst . sc_tbl_lookup_err z tbl+-- | 'fst' of 'sc_tbl_lookup_err'+sc_name_tbl :: Integral i => SC_Table i -> [i] -> SC_Name+sc_name_tbl tbl = fst . sc_tbl_lookup_err tbl  -- | Lookup a set-class name.  The input set is subject to--- 'forte_prime' before lookup.+-- 'forte_prime' of 'z12' before lookup. ----- > sc_name mod12 [0,2,3,6,7] == "5-Z18"--- > sc_name mod12 [0,1,4,6,7,8] == "6-Z17"-sc_name :: Integral i => Z i -> [i] -> SC_Name-sc_name z = sc_name' z sc_table+-- > sc_name [0,2,3,6,7] == "5-Z18"+-- > sc_name [0,1,4,6,7,8] == "6-Z17"+sc_name :: Integral i => [i] -> SC_Name+sc_name = sc_name_tbl sc_table  -- | Long name (ie. with enumeration of prime form). ----- > sc_name_long mod12 [0,1,4,6,7,8] == "6-Z17[012478]"-sc_name_long :: Integral i => Z i -> [i] -> SC_Name-sc_name_long z p =-    let (nm,p') = sc_tbl_lookup_err z sc_table p+-- > sc_name_long [0,1,4,6,7,8] == "6-Z17[012478]"+sc_name_long :: Integral i => [i] -> SC_Name+sc_name_long p =+    let (nm,p') = sc_tbl_lookup_err sc_table p     in nm ++ z16_vec_pp p'  -- | Unicode (non-breaking hyphen) variant.-sc_name_unicode :: Integral i => Z i -> [i] -> SC_Name-sc_name_unicode z = sc_name' z sc_table_unicode+sc_name_unicode :: Integral i => [i] -> SC_Name+sc_name_unicode = sc_name_tbl sc_table_unicode  -- | Lookup a set-class given a set-class name. --@@ -415,6 +415,7 @@ sc :: Num n => SC_Name -> [n] sc n = snd (fromMaybe (error "sc") (find (\(m,_) -> n == m) sc_table)) +-- | The set-class table (Forte prime forms), ie. 'snd' of 'sc_table'. scs :: Num n => [[n]] scs = map snd sc_table @@ -426,7 +427,8 @@  -- | Vector indicating degree of intersection with inversion at each transposition. ----- > tics mod12 [0,2,4,5,7,9] == [3,2,5,0,5,2,3,4,1,6,1,4]+-- > tics z12 [0,2,4,5,7,9] == [3,2,5,0,5,2,3,4,1,6,1,4]+-- > map (tics z12) scs tics :: Integral i => Z i -> [i] -> [Int] tics z p =     let q = z_sro_t_related z (z_sro_invert z 0 p)@@ -436,13 +438,13 @@  -- | Locate /Z/ relation of set class. ----- > fmap (sc_name mod12) (z_relation_of 12 (sc "7-Z12")) == Just "7-Z36"-z_relation_of :: Integral i => i -> [i] -> Maybe [i]-z_relation_of z x =+-- > fmap sc_name (z_relation_of (sc "7-Z12")) == Just "7-Z36"+z_relation_of :: Integral i => [i] -> Maybe [i]+z_relation_of x =     let n = length x         eq_i :: [Integer] -> [Integer] -> Bool         eq_i = (==)-        f y = (x /= y) && (icv z x `eq_i` icv z y)+        f y = (x /= y) && (z_icv z12 x `eq_i` z_icv z12 y)     in case filter f (scs_n n) of          [] -> Nothing          [r] -> Just r
+ Music/Theory/Z/Lewin_1980.hs view
@@ -0,0 +1,50 @@+-- | David Lewin. \"A Response to a Response: On PC Set+-- Relatedness\". /Perspectives of New Music/, 18(1-2):498-502, 1980.+module Music.Theory.Z.Lewin_1980 where++import Data.Int {- base -}+import Data.List {- base -}++import qualified Music.Theory.Z.Castren_1994 as Castren++type Z12 = Int8++-- | REL function with given /ncv/ function (see 't_rel' and 'ti_rel').+rel :: Floating n => (Int -> [a] -> [n]) -> [a] -> [a] -> n+rel ncv x y =+    let n = min (genericLength x) (genericLength y)+        p = map (`ncv` x) [2..n]+        q = map (`ncv` y) [2..n]+        f = zipWith (\i j -> sqrt (i * j))+        pt = sum (map sum p)+        qt = sum (map sum q)+    in sum (map sum (zipWith f p q)) / sqrt (pt * qt)++-- | T-equivalence REL function.+--+-- Kuusi 2001, 7.5.2+--+-- > let (~=) p q = abs (p - q) < 0.001+-- > t_rel [0,1,2,3,4] [0,2,3,6,7] ~= 0.429+-- > t_rel [0,1,2,3,4] [0,2,4,6,8] ~= 0.253+-- > t_rel [0,2,3,6,7] [0,2,4,6,8] ~= 0.324+t_rel :: Floating n => [Z12] -> [Z12] -> n+t_rel = rel Castren.t_n_class_vector++-- | T/I-equivalence REL function.+--+-- Buchler 1998, Fig. 3.38+--+-- > let (~=) p q = abs (p - q) < 0.001+-- > let a = [0,2,3,5,7]::[Z12]+-- > let b = [0,2,3,4,5,8]::[Z12]+-- > let g = [0,1,2,3,5,6,8,10]::[Z12]+-- > let j = [0,2,3,4,5,6,8]::[Z12]+-- > ti_rel a b ~= 0.593+-- > ti_rel a g ~= 0.648+-- > ti_rel a j ~= 0.509+-- > ti_rel b g ~= 0.712+-- > ti_rel b j ~= 0.892+-- > ti_rel g j ~= 0.707+ti_rel :: Floating n => [Z12] -> [Z12] -> n+ti_rel = rel Castren.ti_n_class_vector
+ Music/Theory/Z/Literature.hs view
@@ -0,0 +1,48 @@+-- | Z12 set class database.+module Music.Theory.Z.Literature where++-- | Set class database with descriptors for historically and+-- theoretically significant set classes, indexed by Forte name.+--+-- > lookup "6-Z17" sc_db == Just "All-Trichord Hexachord"+-- > lookup "7-35" sc_db == Just "diatonic collection (d)"+sc_db :: [(String,String)]+sc_db =+    [("4-Z15","All-Interval Tetrachord (see also 4-Z29)")+    ,("4-Z29","All-Interval Tetrachord (see also 4-Z15)")+    ,("6-Z17","All-Trichord Hexachord")+    ,("8-Z15","All-Tetrachord Octochord (see also 8-Z29)")+    ,("8-Z29","All-Tetrachord Octochord (see also 8-Z15)")+    ,("6-1","A-Type All-Combinatorial Hexachord")+    ,("6-8","B-Type All-Combinatorial Hexachord")+    ,("6-32","C-Type All-Combinatorial Hexachord")+    ,("6-7","D-Type All-Combinatorial Hexachord")+    ,("6-20","E-Type All-Combinatorial Hexachord")+    ,("6-35","F-Type All-Combinatorial Hexachord")+    ,("7-35","diatonic collection (d)")+    ,("7-34","ascending melodic minor collection")+    ,("8-28","octotonic collection (Messiaen Mode II)")+    ,("6-35","wholetone collection")+    ,("3-10","diminished triad")+    ,("3-11","major/minor triad")+    ,("3-12","augmented triad")+    ,("4-19","minor major-seventh chord")+    ,("4-20","major-seventh chord")+    ,("4-25","french augmented sixth chord")+    ,("4-28","dimished-seventh chord")+    ,("4-26","minor-seventh chord")+    ,("4-27","half-dimished seventh(P)/dominant-seventh(I) chord")+    ,("6-30","Petrushka Chord {0476a1},3-11 at T6")+    ,("6-34","Mystic Chord {06a492}")+    ,("6-Z44","Schoenberg Signature Set,3-3 at T5 or T7")+    ,("6-Z19","complement of 6-Z44,3-11 at T1 or TB")+    ,("9-12","Messiaen Mode III (nontonic collection)")+    ,("8-9","Messian Mode IV")+    ,("7-31","The only seven-element subset of 8-28. ")+    ,("5-31","The only five-element superset of 4-28.")+    ,("5-33","The only five-element subset of 6-35.")+    ,("7-33","The only seven-element superset of 6-35.")+    ,("5-21","The only five-element subset of 6-20.")+    ,("7-21","The only seven-element superset of 6-20.")+    ,("5-25","The only five-element subset of both 7-35 and 8-28.")+    ,("6-14","Any non-intersecting union of 3-6 and 3-12.") ]
+ Music/Theory/Z/Morris_1974.hs view
@@ -0,0 +1,49 @@+-- | Robert Morris and D. Starr. \"The Structure of All-Interval Series\".+-- /Journal of Music Theory/, 18:364-389, 1974.+module Music.Theory.Z.Morris_1974 where++import Control.Monad {- base -}++import qualified Control.Monad.Logic as L {- logict -}++-- | 'msum' '.' 'map' 'return'.+--+-- > L.observeAll (fromList [1..7]) == [1..7]+fromList :: MonadPlus m => [a] -> m a+fromList = msum . map return++-- | Interval from /i/ to /j/ in modulo-/n/.+--+-- > let f = int_n 12 in (f 0 11,f 11 0) == (11,1)+int_n :: Integral a => a -> a -> a -> a+int_n n i j = abs ((j - i) `mod` n)++-- | 'L.MonadLogic' all-interval series.+--+-- > map (length . L.observeAll . all_interval_m) [4,6,8,10] == [2,4,24,288]+-- > [0,1,3,2,9,5,10,4,7,11,8,6] `elem` L.observeAll (all_interval_m 12)+-- > length (L.observeAll (all_interval_m 12)) == 3856+all_interval_m :: (MonadPlus m, L.MonadLogic m) => Int -> m [Int]+all_interval_m n =+    let recur k p q = -- k = length p, p = pitch-class sequence, q = interval set+            if k == n+            then return (reverse p)+            else do i <- fromList [1 .. n - 1]+                    guard (i `notElem` p)+                    let j = head p+                        m = int_n n i j+                    guard (m `notElem` q)+                    recur (k + 1) (i : p) (m : q)+    in recur 1 [0] []++{- | 'L.observeAll' of 'all_interval_m'.++> let r = [[0,1,5,2,4,3],[0,2,1,4,5,3],[0,4,5,2,1,3],[0,5,1,4,2,3]]+> all_interval 6 == r++> d_dx_n n l = zipWith (int_n n) l (tail l)+> map (d_dx_n 6) r == [[1,4,3,2,5],[2,5,3,1,4],[4,1,3,5,2],[5,2,3,4,1]]++-}+all_interval :: Int -> [[Int]]+all_interval = L.observeAll . all_interval_m
+ Music/Theory/Z/Morris_1987.hs view
@@ -0,0 +1,12 @@+-- | Robert Morris. /Composition with Pitch-Classes: A Theory of+-- Compositional Design/. Yale University Press, New Haven, 1987.+module Music.Theory.Z.Morris_1987 where++import Music.Theory.List {- hmt -}+import Music.Theory.Z {- hmt -}++-- | @INT@ operator.+--+-- > map (int z12) [[0,1,3,6,10],[3,7,0]] == [[1,2,3,4],[4,5]]+int :: Integral i => Z i -> [i] -> [i]+int z = d_dx_by (z_sub z)
+ Music/Theory/Z/Morris_1987/Parse.hs view
@@ -0,0 +1,19 @@+-- | Parsers for pitch class sets and sequences, and for 'SRO's.+module Music.Theory.Z.Morris_1987.Parse where++import Data.Char {- base -}++-- | Parse a /pitch class object/ string.  Each 'Char' is either a+-- number, a space which is ignored, or a letter name for the numbers+-- 10 ('t' or 'a' or 'A') or 11 ('e' or 'B' or 'b').+--+-- > pco "13te" == [1,3,10,11]+-- > pco "13te" == pco "13ab"+pco :: Num n => String -> [n]+pco s =+    let s' = dropWhile isSpace s+        s'' = takeWhile (`elem` "0123456789taAebB") s'+        f c | c `elem` "taA" = 10+            | c `elem` "ebB" = 11+            | otherwise = fromInteger (read [c])+    in map f s''
+ Music/Theory/Z/Rahn_1980.hs view
@@ -0,0 +1,29 @@+-- | John Rahn. /Basic Atonal Theory/. Longman, New York, 1980.+module Music.Theory.Z.Rahn_1980 where++import qualified Music.Theory.Z.Forte_1973 as Forte_1973 {- hmt -}+import Music.Theory.Z {- hmt -}++-- | Rahn prime form (comparison is rightmost inwards).+--+-- > rahn_cmp [0,1,3,6,8,9] [0,2,3,6,7,9] == GT+rahn_cmp :: Ord a => [a] -> [a] -> Ordering+rahn_cmp p q = compare (reverse p) (reverse q)++-- | Rahn prime form, ie. 'Forte_1973.ti_cmp_prime' of 'rahn_cmp'.+--+-- > z_rahn_prime z12 [0,1,3,6,8,9] == [0,2,3,6,7,9]+z_rahn_prime :: Integral i => Z i -> [i] -> [i]+z_rahn_prime z = Forte_1973.z_ti_cmp_prime z rahn_cmp++-- | The six sets where the Forte and Rahn prime forms differ.+--   Given here in Forte prime form.+--+-- > all (\p -> Forte_1973.forte_prime z12 p /= rahn_prime z12 p) rahn_forte_diff == True+rahn_forte_diff :: Num n => [[n]]+rahn_forte_diff =+  [[0,1,3,7,8] -- #5+  ,[0,1,3,5,8,9],[0,1,3,6,8,9] -- #6+  ,[0,1,2,4,7,8,9],[0,1,2,3,5,8,9] -- #7+  ,[0,1,2,4,5,7,9,10] -- #8+  ]
Music/Theory/Z/Read_1978.hs view
@@ -7,84 +7,99 @@ import Data.Char {- base -} import Data.List {- base -} import Data.Maybe {- base -}--import qualified Music.Theory.List as T {- hmt -}+import Data.Word {- base -} +import qualified Music.Theory.List as List {- hmt -} import qualified Music.Theory.Z as Z {- hmt -}-import qualified Music.Theory.Z.SRO as Z {- hmt -}+import qualified Music.Theory.Z.Sro as Sro {- hmt -}  -- | Coding.-type Code = Int+type Code = Word64 +-- | Number of bits at 'Code'.+code_len :: Num n => n+code_len = 64+ -- | Bit array.-type Array = [Bool]+type Bit_Array = [Bool] --- | Pretty printer for 'Array'.-array_pp :: Array -> String-array_pp = map intToDigit . map fromEnum+-- | Logical complement.+bit_array_complement :: Bit_Array -> Bit_Array+bit_array_complement = map not --- | Parse PP of 'Array'.+-- | Pretty printer for 'Bit_Array'.+bit_array_pp :: Bit_Array -> String+bit_array_pp = map (intToDigit . fromEnum)++-- | Parse PP of 'Bit_Array'. ----- > parse_array "01001" == [False,True,False,False,True]-parse_array :: String -> Array-parse_array = map (toEnum . digitToInt)+-- > bit_array_parse "01001" == [False,True,False,False,True]+bit_array_parse :: String -> Bit_Array+bit_array_parse = map (toEnum . digitToInt) --- | Generate 'Code' from 'Array', the coding is most to least significant.+-- * MSB (BIG-ENDIAN)++-- | Generate 'Code' from 'Bit_Array', the coding is most to least significant. ----- > array_to_code (map toEnum [1,1,0,0,1,0,0,0,1,1,1,0,0]) == 6428-array_to_code :: Array -> Code-array_to_code a =-    let n = length a-        f e j = if e then 2 ^ (n - j - 1) else 0-    in sum (zipWith f a [0..])+-- > map (bit_array_to_code . bit_array_parse) (words "000 001 010 011 100 101 110 111") == [0..7]+-- > bit_array_to_code (bit_array_parse "1100100011100") == 6428+bit_array_to_code :: Bit_Array -> Code+bit_array_to_code a =+  let n = length a+      f e j = if e then 2 ^ (n - j - 1) else 0+  in if n > code_len+     then error "bit_array_to_code: > SZ"+     else sum (zipWith f a [0..]) --- | Inverse of 'array_to_code'.+-- | Inverse of 'bit_array_to_code'. ----- > code_to_array 13 6428 == map toEnum [1,1,0,0,1,0,0,0,1,1,1,0,0]-code_to_array :: Int -> Code -> Array-code_to_array n c = map (testBit c) [n - 1, n - 2 .. 0]+-- > code_to_bit_array 13 6428 == bit_array_parse "1100100011100"+code_to_bit_array :: Int -> Code -> Bit_Array+code_to_bit_array n c =+  if n > code_len+  then error "code_to_bit_array: > SZ"+  else map (testBit c) [n - 1, n - 2 .. 0] --- | Array to set.+-- | 'Bit_Array' to set. ----- > array_to_set (map toEnum [1,1,0,0,1,0,0,0,1,1,1,0,0]) == [0,1,4,8,9,10]--- > encode [0,1,4,8,9,10] == 1811-array_to_set :: Integral i => [Bool] -> [i]-array_to_set =+-- > bit_array_to_set (bit_array_parse "1100100011100") == [0,1,4,8,9,10]+-- > set_to_code 13 [0,1,4,8,9,10] == 6428+bit_array_to_set :: Integral i => Bit_Array -> [i]+bit_array_to_set =     let f (i,e) = if e then Just i else Nothing     in mapMaybe f . zip [0..] --- | Inverse of 'array_to_set', /z/ is the degree of the array.-set_to_array :: Integral i => i -> [i] -> Array-set_to_array z p = map (`elem` p) [0 .. z - 1]+-- | Inverse of 'bit_array_to_set', /z/ is the degree of the array.+set_to_bit_array :: Integral i => i -> [i] -> Bit_Array+set_to_bit_array z p =+  if z > code_len+  then error "set_to_bit_array: > SZ"+  else map (`elem` p) [0 .. z - 1] --- | 'array_to_code' of 'set_to_array'.+-- | 'bit_array_to_code' of 'set_to_bit_array'. -- -- > set_to_code 12 [0,2,3,5] == 2880--- > map (set_to_code 12) (T.z_ti_related (flip mod 12) [0,2,3,5])+-- > map (set_to_code 12) (Sro.z_sro_ti_related (flip mod 12) [0,2,3,5]) set_to_code :: Integral i => i -> [i] -> Code-set_to_code z = array_to_code . set_to_array z---- | Logical complement.-array_complement :: Array -> Array-array_complement = map not+set_to_code z = bit_array_to_code . set_to_bit_array z  -- | The /prime/ form is the 'maximum' encoding. ----- > array_is_prime (set_to_array 12 [0,2,3,5]) == False-array_is_prime :: Array -> Bool-array_is_prime a =-    let c = array_to_code a-        p = array_to_set a+-- > bit_array_is_prime (set_to_bit_array 12 [0,2,3,5]) == False+bit_array_is_prime :: Bit_Array -> Bool+bit_array_is_prime a =+    let c = bit_array_to_code a+        p = bit_array_to_set a         n = length a-        z = flip mod n-        u = maximum (map (set_to_code n) (Z.z_sro_ti_related z p))+        z = Z.Z n+        u = maximum (map (set_to_code n) (Sro.z_sro_ti_related z p))     in c == u  -- | The augmentation rule adds @1@ in each empty slot at end of array. ----- > map array_pp (array_augment (parse_array "01000")) == ["01100","01010","01001"]-array_augment :: Array -> [Array]-array_augment a =+-- > map bit_array_pp (bit_array_augment (bit_array_parse "01000")) == ["01100","01010","01001"]+bit_array_augment :: Bit_Array -> [Bit_Array]+bit_array_augment a =     let (z,a') = break id (reverse a)         a'' = reverse a'         n = length z@@ -93,55 +108,61 @@     in map (a'' ++) x  -- | Enumerate first half of the set-classes under given /prime/ function.--- The second half can be derived as the complement of the first.+--   The second half can be derived as the complement of the first. ----- > import Music.Theory.Z12.Forte_1973+-- > import Music.Theory.Z.Forte_1973 -- > length scs == 224 -- > map (length . scs_n) [0..12] == [1,1,6,12,29,38,50,38,29,12,6,1,1] ----- > let z12 = map (fmap (map array_to_set)) (enumerate_half array_is_prime 12)+-- > let z12 = map (fmap (map bit_array_to_set)) (enumerate_half bit_array_is_prime 12) -- > map (length . snd) z12 == [1,1,6,12,29,38,50] -- -- This can become slow, edit /z/ to find out.  It doesn't matter -- about /n/.  This can be edited so that small /n/ would run quickly -- even for large /z/. ----- > fmap (map array_to_set) (lookup 5 (enumerate_half array_is_prime 16))-enumerate_half :: (Array -> Bool) -> Int -> [(Int,[Array])]+-- > fmap (map bit_array_to_set) (lookup 5 (enumerate_half bit_array_is_prime 16))+enumerate_half :: (Bit_Array -> Bool) -> Int -> [(Int,[Bit_Array])] enumerate_half pr n =     let a0 = replicate n False         f k a = if k >= n `div` 2                 then []-                else let r = filter pr (array_augment a)+                else let r = filter pr (bit_array_augment a)                      in (k + 1,r) : concatMap (f (k + 1)) r         jn l = case l of                  (x,y):l' -> (x,concat (y : map snd l'))                  _ -> error ""-        post_proc = map jn . T.group_on fst . sortOn fst+        post_proc = map jn . List.group_on fst . sortOn fst     in post_proc ((0,[a0]) : f 0 a0) --- * Alternate (reverse) form.+-- * LSB - LITTLE-ENDIAN +-- | If the size of the set is '>' 'code_len' then 'error', else 'id'.+set_coding_validate :: [t] -> [t]+set_coding_validate l = if length l <= code_len then l else error "set_coding_validate: SIZE"+ -- | Encoder for 'encode_prime'. ----- > encode [0,1,3,6,8,9] == 843-encode :: Integral i => [i] -> Code-encode = sum . map (2 ^)+-- > map set_encode [[0,1,3,7,8],[0,1,3,6,8,9]] == [395,843]+--+-- > map (set_to_code 12) [[0,1,3,7,8],[0,1,3,6,8,9]] == [3352,3372]+set_encode :: Integral i => [i] -> Code+set_encode = sum . map (2 ^) . set_coding_validate  -- | Decoder for 'encode_prime'. ----- > decode 12 843 == [0,1,3,6,8,9]-decode :: Integral i => i -> Code -> [i]-decode z n =-    let f i = (i,testBit n (fromIntegral i))+-- > map (set_decode 12) [395,843] == [[0,1,3,7,8],[0,1,3,6,8,9]]+set_decode :: Integral i => Int -> Code -> [i]+set_decode z n =+    let f i = (fromIntegral i,testBit n i)     in map fst (filter snd (map f [0 .. z - 1]))  -- | Binary encoding prime form algorithm, equalivalent to Rahn. ----- > encode_prime Z.mod12 [0,1,3,6,8,9] == [0,2,3,6,7,9]--- > Music.Theory.Z12.Rahn_1980.rahn_prime [0,1,3,6,8,9] == [0,2,3,6,7,9]-encode_prime :: Integral i => Z.Z i -> [i] -> [i]-encode_prime z s =-    let t = map (\x -> Z.z_sro_tn z x s) (Z.z_univ z)-        c = t ++ map (Z.z_sro_invert z 0) t-    in decode (Z.z_modulus z) (minimum (map encode c))+-- > set_encode_prime Z.z12 [0,1,3,6,8,9] == [0,2,3,6,7,9]+-- > Music.Theory.Z.Rahn_1980.rahn_prime Z.z12 [0,1,3,6,8,9] == [0,2,3,6,7,9]+set_encode_prime :: Integral i => Z.Z i -> [i] -> [i]+set_encode_prime z s =+    let t = map (\x -> Sro.z_sro_tn z x s) (Z.z_univ z)+        c = t ++ map (Sro.z_sro_invert z 0) t+    in set_decode (fromIntegral (Z.z_modulus z)) (minimum (map set_encode c))
− Music/Theory/Z/SRO.hs 
@@ -1,189 +0,0 @@--- | Serial (ordered) pitch-class operations on 'Z'.-module Music.Theory.Z.SRO where--import Data.List {- base -}-import qualified Text.ParserCombinators.Parsec as P {- parsec -}--import qualified Music.Theory.List as T-import qualified Music.Theory.Parse as T--import Music.Theory.Z---- | Serial operator,of the form rRTMI.-data SRO t = SRO {sro_r :: Int-                 ,sro_R :: Bool-                 ,sro_T :: t-                 ,sro_M :: Bool-                 ,sro_I :: Bool}-             deriving (Eq,Show)---- | Printer in 'rnRTnMI' form.-sro_pp :: Show t => SRO t -> String-sro_pp (SRO rN r tN m i) =-    concat [if rN /= 0 then 'r' : show rN else ""-           ,if r then "R" else ""-           ,'T' : show tN-           ,if m then "M" else ""-           ,if i then "I" else ""]--p_sro :: Integral t => P.GenParser Char () (SRO t)-p_sro = do-  let rot = P.option 0 (P.char 'r' >> T.parse_int)-  r <- rot-  r' <- T.is_char 'R'-  _ <- P.char 'T'-  t <- T.parse_int-  m <- T.is_char 'M'-  i <- T.is_char 'I'-  P.eof-  return (SRO r r' t m i)---- | Parse a Morris format serial operator descriptor.------ > sro_parse "r2RT3MI" == SRO 2 True 3 True True-sro_parse :: Integral i => String -> SRO i-sro_parse =-    either (\e -> error ("sro_parse failed\n" ++ show e)) id .-    P.parse p_sro ""---- | The total set of serial operations.------ > let u = z_sro_univ 3 mod12--- > zip (map sro_pp u) (map (\o -> z_sro_apply 5 mod12 o [0,1,3]) u)-z_sro_univ :: Integral i => Int -> Z i -> [SRO i]-z_sro_univ n_rot z =-    [SRO r r' t m i |-     r <- [0 .. n_rot - 1],-     r' <- [False,True],-     t <- z_univ z,-     m <- [False,True],-     i <- [False,True]]---- | The set of transposition 'SRO's.-z_sro_Tn :: Integral i => Z i -> [SRO i]-z_sro_Tn z = [SRO 0 False n False False | n <- z_univ z]---- | The set of transposition and inversion 'SRO's.-z_sro_TnI :: Integral i => Z i -> [SRO i]-z_sro_TnI z =-    [SRO 0 False n False i |-     n <- z_univ z,-     i <- [False,True]]---- | The set of retrograde and transposition and inversion 'SRO's.-z_sro_RTnI :: Integral i => Z i -> [SRO i]-z_sro_RTnI z =-    [SRO 0 r n False i |-     r <- [True,False],-     n <- z_univ z,-     i <- [False,True]]---- | The set of transposition, @M5@ and inversion 'SRO's.-z_sro_TnMI :: Integral i => Z i -> [SRO i]-z_sro_TnMI z =-    [SRO 0 False n m i |-     n <- z_univ z,-     m <- [True,False],-     i <- [True,False]]---- | The set of retrograde,transposition,@M5@ and inversion 'SRO's.-z_sro_RTnMI :: Integral i => Z i -> [SRO i]-z_sro_RTnMI z =-    [SRO 0 r n m i |-     r <- [True,False],-     n <- z_univ z,-     m <- [True,False],-     i <- [True,False]]---- * Serial operations---- | Apply SRO.  M is ordinarily 5, but can be specified here.------ > z_sro_apply 5 mod12 (SRO 1 True 1 True False) [0,1,2,3] == [11,6,1,4]--- > z_sro_apply 5 mod12 (SRO 1 False 4 True True) [0,1,2,3] == [11,6,1,4]-z_sro_apply :: Integral i => i -> Z i -> SRO i -> [i] -> [i]-z_sro_apply mn z (SRO r r' t m i) x =-    let x1 = if i then z_sro_invert z 0 x else x-        x2 = if m then z_sro_mn z mn x1 else x1-        x3 = z_sro_tn z t x2-        x4 = if r' then reverse x3 else x3-    in T.rotate_left r x4---- | Transpose /p/ by /n/.------ > z_sro_tn mod5 4 [0,1,4] == [4,0,3]--- > z_sro_tn mod12 4 [1,5,6] == [5,9,10]-z_sro_tn :: (Integral i, Functor f) => Z i -> i -> f i -> f i-z_sro_tn z n = fmap (z_add z n)---- | Invert /p/ about /n/.------ > z_sro_invert mod5 0 [0,1,4] == [0,4,1]--- > z_sro_invert mod12 6 [4,5,6] == [8,7,6]--- > z_sro_invert mod12 0 [0,1,3] == [0,11,9]------ > import Data.Word {- base -}--- > z_sro_invert mod12 (0::Word8) [1,4,8]-z_sro_invert :: (Integral i, Functor f) => Z i -> i -> f i -> f i-z_sro_invert z n = fmap (\p -> z_sub z n (z_sub z p  n))---- | Composition of 'invert' about @0@ and 'tn'.------ > z_sro_tni mod5 1 [0,1,3] == [1,0,3]--- > z_sro_tni mod12 4 [1,5,6] == [3,11,10]--- > (z_sro_invert mod12 0 . z_sro_tn mod12 4) [1,5,6] == [7,3,2]-z_sro_tni :: (Integral i, Functor f) => Z i -> i -> f i -> f i-z_sro_tni z n = z_sro_tn z n . z_sro_invert z 0---- | Modulo multiplication.------ > z_sro_mn mod12 11 [0,1,4,9] == z_tni mod12 0 [0,1,4,9]-z_sro_mn :: (Integral i, Functor f) => Z i -> i -> f i -> f i-z_sro_mn z n = fmap (z_mul z n)---- | T-related sequences of /p/.------ > length (z_sro_t_related mod12 [0,3,6,9]) == 12--- > z_sro_t_related mod5 [0,2] == [[0,2],[1,3],[2,4],[3,0],[4,1]]-z_sro_t_related :: (Integral i, Functor f) => Z i -> f i -> [f i]-z_sro_t_related z p = fmap (\n -> z_sro_tn z n p) (z_univ z)---- | T\/I-related sequences of /p/.------ > length (z_sro_ti_related mod12 [0,1,3]) == 24--- > length (z_sro_ti_related mod12 [0,3,6,9]) == 24--- > z_sro_ti_related mod12 [0] == map return [0..11]-z_sro_ti_related :: (Eq (f i), Integral i, Functor f) => Z i -> f i -> [f i]-z_sro_ti_related z p = nub (z_sro_t_related z p ++ z_sro_t_related z (z_sro_invert z 0 p))---- | R\/T\/I-related sequences of /p/.------ > length (z_sro_rti_related mod12 [0,1,3]) == 48--- > length (z_sro_rti_related mod12 [0,3,6,9]) == 24-z_sro_rti_related :: Integral i => Z i -> [i] -> [[i]]-z_sro_rti_related z p = let q = z_sro_ti_related z p in nub (q ++ map reverse q)---- * Sequence operations---- | Variant of 'tn', transpose /p/ so first element is /n/.------ > z_sro_tn_to mod12 5 [0,1,3] == [5,6,8]--- > map (z_sro_tn_to mod12 0) [[0,1,3],[1,3,0],[3,0,1]]-z_sro_tn_to :: Integral i => Z i -> i -> [i] -> [i]-z_sro_tn_to z n p =-    case p of-      [] -> []-      x:xs -> n : z_sro_tn z (z_sub z n x) xs---- | Variant of 'invert', inverse about /n/th element.------ > map (z_sro_invert_ix mod12 0) [[0,1,3],[3,4,6]] == [[0,11,9],[3,2,0]]--- > map (z_sro_invert_ix mod12 1) [[0,1,3],[3,4,6]] == [[2,1,11],[5,4,2]]-z_sro_invert_ix :: Integral i => Z i -> Int -> [i] -> [i]-z_sro_invert_ix z n p = z_sro_invert z (p !! n) p---- | The standard t-matrix of /p/.------ > z_tmatrix mod12 [0,1,3] == [[0,1,3],[11,0,2],[9,10,0]]-z_tmatrix :: Integral i => Z i -> [i] -> [[i]]-z_tmatrix z p = map (\n -> z_sro_tn z n p) (z_sro_tn_to z 0 (z_sro_invert_ix z 0 p))
+ Music/Theory/Z/Sro.hs view
@@ -0,0 +1,219 @@+-- | Serial (ordered) pitch-class operations on 'Z'.+module Music.Theory.Z.Sro where++import Data.List {- base -}++import qualified Text.Parsec as P {- parsec -}++import qualified Music.Theory.List as List {- hmt -}+import qualified Music.Theory.Parse as Parse {- hmt -}++import Music.Theory.Z++-- | Serial operator,of the form rRTMI.+data Sro t = Sro {sro_r :: Int+                 ,sro_R :: Bool+                 ,sro_T :: t+                 ,sro_M :: t -- 1 5+                 ,sro_I :: Bool}+             deriving (Eq,Show)++-- | Printer in 'rnRTnMI' form.+sro_pp :: (Show t,Eq t,Num t) => Sro t -> String+sro_pp (Sro rN r tN m i) =+    concat [if rN /= 0 then 'r' : show rN else ""+           ,if r then "R" else ""+           ,'T' : show tN+           ,if m == 5 then "M" else if m == 1 then "" else error "sro_pp: M?"+           ,if i then "I" else ""]++-- | Parser for Sro.+p_sro :: Integral t => t -> Parse.P (Sro t)+p_sro m_mul = do+  let rot = P.option 0 (P.char 'r' >> Parse.parse_int)+  r <- rot+  r' <- Parse.is_char 'R'+  _ <- P.char 'T'+  t <- Parse.parse_int+  m <- Parse.is_char 'M'+  i <- Parse.is_char 'I'+  P.eof+  return (Sro r r' t (if m then m_mul else 1) i)++-- | Parse a Morris format serial operator descriptor.+--+-- > sro_parse 5 "r2RT3MI" == Sro 2 True 3 5 True+sro_parse :: Integral i => i -> String -> Sro i+sro_parse m =+    either (\e -> error ("sro_parse failed\n" ++ show e)) id .+    P.parse (p_sro m) ""++-- * Z++-- | The total set of serial operations.+--+-- > let u = z_sro_univ 3 5 z12+-- > zip (map sro_pp u) (map (\o -> z_sro_apply z12 o [0,1,3]) u)+z_sro_univ :: Integral i => Int -> i -> Z i -> [Sro i]+z_sro_univ n_rot m_mul z =+    [Sro r r' t m i |+     r <- [0 .. n_rot - 1],+     r' <- [False,True],+     t <- z_univ z,+     m <- [1,m_mul],+     i <- [False,True]]++-- | The set of transposition 'Sro's.+z_sro_Tn :: Integral i => Z i -> [Sro i]+z_sro_Tn z = [Sro 0 False n 1 False | n <- z_univ z]++-- | The set of transposition and inversion 'Sro's.+z_sro_TnI :: Integral i => Z i -> [Sro i]+z_sro_TnI z =+    [Sro 0 False n 1 i |+     n <- z_univ z,+     i <- [False,True]]++-- | The set of retrograde and transposition and inversion 'Sro's.+z_sro_RTnI :: Integral i => Z i -> [Sro i]+z_sro_RTnI z =+    [Sro 0 r n 1 i |+     r <- [True,False],+     n <- z_univ z,+     i <- [False,True]]++-- | The set of transposition, @M@ and inversion 'Sro's.+z_sro_TnMI :: Integral i => i -> Z i -> [Sro i]+z_sro_TnMI m_mul z =+    [Sro 0 False n m i |+     n <- z_univ z,+     m <- [1,m_mul],+     i <- [True,False]]++-- | The set of retrograde,transposition,@M5@ and inversion 'Sro's.+z_sro_RTnMI :: Integral i => i -> Z i -> [Sro i]+z_sro_RTnMI m_mul z =+    [Sro 0 r n m i |+     r <- [True,False],+     n <- z_univ z,+     m <- [1,m_mul],+     i <- [True,False]]++-- * Serial operations++-- | Apply Sro.+--+-- > z_sro_apply z12 (Sro 1 True 1 5 False) [0,1,2,3] == [11,6,1,4]+-- > z_sro_apply z12 (Sro 1 False 4 5 True) [0,1,2,3] == [11,6,1,4]+z_sro_apply :: Integral i => Z i -> Sro i -> [i] -> [i]+z_sro_apply z (Sro r r' t m i) x =+    let x1 = if i then z_sro_invert z 0 x else x+        x2 = if m == 1 then x1 else z_sro_mn z m x1+        x3 = z_sro_tn z t x2+        x4 = if r' then reverse x3 else x3+    in List.rotate_left r x4++-- | Find 'Sro's that map /x/ to /y/ given /m/ and /z/.+--+-- > map sro_pp (z_sro_rel 5 z12 [0,1,2,3] [11,6,1,4]) == ["r1T4MI","r1RT1M"]+z_sro_rel :: (Ord t,Integral t) => t -> Z t -> [t] -> [t] -> [Sro t]+z_sro_rel m z x y = filter (\o -> z_sro_apply z o x == y) (z_sro_univ (length x) m z)++-- * Plain++-- | Transpose /p/ by /n/.+--+-- > z_sro_tn z5 4 [0,1,4] == [4,0,3]+-- > z_sro_tn z12 4 [1,5,6] == [5,9,10]+z_sro_tn :: (Integral i, Functor f) => Z i -> i -> f i -> f i+z_sro_tn z n = fmap (z_add z n)++-- | Invert /p/ about /n/.+--+-- > z_sro_invert z5 0 [0,1,4] == [0,4,1]+-- > z_sro_invert z12 6 [4,5,6] == [8,7,6]+-- > map (z_sro_invert z12 0) [[0,1,3],[1,4,8]] == [[0,11,9],[11,8,4]]+--+-- > import Data.Word {- base -}+-- > z_sro_invert z12 (0::Word8) [1,4,8] == [3,0,8]+z_sro_invert :: (Integral i, Functor f) => Z i -> i -> f i -> f i+z_sro_invert z n = fmap (\p -> z_sub z n (z_sub z p  n))++-- | Composition of 'invert' about @0@ and 'tn'.+--+-- > z_sro_tni z5 1 [0,1,3] == [1,0,3]+-- > z_sro_tni z12 4 [1,5,6] == [3,11,10]+-- > (z_sro_invert z12 0 . z_sro_tn z12 4) [1,5,6] == [7,3,2]+z_sro_tni :: (Integral i, Functor f) => Z i -> i -> f i -> f i+z_sro_tni z n = z_sro_tn z n . z_sro_invert z 0++-- | Modulo multiplication.+--+-- > z_sro_mn z12 11 [0,1,4,9] == z_sro_tni z12 0 [0,1,4,9]+z_sro_mn :: (Integral i, Functor f) => Z i -> i -> f i -> f i+z_sro_mn z n = fmap (z_mul z n)++-- | M5, ie. 'mn' @5@.+--+-- > z_sro_m5 z12 [0,1,3] == [0,5,3]+z_sro_m5 :: (Integral i, Functor f) => Z i -> f i -> f i+z_sro_m5 z = z_sro_mn z 5++-- | T-related sequences of /p/.+--+-- > length (z_sro_t_related z12 [0,3,6,9]) == 12+-- > z_sro_t_related z5 [0,2] == [[0,2],[1,3],[2,4],[3,0],[4,1]]+z_sro_t_related :: (Integral i, Functor f) => Z i -> f i -> [f i]+z_sro_t_related z p = fmap (\n -> z_sro_tn z n p) (z_univ z)++-- | T\/I-related sequences of /p/.+--+-- > length (z_sro_ti_related z12 [0,1,3]) == 24+-- > length (z_sro_ti_related z12 [0,3,6,9]) == 24+-- > z_sro_ti_related z12 [0] == map return [0..11]+z_sro_ti_related :: (Eq (f i), Integral i, Functor f) => Z i -> f i -> [f i]+z_sro_ti_related z p = nub (z_sro_t_related z p ++ z_sro_t_related z (z_sro_invert z 0 p))++-- | R\/T\/I-related sequences of /p/.+--+-- > length (z_sro_rti_related z12 [0,1,3]) == 48+-- > length (z_sro_rti_related z12 [0,3,6,9]) == 24+z_sro_rti_related :: Integral i => Z i -> [i] -> [[i]]+z_sro_rti_related z p = let q = z_sro_ti_related z p in nub (q ++ map reverse q)++-- | T\/M\/I-related sequences of /p/, duplicates removed.+z_sro_tmi_related :: Integral i => Z i -> [i] -> [[i]]+z_sro_tmi_related z p = let q = z_sro_ti_related z p in nub (q ++ map (z_sro_m5 z) q)++-- | R\/T\/M\/I-related sequences of /p/, duplicates removed.+z_sro_rtmi_related :: Integral i => Z i -> [i] -> [[i]]+z_sro_rtmi_related z p = let q = z_sro_tmi_related z p in nub (q ++ map reverse q)++-- | r\/R\/T\/M\/I-related sequences of /p/, duplicates removed.+z_sro_rrtmi_related :: Integral i => Z i -> [i] -> [[i]]+z_sro_rrtmi_related z p = nub (concatMap (z_sro_rtmi_related z) (List.rotations p))++-- * Sequence operations++-- | Variant of 'tn', transpose /p/ so first element is /n/.+--+-- > z_sro_tn_to z12 5 [0,1,3] == [5,6,8]+-- > map (z_sro_tn_to z12 0) [[0,1,3],[1,3,0],[3,0,1]] == [[0,1,3],[0,2,11],[0,9,10]]+z_sro_tn_to :: Integral i => Z i -> i -> [i] -> [i]+z_sro_tn_to z n p =+    case p of+      [] -> []+      x:xs -> n : z_sro_tn z (z_sub z n x) xs++-- | Variant of 'invert', inverse about /n/th element.+--+-- > map (z_sro_invert_ix z12 0) [[0,1,3],[3,4,6]] == [[0,11,9],[3,2,0]]+-- > map (z_sro_invert_ix z12 1) [[0,1,3],[3,4,6]] == [[2,1,11],[5,4,2]]+z_sro_invert_ix :: Integral i => Z i -> Int -> [i] -> [i]+z_sro_invert_ix z n p = z_sro_invert z (p !! n) p++-- | The standard t-matrix of /p/.+--+-- > z_tmatrix z12 [0,1,3] == [[0,1,3],[11,0,2],[9,10,0]]+z_tmatrix :: Integral i => Z i -> [i] -> [[i]]+z_tmatrix z p = map (\n -> z_sro_tn z n p) (z_sro_tn_to z 0 (z_sro_invert_ix z 0 p))
− Music/Theory/Z/TTO.hs 
@@ -1,75 +0,0 @@-module Music.Theory.Z.TTO where--import Data.List {- base -}-import Data.Maybe {- base -}-import qualified Text.ParserCombinators.Parsec as P {- parsec -}--import qualified Music.Theory.Parse as T-import qualified Music.Theory.Set.List as T-import Music.Theory.Z---- | Twelve-tone operator, of the form TMI.-data TTO t = TTO {tto_T :: t,tto_M :: Bool,tto_I :: Bool}-             deriving (Eq,Show)--tto_identity :: Num t => TTO t-tto_identity = TTO 0 False False---- | Pretty printer.-tto_pp :: Show t => TTO t -> String-tto_pp (TTO t m i) = concat ['T' : show t,if m then "M" else "",if i then "I" else ""]--p_tto :: Integral t => P.GenParser Char () (TTO t)-p_tto = do-  _ <- P.char 'T'-  t <- T.parse_int-  m <- T.is_char 'M'-  i <- T.is_char 'I'-  P.eof-  return (TTO t m i)---- | Parser, transposition must be decimal.------ > map (tto_pp . tto_parse) (words "T5 T3I T11M T9MI")-tto_parse :: Integral i => String -> TTO i-tto_parse = either (\e -> error ("tto_parse failed\n" ++ show e)) id . P.parse p_tto ""---- | The set of all 'TTO', given 'Z' function.------ > length (z_tto_univ mod12) == 48--- > map tto_pp (z_tto_univ mod12)-z_tto_univ :: Integral t => Z t -> [TTO t]-z_tto_univ z = [TTO t m i | m <- [False,True], i <- [False,True], t <- z_univ z]---- | M is ordinarily 5, but can be specified here.------ > map (z_tto_f 5 mod12 (tto_parse "T1M")) [0,1,2,3] == [1,6,11,4]-z_tto_f :: Integral t => t -> Z t -> TTO t -> (t -> t)-z_tto_f mn z (TTO t m i) =-    let i_f = if i then z_negate z else id-        m_f = if m then z_mul z mn else id-        t_f = if t > 0 then z_add z t else id-    in t_f . m_f . i_f---- | 'sort' of 'map' 'z_tto_f'.------ > z_tto_apply 5 mod12 (tto_parse "T1M") [0,1,2,3] == [1,4,6,11]-z_tto_apply :: Integral t => t -> Z t -> TTO t -> [t] -> [t]-z_tto_apply mn z o = sort . map (z_tto_f mn z o)--tto_apply :: Integral t => t -> TTO t -> [t] -> [t]-tto_apply mn = z_tto_apply mn id---- | Find 'TTO' that that map /x/ to /y/ given /m/ and /z/.------ > map tto_pp (z_tto_rel 5 mod12 [0,1,2,3] [6,4,1,11]) == ["T1M","T4MI"]-z_tto_rel :: (Ord t,Integral t) => t -> Z t -> [t] -> [t] -> [TTO t]-z_tto_rel m z x y =-    let q = T.set y-    in mapMaybe (\o -> if z_tto_apply m z o x == q then Just o else Nothing) (z_tto_univ z)---- | 'nub' of 'sort' of 'map' /z/.------ > map (z_pcset mod12) [[0,6],[6,12],[12,18]] == replicate 3 [0,6]-z_pcset :: Ord t => Z t -> [t] -> [t]-z_pcset z = nub . sort . map z
+ Music/Theory/Z/Tto.hs view
@@ -0,0 +1,147 @@+-- | Generalised twelve-tone operations on un-ordered pitch-class sets with arbitrary Z.+module Music.Theory.Z.Tto where++import Data.List {- base -}+import Data.Maybe {- base -}++import qualified Text.Parsec as P {- parsec -}++import qualified Music.Theory.Parse as Parse {- hmt -}++import Music.Theory.Z {- hmt -}++-- * Tto++-- | Twelve-tone operator, of the form TMI.+data Tto t = Tto {tto_T :: t,tto_M :: t,tto_I :: Bool}+             deriving (Eq,Show)++-- | T0+tto_identity :: Num t => Tto t+tto_identity = Tto 0 1 False++-- | Pretty printer.  It is an error here is M is not 1 or 5.+tto_pp :: (Show t,Num t,Eq t) => Tto t -> String+tto_pp (Tto t m i) =+  concat ['T' : show t+         ,if m == 1 then "" else if m == 5 then "M" else error "tto_pp: M?"+         ,if i then "I" else ""]++-- | Parser for Tto, requires value for M (ordinarily 5 for 12-tone Tto).+p_tto :: Integral t => t -> Parse.P (Tto t)+p_tto m_mul = do+  _ <- P.char 'T'+  t <- Parse.parse_int+  m <- Parse.is_char 'M'+  i <- Parse.is_char 'I'+  P.eof+  return (Tto t (if m then m_mul else 1) i)++-- | Parser, transposition must be decimal.+--+-- > map (tto_pp . tto_parse 5) (words "T5 T3I T11M T9MI") == ["T5","T3I","T11M","T9MI"]+tto_parse :: Integral i => i -> String -> Tto i+tto_parse m = either (\e -> error ("tto_parse failed\n" ++ show e)) id . P.parse (p_tto m) ""++-- | Set M at Tto.+tto_M_set :: Integral t => t -> Tto t -> Tto t+tto_M_set m (Tto t _ i) = Tto t m i++-- * Z++-- | The set of all 'Tto', given 'Z'.+--+-- > length (z_tto_univ 5 z12) == 48+-- > map tto_pp (z_tto_univ 5 z12)+z_tto_univ :: Integral t => t -> Z t -> [Tto t]+z_tto_univ m_mul z = [Tto t m i | m <- [1,m_mul], i <- [False,True], t <- z_univ z]++-- | Apply Tto to pitch-class.+--+-- > map (z_tto_f z12 (tto_parse 5 "T1M")) [0,1,2,3] == [1,6,11,4]+z_tto_f :: Integral t => Z t -> Tto t -> (t -> t)+z_tto_f z (Tto t m i) =+    let i_f = if i then z_negate z else id+        m_f = if m == 1 then id else z_mul z m+        t_f = if t > 0 then z_add z t else id+    in t_f . m_f . i_f++-- | 'nub' of 'sort' of 'z_tto_f'.  (nub because M may be 0).+--+-- > z_tto_apply z12 (tto_parse 5 "T1M") [0,1,2,3] == [1,4,6,11]+z_tto_apply :: Integral t => Z t -> Tto t -> [t] -> [t]+z_tto_apply z o = nub . sort . map (z_tto_f z o)++-- | Find 'Tto's that map pc-set /x/ to pc-set /y/ given /m/ and /z/.+--+-- > map tto_pp (z_tto_rel 5 z12 [0,1,2,3] [1,4,6,11]) == ["T1M","T4MI"]+z_tto_rel :: (Ord t,Integral t) => t -> Z t -> [t] -> [t] -> [Tto t]+z_tto_rel m z x y =+  let f o = if z_tto_apply z o x == y then Just o else Nothing+  in mapMaybe f (z_tto_univ m z)++-- * Plain++-- | 'nub' of 'sort' of 'z_mod' of /z/.+--+-- > z_pcset z12 [1,13] == [1]+-- > map (z_pcset z12) [[0,6],[6,12],[12,18]] == replicate 3 [0,6]+z_pcset :: (Integral t,Ord t) => Z t -> [t] -> [t]+z_pcset z = nub . sort . map (z_mod z)++-- | Transpose by n.+--+-- > z_tto_tn z12 4 [1,5,6] == [5,9,10]+-- > z_tto_tn z12 4 [0,4,8] == [0,4,8]+z_tto_tn :: Integral i => Z i -> i -> [i] -> [i]+z_tto_tn z n = sort . map (z_add z n)++-- | Invert about n.+--+-- > z_tto_invert z12 6 [4,5,6] == [6,7,8]+-- > z_tto_invert z12 0 [0,1,3] == [0,9,11]+z_tto_invert :: Integral i => Z i -> i -> [i] -> [i]+z_tto_invert z n = sort . map (\p -> z_sub z n (z_sub z p n))++-- | Composition of 'z_tto_invert' about @0@ and 'z_tto_tn'.+--+-- > z_tto_tni z12 4 [1,5,6] == [3,10,11]+-- > (z_tto_invert z12 0 . z_tto_tn z12 4) [1,5,6] == [2,3,7]+z_tto_tni :: Integral i => Z i -> i -> [i] -> [i]+z_tto_tni z n = z_tto_tn z n . z_tto_invert z 0++-- | Modulo-z multiplication+--+-- > z_tto_mn z12 11 [0,1,4,9] == z_tto_invert z12 0 [0,1,4,9]+z_tto_mn :: Integral i => Z i -> i -> [i] -> [i]+z_tto_mn z n = sort . map (z_mul z n)++-- | M5, ie. 'mn' @5@.+--+-- > z_tto_m5 z12 [0,1,3] == [0,3,5]+z_tto_m5 :: Integral i => Z i -> [i] -> [i]+z_tto_m5 z = z_tto_mn z 5++-- * Sequence++-- | T-related sets of /p/.+z_tto_t_related_seq :: Integral i => Z i -> [i] -> [[i]]+z_tto_t_related_seq z p = map (\q -> z_tto_tn z q p) [0..11]++-- | Unique elements of 'z_tto_t_related_seq'.+--+-- > length (z_tto_t_related z12 [0,1,3]) == 12+-- > z_tto_t_related z12 [0,3,6,9] == [[0,3,6,9],[1,4,7,10],[2,5,8,11]]+z_tto_t_related :: Integral i => Z i -> [i] -> [[i]]+z_tto_t_related z = nub . z_tto_t_related_seq z++-- | T\/I-related set of /p/.+z_tto_ti_related_seq :: Integral i => Z i -> [i] -> [[i]]+z_tto_ti_related_seq z p = z_tto_t_related z p ++ z_tto_t_related z (z_tto_invert z 0 p)++-- | Unique elements of 'z_tto_ti_related_seq'.+--+-- > length (z_tto_ti_related z12 [0,1,3]) == 24+-- > z_tto_ti_related z12 [0,3,6,9] == [[0,3,6,9],[1,4,7,10],[2,5,8,11]]+z_tto_ti_related :: Integral i => Z i -> [i] -> [[i]]+z_tto_ti_related z = nub . z_tto_ti_related_seq z
− Music/Theory/Z12.hs 
@@ -1,111 +0,0 @@-{-# Language DataKinds #-}-{- | Z12--Z12 are modulo 12 integers.--> map signum [-1,0::Z12,1] == [1,0,1]-> map abs [-1,0::Z12,1] == [11,0,1]--Aspects of the 'Enum' instance are cyclic.--> pred (0::Z12) == 11-> succ (11::Z12) == 0--'Bounded' works--> [minBound::Z12 .. maxBound] == [0::Z12 .. 11]---}-module Music.Theory.Z12 where--import Data.Char {- base -}-import Data.List {- base -}-import qualified Data.Modular as M {- modular-arithmetic -}-import qualified GHC.TypeLits as L {- base -}--import qualified Music.Theory.List as T {- hmt -}---- | 'Mod' 'Int'.-type Z n = M.Mod Int n---- | 'Z' 12.------ > map negate [0::Z12 .. 0xB] == [0,0xB,0xA,9,8,7,6,5,4,3,2,1]--- > map (+ 5) [0::Z12 .. 11] == [5,6,7,8,9,0xA,0xB,0,1,2,3,4]-type Z12 = M.Mod Int 12---- | Cyclic form of 'enumFromThenTo'.------ > [9::Z12,11 .. 3] == []--- > enumFromThenTo_cyc (9::Z12) 11 3 == [9,11,1,3]-enumFromThenTo_cyc :: L.KnownNat n => Z n -> Z n -> Z n -> [Z n]-enumFromThenTo_cyc n m o =-    let m' = m + (m - n)-    in case compare m' o of-         LT -> n : enumFromThenTo_cyc m m' o-         EQ -> [n,m,o]-         GT -> [n,m]---- | Cyclic form of 'enumFromTo'.------ > [9::Z12 .. 3] == []--- > enumFromTo_cyc (9::Z12) 3 == [9,10,11,0,1,2,3]-enumFromTo_cyc :: L.KnownNat n => Z n -> Z n -> [Z n]-enumFromTo_cyc n m =-    let n' = succ n-    in if n' == m then [n,m] else n : enumFromTo_cyc n' m--{---}---- | Convert integral to 'Z12'.------ > map to_Z12 [-9,-3,0,13] == [3,9,0,1]-to_Z12 :: Integral i => i -> Z12-to_Z12 = M.toMod . fromIntegral--int_to_Z12 :: Int -> Z12-int_to_Z12 = to_Z12---- | Convert 'Z12' to integral.-from_Z12 :: Integral i => Z12 -> i-from_Z12 = fromIntegral . M.unMod--int_from_Z12 :: Z12 -> Int-int_from_Z12 = from_Z12---- | Z12 not in set.------ > complement [0,2,4,5,7,9,11] == [1,3,6,8,10]-complement :: [Z12] -> [Z12]-complement = (\\) [0 .. 11]---- | Z12 to character (10 -> A, 11 -> B).------ > map z12_to_char [0 .. 11] == "0123456789AB"-z12_to_char :: Z12 -> Char-z12_to_char = toUpper . intToDigit . M.unMod---- | Z12 to character (10 -> A, 11 -> B).------ > map char_to_z12 "0123456789AB" == [0..11]-char_to_z12 :: Char -> Z12-char_to_z12 = to_Z12 . digitToInt---- | Unordered set notation (braces).------ > z12_set_pp [0,1,3] == "{013}"-z12_set_pp :: [Z12] -> String-z12_set_pp = T.bracket ('{','}') . map z12_to_char---- | Ordered sequence notation (angle brackets).------ > z12_seq_pp [0,1,3] == "<013>"-z12_seq_pp :: [Z12] -> String-z12_seq_pp = T.bracket ('<','>') . map z12_to_char---- | Ordered vector notation (square brackets).------ > z12_vec_pp [0,1,3] == "[013]"-z12_vec_pp :: [Z12] -> String-z12_vec_pp = T.bracket ('[',']') . map z12_to_char
− Music/Theory/Z12/Castren_1994.hs 
@@ -1,151 +0,0 @@--- | Marcus Castrén. /RECREL: A Similarity Measure for Set-Classes/. PhD--- thesis, Sibelius Academy, Helsinki, 1994.-module Music.Theory.Z12.Castren_1994 where--import Data.List {- base -}-import Data.Maybe {- base -}-import Data.Ratio {- base -}--import qualified Music.Theory.List as T-import Music.Theory.Z (mod12)-import qualified Music.Theory.Z.SRO as T-import qualified Music.Theory.Z.Forte_1973 as T--type Z12 = Int---- | Is /p/ symmetrical under inversion.------ > map inv_sym (T.scs_n 2) == [True,True,True,True,True,True]--- > map (fromEnum.inv_sym) (T.scs_n 3) == [1,0,0,0,0,1,0,0,1,1,0,1]-inv_sym :: [Z12] -> Bool-inv_sym x = x `elem` map (\i -> sort (T.z_sro_tn mod12 i (T.z_sro_invert mod12 0 x))) [0..11]---- | If /p/ is not 'inv_sym' then @(p,invert 0 p)@ else 'Nothing'.------ > sc_t_ti [0,2,4] == Nothing--- > sc_t_ti [0,1,3] == Just ([0,1,3],[0,2,3])-sc_t_ti :: [Z12] -> Maybe ([Z12], [Z12])-sc_t_ti p =-    if inv_sym p-    then Nothing-    else Just (p,T.t_prime mod12 (T.z_sro_invert mod12 0 p))---- | Transpositional equivalence variant of Forte's 'sc_table'.  The--- inversionally related classes are distinguished by labels @A@ and--- @B@; the class providing the /best normal order/ (Forte 1973) is--- always the @A@ class. If neither @A@ nor @B@ appears in the name of--- a set-class, it is inversionally symmetrical.------ > (length T.sc_table,length t_sc_table) == (224,352)--- > lookup "5-Z18B" t_sc_table == Just [0,2,3,6,7]-t_sc_table :: [(T.SC_Name,[Z12])]-t_sc_table =-    let f x = let nm = T.sc_name mod12 x-              in case sc_t_ti x of-                   Nothing -> [(nm,x)]-                   Just (p,q) -> [(nm++"A",p),(nm++"B",q)]-    in concatMap f T.scs---- | Lookup a set-class name.  The input set is subject to--- 't_prime' before lookup.------ > t_sc_name [0,2,3,6,7] == "5-Z18B"--- > t_sc_name [0,1,4,6,7,8] == "6-Z17B"-t_sc_name :: [Z12] -> T.SC_Name-t_sc_name p =-    let n = find (\(_,q) -> T.t_prime mod12 p == q) t_sc_table-    in fst (fromJust n)---- | Lookup a set-class given a set-class name.------ > t_sc "6-Z17A" == [0,1,2,4,7,8]-t_sc :: T.SC_Name -> [Z12]-t_sc n = snd (fromJust (find (\(m,_) -> n == m) t_sc_table))---- | List of set classes.-t_scs :: [[Z12]]-t_scs = map snd t_sc_table---- | Cardinality /n/ subset of 't_scs'.------ > map (length . t_scs_n) [2..10] == [6,19,43,66,80,66,43,19,6]-t_scs_n :: Integral i => i -> [[Z12]]-t_scs_n n = filter ((== n) . genericLength) t_scs---- | T-related /q/ that are subsets of /p/.------ > t_subsets [0,1,2,3,4] [0,1]  == [[0,1],[1,2],[2,3],[3,4]]--- > t_subsets [0,1,2,3,4] [0,1,4] == [[0,1,4]]--- > t_subsets [0,2,3,6,7] [0,1,4] == [[2,3,6]]-t_subsets :: [Z12] -> [Z12] -> [[Z12]]-t_subsets x a = filter (`T.is_subset` x) (map sort (T.z_sro_t_related mod12 a))---- | T\/I-related /q/ that are subsets of /p/.------ > ti_subsets [0,1,2,3,4] [0,1]  == [[0,1],[1,2],[2,3],[3,4]]--- > ti_subsets [0,1,2,3,4] [0,1,4] == [[0,1,4],[0,3,4]]--- > ti_subsets [0,2,3,6,7] [0,1,4] == [[2,3,6],[3,6,7]]-ti_subsets :: [Z12] -> [Z12] -> [[Z12]]-ti_subsets x a = filter (`T.is_subset` x) (nub (map sort (T.z_sro_ti_related mod12 a)))---- | Trivial run length encoder.------ > rle "abbcccdde" == [(1,'a'),(2,'b'),(3,'c'),(2,'d'),(1,'e')]-rle :: (Eq a,Integral i) => [a] -> [(i,a)]-rle =-    let f x = (genericLength x,head x)-    in map f . group---- | Inverse of 'rle'.------ > rle_decode [(5,'a'),(4,'b')] == "aaaaabbbb"-rle_decode :: (Integral i) => [(i,a)] -> [a]-rle_decode =-    let f (i,j) = genericReplicate i j-    in concatMap f---- | Length of /rle/ encoded sequence.------ > rle_length [(5,'a'),(4,'b')] == 9-rle_length :: (Integral i) => [(i,a)] -> i-rle_length = sum . map fst---- | T-equivalence /n/-class vector (subset-class vector, nCV).------ > t_n_class_vector 2 [0..4] == [4,3,2,1,0,0]--- > rle (t_n_class_vector 3 [0..4]) == [(1,3),(2,2),(2,1),(4,0),(1,1),(9,0)]--- > rle (t_n_class_vector 4 [0..4]) == [(1,2),(3,1),(39,0)]-t_n_class_vector :: (Num a, Integral i) => i -> [Z12] -> [a]-t_n_class_vector n x =-    let a = t_scs_n n-    in map (genericLength . t_subsets x) a---- | T\/I-equivalence /n/-class vector (subset-class vector, nCV).------ > ti_n_class_vector 2 [0..4] == [4,3,2,1,0,0]--- > ti_n_class_vector 3 [0,1,2,3,4] == [3,4,2,0,0,1,0,0,0,0,0,0]--- > rle (ti_n_class_vector 4 [0,1,2,3,4]) == [(2,2),(1,1),(26,0)]-ti_n_class_vector :: (Num b, Integral i) => i -> [Z12] -> [b]-ti_n_class_vector n x =-    let a = T.scs_n n-    in map (genericLength . ti_subsets x) a---- | 'icv' scaled by sum of /icv/.------ > dyad_class_percentage_vector [0,1,2,3,4] == [40,30,20,10,0,0]--- > dyad_class_percentage_vector [0,1,4,5,7] == [20,10,20,20,20,10]-dyad_class_percentage_vector :: Integral i => [Z12] -> [i]-dyad_class_percentage_vector p =-    let p' = T.icv 12 p-    in map (sum p' *) p'---- | /rel/ metric.------ > rel [0,1,2,3,4] [0,1,4,5,7] == 40--- > rel [0,1,2,3,4] [0,2,4,6,8] == 60--- > rel [0,1,4,5,7] [0,2,4,6,8] == 60-rel :: Integral i => [Z12] -> [Z12] -> Ratio i-rel x y =-    let x' = dyad_class_percentage_vector x-        y' = dyad_class_percentage_vector y-    in sum (map abs (zipWith (-) x' y')) % 2
− Music/Theory/Z12/Drape_1999.hs 
@@ -1,588 +0,0 @@--- | Haskell implementations of @pct@ operations.--- See <http://slavepianos.org/rd/t/pct>.-module Music.Theory.Z12.Drape_1999 where--import Data.Function {- base -}-import Data.List {- base -}-import Data.Maybe {- base -}-import Safe {- safe -}--import qualified Music.Theory.List as T-import qualified Music.Theory.Set.List as T-import qualified Music.Theory.Tuple as T--import qualified Music.Theory.Z as Z-import qualified Music.Theory.Z.SRO as Z-import qualified Music.Theory.Z.TTO as Z--import Music.Theory.Z12 (Z12)-import qualified Music.Theory.Z12 as Z12-import qualified Music.Theory.Z12.Forte_1973 as Z12-import qualified Music.Theory.Z12.TTO as Z12-import qualified Music.Theory.Z12.SRO as Z12---- | Cardinality filter------ > cf [0,3] (cg [1..4]) == [[1,2,3],[1,2,4],[1,3,4],[2,3,4],[]]-cf :: (Integral n) => [n] -> [[a]] -> [[a]]-cf ns = filter (\p -> genericLength p `elem` ns)---- | Combinatorial sets formed by considering each set as possible--- values for slot.------ > cgg [[0,1],[5,7],[3]] == [[0,5,3],[0,7,3],[1,5,3],[1,7,3]]--- > let n = "01" in cgg [n,n,n] == ["000","001","010","011","100","101","110","111"]-cgg :: [[a]] -> [[a]]-cgg l =-    case l of-      x:xs -> [ y:z | y <- x, z <- cgg xs ]-      _ -> [[]]---- | Combinations generator, ie. synonym for 'T.powerset'.------ > sort (cg [0,1,3]) == [[],[0],[0,1],[0,1,3],[0,3],[1],[1,3],[3]]-cg :: [a] -> [[a]]-cg = T.powerset---- | Powerset filtered by cardinality.------ >>> pct cg -r3 0159--- 015--- 019--- 059--- 159------ > cg_r 3 [0,1,5,9] == [[0,1,5],[0,1,9],[0,5,9],[1,5,9]]-cg_r :: (Integral n) => n -> [a] -> [[a]]-cg_r n = cf [n] . cg--{- | Chain pcsegs.-->>> echo 024579 | pct chn T0 3 | sort -u-579468 (RT8M)-579A02 (T5)--> chn_t0 3 [0,2,4,5,7,9] == [[5,7,9,10,0,2],[5,7,9,4,6,8]]-->>> echo 02457t | pct chn T0 2-7A0135 (RT5I)-7A81B9 (RT9MI)--> chn_t0 2 [0,2,4,5,7,10] == [[7,10,0,1,3,5],[7,10,8,1,11,9]]---}-chn_t0 :: Int -> [Z12] -> [[Z12]]-chn_t0 n p =-    let f q = T.take_right n p == take n q-    in filter f (Z12.sro_rtmi_related p)--{- | Cyclic interval segment.-->>> echo 014295e38t76 | pct cisg-13A7864529B6--> ciseg [0,1,4,2,9,5,11,3,8,10,7,6] == [1,3,10,7,8,6,4,5,2,9,11,6]---}-ciseg :: [Z12] -> [Z12]-ciseg = T.d_dx . cyc---- | Synonynm for 'complement'.------ >>> pct cmpl 02468t--- 13579B------ > cmpl [0,2,4,6,8,10] == [1,3,5,7,9,11]-cmpl :: [Z12] -> [Z12]-cmpl = Z12.complement---- | Form cycle.------ >>> echo 056 | pct cyc--- 0560------ > cyc [0,5,6] == [0,5,6,0]-cyc :: [a] -> [a]-cyc l =-    case l of-      [] -> []-      x:xs -> (x:xs) ++ [x]---- | Diatonic set name. 'd' for diatonic set, 'm' for melodic minor--- set, 'o' for octotonic set.-d_nm :: (Integral a) => [a] -> Maybe Char-d_nm x =-    case x of-      [0,2,4,5,7,9,11] -> Just 'd'-      [0,2,3,5,7,9,11] -> Just 'm'-      [0,1,3,4,6,7,9,10] -> Just 'o'-      _ -> Nothing---- | Diatonic implications.-dim :: [Z12] -> [(Z12,[Z12])]-dim p =-    let g (i,q) = T.is_subset p (Z12.tto_tn i q)-        f = filter g . zip [0..11] . repeat-        d = [0,2,4,5,7,9,11]-        m = [0,2,3,5,7,9,11]-        o = [0,1,3,4,6,7,9,10]-    in f d ++ f m ++ f o---- | Variant of 'dim' that is closer to the 'pct' form.------ >>> pct dim 016--- T1d--- T1m--- T0o------ > dim_nm [0,1,6] == [(1,'d'),(1,'m'),(0,'o')]-dim_nm :: [Z12] -> [(Z12,Char)]-dim_nm =-    let pk f (i,j) = (i,f j)-    in nubBy ((==) `on` snd) .-       map (pk (fromMaybe (error "dim_mn") . d_nm)) .-       dim---- | Diatonic interval set to interval set.------ >>> pct dis 24--- 1256------ > dis [2,4] == [1,2,5,6]-dis :: (Integral t) => [Int] -> [t]-dis =-    let is = [[], [], [1,2], [3,4], [5,6], [6,7], [8,9], [10,11]]-    in concatMap (\j -> is !! j)---- | Degree of intersection.------ >>> echo 024579e | pct doi 6 | sort -u--- 024579A--- 024679B------ > let p = [0,2,4,5,7,9,11]--- > in doi 6 p p == [[0,2,4,5,7,9,10],[0,2,4,6,7,9,11]]------ >>> echo 01234 | pct doi 2 7-35 | sort -u--- 13568AB------ > doi 2 (T.sc "7-35") [0,1,2,3,4] == [[1,3,5,6,8,10,11]]-doi :: Int -> [Z12] -> [Z12] -> [[Z12]]-doi n p q =-    let f j = [Z12.tto_tn j p,Z12.tto_tni j p]-        xs = concatMap f [0..11]-    in T.set (filter (\x -> length (x `intersect` q) == n) xs)---- | Forte name.-fn :: [Z12] -> String-fn = Z12.sc_name---- | Z12 cycles.-frg_cyc :: T.T6 [[Z12]]-frg_cyc =-    let c1 = [[0..11]]-        c2 = map (\n -> map (+ n) [0,2..10]) [0..1]-        c3 = map (\n -> map (+ n) [0,3..9]) [0..2]-        c4 = map (\n -> map (+ n) [0,4..8]) [0..3]-        c5 = map (map (* 5)) c1-        c6 = map (\n -> map (+ n) [0,6]) [0..5]-    in (c1,c2,c3,c4,c5,c6)---- | Fragmentation of cycles.-frg :: [Z12] -> T.T6 [String]-frg p =-    let f = map (\n -> if n `elem` p then Z12.z12_to_char n else '-')-    in T.t6_map (map f) frg_cyc--ic_cycle_vector :: [Z12] -> T.T6 [Int]-ic_cycle_vector p =-    let f str = let str' = if length str > 2 then T.close str else str-                in length (filter (\(x,y) -> x /= '-' && y /= '-') (T.adj2 1 str'))-    in T.t6_map (map f) (frg p)---- | Pretty printer for 'ic_cycle_vector'.------ > let r = "IC cycle vector: <1> <22> <111> <1100> <5> <000000>"--- > in ic_cycle_vector_pp (ic_cycle_vector [0,2,4,5,7,9]) == r-ic_cycle_vector_pp :: T.T6 [Int] -> String-ic_cycle_vector_pp = ("IC cycle vector: " ++) . unwords . T.t6_to_list . T.t6_map Z.z16_seq_pp--frg_hdr :: [String]-frg_hdr = map (\n -> "Fragmentation of " ++ show n ++ "-cycle(s)") [1::Int .. 6]--{-| Fragmentation of cycles.-->>> pct frg 024579-Fragmentation of 1-cycle(s):  [0-2-45-7-9--]-Fragmentation of 2-cycle(s):  [024---] [--579-]-Fragmentation of 3-cycle(s):  [0--9] [-47-] [25--]-Fragmentation of 4-cycle(s):  [04-] [-59] [2--] [-7-]-Fragmentation of 5-cycle(s):  [05------4927]-Fragmentation of 6-cycle(s):  [0-] [-7] [2-] [-9] [4-] [5-]-IC cycle vector: <1> <22> <111> <1100> <5> <000000>--> putStrLn $ frg_pp [0,2,4,5,7,9]--}-frg_pp :: [Z12] -> String-frg_pp =-    let f = unwords . map (\p -> T.bracket ('[',']') p)-        g x y = x ++ ": " ++ y-    in unlines . zipWith g frg_hdr . T.t6_to_list . T.t6_map f . frg---- | Embedded segment search.------ >>> echo 23A | pct ess 0164325--- 2B013A9--- 923507A------ > ess [0,1,6,4,3,2,5] [2,3,10] == [[9,2,3,5,0,7,10],[2,11,0,1,3,10,9]]-ess :: [Z12] -> [Z12] -> [[Z12]]-ess p q = filter (`T.is_embedding` q) (Z12.sro_rtmi_related p)---- | Can the set-class q (under prime form algorithm pf) be---   drawn from the pcset p.-has_sc_pf :: (Integral a) => ([a] -> [a]) -> [a] -> [a] -> Bool-has_sc_pf pf p q =-    let n = length q-    in pf q `elem` map pf (cf [n] (cg p))---- | Can the set-class q be drawn from the pcset p.------ > let d = [0,2,4,5,7,9,11] in has_sc d (complement d) == True--- > has_sc [] [] == True-has_sc :: [Z12] -> [Z12] -> Bool-has_sc = has_sc_pf Z12.forte_prime---- | Interval cycle filter.------ >>> echo 22341 | pct icf--- 22341------ > icf [[2,2,3,4,1]] == [[2,2,3,4,1]]-icf :: (Num a,Eq a) => [[a]] -> [[a]]-icf = filter ((== 12) . sum)---- | Interval class set to interval sets.------ >>> pct ici -c 123--- 123--- 129--- 1A3--- 1A9------ > ici_c [1,2,3] == [[1,2,3],[1,2,9],[1,10,3],[1,10,9]]-ici :: (Num t) => [Int] -> [[t]]-ici xs =-    let is j = [[0], [1,11], [2,10], [3,9], [4,8], [5,7], [6]] !! j-        ys = map is xs-    in cgg ys---- | Interval class set to interval sets, concise variant.------ > ici_c [1,2,3] == [[1,2,3],[1,2,9],[1,10,3],[1,10,9]]-ici_c :: [Int] -> [[Int]]-ici_c [] = []-ici_c (x:xs) = map (x:) (ici xs)---- | Interval-class segment.------ >>> pct icseg 013265e497t8--- 12141655232------ > icseg [0,1,3,2,6,5,11,4,9,7,10,8] == [1,2,1,4,1,6,5,5,2,3,2]-icseg :: [Z12] -> [Z12]-icseg = map Z12.ic . iseg---- | Interval segment (INT).-iseg :: [Z12] -> [Z12]-iseg = T.d_dx---- | Imbrications.------ > let r = [[[0,2,4],[2,4,5],[4,5,7],[5,7,9]]--- >         ,[[0,2,4,5],[2,4,5,7],[4,5,7,9]]]--- > in imb [3,4] [0,2,4,5,7,9] == r-imb :: (Integral n) => [n] -> [a] -> [[[a]]]-imb cs p =-    let g n = (== n) . genericLength-        f ps n = filter (g n) (map (genericTake n) ps)-    in map (f (tails p)) cs--{- | 'issb' gives the set-classes that can append to 'p' to give 'q'.-->>> pct issb 3-7 6-32-3-7-3-2-3-11--> issb (T.sc "3-7") (T.sc "6-32") == ["3-2","3-7","3-11"]---}-issb :: [Z12] -> [Z12] -> [String]-issb p q =-    let k = length q - length p-        f = any id . map (\x -> Z12.forte_prime (p ++ x) == q) . Z12.tto_ti_related-    in map Z12.sc_name (filter f (cf [k] Z12.scs))---- | Matrix search.------ >>> pct mxs 024579 642 | sort -u--- 6421B9--- B97642------ > T.set (mxs [0,2,4,5,7,9] [6,4,2]) == [[6,4,2,1,11,9],[11,9,7,6,4,2]]-mxs :: [Z12] -> [Z12] -> [[Z12]]-mxs p q = filter (q `isInfixOf`) (Z12.sro_rti_related p)---- | Normalize.------ >>> pct nrm 0123456543210--- 0123456------ > nrm [0,1,2,3,4,5,6,5,4,3,2,1,0] == [0,1,2,3,4,5,6]-nrm :: (Ord a) => [a] -> [a]-nrm = T.set---- | Normalize, retain duplicate elements.-nrm_r :: (Ord a) => [a] -> [a]-nrm_r = sort--{- | Pitch-class invariances (called @pi@ at @pct@).-->>> pct pi 0236 12-pcseg 0236-pcseg 6320-pcseg 532B-pcseg B235--> pci [1,2] [0,2,3,6] == [[0,2,3,6],[5,3,2,11],[6,3,2,0],[11,2,3,5]]---}-pci :: [Int] -> [Z12] -> [[Z12]]-pci i p =-    let f q = T.set (map (q !!) i)-    in filter (\q -> f q == f p) (Z12.sro_rti_related p)---- | Relate sets (TnMI).------ >>> pct rs 0123 641e--- T1M------ > rs [0,1,2,3] [6,4,1,11] == [(Z.tto_parse "T1M",[1,6,11,4])--- >                            ,(Z.tto_parse "T4MI",[4,11,6,1])]-rs :: [Z12] -> [Z12] -> [(Z.TTO Z12, [Z12])]-rs x y =-    let xs = map (\o -> (o,Z.z_tto_apply 5 id o x)) (Z.z_tto_univ id)-        q = T.set y-    in filter (\(_,p) -> T.set p == q) xs--rs1 :: [Z12] -> [Z12] -> Maybe (Z.TTO Z12)-rs1 p = fmap fst . headMay . rs p--{- | Relate segments.-->>> pct rsg 156 3BA-T4I--> rsg [1,5,6] [3,11,10] == [Z.sro_parse "T4I",Z.sro_parse "r1RT4MI"]-->>> pct rsg 0123 05t3-T0M--> rsg [0,1,2,3] [0,5,10,3] == [Z.sro_parse "T0M",Z.sro_parse "RT3MI"]-->>> pct rsg 0123 4e61-RT1M--> rsg [0,1,2,3] [4,11,6,1] == [Z.sro_parse "T4MI",Z.sro_parse "RT1M"]-->>> echo e614 | pct rsg 0123-r3RT1M--> rsg [0,1,2,3] [11,6,1,4] == [Z.sro_parse "r1T4MI",Z.sro_parse "r1RT1M"]---}-rsg :: [Z12] -> [Z12] -> [Z.SRO Z12]-rsg x y = filter (\o -> sro o x == y) (Z.z_sro_univ (length x) id)---- | Subsets.-sb :: [[Z12]] -> [[Z12]]-sb xs =-    let f p = all id (map (`has_sc` p) xs)-    in filter f Z12.scs--{- | scc = set class completion-->>> pct scc 6-32 168-35A-49B-3AB-34B--> scc (Z12.sc "6-32") [1,6,8] == [[3,5,10],[4,9,11],[3,10,11],[3,4,11]]---}-scc :: [Z12] -> [Z12] -> [[Z12]]-scc r p = map (\\ p) (filter (T.is_subset p) (Z12.tto_ti_related r))--si_hdr :: [String]-si_hdr =-    ["pitch-class-set"-    ,"set-class"-    ,"interval-class-vector"-    ,"tics"-    ,"complement"-    ,"multiplication-by-five-transform"]--type SI = ([Z12],Z.TTO Z12,[Z12])---- > si_raw [0,5,3,11]-si_raw :: [Z12] -> (SI,[Z12],[Int],SI,SI)-si_raw p =-    let n = length p-        p_icv = Z12.to_Z12 n : Z12.icv p-        gen_si x = let x_f = Z12.forte_prime x-                       Just x_o = rs1 x_f x-                   in (nub (sort x),x_o,x_f)-    in (gen_si p,p_icv,tics p,gen_si (Z12.complement p),gen_si (map (* 5) p))--si_raw_pp :: [Z12] -> [String]-si_raw_pp p =-    let pf_pp concise (x_o,x_f) =-            concat [Z.tto_pp x_o," ",Z12.sc_name x_f-                   ,if concise then "" else Z12.z12_vec_pp x_f]-        si_pp (x,x_o,x_f) = concat [Z12.z12_set_pp x," (",pf_pp True (x_o,x_f),")"]-        ((p',p_o,p_f),p_icv,p_tics,c,m) = si_raw p-    in [Z12.z12_set_pp p'-       ,pf_pp False (p_o,p_f)-       ,Z12.z12_vec_pp p_icv-       ,Z.z16_vec_pp p_tics-       ,si_pp c-       ,si_pp m]---- | Set information.------ > putStr $ unlines $ si [0,5,3,11]-si :: [Z12] -> [String]-si p = zipWith (\k v -> concat [k,": ",v]) si_hdr (si_raw_pp p)--{- | Super set-class.-->>> pct spsc 4-11 4-12-5-26[02458]--> spsc [Z12.sc "4-11",Z12.sc "4-12"] == [[0,2,4,5,8]]-->>> pct spsc 3-11 3-8-4-27[0258]-4-Z29[0137]--> spsc [Z12.sc "3-11",Z12.sc "3-8"] == [[0,2,5,8],[0,1,3,7]]-->>> pct spsc `pct fl 3`-6-Z17[012478]--> spsc (cf [3] Z12.scs) == [[0,1,2,4,7,8]]---}-spsc :: [[Z12]] -> [[Z12]]-spsc xs =-    let f y = all (y `has_sc`) xs-        g = (==) `on` length-    in (head . groupBy g . filter f) Z12.scs--{- | sra = stravinsky rotational array-->>> echo 019BA7 | pct sra-019BA7-08A96B-021A34-0B812A-0923B1-056243--> let r = [[0,1,9,11,10,7],[0,8,10,9,6,11],[0,2,1,10,3,4]->        ,[0,11,8,1,2,10],[0,9,2,3,11,1],[0,5,6,2,4,3]]-> in sra [0,1,9,11,10,7] == r---}-sra :: [Z12] -> [[Z12]]-sra = map (Z12.sro_tn_to 0) . T.rotations--{- | Serial operation.-->>> echo 156 | pct sro T4-59A--> sro (Z.sro_parse "T4") [1,5,6] == [5,9,10]-->>> echo 024579 | pct sro RT4I-79B024--> sro (Z.SRO 0 True 4 False True) [0,2,4,5,7,9] == [7,9,11,0,2,4]-->>> echo 156 | pct sro T4I-3BA--> sro (Z.sro_parse "T4I") [1,5,6] == [3,11,10]-> sro (Z.SRO 0 False 4 False True) [1,5,6] == [3,11,10]-->>> echo 156 | pct sro T4  | pct sro T0I-732--> (sro (Z.sro_parse "T0I") . sro (Z.sro_parse "T4")) [1,5,6] == [7,3,2]-->>> echo 024579 | pct sro RT4I-79B024--> sro (Z.sro_parse "RT4I") [0,2,4,5,7,9] == [7,9,11,0,2,4]---}-sro :: Z.SRO Z12 -> [Z12] -> [Z12]-sro o = Z.z_sro_apply 5 id o---- | Vector indicating degree of intersection with inversion at each transposition.------ > tics [0,2,4,5,7,9] == [3,2,5,0,5,2,3,4,1,6,1,4]--- > map tics Z12.scs-tics :: [Z12] -> [Int]-tics p =-    let q = Z12.tto_t_related (Z12.tto_invert 0 p)-    in map (length . intersect p) q--{- | tmatrix-->>> pct tmatrix 1258--1258-0147-9A14-67A1--> tmatrix [1,2,5,8] == [[1,2,5,8],[0,1,4,7],[9,10,1,4],[6,7,10,1]]---}-tmatrix :: [Z12] -> [[Z12]]-tmatrix p =-    let i = map negate (T.d_dx p)-    in map (\n -> map (+ n) p) (T.dx_d 0 i)---{- | trs = transformations search.  Search all RTnMI of /p/ for /q/.-->>> echo 642 | pct trs 024579 | sort -u-531642-6421B9-642753-B97642--> let r = [[5,3,1,6,4,2],[6,4,2,1,11,9],[6,4,2,7,5,3],[11,9,7,6,4,2]]-> in sort (trs [0,2,4,5,7,9] [6,4,2]) == r---}-trs :: [Z12] -> [Z12] -> [[Z12]]-trs p q = filter (q `isInfixOf`) (Z12.sro_rtmi_related p)---- > trs_m [0,2,4,5,7,9] [6,4,2] == [[6,4,2,1,11,9],[11,9,7,6,4,2]]-trs_m :: [Z12] -> [Z12] -> [[Z12]]-trs_m p q = filter (q `isInfixOf`) (Z12.sro_rti_related p)
− Music/Theory/Z12/Forte_1973.hs 
@@ -1,341 +0,0 @@--- | Allen Forte. /The Structure of Atonal Music/. Yale University--- Press, New Haven, 1973.-module Music.Theory.Z12.Forte_1973 where--import qualified Music.Theory.Z.Forte_1973 as Z-import Music.Theory.Z12---- * Prime form---- | T-related rotations of /p/.------ > t_rotations [0,1,3] == [[0,1,3],[0,2,11],[0,9,10]]-t_rotations :: [Z12] -> [[Z12]]-t_rotations = Z.t_rotations id---- | T\/I-related rotations of /p/.------ > ti_rotations [0,1,3] == [[0,1,3],[0,2,11],[0,9,10]--- >                         ,[0,9,11],[0,2,3],[0,1,10]]-ti_rotations :: [Z12] -> [[Z12]]-ti_rotations = Z.ti_rotations id---- | Forte prime form, ie. 'cmp_prime' of 'forte_cmp'.------ > forte_prime [0,1,3,6,8,9] == [0,1,3,6,8,9]--- > forte_prime [0,2,3,6,7] == [0,1,4,5,7]-forte_prime :: [Z12] -> [Z12]-forte_prime = Z.forte_prime id---- | Transpositional equivalence prime form, ie. 't_cmp_prime' of--- 'forte_cmp'.------ > (forte_prime [0,2,3],t_prime [0,2,3]) == ([0,1,3],[0,2,3])-t_prime :: [Z12] -> [Z12]-t_prime = Z.t_prime id---- * Set Class Table--type SC_Name = Z.SC_Name---- | The set-class table (Forte prime forms).------ > length sc_table == 224-sc_table :: [(SC_Name,[Z12])]-sc_table = Z.sc_table---- | Lookup a set-class name.  The input set is subject to--- 'forte_prime' before lookup.------ > sc_name [0,2,3,6,7] == "5-Z18"--- > sc_name [0,1,4,6,7,8] == "6-Z17"-sc_name :: [Z12] -> SC_Name-sc_name = Z.sc_name id---- > sc_name_long [0,1,4,6,7,8] == "6-Z17[012478]"-sc_name_long :: [Z12] -> SC_Name-sc_name_long = Z.sc_name_long id---- | Lookup a set-class given a set-class name.------ > sc "6-Z17" == [0,1,2,4,7,8]-sc :: SC_Name -> [Z12]-sc = Z.sc--{- | List of set classes (the set class universe).--> let r = [("0-1",[0,0,0,0,0,0])->         ,("1-1",[0,0,0,0,0,0])->         ,("2-1",[1,0,0,0,0,0])->         ,("2-2",[0,1,0,0,0,0])->         ,("2-3",[0,0,1,0,0,0])->         ,("2-4",[0,0,0,1,0,0])->         ,("2-5",[0,0,0,0,1,0])->         ,("2-6",[0,0,0,0,0,1])->         ,("3-1",[2,1,0,0,0,0])->         ,("3-2",[1,1,1,0,0,0])->         ,("3-3",[1,0,1,1,0,0])->         ,("3-4",[1,0,0,1,1,0])->         ,("3-5",[1,0,0,0,1,1])->         ,("3-6",[0,2,0,1,0,0])->         ,("3-7",[0,1,1,0,1,0])->         ,("3-8",[0,1,0,1,0,1])->         ,("3-9",[0,1,0,0,2,0])->         ,("3-10",[0,0,2,0,0,1])->         ,("3-11",[0,0,1,1,1,0])->         ,("3-12",[0,0,0,3,0,0])->         ,("4-1",[3,2,1,0,0,0])->         ,("4-2",[2,2,1,1,0,0])->         ,("4-3",[2,1,2,1,0,0])->         ,("4-4",[2,1,1,1,1,0])->         ,("4-5",[2,1,0,1,1,1])->         ,("4-6",[2,1,0,0,2,1])->         ,("4-7",[2,0,1,2,1,0])->         ,("4-8",[2,0,0,1,2,1])->         ,("4-9",[2,0,0,0,2,2])->         ,("4-10",[1,2,2,0,1,0])->         ,("4-11",[1,2,1,1,1,0])->         ,("4-12",[1,1,2,1,0,1])->         ,("4-13",[1,1,2,0,1,1])->         ,("4-14",[1,1,1,1,2,0])->         ,("4-Z15",[1,1,1,1,1,1])->         ,("4-16",[1,1,0,1,2,1])->         ,("4-17",[1,0,2,2,1,0])->         ,("4-18",[1,0,2,1,1,1])->         ,("4-19",[1,0,1,3,1,0])->         ,("4-20",[1,0,1,2,2,0])->         ,("4-21",[0,3,0,2,0,1])->         ,("4-22",[0,2,1,1,2,0])->         ,("4-23",[0,2,1,0,3,0])->         ,("4-24",[0,2,0,3,0,1])->         ,("4-25",[0,2,0,2,0,2])->         ,("4-26",[0,1,2,1,2,0])->         ,("4-27",[0,1,2,1,1,1])->         ,("4-28",[0,0,4,0,0,2])->         ,("4-Z29",[1,1,1,1,1,1])->         ,("5-1",[4,3,2,1,0,0])->         ,("5-2",[3,3,2,1,1,0])->         ,("5-3",[3,2,2,2,1,0])->         ,("5-4",[3,2,2,1,1,1])->         ,("5-5",[3,2,1,1,2,1])->         ,("5-6",[3,1,1,2,2,1])->         ,("5-7",[3,1,0,1,3,2])->         ,("5-8",[2,3,2,2,0,1])->         ,("5-9",[2,3,1,2,1,1])->         ,("5-10",[2,2,3,1,1,1])->         ,("5-11",[2,2,2,2,2,0])->         ,("5-Z12",[2,2,2,1,2,1])->         ,("5-13",[2,2,1,3,1,1])->         ,("5-14",[2,2,1,1,3,1])->         ,("5-15",[2,2,0,2,2,2])->         ,("5-16",[2,1,3,2,1,1])->         ,("5-Z17",[2,1,2,3,2,0])->         ,("5-Z18",[2,1,2,2,2,1])->         ,("5-19",[2,1,2,1,2,2])->         ,("5-20",[2,1,1,2,3,1])->         ,("5-21",[2,0,2,4,2,0])->         ,("5-22",[2,0,2,3,2,1])->         ,("5-23",[1,3,2,1,3,0])->         ,("5-24",[1,3,1,2,2,1])->         ,("5-25",[1,2,3,1,2,1])->         ,("5-26",[1,2,2,3,1,1])->         ,("5-27",[1,2,2,2,3,0])->         ,("5-28",[1,2,2,2,1,2])->         ,("5-29",[1,2,2,1,3,1])->         ,("5-30",[1,2,1,3,2,1])->         ,("5-31",[1,1,4,1,1,2])->         ,("5-32",[1,1,3,2,2,1])->         ,("5-33",[0,4,0,4,0,2])->         ,("5-34",[0,3,2,2,2,1])->         ,("5-35",[0,3,2,1,4,0])->         ,("5-Z36",[2,2,2,1,2,1])->         ,("5-Z37",[2,1,2,3,2,0])->         ,("5-Z38",[2,1,2,2,2,1])->         ,("6-1",[5,4,3,2,1,0])->         ,("6-2",[4,4,3,2,1,1])->         ,("6-Z3",[4,3,3,2,2,1])->         ,("6-Z4",[4,3,2,3,2,1])->         ,("6-5",[4,2,2,2,3,2])->         ,("6-Z6",[4,2,1,2,4,2])->         ,("6-7",[4,2,0,2,4,3])->         ,("6-8",[3,4,3,2,3,0])->         ,("6-9",[3,4,2,2,3,1])->         ,("6-Z10",[3,3,3,3,2,1])->         ,("6-Z11",[3,3,3,2,3,1])->         ,("6-Z12",[3,3,2,2,3,2])->         ,("6-Z13",[3,2,4,2,2,2])->         ,("6-14",[3,2,3,4,3,0])->         ,("6-15",[3,2,3,4,2,1])->         ,("6-16",[3,2,2,4,3,1])->         ,("6-Z17",[3,2,2,3,3,2])->         ,("6-18",[3,2,2,2,4,2])->         ,("6-Z19",[3,1,3,4,3,1])->         ,("6-20",[3,0,3,6,3,0])->         ,("6-21",[2,4,2,4,1,2])->         ,("6-22",[2,4,1,4,2,2])->         ,("6-Z23",[2,3,4,2,2,2])->         ,("6-Z24",[2,3,3,3,3,1])->         ,("6-Z25",[2,3,3,2,4,1])->         ,("6-Z26",[2,3,2,3,4,1])->         ,("6-27",[2,2,5,2,2,2])->         ,("6-Z28",[2,2,4,3,2,2])->         ,("6-Z29",[2,2,4,2,3,2])->         ,("6-30",[2,2,4,2,2,3])->         ,("6-31",[2,2,3,4,3,1])->         ,("6-32",[1,4,3,2,5,0])->         ,("6-33",[1,4,3,2,4,1])->         ,("6-34",[1,4,2,4,2,2])->         ,("6-35",[0,6,0,6,0,3])->         ,("6-Z36",[4,3,3,2,2,1])->         ,("6-Z37",[4,3,2,3,2,1])->         ,("6-Z38",[4,2,1,2,4,2])->         ,("6-Z39",[3,3,3,3,2,1])->         ,("6-Z40",[3,3,3,2,3,1])->         ,("6-Z41",[3,3,2,2,3,2])->         ,("6-Z42",[3,2,4,2,2,2])->         ,("6-Z43",[3,2,2,3,3,2])->         ,("6-Z44",[3,1,3,4,3,1])->         ,("6-Z45",[2,3,4,2,2,2])->         ,("6-Z46",[2,3,3,3,3,1])->         ,("6-Z47",[2,3,3,2,4,1])->         ,("6-Z48",[2,3,2,3,4,1])->         ,("6-Z49",[2,2,4,3,2,2])->         ,("6-Z50",[2,2,4,2,3,2])->         ,("7-1",[6,5,4,3,2,1])->         ,("7-2",[5,5,4,3,3,1])->         ,("7-3",[5,4,4,4,3,1])->         ,("7-4",[5,4,4,3,3,2])->         ,("7-5",[5,4,3,3,4,2])->         ,("7-6",[5,3,3,4,4,2])->         ,("7-7",[5,3,2,3,5,3])->         ,("7-8",[4,5,4,4,2,2])->         ,("7-9",[4,5,3,4,3,2])->         ,("7-10",[4,4,5,3,3,2])->         ,("7-11",[4,4,4,4,4,1])->         ,("7-Z12",[4,4,4,3,4,2])->         ,("7-13",[4,4,3,5,3,2])->         ,("7-14",[4,4,3,3,5,2])->         ,("7-15",[4,4,2,4,4,3])->         ,("7-16",[4,3,5,4,3,2])->         ,("7-Z17",[4,3,4,5,4,1])->         ,("7-Z18",[4,3,4,4,4,2])->         ,("7-19",[4,3,4,3,4,3])->         ,("7-20",[4,3,3,4,5,2])->         ,("7-21",[4,2,4,6,4,1])->         ,("7-22",[4,2,4,5,4,2])->         ,("7-23",[3,5,4,3,5,1])->         ,("7-24",[3,5,3,4,4,2])->         ,("7-25",[3,4,5,3,4,2])->         ,("7-26",[3,4,4,5,3,2])->         ,("7-27",[3,4,4,4,5,1])->         ,("7-28",[3,4,4,4,3,3])->         ,("7-29",[3,4,4,3,5,2])->         ,("7-30",[3,4,3,5,4,2])->         ,("7-31",[3,3,6,3,3,3])->         ,("7-32",[3,3,5,4,4,2])->         ,("7-33",[2,6,2,6,2,3])->         ,("7-34",[2,5,4,4,4,2])->         ,("7-35",[2,5,4,3,6,1])->         ,("7-Z36",[4,4,4,3,4,2])->         ,("7-Z37",[4,3,4,5,4,1])->         ,("7-Z38",[4,3,4,4,4,2])->         ,("8-1",[7,6,5,4,4,2])->         ,("8-2",[6,6,5,5,4,2])->         ,("8-3",[6,5,6,5,4,2])->         ,("8-4",[6,5,5,5,5,2])->         ,("8-5",[6,5,4,5,5,3])->         ,("8-6",[6,5,4,4,6,3])->         ,("8-7",[6,4,5,6,5,2])->         ,("8-8",[6,4,4,5,6,3])->         ,("8-9",[6,4,4,4,6,4])->         ,("8-10",[5,6,6,4,5,2])->         ,("8-11",[5,6,5,5,5,2])->         ,("8-12",[5,5,6,5,4,3])->         ,("8-13",[5,5,6,4,5,3])->         ,("8-14",[5,5,5,5,6,2])->         ,("8-Z15",[5,5,5,5,5,3])->         ,("8-16",[5,5,4,5,6,3])->         ,("8-17",[5,4,6,6,5,2])->         ,("8-18",[5,4,6,5,5,3])->         ,("8-19",[5,4,5,7,5,2])->         ,("8-20",[5,4,5,6,6,2])->         ,("8-21",[4,7,4,6,4,3])->         ,("8-22",[4,6,5,5,6,2])->         ,("8-23",[4,6,5,4,7,2])->         ,("8-24",[4,6,4,7,4,3])->         ,("8-25",[4,6,4,6,4,4])->         ,("8-26",[4,5,6,5,6,2])->         ,("8-27",[4,5,6,5,5,3])->         ,("8-28",[4,4,8,4,4,4])->         ,("8-Z29",[5,5,5,5,5,3])->         ,("9-1",[8,7,6,6,6,3])->         ,("9-2",[7,7,7,6,6,3])->         ,("9-3",[7,6,7,7,6,3])->         ,("9-4",[7,6,6,7,7,3])->         ,("9-5",[7,6,6,6,7,4])->         ,("9-6",[6,8,6,7,6,3])->         ,("9-7",[6,7,7,6,7,3])->         ,("9-8",[6,7,6,7,6,4])->         ,("9-9",[6,7,6,6,8,3])->         ,("9-10",[6,6,8,6,6,4])->         ,("9-11",[6,6,7,7,7,3])->         ,("9-12",[6,6,6,9,6,3])->         ,("10-1",[9,8,8,8,8,4])->         ,("10-2",[8,9,8,8,8,4])->         ,("10-3",[8,8,9,8,8,4])->         ,("10-4",[8,8,8,9,8,4])->         ,("10-5",[8,8,8,8,9,4])->         ,("10-6",[8,8,8,8,8,5])->         ,("11-1",[10,10,10,10,10,5])->         ,("12-1",[12,12,12,12,12,6])]-> in let icvs = map icv scs in zip (map sc_name scs) icvs == r---}-scs :: [[Z12]]-scs = Z.scs---- | Cardinality /n/ subset of 'scs'.------ > map (length . scs_n) [1..11] == [1,6,12,29,38,50,38,29,12,6,1]-scs_n :: Integral i => i -> [[Z12]]-scs_n = Z.scs_n---- * BIP Metric---- | Basic interval pattern, see Allen Forte \"The Basic Interval Patterns\"--- /JMT/ 17/2 (1973):234-272------ >>> pct bip 0t95728e3416--- 11223344556------ > bip [0,10,9,5,7,2,8,11,3,4,1,6] == [1,1,2,2,3,3,4,4,5,5,6]--- > bip (pco "0t95728e3416") == [1,1,2,2,3,3,4,4,5,5,6]-bip :: [Z12] -> [Z12]-bip = map int_to_Z12 . Z.bip 12 . map int_from_Z12---- * ICV Metric---- | Interval class of Z12 interval /i/.------ > map ic [5,6,7] == [5,6,5]--- > map ic [-13,-1,0,1,13] == [1,1,0,1,1]-ic :: Z12 -> Z12-ic = int_to_Z12 . Z.ic 12 . int_from_Z12---- | Forte notation for interval class vector.------ > icv [0,1,2,4,7,8] == [3,2,2,3,3,2]-icv :: Integral i => [Z12] -> [i]-icv = map fromInteger . Z.icv 12 . map int_from_Z12---- | Type specialise...-icv' :: [Z12] -> [Int]-icv' = icv---- * Z-relation---- | Locate /Z/ relation of set class.------ > fmap sc_name (z_relation_of (sc "7-Z12")) == Just "7-Z36"-z_relation_of :: [Z12] -> Maybe [Z12]-z_relation_of = fmap (map int_to_Z12) . Z.z_relation_of 12 . map int_from_Z12
− Music/Theory/Z12/Lewin_1980.hs 
@@ -1,48 +0,0 @@--- | David Lewin. \"A Response to a Response: On PC Set--- Relatedness\". /Perspectives of New Music/, 18(1-2):498-502, 1980.-module Music.Theory.Z12.Lewin_1980 where--import Data.List-import qualified Music.Theory.Z12.Castren_1994 as C--type Z12 = Int---- | REL function with given /ncv/ function (see 't_rel' and 'ti_rel').-rel :: Floating n => (Int -> [a] -> [n]) -> [a] -> [a] -> n-rel ncv x y =-    let n = min (genericLength x) (genericLength y)-        p = map (`ncv` x) [2..n]-        q = map (`ncv` y) [2..n]-        f = zipWith (\i j -> sqrt (i * j))-        pt = sum (map sum p)-        qt = sum (map sum q)-    in sum (map sum (zipWith f p q)) / sqrt (pt * qt)---- | T-equivalence REL function.------ Kuusi 2001, 7.5.2------ > let (~=) p q = abs (p - q) < 1e-2--- > t_rel [0,1,2,3,4] [0,2,3,6,7] ~= 0.44--- > t_rel [0,1,2,3,4] [0,2,4,6,8] ~= 0.28--- > t_rel [0,2,3,6,7] [0,2,4,6,8] ~= 0.31-t_rel :: Floating n => [Z12] -> [Z12] -> n-t_rel = rel C.t_n_class_vector---- | T/I-equivalence REL function.------ Buchler 1998, Fig. 3.38------ > let (~=) p q = abs (p - q) < 1e-3--- > let a = [0,2,3,5,7]::[Z12]--- > let b = [0,2,3,4,5,8]::[Z12]--- > let g = [0,1,2,3,5,6,8,10]::[Z12]--- > let j = [0,2,3,4,5,6,8]::[Z12]--- > ti_rel a b ~= 0.593--- > ti_rel a g ~= 0.648--- > ti_rel a j ~= 0.509--- > ti_rel b g ~= 0.712--- > ti_rel b j ~= 0.892--- > ti_rel g j ~= 0.707-ti_rel :: Floating n => [Z12] -> [Z12] -> n-ti_rel = rel C.ti_n_class_vector
− Music/Theory/Z12/Literature.hs 
@@ -1,48 +0,0 @@--- | Z12 set class database.-module Music.Theory.Z12.Literature where---- | Set class database with descriptors for historically and--- theoretically significant set classes, indexed by Forte name.------ > lookup "6-Z17" sc_db == Just "All-Trichord Hexachord"--- > lookup "7-35" sc_db == Just "diatonic collection (d)"-sc_db :: [(String,String)]-sc_db =-    [("4-Z15","All-Interval Tetrachord (see also 4-Z29)")-    ,("4-Z29","All-Interval Tetrachord (see also 4-Z15)")-    ,("6-Z17","All-Trichord Hexachord")-    ,("8-Z15","All-Tetrachord Octochord (see also 8-Z29)")-    ,("8-Z29","All-Tetrachord Octochord (see also 8-Z15)")-    ,("6-1","A-Type All-Combinatorial Hexachord")-    ,("6-8","B-Type All-Combinatorial Hexachord")-    ,("6-32","C-Type All-Combinatorial Hexachord")-    ,("6-7","D-Type All-Combinatorial Hexachord")-    ,("6-20","E-Type All-Combinatorial Hexachord")-    ,("6-35","F-Type All-Combinatorial Hexachord")-    ,("7-35","diatonic collection (d)")-    ,("7-34","ascending melodic minor collection")-    ,("8-28","octotonic collection (Messiaen Mode II)")-    ,("6-35","wholetone collection")-    ,("3-10","diminished triad")-    ,("3-11","major/minor triad")-    ,("3-12","augmented triad")-    ,("4-19","minor major-seventh chord")-    ,("4-20","major-seventh chord")-    ,("4-25","french augmented sixth chord")-    ,("4-28","dimished-seventh chord")-    ,("4-26","minor-seventh chord")-    ,("4-27","half-dimished seventh(P)/dominant-seventh(I) chord")-    ,("6-30","Petrushka Chord {0476a1},3-11 at T6")-    ,("6-34","Mystic Chord {06a492}")-    ,("6-Z44","Schoenberg Signature Set,3-3 at T5 or T7")-    ,("6-Z19","complement of 6-Z44,3-11 at T1 or TB")-    ,("9-12","Messiaen Mode III (nontonic collection)")-    ,("8-9","Messian Mode IV")-    ,("7-31","The only seven-element subset of 8-28. ")-    ,("5-31","The only five-element superset of 4-28.")-    ,("5-33","The only five-element subset of 6-35.")-    ,("7-33","The only seven-element superset of 6-35.")-    ,("5-21","The only five-element subset of 6-20.")-    ,("7-21","The only seven-element superset of 6-20.")-    ,("5-25","The only five-element subset of both 7-35 and 8-28.")-    ,("6-14","Any non-intersecting union of 3-6 and 3-12.") ]
− Music/Theory/Z12/Morris_1974.hs 
@@ -1,36 +0,0 @@--- | Robert Morris and D. Starr. \"The Structure of All-Interval Series\".--- /Journal of Music Theory/, 18:364-389, 1974.-module Music.Theory.Z12.Morris_1974 where--import qualified Control.Monad.Logic as L {- logict -}---- | 'L.msum' '.' 'map' 'return'.------ > L.observeAll (fromList [1..7]) == [1..7]-fromList :: L.MonadPlus m => [a] -> m a-fromList = L.msum . map return---- | 'L.MonadLogic' all-interval series.------ > map (length . L.observeAll . all_interval_m) [4,6,8,10] == [2,4,24,288]--- > [0,1,3,2,9,5,10,4,7,11,8,6] `elem` L.observeAll (all_interval_m 12)--- > length (L.observeAll (all_interval_m 12)) == 3856-all_interval_m :: L.MonadLogic m => Int -> m [Int]-all_interval_m n =-    let recur k p q = -- k = length p-            if k == n-            then return (reverse p)-            else do i <- fromList [1 .. n - 1]-                    L.guard (i `notElem` p)-                    let j:_ = p-                        m = abs ((i - j) `mod` n)-                    L.guard (m `notElem` q)-                    recur (k + 1) (i : p) (m : q)-    in recur 1 [0] []---- | 'L.observeAll' of 'all_interval_m'.------ > let r = [[0,1,5,2,4,3],[0,2,1,4,5,3],[0,4,5,2,1,3],[0,5,1,4,2,3]]--- > in all_interval 6 == r-all_interval :: Int -> [[Int]]-all_interval = L.observeAll . all_interval_m
− Music/Theory/Z12/Morris_1987.hs 
@@ -1,12 +0,0 @@--- | Robert Morris. /Composition with Pitch-Classes: A Theory of--- Compositional Design/. Yale University Press, New Haven, 1987.-module Music.Theory.Z12.Morris_1987 where--import Music.Theory.List-import Music.Theory.Z12---- | @INT@ operator.------ > int [0,1,3,6,10] == [1,2,3,4]-int :: [Z12] -> [Z12]-int = d_dx
− Music/Theory/Z12/Morris_1987/Parse.hs 
@@ -1,21 +0,0 @@--- | Parsers for pitch class sets and sequences, and for 'SRO's.-module Music.Theory.Z12.Morris_1987.Parse where--import Data.Char {- base -}--import Music.Theory.Z12---- | Parse a /pitch class object/ string.  Each 'Char' is either a--- number, a space which is ignored, or a letter name for the numbers--- 10 ('t' or 'a' or 'A') or 11 ('e' or 'B' or 'b').------ > pco "13te" == [1,3,10,11]--- > pco "13te" == pco "13ab"-pco :: String -> [Z12]-pco s =-    let s' = dropWhile isSpace s-        s'' = takeWhile (`elem` "0123456789taAebB") s'-        f c | c `elem` "taA" = 10-            | c `elem` "ebB" = 11-            | otherwise = fromInteger (read [c])-    in map f s''
− Music/Theory/Z12/Rahn_1980.hs 
@@ -1,25 +0,0 @@--- | John Rahn. /Basic Atonal Theory/. Longman, New York, 1980.-module Music.Theory.Z12.Rahn_1980 where--import Music.Theory.Z12-import qualified Music.Theory.Z.Forte_1973 as Z---- | Rahn prime form (comparison is rightmost inwards).------ > rahn_cmp [0,1,3,6,8,9] [0,2,3,6,7,9] == GT-rahn_cmp :: Ord a => [a] -> [a] -> Ordering-rahn_cmp p q = compare (reverse p) (reverse q)---- | Rahn prime form, ie. 'ti_cmp_prime' of 'rahn_cmp'.------ > rahn_prime [0,1,3,6,8,9] == [0,2,3,6,7,9]------ > import Music.Theory.Z12.Forte_1973------ > let s = [[0,1,3,7,8]--- >         ,[0,1,3,6,8,9],[0,1,3,5,8,9]--- >         ,[0,1,2,4,7,8,9]--- >         ,[0,1,2,4,5,7,9,10]]--- > in all (\p -> forte_prime p /= rahn_prime p) s == True-rahn_prime :: [Z12] -> [Z12]-rahn_prime = Z.ti_cmp_prime id rahn_cmp
− Music/Theory/Z12/Read_1978.hs 
@@ -1,28 +0,0 @@--- | Ronald C. Read. \"Every one a winner or how to avoid isomorphism--- search when cataloguing combinatorial configurations.\" /Annals of--- Discrete Mathematics/ 2:107–20, 1978.-module Music.Theory.Z12.Read_1978 where--import Music.Theory.Z12 {- hmt -}-import qualified Music.Theory.Z.Read_1978 as Z {- hmt -}--type Code = Z.Code---- | Encoder for 'encode_prime'.------ > encode [0,1,3,6,8,9] == 843-encode :: [Z12] -> Code-encode = Z.encode---- | Decoder for 'encode_prime'.------ > decode 843 == [0,1,3,6,8,9]-decode :: Code -> [Z12]-decode = Z.decode 12---- | Binary encoding prime form algorithm, equalivalent to Rahn.------ > encode_prime [0,1,3,6,8,9] == [0,2,3,6,7,9]--- > Music.Theory.Z12.Rahn_1980.rahn_prime [0,1,3,6,8,9] == [0,2,3,6,7,9]-encode_prime :: [Z12] -> [Z12]-encode_prime = Z.encode_prime id
− Music/Theory/Z12/SRO.hs 
@@ -1,97 +0,0 @@--- | Serial (ordered) pitch-class operations on 'Z12'.-module Music.Theory.Z12.SRO where--import Data.List {- base -}--import qualified Music.Theory.List as T-import qualified Music.Theory.Z.SRO as Z-import           Music.Theory.Z12---- | Transpose /p/ by /n/.------ > sro_tn 4 [1,5,6] == [5,9,10]-sro_tn :: Z12 -> [Z12] -> [Z12]-sro_tn = Z.z_sro_tn id---- | Invert /p/ about /n/.------ > sro_invert 6 [4,5,6] == [8,7,6]--- > sro_invert 0 [0,1,3] == [0,11,9]-sro_invert :: Z12 -> [Z12] -> [Z12]-sro_invert = Z.z_sro_invert id---- | Composition of 'invert' about @0@ and 'tn'.------ > tni 4 [1,5,6] == [3,11,10]--- > (sro_invert 0 . sro_tn  4) [1,5,6] == [7,3,2]-sro_tni :: Z12 -> [Z12] -> [Z12]-sro_tni = Z.z_sro_tni id---- | Modulo 12 multiplication------ > sro_mn 11 [0,1,4,9] == sro_tni 0 [0,1,4,9]-sro_mn :: Z12 -> [Z12] -> [Z12]-sro_mn = Z.z_sro_mn id---- | M5, ie. 'mn' @5@.------ > sro_m5 [0,1,3] == [0,5,3]-sro_m5 :: [Z12] -> [Z12]-sro_m5 = sro_mn 5---- | T-related sequences of /p/.------ > length (sro_t_related [0,3,6,9]) == 12-sro_t_related :: [Z12] -> [[Z12]]-sro_t_related = Z.z_sro_t_related id---- | T\/I-related sequences of /p/.------ > length (ti_related [0,1,3]) == 24--- > length (ti_related [0,3,6,9]) == 24--- > ti_related [0] == map return [0..11]-sro_ti_related :: [Z12] -> [[Z12]]-sro_ti_related = Z.z_sro_ti_related id---- | R\/T\/I-related sequences of /p/.------ > length (rti_related [0,1,3]) == 48--- > length (rti_related [0,3,6,9]) == 24-sro_rti_related :: [Z12] -> [[Z12]]-sro_rti_related = Z.z_sro_rti_related id---- | T\/M\/I-related sequences of /p/, duplicates removed.-sro_tmi_related :: [Z12] -> [[Z12]]-sro_tmi_related p = let q = sro_ti_related p in nub (q ++ map sro_m5 q)---- | R\/T\/M\/I-related sequences of /p/, duplicates removed.-sro_rtmi_related :: [Z12] -> [[Z12]]-sro_rtmi_related p = let q = sro_tmi_related p in nub (q ++ map reverse q)---- | r\/R\/T\/M\/I-related sequences of /p/, duplicates removed.-sro_rrtmi_related :: [Z12] -> [[Z12]]-sro_rrtmi_related p = nub (concatMap sro_rtmi_related (T.rotations p))---- * Sequence operations---- | Variant of 'tn', transpose /p/ so first element is /n/.------ > sro_tn_to 5 [0,1,3] == [5,6,8]--- > map (sro_tn_to 0) [[0,1,3],[1,3,0],[3,0,1]] == [[0,1,3],[0,2,11],[0,9,10]]-sro_tn_to :: Z12 -> [Z12] -> [Z12]-sro_tn_to = Z.z_sro_tn_to id---- | Variant of 'invert', inverse about /n/th element.------ > map (sro_invert_ix 0) [[0,1,3],[3,4,6]] == [[0,11,9],[3,2,0]]--- > map (sro_invert_ix 1) [[0,1,3],[3,4,6]] == [[2,1,11],[5,4,2]]-sro_invert_ix :: Int -> [Z12] -> [Z12]-sro_invert_ix = Z.z_sro_invert_ix id---- | The standard t-matrix of /p/.------ > tmatrix [0,1,3] == [[0,1,3]--- >                    ,[11,0,2]--- >                    ,[9,10,0]]-tmatrix :: [Z12] -> [[Z12]]-tmatrix = Z.z_tmatrix id
− Music/Theory/Z12/TTO.hs 
@@ -1,59 +0,0 @@--- | Pitch-class set (unordered) operations on 'Z12'.-module Music.Theory.Z12.TTO where--import Data.List {- base -}--import Music.Theory.Z12---- | Map to pitch-class and reduce to set.------ > pcset [1,13] == [1]-pcset :: (Integral a) => [a] -> [Z12]-pcset = nub . sort . map fromIntegral---- | Transpose by n.------ > tto_tn 4 [1,5,6] == [5,9,10]--- > tto_tn 4 [0,4,8] == [0,4,8]-tto_tn :: Z12 -> [Z12] -> [Z12]-tto_tn n = sort . map (+ n)---- | Invert about n.------ > tto_invert 6 [4,5,6] == [6,7,8]--- > tto_invert 0 [0,1,3] == [0,9,11]-tto_invert :: Z12 -> [Z12] -> [Z12]-tto_invert n = sort . map (\p -> n - (p - n))---- | Composition of 'invert' about @0@ and 'tn'.------ > tto_tni 4 [1,5,6] == [3,10,11]--- > (tto_invert 0 . tto_tn 4) [1,5,6] == [2,3,7]-tto_tni :: Z12 -> [Z12] -> [Z12]-tto_tni n = tto_tn n . tto_invert 0---- | Modulo 12 multiplication------ > tto_mn 11 [0,1,4,9] == tto_invert 0 [0,1,4,9]-tto_mn :: Z12 -> [Z12] -> [Z12]-tto_mn n = sort . map (* n)---- | M5, ie. 'mn' @5@.------ > tto_m5 [0,1,3] == [0,3,5]-tto_m5 :: [Z12] -> [Z12]-tto_m5 = tto_mn 5---- | T-related sets of /p/.------ > length (tto_t_related [0,1,3]) == 12--- > tto_t_related [0,3,6,9] == [[0,3,6,9],[1,4,7,10],[2,5,8,11]]-tto_t_related :: [Z12] -> [[Z12]]-tto_t_related p = nub (map (`tto_tn` p) [0..11])---- | T\/I-related set of /p/.------ > length (tto_ti_related [0,1,3]) == 24--- > tto_ti_related [0,3,6,9] == [[0,3,6,9],[1,4,7,10],[2,5,8,11]]-tto_ti_related :: [Z12] -> [[Z12]]-tto_ti_related p = nub (tto_t_related p ++ tto_t_related (tto_invert 0 p))
− README 
@@ -1,21 +0,0 @@-hmt - haskell music theory-----------------------------Music theory operations in [haskell][hs], primarily focused on 'set-theory' and 'common music notation'.--- [hmt-diagrams][hmt-diagrams]--## cli--[db](?t=hmt&e=md/db.md),-[pct](?t=hmt&e=md/pct.md),-[scala](?t=hmt&e=md/scala.md)--[hs]: http://haskell.org/-[hmt-diagrams]:  http://rd.slavepianos.org/?t=hmt-diagrams--© [rohan drape][rd], 2006-2017, [gpl][gpl].--[rd]:  http://rd.slavepianos.org/-[gpl]: http://gnu.org/copyleft/
+ README.md view
@@ -0,0 +1,26 @@+hmt - haskell music theory+--------------------------++[haskell](http://haskell.org/) music theory++requires:++- [hmt-base](http://rohandrape.net/?t=hmt-base)++related:++- [hmt-diagrams](http://rohandrape.net/?t=hmt-diagrams)+- [hmt-texts](http://rohandrape.net/?t=hmt-texts)++## cli++[csv-midi](http://rohandrape.net/?t=hmt&e=md/csv-midi.md),+[db](http://rohandrape.net/?t=hmt&e=md/db.md),+[gl](http://rohandrape.net/?t=hmt&e=md/gl.md),+[gr-planar](http://rohandrape.net/?t=hmt&e=md/gr-planar.md),+[obj](http://rohandrape.net/?t=hmt&e=md/obj.md),+[pct](http://rohandrape.net/?t=hmt&e=md/pct.md),+[ply](http://rohandrape.net/?t=hmt&e=md/ply.md),+[scala](http://rohandrape.net/?t=hmt&e=md/scala.md)++© [rohan drape](http://rohandrape.net/), 2006-2022, [gpl](http://gnu.org/copyleft/).
+ data/csv/mnd/all-notes-off.csv view
@@ -0,0 +1,129 @@+time,on/off,note,velocity,channel,param+0.0000,off,0,0,0,+0.0100,off,1,0,0,+0.0200,off,2,0,0,+0.0300,off,3,0,0,+0.0400,off,4,0,0,+0.0500,off,5,0,0,+0.0600,off,6,0,0,+0.0700,off,7,0,0,+0.0800,off,8,0,0,+0.0900,off,9,0,0,+0.1000,off,10,0,0,+0.1100,off,11,0,0,+0.1200,off,12,0,0,+0.1300,off,13,0,0,+0.1400,off,14,0,0,+0.1500,off,15,0,0,+0.1600,off,16,0,0,+0.1700,off,17,0,0,+0.1800,off,18,0,0,+0.1900,off,19,0,0,+0.2000,off,20,0,0,+0.2100,off,21,0,0,+0.2200,off,22,0,0,+0.2300,off,23,0,0,+0.2400,off,24,0,0,+0.2500,off,25,0,0,+0.2600,off,26,0,0,+0.2700,off,27,0,0,+0.2800,off,28,0,0,+0.2900,off,29,0,0,+0.3000,off,30,0,0,+0.3100,off,31,0,0,+0.3200,off,32,0,0,+0.3300,off,33,0,0,+0.3400,off,34,0,0,+0.3500,off,35,0,0,+0.3600,off,36,0,0,+0.3700,off,37,0,0,+0.3800,off,38,0,0,+0.3900,off,39,0,0,+0.4000,off,40,0,0,+0.4100,off,41,0,0,+0.4200,off,42,0,0,+0.4300,off,43,0,0,+0.4400,off,44,0,0,+0.4500,off,45,0,0,+0.4600,off,46,0,0,+0.4700,off,47,0,0,+0.4800,off,48,0,0,+0.4900,off,49,0,0,+0.5000,off,50,0,0,+0.5100,off,51,0,0,+0.5200,off,52,0,0,+0.5300,off,53,0,0,+0.5400,off,54,0,0,+0.5500,off,55,0,0,+0.5600,off,56,0,0,+0.5700,off,57,0,0,+0.5800,off,58,0,0,+0.5900,off,59,0,0,+0.6000,off,60,0,0,+0.6100,off,61,0,0,+0.6200,off,62,0,0,+0.6300,off,63,0,0,+0.6400,off,64,0,0,+0.6500,off,65,0,0,+0.6600,off,66,0,0,+0.6700,off,67,0,0,+0.6800,off,68,0,0,+0.6900,off,69,0,0,+0.7000,off,70,0,0,+0.7100,off,71,0,0,+0.7200,off,72,0,0,+0.7300,off,73,0,0,+0.7400,off,74,0,0,+0.7500,off,75,0,0,+0.7600,off,76,0,0,+0.7700,off,77,0,0,+0.7800,off,78,0,0,+0.7900,off,79,0,0,+0.8000,off,80,0,0,+0.8100,off,81,0,0,+0.8200,off,82,0,0,+0.8300,off,83,0,0,+0.8400,off,84,0,0,+0.8500,off,85,0,0,+0.8600,off,86,0,0,+0.8700,off,87,0,0,+0.8800,off,88,0,0,+0.8900,off,89,0,0,+0.9000,off,90,0,0,+0.9100,off,91,0,0,+0.9200,off,92,0,0,+0.9300,off,93,0,0,+0.9400,off,94,0,0,+0.9500,off,95,0,0,+0.9600,off,96,0,0,+0.9700,off,97,0,0,+0.9800,off,98,0,0,+0.9900,off,99,0,0,+1.0000,off,100,0,0,+1.0100,off,101,0,0,+1.0200,off,102,0,0,+1.0300,off,103,0,0,+1.0400,off,104,0,0,+1.0500,off,105,0,0,+1.0600,off,106,0,0,+1.0700,off,107,0,0,+1.0800,off,108,0,0,+1.0900,off,109,0,0,+1.1000,off,110,0,0,+1.1100,off,111,0,0,+1.1200,off,112,0,0,+1.1300,off,113,0,0,+1.1400,off,114,0,0,+1.1500,off,115,0,0,+1.1600,off,116,0,0,+1.1700,off,117,0,0,+1.1800,off,118,0,0,+1.1900,off,119,0,0,+1.2000,off,120,0,0,+1.2100,off,121,0,0,+1.2200,off,122,0,0,+1.2300,off,123,0,0,+1.2400,off,124,0,0,+1.2500,off,125,0,0,+1.2600,off,126,0,0,+1.2700,off,127,0,0,
− data/dot/euler-j5-a.dot 
@@ -1,30 +0,0 @@-graph g {-graph [layout="dot",rankdir="TB",nodesep=0.5];-edge [fontsize="8",fontname="century schoolbook"];-node [shape="plaintext",fontsize="10",fontname="century schoolbook"];-R_5_3 [label="A♮\n5:3"];-R_5_4 [label="E♮\n5:4"];-R_15_8 [label="B♮\n15:8"];-R_16_9 [label="B♭\n16:9"];-R_4_3 [label="F♮\n4:3"];-R_1_1 [label="C♮\n1:1"];-R_3_2 [label="G♮\n3:2"];-R_9_8 [label="D♮\n9:8"];-R_64_45 [label="F♯\n64:45"];-R_16_15 [label="C♯\n16:15"];-R_8_5 [label="A♭\n8:5"];-R_6_5 [label="E♭\n6:5"];-R_5_3 -- R_5_4 -- R_15_8;-R_16_9 -- R_4_3 -- R_1_1 -- R_3_2 -- R_9_8;-R_64_45 -- R_16_15 -- R_8_5 -- R_6_5;-R_4_3 -- R_5_3 [label="   (8:5)"];-R_1_1 -- R_5_4 [label="   (8:5)"];-R_3_2 -- R_15_8 [label="   (8:5)"];-R_64_45 -- R_16_9 [label="   (8:5)"];-R_16_15 -- R_4_3 [label="   (8:5)"];-R_8_5 -- R_1_1 [label="   (8:5)"];-R_6_5 -- R_3_2 [label="   (8:5)"];-{rank=min; R_5_3 R_5_4 R_15_8}-{rank=same; R_16_9 R_4_3 R_1_1 R_3_2 R_9_8}-{rank=max; R_64_45 R_16_15 R_8_5 R_6_5}-}
− data/dot/euler-j5-b.dot 
@@ -1,30 +0,0 @@-graph g {-graph [layout="dot",rankdir="TB",nodesep=0.5];-edge [fontsize="8",fontname="century schoolbook"];-node [shape="plaintext",fontsize="10",fontname="century schoolbook"];-R_5_3 [label="A♮\n5:3"];-R_5_4 [label="E♮\n5:4"];-R_15_8 [label="B♮\n15:8"];-R_45_32 [label="F♯\n45:32"];-R_16_9 [label="B♭\n16:9"];-R_4_3 [label="F♮\n4:3"];-R_1_1 [label="C♮\n1:1"];-R_3_2 [label="G♮\n3:2"];-R_9_8 [label="D♮\n9:8"];-R_16_15 [label="C♯\n16:15"];-R_8_5 [label="A♭\n8:5"];-R_6_5 [label="E♭\n6:5"];-R_5_3 -- R_5_4 -- R_15_8 -- R_45_32;-R_16_9 -- R_4_3 -- R_1_1 -- R_3_2 -- R_9_8;-R_16_15 -- R_8_5 -- R_6_5;-R_4_3 -- R_5_3 [label="   (8:5)"];-R_1_1 -- R_5_4 [label="   (8:5)"];-R_3_2 -- R_15_8 [label="   (8:5)"];-R_9_8 -- R_45_32 [label="   (8:5)"];-R_16_15 -- R_4_3 [label="   (8:5)"];-R_8_5 -- R_1_1 [label="   (8:5)"];-R_6_5 -- R_3_2 [label="   (8:5)"];-{rank=min; R_5_3 R_5_4 R_15_8 R_45_32}-{rank=same; R_16_9 R_4_3 R_1_1 R_3_2 R_9_8}-{rank=max; R_16_15 R_8_5 R_6_5}-}
− data/dot/euler-j7.dot 
@@ -1,29 +0,0 @@-graph g {-graph [layout="dot",rankdir="TB",nodesep=0.5];-edge [fontsize="8",fontname="century schoolbook"];-node [shape="plaintext",fontsize="10",fontname="century schoolbook"];-R_5_4 [label="E♮\n5:4"];-R_15_8 [label="B♮\n15:8"];-R_45_32 [label="F♯\n45:32"];-R_135_128 [label="C♯\n135:128"];-R_4_3 [label="F♮\n4:3"];-R_1_1 [label="C♮\n1:1"];-R_3_2 [label="G♮\n3:2"];-R_9_8 [label="D♮\n9:8"];-R_27_16 [label="A♮\n27:16"];-R_14_9 [label="A♭\n14:9"];-R_7_6 [label="E♭\n7:6"];-R_7_4 [label="B♭\n7:4"];-R_5_4 -- R_15_8 -- R_45_32 -- R_135_128;-R_4_3 -- R_1_1 -- R_3_2 -- R_9_8 -- R_27_16;-R_14_9 -- R_7_6 -- R_7_4;-R_1_1 -- R_5_4 [label="   (8:5)"];-R_3_2 -- R_15_8 [label="   (8:5)"];-R_9_8 -- R_45_32 [label="   (8:5)"];-R_27_16 -- R_135_128 [label="   (8:5)"];-R_7_6 -- R_4_3 [label="   (7:4)"];-R_7_4 -- R_1_1 [label="   (7:4)"];-{rank=min; R_5_4 R_15_8 R_45_32 R_135_128}-{rank=same; R_4_3 R_1_1 R_3_2 R_9_8 R_27_16}-{rank=max; R_14_9 R_7_6 R_7_4}-}
− data/dot/euler-wtp.dot 
@@ -1,30 +0,0 @@-graph g {-graph [layout="dot",rankdir="TB",nodesep=0.5];-edge [fontsize="8",fontname="century schoolbook"];-node [shape="plaintext",fontsize="10",fontname="century schoolbook"];-R_49_32 [label="B♭=738\n49:32"];-R_147_128 [label="F♮=240\n147:128"];-R_441_256 [label="C♮=942\n441:256"];-R_1323_1024 [label="G♮=444\n1323:1024"];-R_7_4 [label="C♯=969\n7:4"];-R_21_16 [label="A♭=471\n21:16"];-R_63_32 [label="E♭=1173\n63:32"];-R_189_128 [label="B♭=675\n189:128"];-R_567_512 [label="F♮=177\n567:512"];-R_1_1 [label="E♭=0\n1:1"];-R_3_2 [label="B♭=702\n3:2"];-R_9_8 [label="F♮=204\n9:8"];-R_49_32 -- R_147_128 -- R_441_256 -- R_1323_1024;-R_7_4 -- R_21_16 -- R_63_32 -- R_189_128 -- R_567_512;-R_1_1 -- R_3_2 -- R_9_8;-R_7_4 -- R_49_32 [label="   (8:7)"];-R_21_16 -- R_147_128 [label="   (8:7)"];-R_63_32 -- R_441_256 [label="   (8:7)"];-R_189_128 -- R_1323_1024 [label="   (8:7)"];-R_1_1 -- R_7_4 [label="   (8:7)"];-R_3_2 -- R_21_16 [label="   (8:7)"];-R_9_8 -- R_63_32 [label="   (8:7)"];-{rank=min; R_49_32 R_147_128 R_441_256 R_1323_1024}-{rank=same; R_7_4 R_21_16 R_63_32 R_189_128 R_567_512}-{rank=max; R_1_1 R_3_2 R_9_8}-}
+ data/dot/euler/euler-j5-a.dot view
@@ -0,0 +1,30 @@+graph g {+graph [layout="dot",rankdir="TB",nodesep=0.5];+edge [fontsize="8",fontname="century schoolbook"];+node [shape="plaintext",fontsize="10",fontname="century schoolbook"];+R_5_3 [label="A♮\n5:3"];+R_5_4 [label="E♮\n5:4"];+R_15_8 [label="B♮\n15:8"];+R_16_9 [label="B♭\n16:9"];+R_4_3 [label="F♮\n4:3"];+R_1_1 [label="C♮\n1:1"];+R_3_2 [label="G♮\n3:2"];+R_9_8 [label="D♮\n9:8"];+R_64_45 [label="F♯\n64:45"];+R_16_15 [label="C♯\n16:15"];+R_8_5 [label="A♭\n8:5"];+R_6_5 [label="E♭\n6:5"];+R_5_3 -- R_5_4 -- R_15_8;+R_16_9 -- R_4_3 -- R_1_1 -- R_3_2 -- R_9_8;+R_64_45 -- R_16_15 -- R_8_5 -- R_6_5;+R_4_3 -- R_5_3 [label="   (8:5)"];+R_1_1 -- R_5_4 [label="   (8:5)"];+R_3_2 -- R_15_8 [label="   (8:5)"];+R_64_45 -- R_16_9 [label="   (8:5)"];+R_16_15 -- R_4_3 [label="   (8:5)"];+R_8_5 -- R_1_1 [label="   (8:5)"];+R_6_5 -- R_3_2 [label="   (8:5)"];+{rank=min; R_5_3 R_5_4 R_15_8}+{rank=same; R_16_9 R_4_3 R_1_1 R_3_2 R_9_8}+{rank=max; R_64_45 R_16_15 R_8_5 R_6_5}+}
+ data/dot/euler/euler-j5-b.dot view
@@ -0,0 +1,30 @@+graph g {+graph [layout="dot",rankdir="TB",nodesep=0.5];+edge [fontsize="8",fontname="century schoolbook"];+node [shape="plaintext",fontsize="10",fontname="century schoolbook"];+R_5_3 [label="A♮\n5:3"];+R_5_4 [label="E♮\n5:4"];+R_15_8 [label="B♮\n15:8"];+R_45_32 [label="F♯\n45:32"];+R_16_9 [label="B♭\n16:9"];+R_4_3 [label="F♮\n4:3"];+R_1_1 [label="C♮\n1:1"];+R_3_2 [label="G♮\n3:2"];+R_9_8 [label="D♮\n9:8"];+R_16_15 [label="C♯\n16:15"];+R_8_5 [label="A♭\n8:5"];+R_6_5 [label="E♭\n6:5"];+R_5_3 -- R_5_4 -- R_15_8 -- R_45_32;+R_16_9 -- R_4_3 -- R_1_1 -- R_3_2 -- R_9_8;+R_16_15 -- R_8_5 -- R_6_5;+R_4_3 -- R_5_3 [label="   (8:5)"];+R_1_1 -- R_5_4 [label="   (8:5)"];+R_3_2 -- R_15_8 [label="   (8:5)"];+R_9_8 -- R_45_32 [label="   (8:5)"];+R_16_15 -- R_4_3 [label="   (8:5)"];+R_8_5 -- R_1_1 [label="   (8:5)"];+R_6_5 -- R_3_2 [label="   (8:5)"];+{rank=min; R_5_3 R_5_4 R_15_8 R_45_32}+{rank=same; R_16_9 R_4_3 R_1_1 R_3_2 R_9_8}+{rank=max; R_16_15 R_8_5 R_6_5}+}
+ data/dot/euler/euler-j7.dot view
@@ -0,0 +1,29 @@+graph g {+graph [layout="dot",rankdir="TB",nodesep=0.5];+edge [fontsize="8",fontname="century schoolbook"];+node [shape="plaintext",fontsize="10",fontname="century schoolbook"];+R_5_4 [label="E♮\n5:4"];+R_15_8 [label="B♮\n15:8"];+R_45_32 [label="F♯\n45:32"];+R_135_128 [label="C♯\n135:128"];+R_4_3 [label="F♮\n4:3"];+R_1_1 [label="C♮\n1:1"];+R_3_2 [label="G♮\n3:2"];+R_9_8 [label="D♮\n9:8"];+R_27_16 [label="A♮\n27:16"];+R_14_9 [label="A♭\n14:9"];+R_7_6 [label="E♭\n7:6"];+R_7_4 [label="B♭\n7:4"];+R_5_4 -- R_15_8 -- R_45_32 -- R_135_128;+R_4_3 -- R_1_1 -- R_3_2 -- R_9_8 -- R_27_16;+R_14_9 -- R_7_6 -- R_7_4;+R_1_1 -- R_5_4 [label="   (8:5)"];+R_3_2 -- R_15_8 [label="   (8:5)"];+R_9_8 -- R_45_32 [label="   (8:5)"];+R_27_16 -- R_135_128 [label="   (8:5)"];+R_7_6 -- R_4_3 [label="   (7:4)"];+R_7_4 -- R_1_1 [label="   (7:4)"];+{rank=min; R_5_4 R_15_8 R_45_32 R_135_128}+{rank=same; R_4_3 R_1_1 R_3_2 R_9_8 R_27_16}+{rank=max; R_14_9 R_7_6 R_7_4}+}
+ data/dot/euler/euler-wtp.dot view
@@ -0,0 +1,30 @@+graph g {+graph [layout="dot",rankdir="TB",nodesep=0.5];+edge [fontsize="8",fontname="century schoolbook"];+node [shape="plaintext",fontsize="10",fontname="century schoolbook"];+R_49_32 [label="B♭=738\n49:32"];+R_147_128 [label="F♮=240\n147:128"];+R_441_256 [label="C♮=942\n441:256"];+R_1323_1024 [label="G♮=444\n1323:1024"];+R_7_4 [label="C♯=969\n7:4"];+R_21_16 [label="A♭=471\n21:16"];+R_63_32 [label="E♭=1173\n63:32"];+R_189_128 [label="B♭=675\n189:128"];+R_567_512 [label="F♮=177\n567:512"];+R_1_1 [label="E♭=0\n1:1"];+R_3_2 [label="B♭=702\n3:2"];+R_9_8 [label="F♮=204\n9:8"];+R_49_32 -- R_147_128 -- R_441_256 -- R_1323_1024;+R_7_4 -- R_21_16 -- R_63_32 -- R_189_128 -- R_567_512;+R_1_1 -- R_3_2 -- R_9_8;+R_7_4 -- R_49_32 [label="   (8:7)"];+R_21_16 -- R_147_128 [label="   (8:7)"];+R_63_32 -- R_441_256 [label="   (8:7)"];+R_189_128 -- R_1323_1024 [label="   (8:7)"];+R_1_1 -- R_7_4 [label="   (8:7)"];+R_3_2 -- R_21_16 [label="   (8:7)"];+R_9_8 -- R_63_32 [label="   (8:7)"];+{rank=min; R_49_32 R_147_128 R_441_256 R_1323_1024}+{rank=same; R_7_4 R_21_16 R_63_32 R_189_128 R_567_512}+{rank=max; R_1_1 R_3_2 R_9_8}+}
− data/dot/tj_oh_p012.dot 
@@ -1,30 +0,0 @@-graph g {-graph [layout="dot",rankdir="TB",nodesep=0.5];-edge [fontsize="8",fontname="century schoolbook"];-node [shape="plaintext",fontsize="10",fontname="century schoolbook"];-R_5_3 [label="A♮=884\n5:3"];-R_5_4 [label="E♮=386\n5:4"];-R_15_8 [label="B♮=1088\n15:8"];-R_45_32 [label="F♯=590\n45:32"];-R_16_9 [label="B♭=996\n16:9"];-R_4_3 [label="F♮=498\n4:3"];-R_1_1 [label="C♮=0\n1:1"];-R_3_2 [label="G♮=702\n3:2"];-R_9_8 [label="D♮=204\n9:8"];-R_16_15 [label="C♯=112\n16:15"];-R_8_5 [label="A♭=814\n8:5"];-R_6_5 [label="E♭=316\n6:5"];-R_5_3 -- R_5_4 -- R_15_8 -- R_45_32;-R_16_9 -- R_4_3 -- R_1_1 -- R_3_2 -- R_9_8;-R_16_15 -- R_8_5 -- R_6_5;-R_4_3 -- R_5_3 [label="   (8:5)"];-R_1_1 -- R_5_4 [label="   (8:5)"];-R_3_2 -- R_15_8 [label="   (8:5)"];-R_9_8 -- R_45_32 [label="   (8:5)"];-R_16_15 -- R_4_3 [label="   (8:5)"];-R_8_5 -- R_1_1 [label="   (8:5)"];-R_6_5 -- R_3_2 [label="   (8:5)"];-{rank=min; R_5_3 R_5_4 R_15_8 R_45_32}-{rank=same; R_16_9 R_4_3 R_1_1 R_3_2 R_9_8}-{rank=max; R_16_15 R_8_5 R_6_5}-}
− data/dot/tj_oh_p014.dot 
@@ -1,58 +0,0 @@-graph- g {-graph [start=168732,layout=neato,epsilon=0.000001];-node [shape=plaintext,fontsize=10,fontname="century schoolbook"];-0 [label="C♮"];-1 [label="c♮"];-2 [label="C♯"];-3 [label="c♯"];-4 [label="D♮"];-5 [label="d♮"];-6 [label="E♭"];-7 [label="e♭"];-8 [label="E♮"];-9 [label="e♮"];-10 [label="F♮"];-11 [label="f♮"];-12 [label="F♯"];-13 [label="f♯"];-14 [label="G♮"];-15 [label="g♮"];-16 [label="A♭"];-17 [label="a♭"];-18 [label="A♮"];-19 [label="a♮"];-20 [label="B♮"];-21 [label="b♮"];-22 [label="b♭"];-23 [label="B♭"];-0 -- 1;-0 -- 9;-0 -- 19;-2 -- 3;-2 -- 11;-2 -- 22;-4 -- 5;-4 -- 21;-6 -- 1;-6 -- 7;-6 -- 15;-8 -- 3;-8 -- 9;-8 -- 17;-10 -- 11;-12 -- 13;-12 -- 22;-14 -- 9;-14 -- 15;-14 -- 21;-16 -- 11;-16 -- 17;-18 -- 3;-18 -- 13;-18 -- 19;-20 -- 17;-20 -- 21;-23 -- 5;-23 -- 15;-}
− data/dot/tj_oh_p031.dot 
@@ -1,53 +0,0 @@-graph- g {-graph [layout=neato,epsilon=0.000001];-node [shape=plaintext,fontsize=10,fontname="century schoolbook"];-0 [label="0,2,4,7"];-1 [label="0,2,7,10"];-2 [label="0,2,4,9"];-3 [label="1,3,5,8"];-4 [label="1,3,8,11"];-5 [label="1,3,5,10"];-6 [label="2,4,6,9"];-7 [label="2,4,6,11"];-8 [label="0,5,7,9"];-9 [label="2,5,7,9"];-10 [label="1,6,8,10"];-11 [label="3,6,8,10"];-12 [label="2,7,9,11"];-13 [label="4,7,9,11"];-14 [label="0,3,8,10"];-15 [label="0,5,8,10"];-16 [label="1,4,9,11"];-17 [label="1,6,9,11"];-18 [label="0,2,5,10"];-19 [label="1,3,6,11"];-20 [label="3,5,7,10"];-21 [label="4,6,8,11"];-22 [label="0,3,5,7"];-23 [label="1,4,6,8"];-0 -- 1;-0 -- 2;-2 -- 6;-3 -- 4;-3 -- 5;-5 -- 20;-6 -- 7;-7 -- 21;-8 -- 9;-9 -- 12;-10 -- 11;-12 -- 13;-14 -- 11;-14 -- 15;-16 -- 13;-16 -- 17;-18 -- 1;-18 -- 15;-19 -- 4;-19 -- 17;-22 -- 8;-22 -- 20;-23 -- 10;-23 -- 21;-}
− data/dot/tj_oh_p125.dot 
@@ -1,72 +0,0 @@-graph- g {-graph [layout=neato,epsilon=0.000001];-node [shape=plaintext,fontsize=10,fontname="century schoolbook"];-0 [label="0,4,11"];-1 [label="0,5,11"];-2 [label="1,4,11"];-3 [label="0,5,10"];-4 [label="0,6,10"];-5 [label="1,5,10"];-6 [label="0,6,9"];-7 [label="0,7,9"];-8 [label="1,6,9"];-9 [label="0,7,8"];-10 [label="1,7,8"];-11 [label="1,3,11"];-12 [label="2,3,11"];-13 [label="1,4,10"];-14 [label="2,4,10"];-15 [label="1,5,9"];-16 [label="2,5,9"];-17 [label="1,6,8"];-18 [label="2,6,8"];-19 [label="2,3,10"];-20 [label="2,4,9"];-21 [label="3,4,9"];-22 [label="2,5,8"];-23 [label="3,5,8"];-24 [label="2,6,7"];-25 [label="3,6,7"];-26 [label="3,4,8"];-27 [label="3,5,7"];-28 [label="4,5,7"];-29 [label="4,5,6"];-0 -- 1;-0 -- 2;-3 -- 1;-3 -- 4;-3 -- 5;-6 -- 4;-6 -- 7;-6 -- 8;-9 -- 7;-9 -- 10;-11 -- 2;-11 -- 12;-13 -- 2;-13 -- 5;-13 -- 14;-15 -- 5;-15 -- 8;-15 -- 16;-17 -- 8;-17 -- 10;-17 -- 18;-19 -- 12;-19 -- 14;-20 -- 14;-20 -- 16;-20 -- 21;-22 -- 16;-22 -- 18;-22 -- 23;-24 -- 18;-24 -- 25;-26 -- 21;-26 -- 23;-27 -- 23;-27 -- 25;-27 -- 28;-29 -- 28;-}
− data/dot/tj_oh_p131.dot 
@@ -1,26 +0,0 @@-graph- g {-graph [layout=neato,epsilon=0.000001];-node [shape=plaintext,fontsize=10,fontname="century schoolbook"];-0 [label="6,10,14"];-1 [label="6,11,13"];-2 [label="7,9,14"];-3 [label="7,10,13"];-4 [label="7,11,12"];-5 [label="8,9,13"];-6 [label="8,10,12"];-7 [label="9,10,11"];-0 -- 1;-0 -- 2;-0 -- 3;-1 -- 3;-1 -- 4;-2 -- 3;-2 -- 5;-3 -- 4;-3 -- 5;-3 -- 6;-4 -- 6;-5 -- 6;-6 -- 7;-}
− data/dot/tj_oh_p162.dot 
@@ -1,83 +0,0 @@-graph- g {-edge [len=1.75];-graph [layout=neato,epsilon=0.000001];-node [shape=plaintext,fontsize=10,fontname="century schoolbook"];-0 [label="0,1,2,6"];-1 [label="0,2,5,6"];-2 [label="1,2,4,6"];-3 [label="1,2,6,8"];-4 [label="0,1,3,5"];-5 [label="0,1,5,7"];-6 [label="1,3,4,5"];-7 [label="1,3,5,8"];-8 [label="0,1,4,8"];-9 [label="0,4,5,8"];-10 [label="1,4,5,7"];-11 [label="1,5,7,8"];-12 [label="0,2,3,4"];-13 [label="0,2,3,8"];-14 [label="0,2,4,7"];-15 [label="0,3,4,6"];-16 [label="2,3,4,8"];-17 [label="0,2,7,8"];-18 [label="0,3,6,8"];-19 [label="0,4,6,7"];-20 [label="2,4,7,8"];-21 [label="2,4,5,6"];-22 [label="2,5,6,8"];-23 [label="0,6,7,8"];-24 [label="3,4,6,8"];-25 [label="4,6,7,8"];-26 [label="1,2,3,7"];-27 [label="1,3,6,7"];-28 [label="2,3,5,7"];-29 [label="3,5,6,7"];-0 -- 1;-0 -- 2;-0 -- 3;-1 -- 21;-1 -- 22;-2 -- 3;-2 -- 21;-3 -- 22;-4 -- 5;-4 -- 6;-4 -- 7;-5 -- 10;-5 -- 11;-6 -- 7;-6 -- 10;-7 -- 11;-8 -- 9;-10 -- 11;-12 -- 13;-12 -- 14;-12 -- 15;-12 -- 16;-13 -- 16;-13 -- 17;-13 -- 18;-14 -- 17;-14 -- 19;-14 -- 20;-15 -- 18;-15 -- 19;-15 -- 24;-16 -- 20;-16 -- 24;-17 -- 20;-17 -- 23;-18 -- 23;-18 -- 24;-19 -- 23;-19 -- 25;-20 -- 25;-21 -- 22;-23 -- 25;-24 -- 25;-26 -- 27;-26 -- 28;-27 -- 29;-28 -- 29;-}
− data/scl/dr_itb_etude_1.scl 
@@ -1,41 +0,0 @@-! dr_itb_etude_1.scl-!-...-36-!-1/1-1/1-1/1-1/1-4/3-16/11-16/11-8/5-8/5-16/9-16/9-2/1-2/1-16/7-16/7-16/7-8/3-8/3-3/1-16/5-16/5-32/9-32/9-4/1-4/1-9/2-9/2-5/1-16/3-11/2-6/1-32/5-32/5-7/1-7/1-8/1
+ data/scl/ew_1357_3.scl view
@@ -0,0 +1,28 @@+! ew_1357_3.scl+!+EW, 1-3-5-7-9Genus.pdf, P.3+23+!+81/80+21/20+35/32+9/8+7/6+189/160+5/4+81/64+21/16+27/20+45/32+35/24+3/2+243/160+63/40+5/3+27/16+7/4+567/320+15/8+35/18+63/32+2/1
+ data/scl/ew_Pelogflute_2.scl view
@@ -0,0 +1,14 @@+! ew_Pelogflute_2.scl+!+EW, Pelogflute.pdf, P.2+9+!+16/15+64/55+5/4+4/3+16/11+8/5+128/75+20/11+2/1
+ data/scl/ew_el12_12.scl view
@@ -0,0 +1,17 @@+! ew_el12_12.scl+!+EW, earlylattices12.pdf, P.12+12+!+45/44+12/11+7/6+5/4+14/11+15/11+35/24+14/9+35/22+56/33+15/8+2/1
+ data/scl/ew_el12_7.scl view
@@ -0,0 +1,17 @@+! ew_el12_7.scl+!+EW, earlylattices12.pdf, P.7+12+!+80/77+8/7+77/64+847/640+11/8+10/7+16/11+847/512+128/77+121/64+77/40+2/1
+ data/scl/ew_hel_12.scl view
@@ -0,0 +1,27 @@+! ew_hel_12.scl+!+EW, hel.pdf, P.12+22+!+135/128+13/12+10/9+9/8+7/6+11/9+5/4+81/64+4/3+11/8+45/32+17/12+3/2+405/256+13/8+5/3+27/16+7/4+11/6+15/8+23/12+2/1
+ data/scl/ew_novarotreediamond_1.scl view
@@ -0,0 +1,28 @@+! ew_novarotreediamond_1.scl+!+EW, novavotreediamond.pdf, P.1+23+!+21/20+16/15+10/9+9/8+8/7+7/6+6/5+5/4+21/16+4/3+7/5+10/7+3/2+32/21+8/5+5/3+12/7+7/4+16/9+9/5+15/8+40/21+2/1
+ data/scl/ew_poole.scl view
@@ -0,0 +1,27 @@+! ew_poole.scl+!+EW, 2010/10/scale-for-rod-poole.html+22+!+33/32+21/20+13/12+9/8+7/6+11/9+5/4+14/11+4/3+11/8+7/5+13/9+3/2+14/9+44/27+5/3+27/16+7/4+11/6+15/8+21/11+2/1
+ data/scl/ew_two_22_7.scl view
@@ -0,0 +1,27 @@+! ew_two_22_7.scl+!+EW, 2018/03/an-unusual-22-tone-7-limit-tuning.html+22+!+36/35+16/15+35/32+9/8+7/6+6/5+315/256+245/192+21/16+27/20+7/5+735/512+189/128+49/32+63/40+5/3+12/7+16/9+64/35+15/8+35/18+2/1
+ data/scl/ew_xen3b_3.scl view
@@ -0,0 +1,22 @@+! ew_xen3b_3.scl+!+EW, xen3b.pdf, P.3+17+!+256/243+12/11+9/8+32/27+5/4+81/64+4/3+1024/729+16/11+3/2+128/81+5/3+27/16+16/9+15/8+243/128+2/1
+ data/scl/ew_xen456_9.scl view
@@ -0,0 +1,24 @@+! ew_xen456_9.scl+!+EW, xen456.pdf, P.9+19+!+45/44+16/15+12/11+8/7+32/27+40/33+14/11+4/3+15/11+64/45+16/11+32/21+8/5+18/11+12/7+16/9+20/11+21/11+2/1
− data/scl/hs17.scl 
@@ -1,22 +0,0 @@-! hs17.scl-!-17 tone harmonic series-17-!-2/1-3/1-4/1-5/1-6/1-7/1-8/1-9/1-10/1-11/1-12/1-13/1-14/1-15/1-16/1-17/1-2/1
− data/scl/hs19.scl 
@@ -1,24 +0,0 @@-! hs19.scl-!-19 tone harmonic series-19-!-2/1-3/1-4/1-5/1-6/1-7/1-8/1-9/1-10/1-11/1-12/1-13/1-14/1-15/1-16/1-17/1-18/1-19/1-2/1
− data/scl/hs21.scl 
@@ -1,26 +0,0 @@-! hs21.scl-!-21 tone harmonic series-21-!-2/1-3/1-4/1-5/1-6/1-7/1-8/1-9/1-10/1-11/1-12/1-13/1-14/1-15/1-16/1-17/1-18/1-19/1-20/1-21/1-2/1
− data/scl/hs23.scl 
@@ -1,28 +0,0 @@-! hs23.scl-!-23 tone harmonic series-23-!-2/1-3/1-4/1-5/1-6/1-7/1-8/1-9/1-10/1-11/1-12/1-13/1-14/1-15/1-16/1-17/1-18/1-19/1-20/1-21/1-22/1-23/1-2/1
hmt.cabal view
@@ -1,82 +1,78 @@+cabal-version:     2.4 Name:              hmt-Version:           0.16+Version:           0.20 Synopsis:          Haskell Music Theory-Description:       Haskell music theory library-License:           GPL+Description:       Haskell library for Music Theory+License:           GPL-3.0-only Category:          Music-Copyright:         Rohan Drape, 2006-2017+Copyright:         Rohan Drape, 2006-2022 Author:            Rohan Drape-Maintainer:        rd@slavepianos.org+Maintainer:        rd@rohandrape.net Stability:         Experimental-Homepage:          http://rd.slavepianos.org/t/hmt-Tested-With:       GHC == 8.0.1+Homepage:          http://rohandrape.net/t/hmt+Tested-With:       GHC == 9.2.4 Build-Type:        Simple-Cabal-Version:     >= 1.8 -Data-files:        README+Data-files:        README.md                    data/csv/mnd/*.csv-                   data/dot/*.dot+                   data/dot/euler/*.dot                    data/scl/*.scl  Library-  Build-Depends:   aeson,-                   array,-                   base >= 4.8 && < 5,+  Build-Depends:   array,+                   base >= 4.9 && < 5,                    bytestring,                    colour,                    containers,+                   data-memocombinators,                    data-ordlist,                    directory,                    fgl,                    filepath,+                   hmt-base == 0.20.*,                    lazy-csv,                    logict,-                   modular-arithmetic,                    multiset-comb,                    parsec,-                   permutation,                    primes,+                   process,                    random,                    safe,                    split,-                   text+                   strict,+                   text,+                   time+  Default-Language:Haskell2010   GHC-Options:     -Wall -fwarn-tabs-  Exposed-modules: Music.Theory.Array-                   Music.Theory.Array.Cell_Ref-                   Music.Theory.Array.CSV-                   Music.Theory.Array.CSV.Midi.MND+  Exposed-modules: Music.Theory.Array.Csv.Midi.Cli+                   Music.Theory.Array.Csv.Midi.Mnd+                   Music.Theory.Array.Csv.Midi.Skini                    Music.Theory.Array.Direction-                   Music.Theory.Array.MD-                   Music.Theory.Bits+                   Music.Theory.Array.Square                    Music.Theory.Bjorklund                    Music.Theory.Block_Design.Johnson_2007                    Music.Theory.Braille-                   Music.Theory.Byte                    Music.Theory.Clef-                   Music.Theory.Combinations                    Music.Theory.Contour.Polansky_1992-                   Music.Theory.DB.Common-                   Music.Theory.DB.CSV-                   Music.Theory.DB.JSON-                   Music.Theory.DB.Plain-                   Music.Theory.Directory+                   Music.Theory.Db.Cli+                   Music.Theory.Db.Common+                   Music.Theory.Db.Csv+                   Music.Theory.Db.Plain                    Music.Theory.Duration                    Music.Theory.Duration.Annotation-                   Music.Theory.Duration.CT+                   Music.Theory.Duration.ClickTrack+                   Music.Theory.Duration.Hollos2014                    Music.Theory.Duration.Name                    Music.Theory.Duration.Name.Abbreviation-                   Music.Theory.Duration.RQ-                   Music.Theory.Duration.RQ.Division-                   Music.Theory.Duration.RQ.Tied+                   Music.Theory.Duration.Rq+                   Music.Theory.Duration.Rq.Division+                   Music.Theory.Duration.Rq.Tied                    Music.Theory.Duration.Sequence.Notate                    Music.Theory.Dynamic_Mark-                   Music.Theory.Either-                   Music.Theory.Enum-                   Music.Theory.Function                    Music.Theory.Gamelan                    Music.Theory.Graph.Deacon_1934                    Music.Theory.Graph.Dot-                   Music.Theory.Graph.FGL+                   Music.Theory.Graph.Fgl                    Music.Theory.Graph.Johnson_2014                    Music.Theory.Instrument.Choir                    Music.Theory.Instrument.Names@@ -84,25 +80,21 @@                    Music.Theory.Interval.Barlow_1987                    Music.Theory.Interval.Name                    Music.Theory.Interval.Spelling-                   Music.Theory.IO                    Music.Theory.Key-                   Music.Theory.List-                   Music.Theory.Map-                   Music.Theory.Math-                   Music.Theory.Math.Convert-                   Music.Theory.Math.OEIS-                   Music.Theory.Maybe+                   Music.Theory.List.Logic+                   Music.Theory.Math.Convert.Fx+                   Music.Theory.Math.Nichomachus+                   Music.Theory.Math.Oeis+                   Music.Theory.Math.Prime                    Music.Theory.Meter.Barlow_1987                    Music.Theory.Metric.Buchler_1998                    Music.Theory.Metric.Morris_1980                    Music.Theory.Metric.Polansky_1996-                   Music.Theory.Monad-                   Music.Theory.Ord                    Music.Theory.Parse-                   Music.Theory.Permutations                    Music.Theory.Permutations.List                    Music.Theory.Permutations.Morris_1984                    Music.Theory.Pitch+                   Music.Theory.Pitch.Bark                    Music.Theory.Pitch.Chord                    Music.Theory.Pitch.Name                    Music.Theory.Pitch.Note@@ -112,70 +104,74 @@                    Music.Theory.Pitch.Spelling.Key                    Music.Theory.Pitch.Spelling.Table                    Music.Theory.Random.I_Ching-                   Music.Theory.Read+                   Music.Theory.Random.Jones_1981                    Music.Theory.Set.List                    Music.Theory.Set.Set-                   Music.Theory.Show-                   Music.Theory.String                    Music.Theory.Tempo_Marking                    Music.Theory.Tiling.Canon                    Music.Theory.Tiling.Johnson_2004                    Music.Theory.Tiling.Johnson_2009                    Music.Theory.Time.Bel1990.R-                   Music.Theory.Time.Duration-                   Music.Theory.Time.Notation+                   Music.Theory.Time.KeyKit+                   Music.Theory.Time.KeyKit.Basic+                   Music.Theory.Time.KeyKit.Parser                    Music.Theory.Time.Seq                    Music.Theory.Time_Signature-                   Music.Theory.Tuple                    Music.Theory.Tuning                    Music.Theory.Tuning.Alves_1997-                   Music.Theory.Tuning.DB-                   Music.Theory.Tuning.DB.Alves-                   Music.Theory.Tuning.DB.Gann-                   Music.Theory.Tuning.DB.Microtonal_Synthesis-                   Music.Theory.Tuning.DB.Riley-                   Music.Theory.Tuning.DB.Werckmeister-                   Music.Theory.Tuning.ET-                   Music.Theory.Tuning.Euler+                   Music.Theory.Tuning.Anamark+                   Music.Theory.Tuning.Db+                   Music.Theory.Tuning.Db.Alves+                   Music.Theory.Tuning.Db.Gann+                   Music.Theory.Tuning.Db.Microtonal_Synthesis+                   Music.Theory.Tuning.Db.Riley+                   Music.Theory.Tuning.Db.Werckmeister+                   Music.Theory.Tuning.Efg+                   Music.Theory.Tuning.Et                    Music.Theory.Tuning.Gann_1993+                   Music.Theory.Tuning.Graph.Euler+                   Music.Theory.Tuning.Graph.Iset+                   Music.Theory.Tuning.Hs                    Music.Theory.Tuning.Load                    Music.Theory.Tuning.Meyer_1929+                   Music.Theory.Tuning.Midi+                   Music.Theory.Tuning.Partch                    Music.Theory.Tuning.Polansky_1978                    Music.Theory.Tuning.Polansky_1984                    Music.Theory.Tuning.Polansky_1985c                    Music.Theory.Tuning.Polansky_1990                    Music.Theory.Tuning.Rosenboom_1979                    Music.Theory.Tuning.Scala+                   Music.Theory.Tuning.Scala.Cli+                   Music.Theory.Tuning.Scala.Functions                    Music.Theory.Tuning.Scala.Interval+                   Music.Theory.Tuning.Scala.Kbm+                   Music.Theory.Tuning.Scala.Meta                    Music.Theory.Tuning.Scala.Mode                    Music.Theory.Tuning.Sethares_1994                    Music.Theory.Tuning.Syntonic-                   Music.Theory.Unicode+                   Music.Theory.Tuning.Type+                   Music.Theory.Tuning.Wilson                    Music.Theory.Wyschnegradsky                    Music.Theory.Xenakis.S4                    Music.Theory.Xenakis.Sieve                    Music.Theory.Z                    Music.Theory.Z.Boros_1990+                   Music.Theory.Z.Castren_1994                    Music.Theory.Z.Clough_1979                    Music.Theory.Z.Drape_1999+                   Music.Theory.Z.Drape_1999.Cli                    Music.Theory.Z.Forte_1973+                   Music.Theory.Z.Lewin_1980+                   Music.Theory.Z.Literature+                   Music.Theory.Z.Morris_1974+                   Music.Theory.Z.Morris_1987+                   Music.Theory.Z.Morris_1987.Parse+                   Music.Theory.Z.Rahn_1980                    Music.Theory.Z.Read_1978-                   Music.Theory.Z.TTO-                   Music.Theory.Z.SRO-                   Music.Theory.Z12-                   Music.Theory.Z12.Castren_1994-                   Music.Theory.Z12.Drape_1999-                   Music.Theory.Z12.Forte_1973-                   Music.Theory.Z12.Lewin_1980-                   Music.Theory.Z12.Literature-                   Music.Theory.Z12.Morris_1974-                   Music.Theory.Z12.Morris_1987-                   Music.Theory.Z12.Morris_1987.Parse-                   Music.Theory.Z12.Rahn_1980-                   Music.Theory.Z12.Read_1978-                   Music.Theory.Z12.SRO-                   Music.Theory.Z12.TTO+                   Music.Theory.Z.Tto+                   Music.Theory.Z.Sro  Source-Repository  head-  Type:            darcs-  Location:        http://rd.slavepianos.org/sw/hmt+  Type:            git+  Location:        https://gitlab.com/rd--/hmt