packages feed

hmt 0.15 → 0.20

raw patch · 186 files changed

Files

− Help/hmt.help.lhs 
@@ -1,175 +0,0 @@-# Pct--> import Control.Arrow {- base -}-> import Data.Function {- base -}-> import Data.List {- base -}-> import Data.Maybe {- base -}-> import Music.Theory.List {- hmt -}-> import Music.Theory.Permutations {- hmt -}-> import Music.Theory.Set.List {- hmt -}-> import Music.Theory.Z12.Drape_1999 {- hmt -}-> import Music.Theory.Z12.Forte_1973 {- hmt -}-> import Music.Theory.Z12.Morris_1987 {- hmt -}-> import Music.Theory.Z12.Morris_1987.Parse {- hmt -}-> import Music.Theory.Z12.SRO {- hmt -}--This file illustrates equivalent expressions in pct and hmt terms.--    $ pcom pcseg iseg 01549 | pcom iseg icseg | pcom icseg icset-    145--> (set . map ic . int) [0,1,5,4,9] == [1,4,5]--    $ pcom pcseg pcset 01549 | pcom pcset sc | pcom sc icv | pcom icv icset-    1345--> let icv_icset x = let f x y = if x > 0 then Just y else Nothing->                   in catMaybes (zipWith f x [1..6])-> in (icv_icset . icv . forte_prime) [0,1,5,4,9] == [1,3,4,5]--    $ pg 5-Z17 | bip | sort -u > 5-Z17.bip ; \-      pg 5-Z37 | bip | sort -u > 5-Z37.bip ; \-      comm 5-Z17.bip 5-Z37.bip -1 -2 | wc -l-    16--> let f = nub . map bip . permutations . sc-> in length (f "5-Z17" `intersect` f "5-Z37") == 16--    $ cat ../db.sh-    for sc in $(fl -c $1)-    do-      pg $sc | bip | sort -u > $sc-    done-    $ sh ../db.sh 4-    $ ls-    4-1   4-12  4-16  4-19  4-21  4-24  4-27  4-4   4-7   4-Z15-    4-10  4-13  4-17  4-2   4-22  4-25  4-28  4-5   4-8   4-Z29-    4-11  4-14  4-18  4-20  4-23  4-26  4-3   4-6   4-9--> let {s = filter ((== 4) . length) scs->     ;x = map permutations s}-> in zip (map sc_name s) (map (set . (map bip)) x)--    $ cat view.sh-    for i in $(fl -c $1 | pg | bip | sort -u)-    do-      echo $i":" $(grep -l $i * | sort -t '-' +1  -n | tr "\n" " ")-    done-    $ sh view.sh 4-    111: 4-1-    112: 4-1 4-2 4-3-    113: 4-1 4-3 4-4 4-7-    ...--> let {n = 4->     ;s = filter ((== n) . length) scs->     ;x = map permutations s->     ;z = zip (map sc_name s) (map (set . (map bip)) x)->     ;f b (s,bs) = if b `elem` bs then Just s else Nothing->     ;g b = catMaybes (map (f b) z)->     ;a = set (map bip (concat x))}-> in zip a (map g a)--    $ cyc <  ~/src/pct/lib/scs | epmq \-    > "in cset 89" "is icset 12" "hasnt icseg 11" | scdb-    7-34    ascending melodic minor collection-    7-35    diatonic collection (d)-    8-28    octotonic collection (Messiaen Mode II)--> let {cyc xs = xs ++ [head xs]->     ;a = filter (\p -> length p `elem` [8,9]) (map cyc scs)->     ;b = filter (\p -> set (int p) == [1,2]) a->     ;c = filter (\p -> not ([1,1] `isInfixOf` int p)) b}-> in map (sc_name . nub) c == ["7-34","7-35","8-28"]--    $ epmq < ~/src/pct/lib/univ "in cset 6" "in pcset 579t024" \-    > "has sc 5-35" "hasnt sc 2-6" "notin pcset 024579e"-    02579A--> let {a = cf [6] (powerset [0..11])->     ;b = filter (is_superset [0,2,4,5,7,9,10]) a->     ;c = filter (`has_sc` (sc "5-35")) b->     ;d = filter (not . (`has_sc` (sc "2-6"))) c->     ;e = filter (not . is_superset [0,2,4,5,7,9,11]) d}-> in e == [[0,2,5,7,9,10]]--    $ echo 156 | sro T0I | sro T4-    3BA--> let {i = SRO 0 False 0 False True->     ;t4 = SRO 0 False 4 False False}-> in (sro i >>> sro t4) [1,5,6] == [3,11,10]--    $ echo 156 | sro T4  | sro T0I-    732--> let {i = SRO 0 False 0 False True->     ;t4 = SRO 0 False 4 False False}-> in (sro i . sro t4) [1,5,6] == [7,3,2]--Note that pct uses right rotation rotation.--> sro (SRO 1 True 1 True False) [0,1,2,3] == [11,6,1,4]-> sro (SRO 1 False 4 True True) [0,1,2,3] == [11,6,1,4]--    I = MB; TnI = TnMB,--> mn 11 [0,1,4,9] == tni 0 [0,1,4,9]--    MI = IM = M7 = MBM5; TnMI = TnM7--> sro (rnrtnmi "T0MI") [0,1,4,9] == mn 7 [0,1,4,9]--    T0 = T0M1; Tn = TnM1-    M = M5; TnM = TnM5,--    $ se -c5 123-    12333-    12233-    12223-    11233-    11223-    11123--> expand_set 5 [1,2,3]--> ici [1,2,3]-> cgg [[0],[1,11],[2,10],[3,9],[4,8],[5,7],[6]]--    $ se -c5 1245 | pg | ici | pcom iseg sc | \-      sort -u | epmq "in cset 6" | wc -l-    42--> let {a = expand_set 5 [1,2,4,5]->     ;b = concatMap permutations a->     ;c = concatMap ici b->     ;d = map (forte_prime . dx_d 0) c->     ;e = nub d->     ;f = cf [6] e}-> in length f == 42--    $ imb -c34 024579 | pfmt-    024 245 457 579-    0245 2457 4579--> imb [3,4] [0,2,4,5,7,9]--    $ rs 0123 e614-    T1M-    $ rs 0123 641e416-    T1M--    $ sb 6-32 6-8 | fn | pfmt-    1-1-    2-1 2-2 2-3 2-4 2-5-    3-2 3-4 3-6 3-7 3-9 3-11-    4-10 4-11 4-14 4-22 4-23-    5-23-    $ for i in `cat ~/src/pct/lib/scs | cf 6 | fn` ; \-      do echo $i >> LIST ; sb $i | cf 3 | wc -l >> LIST ; done--> map sc_name (sb [sc "6-32",sc "6-8"])--> let f p = let xs = cf [3] (sb [p])->           in (sc_name p,length xs)-> in map f (cf [6] scs)
− Music/Theory/Array/CSV.hs 
@@ -1,346 +0,0 @@--- | Regular matrix array data, CSV, column & row indexing.-module Music.Theory.Array.CSV where--import Data.Array {- array -}-import Data.Char {- base -}-import Data.Function {- base -}-import Data.List {- base -}-import Data.String {- base -}--import qualified Text.CSV.Lazy.String as C {- lazy-csv -}--import qualified Music.Theory.List as T {- hmt -}---- * Indexing---- | @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 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 = 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---- | 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)---- | 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)]---- * TABLE---- | When reading a CSV file is the first row a header?-type CSV_Has_Header = Bool--type CSV_Delimiter = Char--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 perhaps a header.-type CSV_Table a = (Maybe [String],Table a)---- | Read '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 <- readFile 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' :: (String -> a) -> FilePath -> IO (Table a)-csv_table_read' f = fmap snd . csv_table_read def_csv_opt f---- | Read and process @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)---- > 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)---- | Write 'Table' to @CSV@ file.-csv_table_write :: (a -> String) -> CSV_Opt -> FilePath -> CSV_Table a -> IO ()-csv_table_write f (_,delim,brk,align) fn (hdr,tbl) = do-  let tbl' = csv_table_align align (map (map f) tbl)-      (_,t) = C.toCSVTable (T.mcons hdr tbl')-      s = C.ppDSVTable brk delim t-  writeFile fn s---- | Write 'Table' only (no header).-csv_table_write' :: (a -> String) -> CSV_Opt -> FilePath -> Table a -> IO ()-csv_table_write' f opt fn tbl = csv_table_write f 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 -> Row_Ref -> [a]-table_row t r = t !! row_index r---- | Column data.-table_column :: Table a -> Column_Ref -> [a]-table_column t c = transpose t !! column_index c---- | Lookup value across columns.-table_column_lookup :: Eq a => Table a -> (Column_Ref,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 -> Cell_Ref -> a-table_cell t (c,r) =-    let (r',c') = (row_index r,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 -> (Row_Ref,Column_Range) -> [a]-table_row_segment t (r,c) =-    let (r',c') = (row_index r,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 -> Array Cell_Ref a-table_to_array t =-    let nr = length t-        nc = length (t !! 0)-        bnd = (cell_ref_minima,(toEnum (nc - 1),nr))-        asc = zip (cell_range_row_order bnd) (concat t)-    in array bnd asc---- | 'table_to_array' of 'csv_table_read'.-csv_array_read :: CSV_Opt -> (String -> a) -> FilePath -> IO (Array Cell_Ref a)-csv_array_read opt f fn = fmap (table_to_array . snd) (csv_table_read opt f fn)
− Music/Theory/Array/CSV/Midi.hs 
@@ -1,86 +0,0 @@--- | Functions for reading midi note data from CSV files.-module Music.Theory.Array.CSV.Midi where--import Data.Function {- base -}-import Data.Maybe {- base -}--import qualified Music.Theory.Array.CSV as T {- hmt -}-import qualified Music.Theory.Time.Seq as T {- hmt -}---- | Variant of 'reads' requiring exact match.-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_err :: Read a => String -> a-reads_err str = fromMaybe (error ("could not read: " ++ str)) (reads_exact str)---- | The required header field.-csv_midi_note_data_hdr :: [String]-csv_midi_note_data_hdr = ["time","on/off","note","velocity"]---- | Midi note data, header is @time,on/off,note,velocity@.--- Translation values for on/off are consulted.------ > let fn = "/home/rohan/cvs/uc/uc-26/daily-practice/2014-08-13.1.csv"--- > csv_midi_note_data_read' ("ON","OFF") fn :: IO [(Double,Either String String,Double,Double)]-csv_midi_note_data_read' :: (Read t,Real t,Read n,Real n) => (m,m) -> FilePath -> IO [(t,Either m String,n,n)]-csv_midi_note_data_read' (m_on,m_off) =-    let err x = error ("csv_midi_note_data_read: " ++ x)-        read_md x = case x of-                      "on" -> Left m_on-                      "off" -> Left m_off-                      _ -> Right x-        f m =-            case m of-              [st,md,mnn,amp] -> (reads_err st,read_md md,reads_err mnn,reads_err amp)-              _ -> err "entry?"-        g (hdr,dat) = case hdr of-                        Just hdr' -> if hdr' == csv_midi_note_data_hdr then dat else err "header?"-                        Nothing -> err "no header?"-    in fmap (map f . g) . T.csv_table_read (True,',',False,T.CSV_No_Align) id---- | Variant of 'csv_midi_note_data_read'' that errors on non on/off data.-csv_midi_note_data_read :: (Read t,Real t,Read n,Real n) => (m,m) -> FilePath -> IO [(t,m,n,n)]-csv_midi_note_data_read m =-    let f (t,p,q,r) = (t,either id (error "not on/off") p,q,r)-    in fmap (map f) . csv_midi_note_data_read' m---- | 'Tseq' form of 'csv_read_midi_note_data'.-midi_tseq_read :: (Read t,Real t,Read n,Real n) => FilePath -> IO (T.Tseq t (T.On_Off (n,n)))-midi_tseq_read =-    let mk_node (st,md,mnn,amp) = if md-                                  then (st,T.On (mnn,amp))-                                  else (st,T.Off (mnn,0))-    in fmap (map mk_node) . csv_midi_note_data_read (True,False)---- | Translate from 'Tseq' form to 'Wseq' form.-midi_tseq_to_midi_wseq :: (Num t,Eq n) => T.Tseq t (T.On_Off (n,n)) -> T.Wseq t (n,n)-midi_tseq_to_midi_wseq = T.tseq_on_off_to_wseq ((==) `on` fst)---- | Off-velocity is zero.-midi_wseq_to_midi_tseq :: (Num t,Ord t) => T.Wseq t (n,n) -> T.Tseq t (T.On_Off (n,n))-midi_wseq_to_midi_tseq = T.wseq_on_off---- | Writer.-csv_midi_note_data_write :: (Eq m,Show t,Real t,Show n,Real n) => (m,m) -> FilePath -> [(t,m,n,n)] -> IO ()-csv_midi_note_data_write (m_on,m_off) nm =-    let show_md md = if md == m_on-                     then "on" else if md == m_off-                                    then "off"-                                    else error "csv_midi_note_data_write"-        un_node (st,md,mnn,amp) = [show st,show_md md,show mnn,show amp]-        with_hdr dat = (Just csv_midi_note_data_hdr,dat)-    in T.csv_table_write id T.def_csv_opt nm . with_hdr . map un_node---- | 'Tseq' form of 'csv_midi_note_data_write'.-midi_tseq_write :: (Show t,Real t,Show n,Real n) => FilePath -> T.Tseq t (T.On_Off (n,n)) -> IO ()-midi_tseq_write nm sq =-    let f (t,e) = case e of-                    T.On (n,v) -> (t,True,n,v)-                    T.Off (n,v) -> (t,False,n,v)-        sq' = map f sq-    in csv_midi_note_data_write (True,False) nm sq'
+ 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
@@ -0,0 +1,84 @@+-- | Directions in an array.+module Music.Theory.Array.Direction where++import Data.List {- base -}+import Data.Maybe {- base -}++import qualified Music.Theory.Array.Cell_Ref as T {- hmt -}+import qualified Music.Theory.List as T {- hmt -}++-- * LOC / VEC++-- | (column,row)+type LOC n = (n,n)++-- | (Δcolumn,Δrow), rows /descend/, ie. down is positive, up is negative.+type VEC n = (n,n)++vector_add :: Num n => VEC n -> VEC n -> VEC n+vector_add (c1,r1) (c2,r2) = (c1 + c2,r1 + r2)++vector_sub :: Num n => VEC n -> VEC n -> VEC n+vector_sub (c1,r1) (c2,r2) = (c1 - c2,r1 - r2)++vector_sum :: Num n => [VEC n] -> VEC n+vector_sum = foldl1 vector_add++apply_vec :: Num n => LOC n -> VEC n -> LOC n+apply_vec (c,r) (dc,dr) = (c + dc,r + dr)++-- | Segment 'VEC' into a sequence of unit steps.+--+-- > let r = [[(0,0)],[(0,1)],[(0,1),(-1,0)],[(0,1),(0,1),(0,1),(-1,0),(-1,0)]]+-- > in map segment_vec [(0,0),(0,1),(-1,1),(-2,3)] == r+segment_vec :: Integral n => VEC n -> [VEC n]+segment_vec v =+    case v of+      (0,0) -> [v]+      (c,r) -> genericReplicate (abs r) (0,signum r) ++ genericReplicate (abs c) (signum c,0)++derive_vec :: Num n => LOC n -> LOC n -> VEC n+derive_vec (c1,r1) (c2,r2) = (c2 - c1,r2 - r1)++unfold_path :: Num n => LOC n -> [VEC n] -> [LOC n]+unfold_path = scanl apply_vec++-- * DIRECTION (non-diagonal)++type DIRECTION_S = String++-- | Directions are D=down, L=left, R=right, U=up.+is_direction :: String -> Bool+is_direction = (`elem` "DLRU.") . head++type DIRECTION_C = Char++-- | Reads either S|D W|L E|R N|U, reverse lookup gives SWEN. A period+-- indicates (0,0). S=south, W=west, E=east, N=north.+direction_char_to_vector_tbl :: Num n => [(DIRECTION_C,VEC n)]+direction_char_to_vector_tbl =+    [('.',(0,0))+    ,('S',(0,1)),('W',(-1,0)),('E',(1,0)),('N',(0,-1))+    ,('D',(0,1)),('L',(-1,0)),('R',(1,0)),('U',(0,-1))]++-- > map direction_char_to_vector "LU"+direction_char_to_vector :: Num n => DIRECTION_C -> VEC n+direction_char_to_vector d = fromMaybe (error "dir?") $ lookup d direction_char_to_vector_tbl++-- > let r = [(0,-1),(0,1),(-1,0),(1,0),(-1,-1),(1,1),(-2,0),(-1,-1)]+-- > in map direction_to_vector (words "U D L R UL DR LL LU") == r+direction_to_vector :: Num n => [DIRECTION_C] -> VEC n+direction_to_vector = vector_sum . map direction_char_to_vector++vector_to_direction_char :: (Eq n, Num n) => VEC n -> DIRECTION_C+vector_to_direction_char v =+    let r = T.reverse_lookup v direction_char_to_vector_tbl+    in fromMaybe (error "vec->dir?") r++-- | Direction sequence to cell references.+dir_seq_to_cell_seq :: (String,[String]) -> [String]+dir_seq_to_cell_seq (l,v) =+    let p = map direction_to_vector v+        c = T.parse_cell_index l+    in map (T.cell_ref_pp . T.index_to_cell) (unfold_path c p)+
− Music/Theory/Array/MD.hs 
@@ -1,111 +0,0 @@--- | Regular array data as markdown (MD) tables.-module Music.Theory.Array.MD where--import Data.Char {- base -}-import Data.List {- base -}--import qualified Music.Theory.List as T {- hmt -}---- | Append /k/ to the right of /l/ until result has /n/ places.-pad_right :: a -> Int -> [a] -> [a]-pad_right k n l = take n (l ++ repeat k)---- | Append /k/ to each row of /tbl/ as required to be regular (all--- rows equal length).-make_regular :: a -> [[a]] -> [[a]]-make_regular k tbl =-    let z = maximum (map length tbl)-    in map (pad_right k z) tbl---- | Delete trailing 'Char' where 'isSpace' holds.-delete_trailing_whitespace :: [Char] -> [Char]-delete_trailing_whitespace = reverse . dropWhile isSpace . reverse---- | 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/.------ > md_table_opt False (Nothing,[["a","bc","def"],["ghij","klm","no","p"]])-md_table_opt :: Bool -> MD_Table String -> [String]-md_table_opt pleft (hdr,t) =-    let t' = maybe t (:t) hdr-        c = transpose (make_regular "" t')-        n = map (maximum . map length) c-        ext k s = let pd = replicate (k - length s) ' '-                  in if pleft then pd ++ s else s ++ pd-        m = unwords (map (flip replicate '-') n)-        w = map unwords (transpose (zipWith (map . ext) n c))-        d = map 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---- | '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 t = md_matrix "" (map return "abc") (map (map show) [[1,2,3],[2,3,1],[3,1,2]])-->>> putStrLn $ unlines $ md_table' t-- - - --  a b c-a 1 2 3-b 2 3 1-c 3 1 2-- - - ----}-md_matrix :: a -> [a] -> [[a]] -> MD_Table a-md_matrix nil nm t = md_table_join (Nothing,[nil] : map return nm) (Nothing,nm : t)---- | Variant for 'String' tables where /nil/ is the empty string and--- the header cells are in bold.-md_matrix_bold :: [String] -> [[String]] -> MD_Table String-md_matrix_bold nm t =-    let bold x = "__" ++ x ++ "__"-        nm' = map bold nm-    in md_matrix "" nm' t
+ 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/Bjorklund.hs view
@@ -3,111 +3,138 @@ -- /Journal of Computational Geometry: Theory and Applications/ -- Volume 42, Issue 5, July, 2009 -- (<http://dx.doi.org/10.1016/j.comgeo.2008.04.005>)-module Music.Theory.Bjorklund (bjorklund,xdot,iseq,iseq_str) where+module Music.Theory.Bjorklund where  import Data.List.Split {- split -} -type STEP a = ((Int,Int),([[a]],[[a]]))+import qualified Music.Theory.List as T -left :: STEP a -> STEP a-left ((i,j),(xs,ys)) =+-- | Bjorklund state+type BJORKLUND_ST a = ((Int,Int),([[a]],[[a]]))++-- | 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]--- > xdot (bjorklund (5,9)) == "x.x.x.x.x"------ > let es = [(2,3),(2,5)--- >          ,(3,4),(3,5),(3,8)--- >          ,(4,7),(4,9),(4,12),(4,15)--- >          ,(5,6),(5,7),(5,8),(5,9),(5,11),(5,12),(5,13),(5,16)--- >          ,(6,7),(6,13)--- >          ,(7,8),(7,9),(7,10),(7,12),(7,15),(7,16),(7,17),(7,18)--- >          ,(8,17),(8,19)--- >          ,(9,14),(9,16),(9,22),(9,23)--- >          ,(11,12),(11,24)--- >          ,(13,24)--- >          ,(15,34)]--- > in map (\e -> let e' = bjorklund e in (e,xdot e',iseq_str e')) es------ > [((2,3),"xx.","(12)")--- > ,((2,5),"x.x..","(23)")--- > ,((3,4),"xxx.","(112)")--- > ,((3,5),"x.x.x","(221)")--- > ,((3,8),"x..x..x.","(332)")--- > ,((4,7),"x.x.x.x","(2221)")--- > ,((4,9),"x.x.x.x..","(2223)")--- > ,((4,12),"x..x..x..x..","(3333)")--- > ,((4,15),"x...x...x...x..","(4443)")--- > ,((5,6),"xxxxx.","(11112)")--- > ,((5,7),"x.xx.xx","(21211)")--- > ,((5,8),"x.xx.xx.","(21212)")--- > ,((5,9),"x.x.x.x.x","(22221)")--- > ,((5,11),"x.x.x.x.x..","(22223)")--- > ,((5,12),"x..x.x..x.x.","(32322)")--- > ,((5,13),"x..x.x..x.x..","(32323)")--- > ,((5,16),"x..x..x..x..x...","(33334)")--- > ,((6,7),"xxxxxx.","(111112)")--- > ,((6,13),"x.x.x.x.x.x..","(222223)")--- > ,((7,8),"xxxxxxx.","(1111112)")--- > ,((7,9),"x.xxx.xxx","(2112111)")--- > ,((7,10),"x.xx.xx.xx","(2121211)")--- > ,((7,12),"x.xx.x.xx.x.","(2122122)")--- > ,((7,15),"x.x.x.x.x.x.x..","(2222223)")--- > ,((7,16),"x..x.x.x..x.x.x.","(3223222)")--- > ,((7,17),"x..x.x..x.x..x.x.","(3232322)")--- > ,((7,18),"x..x.x..x.x..x.x..","(3232323)")--- > ,((8,17),"x.x.x.x.x.x.x.x..","(22222223)")--- > ,((8,19),"x..x.x.x..x.x.x..x.","(32232232)")--- > ,((9,14),"x.xx.xx.xx.xx.","(212121212)")--- > ,((9,16),"x.xx.x.x.xx.x.x.","(212221222)")--- > ,((9,22),"x..x.x..x.x..x.x..x.x.","(323232322)")--- > ,((9,23),"x..x.x..x.x..x.x..x.x..","(323232323)")--- > ,((11,12),"xxxxxxxxxxx.","(11111111112)")--- > ,((11,24),"x..x.x.x.x.x..x.x.x.x.x.","(32222322222)")--- > ,((13,24),"x.xx.x.x.x.x.xx.x.x.x.x.","(2122222122222)")--- > ,((15,34),"x..x.x.x.x..x.x.x.x..x.x.x.x..x.x.","(322232223222322)")]+{- | 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_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])]+> let es' = concatMap (\(i,j) -> map ((,) i) j) es+> mapM_ (putStrLn . euler_pp_unicode) es'++> > E(2,3) [××·] (12)+> > E(2,5) [×·×··] (23)+> > E(3,4) [×××·] (112)+> > E(3,5) [×·×·×] (221)+> > E(3,8) [×··×··×·] (332)+> > E(4,7) [×·×·×·×] (2221)+> > E(4,9) [×·×·×·×··] (2223)+> > E(4,12) [×··×··×··×··] (3333)+> > E(4,15) [×···×···×···×··] (4443)+> > E(5,6) [×××××·] (11112)+> > E(5,7) [×·××·××] (21211)+> > E(5,8) [×·××·××·] (21212)+> > E(5,9) [×·×·×·×·×] (22221)+> > E(5,11) [×·×·×·×·×··] (22223)+> > E(5,12) [×··×·×··×·×·] (32322)+> > E(5,13) [×··×·×··×·×··] (32323)+> > E(5,16) [×··×··×··×··×···] (33334)+> > E(6,7) [××××××·] (111112)+> > E(6,13) [×·×·×·×·×·×··] (222223)+> > E(7,8) [×××××××·] (1111112)+> > E(7,9) [×·×××·×××] (2112111)+> > E(7,10) [×·××·××·××] (2121211)+> > E(7,12) [×·××·×·××·×·] (2122122)+> > E(7,15) [×·×·×·×·×·×·×··] (2222223)+> > E(7,16) [×··×·×·×··×·×·×·] (3223222)+> > E(7,17) [×··×·×··×·×··×·×·] (3232322)+> > E(7,18) [×··×·×··×·×··×·×··] (3232323)+> > E(8,17) [×·×·×·×·×·×·×·×··] (22222223)+> > E(8,19) [×··×·×·×··×·×·×··×·] (32232232)+> > E(9,14) [×·××·××·××·××·] (212121212)+> > E(9,16) [×·××·×·×·××·×·×·] (212221222)+> > E(9,22) [×··×·×··×·×··×·×··×·×·] (323232322)+> > E(9,23) [×··×·×··×·×··×·×··×·×··] (323232323)+> > E(11,12) [×××××××××××·] (11111111112)+> > E(11,24) [×··×·×·×·×·×··×·×·×·×·×·] (32222322222)+> > E(13,24) [×·××·×·×·×·×·××·×·×·×·×·] (2122222122222)+> > E(15,34) [×··×·×·×·×··×·×·×·×··×·×·×·×··×·×·] (322232223222322)++-} bjorklund :: (Int,Int) -> [Bool] bjorklund (i,j') =     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_unicode (bjorklund_r 2 (5,16)) == "··×··×··×··×··×·"+bjorklund_r :: Int -> (Int, Int) -> [Bool]+bjorklund_r n = T.rotate_right n . bjorklund++-- | Pretty printer, generalise.+euler_pp_f :: (Bool -> Char) -> (Int,Int) -> String+euler_pp_f f e =+    let r = bjorklund e+    in concat ["E",show e," [",map f r,"] ",iseq_str r]++-- | Unicode form, ie. @×·@.+--+-- > 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_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. ----- > xdot (bjorklund (5,9)) == "x.x.x.x.x"-xdot :: [Bool] -> String-xdot = map (\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_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/Block_Design/Johnson_2007.hs view
@@ -2,7 +2,7 @@ -- Computation in Music, Berlin, May 2007. module Music.Theory.Block_Design.Johnson_2007 where -import Control.Arrow {- base -}+import Control.Arrow ((***)) {- base -} import Data.List {- base -}  import qualified Music.Theory.List as T
+ Music/Theory/Braille.hs view
@@ -0,0 +1,274 @@+-- | <http://en.wikipedia.org/wiki/Braille_Patterns>+module Music.Theory.Braille where++import Data.Char {- base -}+import Data.List {- base -}+import Data.Maybe {- base -}+import Text.Printf {- base -}++-- | Braille coding data.  Elements are: (ASCII HEX,ASCII CHAR,DOT+-- LIST,UNICODE CHAR,MEANING).  The dot numbers are in column order.+type BRAILLE = (Int,Char,[Int],Char,String)++-- | ASCII 'Char' of 'BRAILLE'.+braille_ascii :: BRAILLE -> Char+braille_ascii (_,c,_,_,_) = c++-- | Unicode 'Char' of 'BRAILLE'.+braille_unicode :: BRAILLE -> Char+braille_unicode (_,_,_,c,_) = c++-- | Dot list of 'BRAILLE'.+braille_dots :: BRAILLE -> [Int]+braille_dots (_,_,d,_,_) = d++-- | ASCII Braille table.+--+-- > all id (map (\(x,c,_,_,_) -> x == fromEnum c) braille_table) == True+braille_table :: [BRAILLE]+braille_table =+    [(0x20,' ',[],'⠀'," ")+    ,(0x21,'!',[2,3,4,6],'⠮',"the")+    ,(0x22,'"',[5],'⠐',"contraction")+    ,(0x23,'#',[3,4,5,6],'⠼',"number prefix")+    ,(0x24,'$',[1,2,4,6],'⠫',"ed")+    ,(0x25,'%',[1,4,6],'⠩',"sh")+    ,(0x26,'&',[1,2,3,4,6],'⠯',"and")+    ,(0x27,'\'',[3],'⠄',"'")+    ,(0x28,'(',[1,2,3,5,6],'⠷',"of")+    ,(0x29,')',[2,3,4,5,6],'⠾',"with")+    ,(0x2A,'*',[1,6],'⠡',"ch")+    ,(0x2B,'+',[3,4,6],'⠬',"ing")+    ,(0x2C,',',[6],'⠠',"uppercase prefix")+    ,(0x2D,'-',[3,6],'⠤',"-")+    ,(0x2E,'.',[4,6],'⠨',"italic prefix")+    ,(0x2F,'/',[3,4],'⠌',"st")+    ,(0x30,'0',[3,5,6],'⠴',"”")+    ,(0x31,'1',[2],'⠂',",")+    ,(0x32,'2',[2,3],'⠆',";")+    ,(0x33,'3',[2,5],'⠒',":")+    ,(0x34,'4',[2,5,6],'⠲',".")+    ,(0x35,'5',[2,6],'⠢',"en")+    ,(0x36,'6',[2,3,5],'⠖',"!")+    ,(0x37,'7',[2,3,5,6],'⠶',"( or )")+    ,(0x38,'8',[2,3,6],'⠦',"“ or ?")+    ,(0x39,'9',[3,5],'⠔',"in")+    ,(0x3A,':',[1,5,6],'⠱',"wh")+    ,(0x3B,';',[5,6],'⠰',"letter prefix")+    ,(0x3C,'<',[1,2,6],'⠣',"gh")+    ,(0x3D,'=',[1,2,3,4,5,6],'⠿',"for")+    ,(0x3E,'>',[3,4,5],'⠜',"ar")+    ,(0x3F,'?',[1,4,5,6],'⠹',"th")+    ,(0x40,'@',[4],'⠈',"accent prefix")+    ,(0x41,'A',[1],'⠁',"a")+    ,(0x42,'B',[1,2],'⠃',"b")+    ,(0x43,'C',[1,4],'⠉',"c")+    ,(0x44,'D',[1,4,5],'⠙',"d")+    ,(0x45,'E',[1,5],'⠑',"e")+    ,(0x46,'F',[1,2,4],'⠋',"f")+    ,(0x47,'G',[1,2,4,5],'⠛',"g")+    ,(0x48,'H',[1,2,5],'⠓',"h")+    ,(0x49,'I',[2,4],'⠊',"i")+    ,(0x4A,'J',[2,4,5],'⠚',"j")+    ,(0x4B,'K',[1,3],'⠅',"k")+    ,(0x4C,'L',[1,2,3],'⠇',"l")+    ,(0x4D,'M',[1,3,4],'⠍',"m")+    ,(0x4E,'N',[1,3,4,5],'⠝',"n")+    ,(0x4F,'O',[1,3,5],'⠕',"o")+    ,(0x50,'P',[1,2,3,4],'⠏',"p")+    ,(0x51,'Q',[1,2,3,4,5],'⠟',"q")+    ,(0x52,'R',[1,2,3,5],'⠗',"r")+    ,(0x53,'S',[2,3,4],'⠎',"s")+    ,(0x54,'T',[2,3,4,5],'⠞',"t")+    ,(0x55,'U',[1,3,6],'⠥',"u")+    ,(0x56,'V',[1,2,3,6],'⠧',"v")+    ,(0x57,'W',[2,4,5,6],'⠺',"w")+    ,(0x58,'X',[1,3,4,6],'⠭',"x")+    ,(0x59,'Y',[1,3,4,5,6],'⠽',"y")+    ,(0x5A,'Z',[1,3,5,6],'⠵',"z")+    ,(0x5B,'[',[2,4,6],'⠪',"ow")+    ,(0x5C,'\\',[1,2,5,6],'⠳',"ou")+    ,(0x5D,']',[1,2,4,5,6],'⠻',"er")+    ,(0x5E,'^',[4,5],'⠘',"currency prefix")+    ,(0x5F,'_',[4,5,6],'⠸',"contraction")+    ]++-- | Lookup 'BRAILLE' value for unicode character.+--+-- > braille_lookup_unicode '⠝' == Just (0x4E,'N',[1,3,4,5],'⠝',"n")+braille_lookup_unicode :: Char -> Maybe BRAILLE+braille_lookup_unicode c = find ((== c) . braille_unicode) braille_table++-- | Lookup 'BRAILLE' value for ascii character (case invariant).+--+-- > 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++-- | 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+-- cell, the two cells to the right are the first two cells of the+-- decade shifted right.+--+-- For each decade there are two extra cells that shift+-- the first two cells of the decade right one place.  Subsequent+-- decades are derived by simple transformation of the first.  The+-- second is the first with the addition of dot @3@, the third adds+-- dots @3@ and @6@, the fourth adds dot @6@ and the fifth shifts the+-- first down one row.+--+-- The first decade has the 13 of the 16 4-dot patterns, the remaining+-- 3 are in the fifth decade, that is they are the three 4-dot+-- patterns that are down shifts of a 4-dot pattern.+--+-- > let trimap f (p,q,r) = (f p,f q,f r)+-- > let f = map (fromJust . decode) in map (trimap f) braille_64+braille_64 :: [(String,String,String)]+braille_64 =+    [("⠀","⠁⠃⠉⠙⠑⠋⠛⠓⠊⠚","⠈⠘")+    ,("⠄","⠅⠇⠍⠝⠕⠏⠟⠗⠎⠞","⠌⠜")+    ,("⠤","⠥⠧⠭⠽⠵⠯⠿⠷⠮⠾","⠬⠼")+    ,("⠠","⠡⠣⠩⠹⠱⠫⠻⠳⠪⠺","⠨⠸")+    ,("","⠂⠆⠒⠲⠢⠖⠶⠦⠔⠴","⠐⠰")]++-- | Transcribe ASCII to unicode braille.+--+-- > transcribe_unicode "BRAILLE ASCII CHAR GRID" == "⠃⠗⠁⠊⠇⠇⠑⠀⠁⠎⠉⠊⠊⠀⠉⠓⠁⠗⠀⠛⠗⠊⠙"+-- > transcribe_unicode "BRAILLE HTML TABLE GRID" == "⠃⠗⠁⠊⠇⠇⠑⠀⠓⠞⠍⠇⠀⠞⠁⠃⠇⠑⠀⠛⠗⠊⠙"+transcribe_unicode :: String -> String+transcribe_unicode = map (braille_unicode . fromJust . braille_lookup_ascii)++-- | Generate a character grid using inidicated values for filled and empty cells.+--+-- > let ch = (' ','.')+-- > putStrLn$ transcribe_char_grid ch "BRAILLE ASCII CHAR GRID"+--+-- > let ch = (white_circle,black_circle)+-- > putStrLn$ string_html_table $ transcribe_char_grid ch "BRAILLE HTML TABLE GRID"+transcribe_char_grid :: (Char,Char) -> String -> String+transcribe_char_grid (w,b) =+    unlines .+    map concat .+    transpose .+    map (dots_grid (w,b) . braille_dots . fromJust . braille_lookup_ascii)++-- | Generate 6-dot grid given (white,black) values.+--+-- > dots_grid (0,1) [1,2,3,5] == [[1,0],[1,1],[1,0]]+dots_grid :: (c,c) -> [Int] -> [[c]]+dots_grid (w,b) d =+    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>"+        g x = "<tr>" ++ concatMap f x ++ "</tr>"+        h x = "<table>" ++ concatMap g x ++ "</table>"+    in h (lines s)++{- | Decoding.++> let t0 = ["⠠⠁⠇⠇⠀⠓⠥⠍⠁⠝⠀⠆⠬⠎⠀⠜⠑⠀⠃⠕⠗⠝⠀⠋⠗⠑⠑⠀⠯⠀⠑⠟⠥⠁⠇⠀⠔⠀⠙⠊⠛⠝⠰⠽⠀⠯⠀⠐⠗⠎⠲"+>          ,"⠠⠮⠽⠀⠜⠑⠀⠢⠙⠪⠫⠀⠾⠀⠗⠂⠎⠕⠝⠀⠯⠀⠒⠎⠉⠊⠰⠑⠀⠯⠀⠩⠙⠀⠁⠉⠞⠀⠞⠪⠜⠙⠎⠀⠐⠕⠀⠁⠝⠕⠤"+>          ,"⠮⠗⠀⠔⠀⠁⠀⠸⠎⠀⠷⠀⠃⠗⠕⠮⠗⠓⠕⠕⠙⠲"]++> concatMap (fromMaybe "#" . decode) (concat t0)++-}+decode :: Char -> Maybe String+decode c =+    case braille_lookup_unicode c of+      Just (_,_,_,_,s) -> Just s+      Nothing -> Nothing++-- | Start and end unicode indices.+braille_rng :: Integral i => (i,i)+braille_rng = (0x2800,0x28FF)++-- | All characters, in sequence.+--+-- > length braille_seq == 256+-- > putStrLn braille_seq+braille_seq :: [Char]+braille_seq = let (l,r) = braille_rng in [toEnum l .. toEnum r]++-- | The /n/th character, zero indexed.+braille_char :: Int -> Char+braille_char = toEnum . (+) 0x2800++-- | Two element index, 255 * 255 = 65025 places.+--+-- > map braille_ix [100,300]+braille_ix :: Int -> (Char,Char)+braille_ix n =+    let (i,j) = n `divMod` 255+        f k = braille_char (k + 1)+    in (f i,f j)++-- | HTML character encoding (as hex integer).+--+-- > unwords $ map unicode_html braille_seq+unicode_html :: Char -> String+unicode_html = printf "&#x%x;" . fromEnum++-- * Unicode++-- | White (empty) circle.+white_circle :: Char+white_circle = '○'++-- | Black (filled) circle.+black_circle :: Char+black_circle = '●'++-- | Shaded (hatched) circle.+shaded_circle :: Char+shaded_circle = '◍'++-- * Contractions++-- | Table of one letter contractions.+one_letter_contractions :: [(Char,String)]+one_letter_contractions =+    [('⠃',"but")+    ,('⠉',"can")+    ,('⠙',"do")+    ,('⠑',"every")+    ,('⠋',"from,-self")+    ,('⠛',"go")+    ,('⠓',"have")+    ,('⠚',"just")+    ,('⠅',"knowledge")+    ,('⠇',"like")+    ,('⠍',"more")+    ,('⠝',"not")+    ,('⠏',"people")+    ,('⠟',"quite")+    ,('⠗',"rather")+    ,('⠎',"so")+    ,('⠞',"that")+    ,('⠌',"still")+    ,('⠥',"us")+    ,('⠧',"very")+    ,('⠭',"it")+    ,('⠽',"you")+    ,('⠵',"as")+    ,('⠡',"child")+    ,('⠩',"shall")+    ,('⠹',"this")+    ,('⠱',"which")+    ,('⠳',"out")+    ,('⠺',"will")+    ,('⠆',"be,be-")+    ,('⠒',"con-")+    ,('⠲',"dis-")+    ,('⠢',"enough")+    ,('⠖',"to")+    ,('⠶',"were")+    ,('⠦',"his")+    ,('⠔',"in")+    ,('⠴',"by,was")+    ,('⠤',"com-")+    ]
Music/Theory/Clef.hs view
@@ -1,15 +1,15 @@ -- | Common music notation clefs. module Music.Theory.Clef where -import Music.Theory.Pitch-import Music.Theory.Pitch.Name+import Music.Theory.Pitch {- hmt -}+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 Music.Theory.Permutations---- | 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 = nk_permutations n k `div` 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 :: Integral t => t -> [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
@@ -10,33 +10,14 @@ import Data.Maybe {- base -} import Data.Ratio {- base -} -import qualified Music.Theory.Set.List as T-import qualified Music.Theory.Permutations.List as T---- * List functions---- | Replace the /i/th value at /ns/ with /x/.------ > replace "test" 2 'n' == "tent"-replace :: Integral i => [a] -> i -> a -> [a]-replace ns i x =-    let f j y = if i == j then x else y-    in zipWith f [0..] ns+import qualified Music.Theory.List as T {- hmt-base -}+import qualified Music.Theory.Ord as T {- hmt-base -} --- | Are all elements equal.------ > all_equal "aaa" == True-all_equal :: Eq a => [a] -> Bool-all_equal xs = all id (zipWith (==) xs (tail xs))+import qualified Music.Theory.Permutations.List as T {- hmt -}+import qualified Music.Theory.Set.List as T {- hmt -}  -- * Indices --- | Compare adjacent elements (p.262) left to right.------ > compare_adjacent [0,1,3,2] == [LT,LT,GT]-compare_adjacent :: Ord a => [a] -> [Ordering]-compare_adjacent xs = zipWith compare xs (tail xs)- -- | Construct set of /n/ '-' @1@ adjacent indices, left right order. -- -- > adjacent_indices 5 == [(0,1),(1,2),(2,3),(3,4)]@@ -51,36 +32,6 @@     let n' = n - 1     in [(i,j) | i <- [0 .. n'], j <- [i + 1 .. n']] --- * 'Enum' functions---- | 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---- * 'Ordering' functions---- | Specialised 'genericFromEnum'.-ord_to_int :: Integral a => Ordering -> a-ord_to_int = genericFromEnum---- | Specialised 'genericToEnum'.-int_to_ord :: Integral a => a -> Ordering-int_to_ord = genericToEnum---- | 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- -- * Matrix  -- | A list notation for matrices.@@ -109,7 +60,7 @@ data Contour_Half_Matrix =     Contour_Half_Matrix {contour_half_matrix_n :: Int                         ,contour_half_matrix_m :: Matrix Ordering}-    deriving (Eq)+    deriving (Eq,Ord)  -- | Half 'Matrix' of contour given comparison function /f/. --@@ -183,7 +134,7 @@ -- > let c = ["abc","bbb","cba"] -- > in map (uniform.contour_description) c == [True,True,True] uniform :: Contour_Description -> Bool-uniform (Contour_Description _ m) = all_equal (M.elems m)+uniform (Contour_Description _ m) = T.all_equal (M.elems m)  -- | 'True' if contour does not containt any 'EQ' elements. --@@ -317,7 +268,7 @@                                             LT -> i' + adjustment j'                                             EQ -> i'                                             GT -> i' - adjustment j'-                                in Just (replace ns j j'')+                                in Just (T.replace_at ns j j'')         refine [] ns = ns         refine (i:is) ns = case step i ns of                              Nothing -> refine is ns@@ -330,7 +281,7 @@ -- > in draw_contour (contour_description_invert c) == [3,2,0,1] contour_description_invert :: Contour_Description -> Contour_Description contour_description_invert (Contour_Description n m) =-    Contour_Description n (M.map ord_invert m)+    Contour_Description n (M.map T.ord_invert m)  -- * Construction @@ -499,5 +450,5 @@ ex_4 =     let ns :: [[Int]]         ns = [[2,2,2,1],[2,2,0],[0,0],[1]]-        ns' = map (map int_to_ord) ns+        ns' = map (map T.int_to_ord) ns     in half_matrix_to_description (Contour_Half_Matrix 5 ns')
+ 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/Duration.hs view
@@ -1,22 +1,32 @@ -- | 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 -} +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 duration_meq p q = multiplier p == multiplier q +-- | Is multiplier the identity (ie. @1@)?+duration_m1 :: Duration -> Bool+duration_m1 = (== 1) . multiplier+ -- | Compare durations with equal multipliers. duration_compare_meq :: Duration -> Duration -> Maybe Ordering duration_compare_meq y0 y1 =@@ -40,158 +50,167 @@ instance Ord Duration where     compare = duration_compare_meq_err -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)--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)- -- | True if neither duration is dotted. no_dots :: (Duration, Duration) -> Bool 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 (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' :: Duration -> Duration -> Duration-sum_dur' y0 y1 =+sum_dur_err :: Duration -> Duration -> Duration+sum_dur_err y0 y1 =     let y2 = sum_dur y0 y1         err = error ("sum_dur': " ++ show (y0,y1))     in fromMaybe err y2 --- | Give @MusicXML@ type for division.+{- | 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]++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 :: [(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 :: 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 -> 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++-- | 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 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 =-    case x of-      256 -> "256th"-      128 -> "128th"-      64 -> "64th"-      32 -> "32nd"-      16 -> "16th"-      8 -> "eighth"-      4 -> "quarter"-      2 -> "half"-      1 -> "whole"-      0 -> "breve"-      -1 -> "long"-      _ -> error ("whole_note_division_to_musicxml_type: " ++ show x)+    T.lookup_err_msg "division_musicxml_tbl" x division_musicxml_tbl  -- | Variant of 'whole_note_division_to_musicxml_type' extracting--- 'division' from 'Duration'.+-- 'division' from 'Duration', dots & multipler are ignored. ----- > duration_to_musicxml_type quarter_note == "quarter"+-- > duration_to_musicxml_type (Duration 4 0 1) == "quarter" duration_to_musicxml_type :: Duration -> String duration_to_musicxml_type = whole_note_division_to_musicxml_type . division --- | Give /Lilypond/ notation for 'Duration'.  Note that the duration--- multiplier is /not/ written.+-- * Unicode++-- | Table giving @Unicode@ symbols for divisions.+division_unicode_tbl :: [(Integer,Char)]+division_unicode_tbl = zip [0,1,2,4,8,16,32,64,128,256] "𝅜𝅝𝅗𝅥𝅘𝅥𝅘𝅥𝅮𝅘𝅥𝅯𝅘𝅥𝅰𝅘𝅥𝅱𝅘𝅥𝅲"++-- | Lookup 'division_unicode_tbl'. ----- > import Music.Theory.Duration.Name--- > map duration_to_lilypond_type [half_note,dotted_quarter_note] == ["2","4."]+-- > map whole_note_division_to_unicode_symbol [1,2,4,8] == "𝅝𝅗𝅥𝅘𝅥𝅘𝅥𝅮"+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++-- | Give Unicode string for 'Duration'. The duration multiplier is /not/ written.+--+-- > map duration_to_unicode [Duration 1 2 1,Duration 4 1 1] == ["𝅝𝅭𝅭","𝅘𝅥𝅭"]+duration_to_unicode :: Duration -> String+duration_to_unicode (Duration dv d _) =+    let dv' = whole_note_division_to_unicode_symbol dv+    in dv' : replicate (fromIntegral d) '𝅭'++-- * Lilypond++-- | 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 duration_to_lilypond_type (Duration dv d _) =     let dv' = if dv == 0 then "\\breve" else show dv     in dv' ++ replicate (fromIntegral d) '.' --- | Calculate number of beams at notated division.------ > whole_note_division_to_beam_count 32 == Just 3-whole_note_division_to_beam_count :: Integer -> Maybe Integer-whole_note_division_to_beam_count x =-    let t = [(256,6),(128,5),(64,4),(32,3),(16,2),(8,1)-            ,(4,0),(2,0),(1,0),(0,0),(-1,0)]-    in lookup x t+-- * Humdrum --- | Calculate number of beams at 'Duration'.------ > map duration_beam_count [half_note,sixteenth_note] == [0,2]-duration_beam_count :: Duration -> Integer-duration_beam_count (Duration x _ _) =-    let err = error "duration_beam_count"-        bc = whole_note_division_to_beam_count x-    in fromMaybe err bc+{- | Duration to @**recip@ notation. -whole_note_division_pp :: Integer -> Maybe Char-whole_note_division_pp x =-    let t = [(16,'s'),(8,'e'),(4,'q'),(2,'h'),(1,'w')]-    in lookup x t+<http://humdrum.org/Humdrum/representations/recip.rep.html> --- > import Music.Theory.Duration.Name.Abbreviation--- > map duration_pp [q,h',e''] == [Just "q",Just "h'",Just "e''"]-duration_pp :: Duration -> Maybe String-duration_pp (Duration x d m) =-    let d' = genericReplicate d '\''-        m' = case (numerator m,denominator m) of-               (1,1) -> ""-               (1,i) -> '/' : show i-               (i,j) -> '*' : show i ++ "/" ++ show j-    in case whole_note_division_pp x of-         Just x' -> Just (x' : d' ++ m')-         _ -> Nothing+> let d = map (\z -> Duration z 0 1) [0,1,2,4,8,16,32]+> map duration_recip_pp d == ["0","1","2","4","8","16","32"] --- | Duration to @**recip@ notation.------ 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"]------ > 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."]+> let d = [Duration 1 1 (1/3),Duration 4 1 1,Duration 4 1 (2/3)]+> map duration_recip_pp d == ["3.","4.","6."]+-} duration_recip_pp :: Duration -> String duration_recip_pp (Duration x d m) =     let (mn,md) = (numerator m,denominator m)@@ -199,3 +218,43 @@     in if denominator r == 1        then show (numerator r) ++ genericReplicate d '.'        else error (show ("duration_recip_pp",x,d,m,r))++-- * Letter++{- | 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")]++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 '.'+        m' = case (numerator m,denominator m) of+               (1,1) -> ""+               (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
@@ -3,11 +3,12 @@  import Data.Maybe {- base -} import Data.Ratio {- base -}-import qualified Data.Traversable as T {- base -} import Data.Tree {- containers -} +import qualified Music.Theory.List as L {- hmt-base -}+ import Music.Theory.Duration-import Music.Theory.Duration.RQ+import Music.Theory.Duration.Rq  -- | Standard music notation durational model annotations data D_Annotation = Tie_Right@@ -57,58 +58,12 @@ 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)     in zipWith jn (map fn x) ts --- | Transform predicates into 'Ordering' predicate such that if /f/--- holds then 'LT', if /g/ holds then 'GT' else 'EQ'.------ > map (begin_end_cmp (== '{') (== '}')) "{a}" == [LT,EQ,GT]-begin_end_cmp :: (t -> Bool) -> (t -> Bool) -> t -> Ordering-begin_end_cmp f g x = if f x then LT else if g x then GT else EQ---- | Variant of 'begin_end_cmp', predicates are constructed by '=='.------ > map (begin_end_cmp_eq '{' '}') "{a}" == [LT,EQ,GT]-begin_end_cmp_eq :: Eq t => t -> t -> t -> Ordering-begin_end_cmp_eq p q = begin_end_cmp (== p) (== q)---- | 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 (begin_end_cmp_eq '{' '}') l}--- > in catMaybes (flatten t) == l------ > let d = putStrLn . drawTree . fmap show--- > in d (group_tree (begin_end_cmp_eq '(' ')') "a(b(cd)ef)ghi")-group_tree :: (a -> Ordering) -> [a] -> Tree (Maybe a)-group_tree 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)-        push (r,z) e = case z of-                         h:z' -> (r,insert_e h (unit e) : z')-                         [] -> (unit e : r,[])-        open (r,z) = (r,nil:z)-        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' -> case f e of-                        LT -> go (push (open st) e) x'-                        EQ -> go (push st e) x'-                        GT -> go (close (push st e)) x'-    in go ([],[])- -- | Group tuplets into a 'Tree'.  Branch nodes have label 'Nothing', -- leaf nodes label 'Just' 'Duration_A'. --@@ -121,9 +76,7 @@ -- >         ,(q,[])] -- > in catMaybes (flatten (da_group_tuplets d)) == d da_group_tuplets :: [Duration_A] -> Tree (Maybe Duration_A)-da_group_tuplets =-    let f = begin_end_cmp da_begins_tuplet da_ends_tuplet-    in group_tree f+da_group_tuplets = L.group_tree (da_begins_tuplet,da_ends_tuplet)  -- | Variant of 'break' that places separator at left. --@@ -165,22 +118,11 @@                    in Right (d : t) : da_group_tuplets_nn x''               else Left d : da_group_tuplets_nn x' --- | Keep right variant of 'zipWith', 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 []- -- | Keep right variant of 'zip', unused rhs values are returned. -- -- > zip_kr [1..4] ['a'..'f'] == ([(1,'a'),(2,'b'),(3,'c'),(4,'d')],"ef") zip_kr :: [a] -> [b] -> ([(a,b)],[b])-zip_kr = zip_with_kr (,)+zip_kr = L.zip_with_kr (,)  -- | 'zipWith' variant that adopts the shape of the lhs. --@@ -192,31 +134,9 @@     case (p,q) of       (e:p',i:q') -> case e of                        Left j -> Left (f j i) : nn_reshape f p' q'-                       Right j -> let (j',q'') = zip_with_kr f j q+                       Right j -> let (j',q'') = L.zip_with_kr f j q                                   in Right j' : nn_reshape f p' q''       _ -> []---- | Replace elements at 'Traversable' with result of joining with--- elements from list.-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  -- | Does /a/ have 'Tie_Left' and 'Tie_Right'? d_annotated_tied_lr :: [D_Annotation] -> (Bool,Bool)
− 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..]) 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..] 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
@@ -1,8 +1,9 @@--- | 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--- dotted 'eighth_note'.+-- dotted 'eighth_note'.  The prefix is @_@ not @d@ since @d4@ etc. are+-- also note names. -- -- > zipWith duration_compare_meq [e,e,e,e'] [e,s,q,e] == [EQ,GT,LT,GT] -- > zipWith sum_dur [e,q,q'] [e,e,e] == [Just q,Just q',Just h]
− Music/Theory/Duration/RQ.hs 
@@ -1,187 +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-import Music.Theory.Duration.Name---- | Rational Quarter-Note-type RQ = Rational---- | 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 =-    case (numerator x,denominator x) of-      (1,8) -> Just thirtysecond_note-      (3,16) -> Just dotted_thirtysecond_note-      (1,4) -> Just sixteenth_note-      (3,8) -> Just dotted_sixteenth_note-      (1,2) -> Just eighth_note-      (3,4) -> Just dotted_eighth_note-      (1,1) -> Just quarter_note-      (3,2) -> Just dotted_quarter_note-      (2,1) -> Just half_note-      (3,1) -> Just dotted_half_note-      (7,2) -> Just double_dotted_half_note-      (4,1) -> Just whole_note-      (6,1) -> Just dotted_whole_note-      (8,1) -> Just breve-      (12,1) -> Just dotted_breve-      _ -> Nothing---- | 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').@@ -17,54 +17,31 @@ -- 5. Ascribe values to notated durations, see 'ascribe'. module Music.Theory.Duration.Sequence.Notate where -import Control.Applicative {- base -}-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@@ -76,13 +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@@ -96,7 +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@@ -104,12 +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@@ -161,21 +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@@ -187,24 +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) ->@@ -215,57 +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@@ -275,10 +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]@@ -288,13 +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)@@ -302,82 +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) .@@ -386,59 +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@@ -449,39 +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))@@ -489,31 +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))@@ -534,7 +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)@@ -543,13 +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@@ -642,10 +617,18 @@                 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 +-- | Run simplifier until it reaches a fix-point, or for at most 'limit' passes.+m_simplify_fix :: Int -> Simplify_P -> Time_Signature -> [Duration_A] -> [Duration_A]+m_simplify_fix limit p ts d =+    let d' = m_simplify p ts d+    in if d == d' || limit == 1+       then d'+       else m_simplify_fix (limit - 1) p ts d'+ -- | Pulse simplifier predicate, which is 'const' 'True'. p_simplify_rule :: Simplify_P p_simplify_rule = const True@@ -660,13 +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'. @@ -674,23 +657,22 @@ >      ts_p = [[1/2,1,1/2],[1/2,1]] >      rq = map (/6) [1,1,1,1,1,1,4,1,2,1,1,2,1,3] >      sr x = T.default_rule [] x->  in T.notate_rqp sr ts (Just ts_p) rq+>  in T.notate_rqp 4 sr ts (Just ts_p) rq  -}-notate_rqp :: Simplify_P -> [Time_Signature] -> Maybe [[RQ]] -> [RQ] ->+notate_rqp :: Int -> Simplify_P -> [Time_Signature] -> Maybe [[Rq]] -> [Rq] ->               Either String [[Duration_A]]-notate_rqp r ts ts_p x = do+notate_rqp limit r ts ts_p x = do   let ts_p' = fromMaybe (map ts_divisions ts) ts_p   mm <- to_divisions_rq ts_p' x   dd <- mm_notate mm-  return (zipWith (m_simplify r) ts dd)+  return (zipWith (m_simplify_fix limit r) ts dd)  -- | Variant of 'notate_rqp' without pulse divisions (derive). ----- > notate (default_rule [((3,2),0,(2,2)),((3,2),0,(4,2))]) [(3,2)] [6]-notate :: Simplify_P -> [Time_Signature] -> [RQ] ->-          Either String [[Duration_A]]-notate r ts x = notate_rqp r ts Nothing x+-- > 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 = notate_rqp limit r ts Nothing  -- * Ascribe @@ -772,17 +754,17 @@                in r : mm_ascribe mm' x'  -- | 'mm_ascribe of 'notate'.-notate_mm_ascribe :: Show a => [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 r ts rqp d p =-    let n = notate_rqp (default_rule r) ts rqp d+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 => [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+notate_mm_ascribe_err = either error id .::::: notate_mm_ascribe  -- | Group elements as /chords/ where a chord element is indicated by -- the given predicate.
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,Eq 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/Function.hs 
@@ -1,52 +0,0 @@--- | "Data.Function" related functions.-module Music.Theory.Function where---- * 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.------ > 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
@@ -0,0 +1,372 @@+-- | Gamelan instruments and pitch structures.+module Music.Theory.Gamelan where++import Data.Char {- base -}+import Data.Function {- base -}+import Data.List {- base -}+import Data.Maybe {- base -}+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.Pitch as T {- hmt -}+import qualified Music.Theory.Tuning as T {- hmt -}+import qualified Music.Theory.Tuning.Et as T {- hmt-diagrams -}++-- | 'fromJust' with error message.+fromJust_err :: String -> Maybe a -> a+fromJust_err err = fromMaybe (error err)++-- | 'approxRational' of 0.01.+near_rat :: Double -> Rational+near_rat = flip approxRational 0.01++-- * Gamelan++-- | Enumeration of gamelan instrument families.+data Instrument_Family+    = Bonang+    | Gambang+    | Gender+    | Gong+    | Saron+      deriving (Enum,Bounded,Eq,Ord,Show,Read)++-- | Universe+instrument_family_set :: [Instrument_Family]+instrument_family_set = T.enum_univ++-- | Enumeration of Gamelan instruments.+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)+    | Gong_Ageng -- ^ Gong Ageng (hanging gong, low)+    | Gong_Suwukan -- ^ Gong Suwukan (hanging gong, middle)+    | Kempul -- ^ Kempul (hanging gong, middle)+    | Kempyang -- ^ Kempyang (horizontal gong, high)+    | Kenong -- ^ Kenong (horizontal gong, low)+    | 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 -> Instrument_Family+instrument_family nm =+    case nm of+      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 =+    let f c = if c == '_' then ' ' else c+    in map f . show++-- | 'Clef' appropriate for 'Instrument_Name'.+instrument_name_clef :: Integral i => Instrument_Name -> T.Clef i+instrument_name_clef nm =+    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+      Gong_Ageng -> T.Clef T.Bass 0+      Gong_Suwukan -> T.Clef T.Bass 0+      Kempul -> T.Clef T.Bass 0+      Kempyang -> T.Clef T.Treble 1+      Kenong -> T.Clef T.Treble 0+      Ketuk -> T.Clef T.Alto 0+      Saron_Barung -> T.Clef T.Treble 0+      Saron_Demung -> T.Clef T.Treble 0+      Saron_Panerus -> T.Clef T.Treble 1++instrument_name_clef_plain :: Integral i => Instrument_Name -> T.Clef i+instrument_name_clef_plain = T.clef_zero . instrument_name_clef++-- | 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)+        o' = if o < 0+             then genericReplicate (abs o) '-'+             else genericReplicate o '+'+    in o' ++ [d']++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,Show)++-- | 'pitch_degree' of 'note_pitch'.+note_degree :: Note -> Degree+note_degree = pitch_degree . note_pitch++-- | 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++-- | 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 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 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 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 t -> Maybe T.Pitch+tone_24et_pitch =+    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 -> T.Pitch+tone_24et_pitch' = fromJust_err "tone_24et_pitch" . tone_24et_pitch++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 -> T.Pitch_Detune+tone_24et_pitch_detune' = fromJust_err "tone_24et_pitch_detune" . tone_24et_pitch_detune++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 t -> Rational+tone_24et_fmidi = near_rat . T.pitch_to_fmidi . tone_24et_pitch'++tone_12et_pitch :: Tone t -> Maybe T.Pitch+tone_12et_pitch =+    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 -> T.Pitch+tone_12et_pitch' = fromJust_err "tone_12et_pitch" . tone_12et_pitch++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 -> 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 t -> Rational+tone_12et_fmidi = near_rat . T.pitch_to_fmidi . tone_12et_pitch'++tone_family :: Tone t -> Instrument_Family+tone_family = instrument_family . tone_instrument_name++tone_in_family :: Instrument_Family -> Tone t -> Bool+tone_in_family c t = tone_family t == c++select_tones :: Instrument_Family -> [Tone t] -> [Maybe (Tone t)]+select_tones c =+    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 t -> Tone_Set t+tone_subset (fm,sc) =+    let f t = tone_family t `elem` fm &&+              fromJust_err "tone_subset" (tone_scale t) `elem` sc+    in filter f++data Instrument = Instrument {instrument_name :: Instrument_Name+                             ,instrument_scale :: Maybe Scale+                             ,instrument_pitches :: Maybe [Pitch]+                             ,instrument_frequencies :: Maybe [Frequency]}+                  deriving (Eq,Show)++type Tone_Set t = [Tone t]+type Tone_Group t = [Tone_Set t]+type Gamelan = [Instrument]++tone_scale :: Tone t -> Maybe Scale+tone_scale = fmap note_scale . tone_note++tone_pitch :: Tone t -> Maybe Pitch+tone_pitch = fmap note_pitch . tone_note++tone_degree :: Tone t -> Maybe Degree+tone_degree = fmap pitch_degree . tone_pitch++tone_degree' :: Tone t -> Degree+tone_degree' = fromJust_err "tone_degree" . tone_degree++tone_octave :: Tone t -> Maybe Octave+tone_octave = fmap pitch_octave . tone_pitch++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 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 t -> Bool+tone_family_class_p (fm,sc) t =+    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 -> 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)+    in filter near_t t++-- | Compare 'Tone's by frequency.  'Tone's without frequency compare+-- as if at frequency @0@.+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'.+map_maybe_uniform :: (a -> Maybe b) -> [a] -> Maybe [b]+map_maybe_uniform f x =+    let x' = map f x+    in if any isNothing x' then Nothing else Just (catMaybes x')++instrument :: Tone_Set t -> Instrument+instrument c =+    let sf = fmap note_scale . tone_note+        pf = fmap note_pitch . tone_note+        pm = map_maybe_uniform pf c+        fm = map_maybe_uniform tone_frequency c+        (p,f) = case (pm,fm) of+                  (Just i,Just j) -> let (i',j') = unzip (sort (zip i j))+                                     in (Just i',Just j')+                  _ -> (pm,fm)+    in case c of+         t:_ -> Instrument (tone_instrument_name t) (sf t) p f+         [] -> undefined++instruments :: Tone_Set t -> [Instrument]+instruments c =+    let c' = sortBy (compare `on` tone_instrument_name) c+        c'' = groupBy ((==) `on` tone_class) c'+    in map instrument c''++instrument_gamut :: Instrument -> Maybe (Pitch,Pitch)+instrument_gamut =+    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 = elemIndex d (scale_degrees s)++-- * Tone set++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 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
@@ -0,0 +1,133 @@+-- | Geometrical Drawings+--+-- A. Bernard Deacon and Camilla H. Wedgwood. “Geometrical Drawings+-- from Malekula and Other Islands of the New Hebrides”. The Journal+-- of the Royal Anthropological Institute of Great Britain and+-- 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-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 -}++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.fgl_to_udot opt (T.gr_pp_label_v pp) (T.g_from_edges 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.Edge String],[T.Dot_Attr],FilePath)++-- * E+g1 :: G+g1 =+    let c1 = words "A1 B2 A3 B4 C3 B2 C1 D2 C3 D4 D3 D2 D1 C2 D3 C4 B3 C2 B1 A2 B3 A4 A3 A2 A1"+        o1 = [("node:shape","circle"),("edge:len","1.5"),("edge:fontsize","7")]+    in (T.adj2 1 c1,o1,"E")++-- * D+g2 :: G+g2 =+    let c2' = words "B3 C2 = C3 B2 A1 = A2 B1 C2 = C1 B2 A3 = A2 B3 C3 C2 B2 B3 ~ C3 ~ C2 C1 == C3 C2 C1 B1 B2 C2 ~ C1 ~ B1 A1 C1 B1 A1 A2 B2 B1 ~ A1 ~ A2 A3 == A1 A2 A3 B3 B2 A2 ~ A3 ~ B3 C3 C3 ~~ C1 ~~ A1 ~~ A3 A3 B3"+        c2 = filter T.is_cell_ref c2'+        o2 = [("node:shape","circle"),("edge:len","3"),("edge:fontsize","7")]+    in (T.adj2 1 c2,o2,"D")++-- * A+g4 :: G+g4 =+    let c4' = words "B1 C2 C3 B3 B2 C2 ~~ C3 C2 ~~ C1 C2 C2 B3 A3 A2 B2 B3 ~~ A3 B3 ~~ C3 B3 B3 A2 A1 B1 B2 A2 ~~ A1 A2 ~~ A3 A2 A2 B1 C1 C2 B2 B1 ~~ C1 B1 ~~ A1 B1 B1"+        c4 = filter T.is_cell_ref c4'+        o4 = [("node:shape","circle"),("edge:len","3"),("edge:fontsize","7")]+    in (T.adj2 1 c4,o4,"A")++g6 :: G+g6 =+    let c6' = words "B1 C2 B2 C1 B1 A2 B2 A1 B1 B2 B3 B3 B3 B3 B2 B1 B0 B0 B0 B0 B1 C1 ~~~ C2 B2 B2 B2 A2 ~~~ A1 B1 B1 B1"+        c6 = filter T.is_cell_ref c6'+        o6 = [("node:shape","circle"),("edge:len","3"),("edge:fontsize","7")]+    in (T.adj2 1 c6,o6,"B")++g8 :: G+g8 =+    let c8' = words "C2 B1 B1 A2 ~ (04) B1 B2 B3 ~ (08) C2 B3 B3 A2 ~ (13) B3 B2 A2 (17) A3 A3 B2 C1 C1 C2 B2 B1 ~ (23) C2 B2 A2 A1 A1 B2 C3 C3 C2"+        c8 = filter T.is_cell_ref c8'+        o8 = [("node:shape","circle"),("edge:len","3"),("edge:fontsize","7")]+    in (T.adj2 1 c8,o8,"C")++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 = 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")++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 = 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")]+    in (e10,o10,"G")++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 = 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")]+    in (e11,o11,"H")++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 = 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")]+    in (e12,o12,"I")++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 = 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")]+    in (e13,o13,"J")++g_all :: [G]+g_all = [g1,g2,g4,g6,g8,g9,g10,g11,g12,g13]++-- G = unlabeled, GL = labeled+-- GC = collated, GF = filtered (unique edges)+-- GD = directed+wr :: G -> IO ()+wr (e,o,nm) = do+  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_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_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)))+-}++wr_all :: IO ()+wr_all = mapM_ wr g_all
+ Music/Theory/Graph/Dot.hs view
@@ -0,0 +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 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 -}++import qualified Music.Theory.Graph.Fgl as T {- hmt -}++-- * 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.+--+-- > map is_symbol ["sym","Sym2","3sym","1",""] == [True,True,False,False,False]+is_symbol :: String -> Bool+is_symbol = s_classify isAlpha isAlphaNum (const True)++-- | Number rule.+--+-- > 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 is_symbol s || is_number s then s else concat ["\"",s,"\""]++-- * 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.+--+-- > 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),"]"]++-- | Merge attributes, left-biased.+dot_attr_ext :: [Dot_Attr] -> [Dot_Attr] -> [Dot_Attr]+dot_attr_ext = List.assoc_merge++-- | graph|node|edge+type Dot_Type = String++-- | (type,[attr])+type Dot_Attr_Set = (Dot_Type,[Dot_Attr])++-- | 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]++-- | type:attr (type = graph|node|edge)+type Dot_Meta_Key = String++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 List.collate c++-- | 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)]++-- * Graph++-- | Graph pretty-printer, (v -> [attr],e -> [attr])+type Graph_Pp v e = ((Int,v) -> [Dot_Attr],((Int,Int),e) -> [Dot_Attr])++-- | 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)++-- | 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)++-- | 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+      _ -> List.bracket ('{','}') (intercalate "," (map show l))++-- | Graph type, directed or un-directed.+data Graph_Type = Graph_Digraph | Graph_Ugraph++g_type_to_string :: Graph_Type -> String+g_type_to_string ty =+    case ty of+      Graph_Digraph -> "digraph"+      Graph_Ugraph -> "graph"++g_type_to_edge_symbol :: Graph_Type -> String+g_type_to_edge_symbol ty =+    case ty of+      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_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 opt)+              ,map v_f v+              ,map e_f e+              ,["}"]]++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 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
@@ -0,0 +1,635 @@+-- | Tom Johnson. /Other Harmony: Beyond Tonal and Atonal/. Editions 75, 2014.+module Music.Theory.Graph.Johnson_2014 where++import Control.Monad {- base -}+import Data.Int {- base -}+import Data.List {- base -}+import Data.Maybe {- base -}++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.Key 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.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 = Int8++dif :: Num a => (a, a) -> a+dif = uncurry (-)++absdif :: Num a => (a, a) -> a+absdif = abs . dif++-- | interval (0,11) to interval class (0,6)+i_to_ic :: (Num a, Ord a) => a -> a+i_to_ic n = if n > 6 then 12 - n else n++p2_and :: (t -> u -> Bool) -> (t -> u -> Bool) -> t -> u -> Bool+p2_and p q i j = p i j && q i j++-- | degree of intersection+doi :: Eq t => [t] -> [t] -> Int+doi p = length . intersect p++doi_of :: Eq t => Int -> [t] -> [t] -> Bool+doi_of n p = (==) n . doi p++-- | The sum of the pointwise absolute difference.+loc_dif :: Num t => [t] -> [t] -> t+loc_dif p q = let f i j = abs (i - j) in sum (zipWith f p q)++loc_dif_of :: (Eq t, Num t) => t -> [t] -> [t] -> Bool+loc_dif_of n p q = loc_dif p q == n++loc_dif_in :: (Eq t, Num t) => [t] -> [t] -> [t] -> Bool+loc_dif_in n p q = loc_dif p q `elem` n++-- | The number of places that are, pointwise, not equal.+--+-- > loc_dif_n "test" "pest" == 1+loc_dif_n :: (Eq t,Num i) => [t] -> [t] -> i+loc_dif_n p q =+    let f i j = if i == j then 0 else 1+    in sum (zipWith f p q)++loc_dif_n_of :: Eq t => Int -> [t] -> [t] -> Bool+loc_dif_n_of n p q = loc_dif_n p q == n++-- > 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 (zipWith (curry absdif) p x)+    in minimum (map f (permutations q))++min_vl_of :: (Num a, Ord a) => a -> [a] -> [a] -> Bool+min_vl_of n p q = min_vl p q == n++min_vl_in :: (Num a, Ord a) => [a] -> [a] -> [a] -> Bool+min_vl_in n p q = min_vl p q `elem` n++combinations2 :: Ord t => [t] -> [(t, t)]+combinations2 p = [(i,j) | i <- p, j <- p, i < j]++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+m_get m i = fromMaybe (error "get") (M.lookup i m)++-- | degree of intersection+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++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 :: 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_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++-- > 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+        l1 = T.tun_seq 4 (3/2) (f (1 * 2/3 * 5/4))+        l2 = T.tun_seq 5 (3/2) (f (1 * 2/3 * 2/3))+        l3 = T.tun_seq 3 (3/2) (f (1 * 2/3 * 4/5))+        (c1,c2) = T.euler_align_rat (5/4,5/4) (l1,l2,l3)+    in ([l1,l2,l3],c1 ++ c2)++p12_euler_plane_gr :: [String]+p12_euler_plane_gr = T.euler_plane_to_dot_rat (0,True) p12_euler_plane++-- * 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 (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 = 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 T.z12 p31_f_4_22))++p31_gr :: [String]+p31_gr = gen_graph_ul [] set_pp p31_e_set++-- * P.114++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 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 =+  [("p114.0.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]))+  ,("p114.3.dot",p114_mk_gr 1.5 (loc_dif_n_of 1))+  ,("p114.4.dot",p114_mk_gr 1.5 (loc_dif_of 1))+  ,("p114.5.dot",p114_mk_gr 1.5 (loc_dif_of 2))+  ,("p114.6.dot",p114_mk_gr 1.5 (loc_dif_in [1,2]))+  ,("p114.7.dot",p114_mk_gr 1.5 (loc_dif_in [1,2,3]))+  ,("p114.8.dot",p114_mk_gr 1.5 (min_vl_in [1,2,3]))+  ,("p114.9.dot",p114_mk_gr 2.0 (min_vl_in [1,2,3,4]))+  ]++-- * P.125++p125_gr :: [String]+p125_gr =+    let t :: [[Int]]+        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))+    in gen_graph_ul [] set_pp (T.e_univ_select_u_edges (doi_of 2) ch)++-- * P.131++p131_gr :: [String]+p131_gr =+    let c = let u = [6::Int .. 14]+            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++p148_mk_gr :: ([Int] -> [Int] -> Bool) -> [String]+p148_mk_gr f =+    let mid_set_pp :: [Int] -> String+        mid_set_pp = concatMap show . take 3 . drop 1+        i_seq :: Num i => [[i]]+        i_seq = permutations [1,2,3,4]+        p_seq :: (Ord i,Num i) => [[i]]+        p_seq = sort (map (T.dx_d 0) i_seq)+    in gen_graph_ul [("edge:len","1.75")] mid_set_pp (T.e_univ_select_u_edges f p_seq)++p148_gr_set :: [(String,[String])]+p148_gr_set =+  [("p148.0.dot",p148_mk_gr (doi_of 4))+  ,("p148.1.dot",p148_mk_gr (min_vl_in [1]))+  ,("p148.2.dot",p148_mk_gr (min_vl_in [1,2]))+  ,("p148.3.dot",p148_mk_gr (p2_and (doi_of 4) (min_vl_in [1])))+  ,("p148.4.dot",p148_mk_gr (p2_and (doi_of 4) (min_vl_in [1,2])))+  ,("p148.5.dot",p148_mk_gr (loc_dif_n_of 1))+  ,("p148.6.dot",p148_mk_gr (loc_dif_of 1))+  ]++-- * 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 opt = [("graph:layout","neato")+              ,("edge:len","1.75")]+    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 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",p172_g1)+    ,("p172.1.dot",p172_g2)+    ,("p172.2.dot",p172_g3)+    ,("p172.3.dot",p172_g4)]++-- * P.177++-- > map (partition_ic 4) p_set+-- > map (partition_ic 6) p_set+partition_ic :: (Num t, Ord t, Show t) => t -> [t] -> ([t], [t])+partition_ic n p =+    case find ((== n) . i_to_ic . absdif) (combinations2 p) of+      Just (i,j) -> let q = sort [i,j] in (q,sort (p \\ q))+      Nothing -> error (show ("partition_ic",n,p))++p177_gr_set :: [(String,[String])]+p177_gr_set =+    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_label_v set_pp+             gr = T.g_from_edges (map (partition_ic 6) p_set)+         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 "/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)+  f ("p131.dot",p131_gr)+  mapM_ f p148_gr_set+  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/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
@@ -0,0 +1,114 @@+module Music.Theory.Instrument.Names where++import Data.List.Split {- split -}++-- | (family,abbreviations,names,transpositions)+instrument_db' :: [(String,String,String,String)]+instrument_db' =+    [("br","b.tbn","bass trombone","")+    ,("br","b.tuba","bass tuba","")+    ,("br","euph","euphonium","")+    ,("br","hn","french horn","F")+    ,("br","tbn;trm","trombone","")+    ,("br","tb;tba","tuba","")+    ,("br","tpt","trumpet","B♭")+    ,("br","t.tbn","tenor trombone","")+    ,("br","crt","cornet","")+    ,("br","fgh;flhn","flugel horn","")+    ,("br","p.tpt","piccolo trumpet","")+    ,("el","cd","compact disc","")+    ,("el","el;elec","electronics","")+    ,("el","tp","tape","")+    ,("el","om","ondes martenot","")+    ,("kb","h;hrm","harmonium","")+    ,("kb","e.pf","electric piano","")+    ,("kb","p;pf;pno","piano;pianoforte","")+    ,("kb","o;or;org","organ","")+    ,("kb","kb;kbd","keyboard","")+    ,("kb","cel","celeste","")+    ,("kb","clvd","clavichord","")+    ,("kb","hpd;hpcd","harpsichord","")+    ,("kb","syn","synthesiser","")+    ,("pc","bd","bass drum","")+    ,("pc","btl","bottle","")+    ,("pc","cast","castanets","")+    ,("pc","cbell","cow-bell","")+    ,("pc","bell","bell","chimes")+    ,("pc","clv","clave","")+    ,("pc","crot","crotales","")+    ,("pc","cym","cymbals","")+    ,("pc","dm","drum","")+    ,("pc","gl;glsp","glockenspiel","")+    ,("pc","mcas","maracas","")+    ,("pc","met.bl","metal block","")+    ,("pc","mr;mar","marimba","")+    ,("pc","sd","side drum","")+    ,("pc","sn.dm","snare drum","")+    ,("pc","sus.cym","suspended cymbal","")+    ,("pc","tamb","tambourine","")+    ,("pc","tam","tam tam","")+    ,("pc","t.bells","tubular bells","")+    ,("pc","td","tenor drum","")+    ,("pc","tri;tgl","triangle","")+    ,("pc","tm;timp","timpani","")+    ,("pc","tpl.bl","temple blocks","")+    ,("pc","vb;vib","vibraphone","")+    ,("pc","wdbl","wood block","")+    ,("pc","xyl","xylophone","")+    ,("str","va;vla","viola","")+    ,("str","vc;vlc","cello;violoncello","")+    ,("str","vn;vln","violin","")+    ,("str","cb","contrabass","")+    ,("str","db","double bass","")+    ,("str","vda","viola d'amore","")+    ,("str","b.gtr","bass guitar","")+    ,("str","e.gtr","electric guitar","")+    ,("str","gtr","guitar","")+    ,("str","","lute","")+    ,("str","zith","zither","")+    ,("str","hp","harp","")+    ,("str","dulc","dulcimer","")+    ,("str","mand","mandolin","")+    ,("vc","a;alt","alto","")+    ,("vc","b;bass","bass","")+    ,("vc","mz;mez","mezzo-soprano","")+    ,("vc","n;nar","narrator","")+    ,("vc","s;sop","soprano","")+    ,("vc","t;tn","tenor","")+    ,("vc","v;vc;voc","voice","")+    ,("vc","ch","chorus","")+    ,("vc","ctral","contralto","")+    ,("vc","ctrbs","contrabass","")+    ,("vc","bar","baritone","")+    ,("vc","b.bar","bass baritone","")+    ,("ww","b.cl","bass clarinet","")+    ,("ww","cb.cl","contrabass clarinet","")+    ,("ww","c;cl","clarinet","B♭")+    ,("ww","a.fl","alto flute","G")+    ,("ww","b.fl","bass flute","C")+    ,("ww","bn;bsn","bassoon","")+    ,("ww","f;fl","flute","")+    ,("ww","hb;htb","hautbois","")+    ,("ww","o;ob","oboe","")+    ,("ww","p;picc","piccolo","")+    ,("ww","ca","cor anglais","")+    ,("ww","c.bn","contrabassoon","")+    ,("ww","a.sax","alto saxophone","E♭")+    ,("ww","b.sax","baritone saxophone","E♭")+    ,("ww","b.ob","bass oboe","")+    ,("ww","cfg","contrafagotto","")+    ,("ww","eh;en.hn","english horn","")+    ,("ww","fg","fagotto","")+    ,("ww","rec","recorder","")+    ,("ww","sax","saxophone","")+    ,("ww","s.sax","soprano saxophone","B♭")+    ,("ww","t.sax","tenor saxophone","B♭")+    ,("ww","oca","ocarina","")+    ]++-- | (family,[abbreviations],[names],[transpositions])+instrument_db :: [(String,[String],[String],[String])]+instrument_db =+    let sep = splitOn ";"+        f (fm,ab,nm,tr) = (fm,sep ab,sep nm,sep tr)+    in map f instrument_db'
Music/Theory/Interval.hs view
@@ -4,16 +4,17 @@ import Data.List {- base -} import Data.Maybe {- base -} -import Music.Theory.Pitch-import Music.Theory.Pitch.Note+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)@@ -21,23 +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 :: Octave}+                         ,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 :: Note_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)@@ -65,20 +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@@ -95,65 +96,39 @@                 in if dir == GT then negate n - o else n + o       Nothing -> error "interval_semitones" --- | Inclusive set of 'Note_T' 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 n1 n2 =-    let fn x = toEnum (x `mod` 7)-        n1' = fromEnum n1-        n2' = fromEnum n2-        n2'' = if n1' > n2' then n2' + 7 else n2'-    in map fn [n1' .. n2'']---- | Invert 'Ordering', ie. 'GT' becomes 'LT' and vice versa.------ > map invert_ordering [LT,EQ,GT] == [GT,EQ,LT]-invert_ordering :: Ordering -> Ordering-invert_ordering x =-    case x of-      LT -> GT-      EQ -> EQ-      GT -> LT- -- | 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 :: Pitch -> Pitch -> Interval+-- > 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-        (Pitch n1 _ o1) = p1-        (Pitch n2 _ o2) = p2-        p1' = pitch_to_pc p1-        p2' = pitch_to_pc p2+        (T.Pitch n1 _ o1) = p1+        (T.Pitch n2 _ o2) = p2+        p1' = T.pitch_to_pc p1+        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 }          _ -> Interval ty qu c (o2 - o1 + o_a) --- | Apply 'invert_ordering' to 'interval_direction' of 'Interval'.+-- | Apply 'T.ord_invert' to 'interval_direction' of 'Interval'. -- -- > invert_interval (Interval Third Major LT 1) == Interval Third Major GT 1 invert_interval :: Interval -> Interval-invert_interval (Interval t qu d o) =-    let d' = invert_ordering d-    in Interval t qu d' o+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@@ -177,7 +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)@@ -185,9 +160,9 @@ -- | Transpose a 'Pitch' by an 'Interval'. -- -- > transpose (Interval Third Diminished LT 0) (Pitch C Sharp 4) == Pitch E Flat 4-pitch_transpose :: Interval -> Pitch -> Pitch+pitch_transpose :: Interval -> T.Pitch -> T.Pitch pitch_transpose i ip =-    let (Pitch p_n p_a p_o) = ip+    let (T.Pitch p_n p_a p_o) = ip         (Interval i_t i_q i_d i_o) = i         i_d' = if i_d == GT                then -1@@ -199,10 +174,10 @@              else if p_n' < p_n && i_d == LT                   then 1                   else 0-        ip' = Pitch p_n' p_a (p_o + i_o + oa)+        ip' = T.Pitch p_n' p_a (p_o + i_o + oa)         st = if i_d == GT-             then (pitch_to_pc ip - pitch_to_pc ip') `mod` 12-             else (pitch_to_pc ip' - pitch_to_pc ip) `mod` 12+             then (T.pitch_to_pc ip - T.pitch_to_pc ip') `mod` 12+             else (T.pitch_to_pc ip' - T.pitch_to_pc ip) `mod` 12         ty = if i_d == GT              then interval_ty p_n' p_n              else interval_ty p_n p_n'@@ -210,14 +185,14 @@              in fromMaybe err (interval_q ty (fromIntegral st))         qd = quality_difference qu i_q * i_d'         p_a' = toEnum (fromEnum p_a + (qd * 2))-    in ip' { alteration = p_a' }+    in ip' {T.alteration = p_a'}  -- | Make leftwards (perfect fourth) and and rightwards (perfect -- fifth) circles from 'Pitch'. -- -- > let c = circle_of_fifths (Pitch F Sharp 4) -- > in map pitch_to_pc (snd c) == [6,1,8,3,10,5,12,7,2,9,4,11]-circle_of_fifths :: Pitch -> ([Pitch], [Pitch])+circle_of_fifths :: T.Pitch -> ([T.Pitch], [T.Pitch]) circle_of_fifths x =     let p4 = Interval Fourth Perfect LT 0         p5 = Interval Fifth Perfect LT 0@@ -228,7 +203,7 @@ -- displacement. -- -- > mapMaybe parse_interval_type (map show [1 .. 15])-parse_interval_type :: String -> Maybe (Interval_T,Octave)+parse_interval_type :: String -> Maybe (Interval_Type,T.Octave) parse_interval_type n =     case reads n of       [(n',[])] -> if n' == 0@@ -240,7 +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)@@ -249,11 +224,11 @@ -- 'parse_interval_type'. -- -- > map interval_type_degree [(Third,0),(Second,1),(Unison,2)] == [3,9,15]-interval_type_degree :: (Interval_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.@@ -282,6 +257,10 @@          '+':q:n -> f q n          q:n -> f q n          _ -> Nothing++-- | 'error' variant.+parse_interval_err :: String -> Interval+parse_interval_err = fromMaybe (error "parse_interval") . parse_interval  -- | Pretty printer for intervals, inverse of 'parse_interval'. interval_pp :: Interval -> String
Music/Theory/Interval/Barlow_1987.hs view
@@ -4,12 +4,12 @@ module Music.Theory.Interval.Barlow_1987 where  import Data.List {- base -}-import Data.Maybe {- base -}-import Data.Numbers.Primes {- primes -} import Data.Ratio {- base -} import Text.Printf {- base -} -import Music.Theory.Tuning+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. --@@ -20,157 +20,93 @@         square n = n * n     in 2 * (square (p' - 1) / p') --- | Generate list of factors of /n/ from /x/.------ > factor primes 315 == [3,3,5,7]-factor :: Integral a => [a] -> a -> [a]-factor x n =-    case x of-      [] -> undefined-      i:x' -> 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'.------ > prime_factors 315 == [3,3,5,7]-prime_factors :: Integral a => a -> [a]-prime_factors = factor 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' '.' 'prime_factors'.------ > prime_factors_m 315 == [(3,2),(5,1),(7,1)]-prime_factors_m :: Integral a => a -> [(a,a)]-prime_factors_m = multiplicities . prime_factors---- | 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 :: 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 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 :: Integral t => 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+-- > length (table_2 0.04) == 66 table_2 :: Double -> [Table_2_Row] 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) = (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
@@ -1,33 +1,203 @@ -- | Common music keys. module Music.Theory.Key where +import Control.Monad {- base -}+import Data.Char {- base -} import Data.List {- base -}+import Data.Maybe {- base -} -import Music.Theory.Pitch-import Music.Theory.Pitch.Name-import Music.Theory.Pitch.Note-import Music.Theory.Interval+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.Pitch.Note as T+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) --- | A common music notation key is a 'Note_T', 'Alteration_T',--- 'Mode_T' triple.-type Key = (Note_T,Alteration_T,Mode_T)+-- | 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 -> String+mode_identifier_pp = map toLower . mode_pp++-- | There are two modes, given one return the other.+mode_parallel :: Mode -> Mode+mode_parallel m = if m == Minor_Mode then Major_Mode else Minor_Mode++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', 'Alteration', 'Mode' triple.+type Key = (T.Note,T.Alteration,Mode)++-- | 'Mode' of 'Key'.+key_mode :: Key -> Mode+key_mode (_,_,m) = m++-- | Enumeration of 42 CMN keys.+--+-- > length key_sequence_42 == 7 * 3 * 2+key_sequence_42 :: [Key]+key_sequence_42 =+    let a_seq = [T.Flat,T.Natural,T.Sharp]+        m_seq = [Major_Mode,Minor_Mode]+    in [(n,a,m) | n <- T.note_seq,a <- a_seq,m <- m_seq]++-- | Subset of 'key_sequence' not including very eccentric keys (where+-- there are more than 7 alterations).+--+-- > length key_sequence_30 == 30+key_sequence_30 :: [Key]+key_sequence_30 = filter (maybe False ((< 8) . abs) . key_fifths) key_sequence_42++-- | Parallel key, ie. 'mode_parallel' of 'Key'.+key_parallel :: Key -> Key+key_parallel (n,a,m) = (n,a,mode_parallel m)++-- | Transposition of 'Key'.+key_transpose :: Key -> Int -> Key+key_transpose (n,a,m) x =+    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.+--+-- > let k = [(T.C,T.Natural,Major_Mode),(T.E,T.Natural,Minor_Mode)]+-- > in map (key_lc_uc_pp . key_relative) k == ["a♮","G♮"]+key_relative :: Key -> Key+key_relative k =+    case key_mode k of+      Major_Mode -> key_parallel (key_transpose k 9)+      Minor_Mode -> key_parallel (key_transpose k 3)++-- | Mediant minor of major key.+--+-- > key_mediant (T.C,T.Natural,Major_Mode) == Just (T.E,T.Natural,Minor_Mode)+key_mediant :: Key -> Maybe Key+key_mediant k =+    case key_mode k of+      Major_Mode -> Just (key_parallel (key_transpose k 4))+      _ -> Nothing++-- > fmap key_pc_set (key_lc_uc_parse "E")+key_pc_set :: Integral i => Key -> [i]+key_pc_set (n,a,md) =+    let pc0 = T.note_to_pc n + T.alteration_to_diff_err a+    in sort (map ((`mod` 12) . (+ pc0)) (mode_pc_seq md))++-- | Pretty-printer where 'Minor_Mode' is written in lower case (lc) and+-- alteration symbol is shown using indicated function.+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+    in c' : a_pp a++-- | 'key_lc_pp' with unicode (uc) alteration.+--+-- > map key_lc_uc_pp [(C,Sharp,Minor_Mode),(E,Flat,Major_Mode)] == ["c♯","E♭"]+key_lc_uc_pp :: Key -> String+key_lc_uc_pp = key_lc_pp (return . T.alteration_symbol)++-- | 'key_lc_pp' with ISO alteration.+key_lc_iso_pp :: Key -> String+key_lc_iso_pp = key_lc_pp T.alteration_iso++-- | 'key_lc_pp' with tonh alteration.+--+-- > map key_lc_tonh_pp [(T.C,T.Sharp,Minor_Mode),(T.E,T.Flat,Major_Mode)]+key_lc_tonh_pp :: Key -> String+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) -> [Char]+key_identifier_pp (n,a,m) = map toLower (intercalate "_" [show n,show a,mode_pp m])++-- > import Data.Maybe+-- > mapMaybe note_char_to_key "CdEfGaB"+note_char_to_key :: Char -> Maybe Key+note_char_to_key c =+    let m = if isUpper c then Major_Mode else Minor_Mode+    in fmap (\n -> (n,T.Natural,m)) (T.parse_note_t True c)++-- | Parse 'Key' from /lc-uc/ string.+--+-- > let k = mapMaybe key_lc_uc_parse ["c","E","f♯","ab","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] -> with_a n =<< T.symbol_to_alteration_unicode_plus_iso a+         _ -> Nothing+ -- | Distance along circle of fifths path of indicated 'Key'.  A -- positive number indicates the number of sharps, a negative number -- the number of flats. ----- > key_fifths (A,Natural,Minor_Mode) == 0--- > key_fifths (A,Natural,Major_Mode) == 3--- > key_fifths (C,Natural,Minor_Mode) == -3-key_fifths :: Key -> Int+-- > key_fifths (T.A,T.Natural,Minor_Mode) == Just 0+-- > key_fifths (T.A,T.Natural,Major_Mode) == Just 3+-- > key_fifths (T.C,T.Natural,Minor_Mode) == Just (-3)+-- > key_fifths (T.B,T.Sharp,Minor_Mode) == Just 9+-- > key_fifths (T.E,T.Sharp,Major_Mode) == Just 11+-- > key_fifths (T.B,T.Sharp,Major_Mode) == Nothing+--+-- > zip (map key_lc_iso_pp key_sequence_42) (map key_fifths key_sequence_42)+key_fifths :: Key -> Maybe Int key_fifths (n,a,m) =-    let cf x = let (p,q) = circle_of_fifths x in p ++ q-        eq (Pitch n' a' _) = n == n' && a == a'-        (Just ix) = case m of-                      Major_Mode -> findIndex eq (cf c4)-                      Minor_Mode -> findIndex eq (cf a4)-    in if ix < 13 then negate ix else ix - 12+    let cf x = let (p,q) = T.circle_of_fifths x in p ++ q+        eq (T.Pitch n' a' _) = n == n' && a == a'+        ix = case m of+               Major_Mode -> findIndex eq (cf T.c4)+               Minor_Mode -> findIndex eq (cf T.a4)+    in fmap (\i -> if i < 13 then negate i else i - 12) ix++-- | Table mapping 'Key' to 'key_fifths' value.+key_fifths_tbl :: [(Key,Int)]+key_fifths_tbl =+    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'.+--+-- > let a = [0,1,-1,2,-2,3,-3,4,-4,5,-5]+-- > 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 -> 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)++-- | Given sorted pitch-class set, find simplest implied key in given mode.+--+-- > 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 -> [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 -> [i] -> Maybe Int+implied_fifths md = key_fifths <=< implied_key md++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 -> [i] -> Int+implied_fifths_err md = fromMaybe (error "implied_fifths") . key_fifths . implied_key_err md
− Music/Theory/List.hs 
@@ -1,456 +0,0 @@--- | List functions.-module Music.Theory.List where--import Data.Function {- base -}-import Data.List {- base -}-import qualified Data.List.Ordered as O {- data-ordlist -}-import Data.List.Split {- split -}-import Data.Maybe {- base -}---- | 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]---- | 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---- | 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]---- | 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)]--- > 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 :: [b] -> [b] -> [b]-interleave p q =-    let u (i,j) = [i,j]-    in concatMap u (zip p q)---- | 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)---- | Count occurences of elements in list.------ > histogram "hohoh" == [('h',3),('o',2)]-histogram :: (Ord a,Integral i) => [a] -> [(a,i)]-histogram x =-    let g = group (sort x)-        n = map genericLength g-    in zip (map head g) n---- | 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 . chunksOf n---- * Association lists---- | Given accesors for /key/ and /value/ collate input.------ > let r = [('A',"a"),('B',"bd"),('C',"ce"),('D',"f")]--- > in collate_on fst snd (zip "ABCBCD" "abcdef")-collate_on :: (Eq k,Ord k) => (a -> k) -> (a -> v) -> [a] -> [(k,[v])]-collate_on f g =-    let h l = case l of-                [] -> error "collate_on"-                l0:_ -> (f l0,map g l)-    in map h . groupBy ((==) `on` f) . sortBy (compare `on` f)---- | 'collate_on' of 'fst' and 'snd'.------ > collate (zip [1,2,1] "abc") == [(1,"ac"),(2,"b")]-collate :: Ord a => [(a,b)] -> [(a,[b])]-collate = collate_on fst snd---- | 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'"---- | Integrate, 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 l = if null l then [] else zipWith (-) (tail l) l---- | 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"---- | 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' :: Bool -> (t -> s -> Ordering) -> [(t,t)] -> s -> Maybe (t,t)-find_bounds' scl f l x =-    let g (p,q) = f p x /= GT && f q x == GT-        h (p,q) = f p x /= GT && f q x /= LT-        h' = if scl then h else g-    in case l of-         [] -> Nothing-         [e] -> if h' e then Just e else Nothing-         e:l' -> if g e then Just e else find_bounds' scl f l' x---- | 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 f (adj2 1 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---- | 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 a last element tuple.------ > separate_last [1..5] == ([1..4],5)-separate_last :: [a] -> ([a],a)-separate_last x =-    let e:x' = reverse x-    in (reverse x',e)---- | 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---- | '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---- | '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 = groupBy ((==) `on` isJust)---- | Predicate to determine if all elements of the list are '=='.-all_eq :: Eq n => [n] -> Bool-all_eq = (== 1) . length . nub---- | 'groupBy' of 'sortBy'.------ > 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 = groupBy ((==) `on` f) . sortBy (compare `on` 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---- | Invert 'Ordering'.-ordering_invert :: Ordering -> Ordering-ordering_invert o =-    case o of-      LT -> GT-      EQ -> EQ-      GT -> LT---- | 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 . sortBy (compare `on` 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))---- | 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---- | '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---- * 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)
+ 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/Math.hs 
@@ -1,98 +0,0 @@--- | Math functions.-module Music.Theory.Math where--import Data.Maybe {- base -}-import Data.Ratio {- base -}-import Numeric {- base -}---- | Real (alias for 'Double').-type R = Double---- | <http://reference.wolfram.com/mathematica/ref/FractionalPart.html>-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---- | <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 - fromInteger (floor 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 :: Integral t => 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---- | 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 ""---- | 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
+ 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 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 
@@ -1,80 +0,0 @@--- | Extensions to "Data.Maybe".-module Music.Theory.Maybe where---- import Data.Maybe {- base -}---- | 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,Show 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]-reverse_primes :: (Integral n,Show n) => n -> [n]-reverse_primes n = reverse (genericTake n primes)+-- > length (reverse_primes 14) == 14+reverse_primes :: Integral n => n -> [n]+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 :: (Fractional a,Enum a,Fractional n) => Interval a n -> [a] -> [a] -> n+-- > 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) @@ -149,9 +143,9 @@  -- | 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 :: (Fractional a,Enum a) => Psi a -> Delta n a  -> ([a] -> a) -> [n] -> [n] -> a+-- > 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         l' = fromIntegral l - 1@@ -162,23 +156,23 @@  -- > 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,Enum n,Fractional n) => [a] -> [a] -> n-olm_no_delta = olm (abs_dif dif_r) (abs_ix_dif dif_r) (const 1)+olm_no_delta :: (Real a,Real n,Fractional n) => [a] -> [a] -> n+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 :: (Enum a,Floating a) => [a] -> [a] -> a-olm_no_delta_squared = olm (sqrt_abs_dif (-)) (sqr_abs_ix_dif (-)) (const 1)+olm_no_delta_squared :: Floating a => [a] -> [a] -> a+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)  -- > olm_no_delta_second_order [0,2,4,1,0] [2,3,0,4,1] == 1.0-olm_no_delta_second_order :: (Real a,Enum a,Fractional a) => [a] -> [a] -> a+olm_no_delta_second_order :: (Real a,Fractional a) => [a] -> [a] -> a olm_no_delta_second_order = second_order olm_no_delta  -- p.301 erroneously gives this as sum (map sqrt [2,0,1]) / 3 -- > olm_no_delta_squared_second_order [0,2,4,1,0] [2,3,0,4,1] == sum (map sqrt [4,0,3]) / 3-olm_no_delta_squared_second_order :: (Enum a,Floating a) => [a] -> [a] -> a+olm_no_delta_squared_second_order :: Floating a => [a] -> [a] -> a olm_no_delta_squared_second_order = second_order olm_no_delta_squared  -- | Second order binomial coefficient, p.307@@ -187,19 +181,19 @@ 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. -- -- > ord_hist [LT,GT,GT] == (1,0,2) ord_hist :: Integral t => [Ordering] -> (t,t,t) ord_hist x =-    let h = L.histogram x+    let h = L.generic_histogram x         f n = fromMaybe 0 (lookup n h)     in (f LT,f EQ,f GT) @@ -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 --@@ -256,30 +250,27 @@     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, Num a) => Interval a n -> [a] -> [a] -> (n, n, [n])+ocm_zcm :: Fractional n => Interval a n -> [a] -> [a] -> (n, n, [n]) ocm_zcm f p q =     let p' = concat (C.half_matrix_f f p)         q' = concat (C.half_matrix_f f q)@@ -291,18 +282,18 @@  -- | 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 :: (Fractional a,Enum a,Fractional n) => Interval a n -> [a] -> [a] -> n+-- > 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     in z / c  -- | 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 :: (Ord a,Fractional a,Enum a,Ord n,Fractional n) => Interval a n -> [a] -> [a] -> n+-- > 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     in z / (c * maximum m)
+ Music/Theory/Parse.hs view
@@ -0,0 +1,27 @@+-- | Parsing utilities+module Music.Theory.Parse where++import Data.Maybe {- base -}++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++-- | Boolean 'P' for given 'Char'.+is_char :: Char -> P Bool+is_char = fmap isJust . P.optionMaybe . P.char++-- | 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 
@@ -1,158 +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 :: (Eq a) => 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 :: (Eq a) => [[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))--}
Music/Theory/Permutations/List.hs view
@@ -1,20 +1,46 @@ -- | List permutation functions. module Music.Theory.Permutations.List where -import qualified Math.Combinatorics.Multiset as C-import qualified Music.Theory.Permutations as P+import Data.List {- base -} +import qualified Math.Combinatorics.Multiset as C {- multiset-comb -}++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 :: (Eq a) => [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++-- | Calculate number of permutations of a multiset.+--+-- > 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 = P.factorial (length x)+        d = product $ map P.factorial $ occ x+    in n `div` d
Music/Theory/Permutations/Morris_1984.hs view
@@ -5,32 +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. --@@ -39,55 +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 --- | Parse abbreviated 'Hold' notation, characters are hexedecimal.+numeric_spelling_tbl :: [(Char,Int)]+numeric_spelling_tbl = zip "1234567890ETABCDFGHJKL" [1 .. 22]++-- | Parse abbreviated 'Hold' notation, characters are NOT hexadecimal. ----- > to_abbrev "38A" == [3,8,10]-to_abbrev :: String -> [Int]-to_abbrev = map digitToInt+-- > 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 =@@ -99,6 +117,14 @@                             else Left n : rec (m + 1) l'     in rec 1 +-- | Given two sequences, derive the one-indexed "hold" list.+--+-- > derive_holds ("12345","13254") == [1]+derive_holds :: (Eq a,Enum n,Num n) => ([a],[a]) -> [n]+derive_holds (p,q) =+    let f n (i,j) = if i == j then Just n else Nothing+    in catMaybes (zipWith f [1..] (zip p q))+ -- | Two-tuple to two element list. pair_to_list :: (t,t) -> [t] pair_to_list (p,q) = [p,q]@@ -113,21 +139,21 @@ -- | 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)  -- | Apply abbreviated 'Hold' notation, given cardinality. -- -- > swap_abbrev 8 [3,8] [2,1,4,3,6,5,8,7] == [1,2,4,6,3,8,5,7]-swap_abbrev :: Eq a => Int -> [Int] -> [a] -> [a]+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'.-apply_change :: Eq a => Int -> Change -> [a] -> [a]+apply_change :: Int -> Change -> [a] -> [a] apply_change k p l =     case p of       Swap_All -> swap_all l@@ -139,8 +165,8 @@ -- > 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 :: Eq a => Method -> [a] -> ([a],[[a]])+-- > apply_method cambridgeshire_slow_course_doubles [1..5] == r+apply_method :: Method -> [a] -> ([a],[[a]]) apply_method m l =     let k = length l         f z e = (apply_change k e z,z)@@ -160,57 +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 --- | Cambridgeshire Slow Course Doubles.------ <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 --- | Cambridge Surprise Major.------ <https://rsw.me.uk/blueline/methods/view/Cambridge_Surprise_Major>+-- | <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 --- | Smithsonian Surprise Royal.------ <https://rsw.me.uk/blueline/methods/view/Smithsonian_Surprise_Royal>+-- | <https://rsw.me.uk/blueline/methods/view/Smithsonian_Surprise_Royal> ----- > length (closed_method smithsonian_surprise_royal [1..10]) == 9+-- > 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 = ("-3A-14-5A-16-347A-18-1456-5A-16-7A",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>+--+-- > 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 ecumenical_surprise_maximus_pl
Music/Theory/Pitch.hs view
@@ -4,69 +4,227 @@ import Data.Char {- base -} import Data.Function {- base -} import Data.List {- base -}+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 Music.Theory.Pitch.Note {- hmt -}-import Music.Theory.Pitch.Spelling {- 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 -} --- | Pitch classes are modulo twelve integers.+-- * 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 :: (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)+    else if pc < 0+         then octave_pitchclass_nrm (o-1,pc+12)+         else (o,pc)++-- | Transpose 'Octave_PitchClass' value.+octave_pitchclass_trs :: Integral i => i -> Octave_PitchClass i -> Octave_PitchClass i+octave_pitchclass_trs n (o,pc) =+    let k = pc + n+        (i,j) = k `divMod` 12+    in (o + i,j)++-- | 'Octave_PitchClass' value to integral /midi/ note number.+--+-- > 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'.+--+-- > 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 (0-11) type PitchClass = Int  -- | Octaves are integers, the octave of middle C is @4@. type Octave = Int  -- | 'Octave' and 'PitchClass' duple.-type Octave_PitchClass i = (i,i)-type OctPC = (Octave,PitchClass)+type OctPc = (Octave,PitchClass) +-- | Translate from generic octave & pitch-class duple.+octave_pitchclass_to_octpc :: (Integral pc, Integral oct) => (oct,pc) -> OctPc+octave_pitchclass_to_octpc (oct,pc) = (fromIntegral oct,fromIntegral pc)++-- | Normalise 'OctPc'.+--+-- > octpc_nrm (4,16) == (5,4)+octpc_nrm :: OctPc -> OctPc+octpc_nrm = octave_pitchclass_nrm++-- | Transpose 'OctPc'.+--+-- > octpc_trs 7 (4,9) == (5,4)+-- > octpc_trs (-11) (4,9) == (3,10)+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 (l,r) =+    let (l',r') = (octpc_to_midi l,octpc_to_midi r)+    in map midi_to_octpc [l' .. r']++-- * Midi note number (0 - 127)++{- | 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++-- | 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),(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 = 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_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)++-- | 'fromIntegral' of 'octpc_to_midi'.+octpc_to_fmidi :: (Integral i,Num n) => Octave_PitchClass i -> n+octpc_to_fmidi = fromIntegral . octave_pitchclass_to_midi++-- | Fractional midi to fractional octave pitch-class.+--+-- > fmidi_to_foctpc 69.5 == (4,9.5)+fmidi_to_foctpc :: RealFrac f => f -> (Octave,f)+fmidi_to_foctpc n = let o = (floor n - 12) `div` 12 in (o,n - (fromIntegral (o + 1) * 12))++-- | Octave of fractional midi note number.+fmidi_octave :: RealFrac f => f -> Octave+fmidi_octave = fst . fmidi_to_foctpc++foctpc_to_fmidi :: RealFrac f => (Octave,f) -> f+foctpc_to_fmidi (o,pc) = (fromIntegral (o + 1) * 12) + pc++-- | Move fractional midi note number to indicated octave.+--+-- > map (fmidi_in_octave 1) [59.5,60.5] == [35.5,24.5]+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 :: Note_T-                   ,alteration :: Alteration_T+data Pitch = Pitch {note :: T.Note+                   ,alteration :: T.Alteration                    ,octave :: Octave}            deriving (Eq,Show)  instance Ord Pitch where     compare = pitch_compare --- | Generalised pitch, given by a generalised alteration.-data Pitch' = Pitch' Note_T Alteration_T' Octave-            deriving (Eq,Show)---- | Pretty printer for 'Pitch''.-pitch'_pp :: Pitch' -> String-pitch'_pp (Pitch' n (_,a) o) = show n ++ a ++ show o---- | 'Pitch'' printed without octave.-pitch'_class_pp :: Pitch' -> String-pitch'_class_pp = T.dropWhileRight isDigit . pitch'_pp- -- | 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-    in Pitch n (alteration_clear_quarter_tone a) o+    in Pitch n (T.alteration_clear_quarter_tone a) o  -- | 'Pitch' to 'Octave' and 'PitchClass' notation. -- -- > pitch_to_octpc (Pitch F Sharp 4) == (4,6) pitch_to_octpc :: Integral i => Pitch -> Octave_PitchClass i-pitch_to_octpc = midi_to_octpc . 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-pitch_is_12et = alteration_is_12et . alteration+pitch_is_12et = T.alteration_is_12et . alteration  -- | 'Pitch' to midi note number notation. -- -- > pitch_to_midi (Pitch A Natural 4) == 69 pitch_to_midi :: Integral i => Pitch -> i pitch_to_midi (Pitch n a o) =-    let a' = alteration_to_diff_err a-        n' = note_to_pc n+    let a' = T.alteration_to_diff_err a+        n' = T.note_to_pc n         o' = fromIntegral o     in 12 + o' * 12 + n' + a' @@ -75,17 +233,17 @@ -- > pitch_to_fmidi (Pitch A QuarterToneSharp 4) == 69.5 pitch_to_fmidi :: Fractional n => Pitch -> n pitch_to_fmidi (Pitch n a o) =-    let a' = alteration_to_fdiff a+    let a' = T.alteration_to_fdiff a         o' = fromIntegral o-        n' = fromInteger (note_to_pc n)+        n' = fromInteger (T.note_to_pc n)     in 12 + o' * 12 + n' + a'  -- | Extract 'PitchClass' of 'Pitch' ----- > pitch_to_pc (Pitch A Natural 4) == 9--- > pitch_to_pc (Pitch F Sharp 4) == 6+-- > map pitch_to_pc [Pitch A Natural 4,Pitch F Sharp 4] == [9,6]+-- > map pitch_to_pc [Pitch C Flat 4,Pitch B Sharp 5] == [11,0] pitch_to_pc :: Pitch -> PitchClass-pitch_to_pc (Pitch n a _) = note_to_pc n + alteration_to_diff_err a+pitch_to_pc (Pitch n a _) = (T.note_to_pc n + T.alteration_to_diff_err a) `mod` 12  -- | 'Pitch' comparison, implemented via 'pitch_to_fmidi'. --@@ -95,110 +253,142 @@     let f = pitch_to_fmidi :: Pitch -> Double     in compare `on` f --- | Given 'Spelling' function translate from 'OctPC' notation to--- 'Pitch'.+-- * Spelling++-- | Function to spell a 'PitchClass'.+type Spelling n = n -> (T.Note,T.Alteration)++-- | Variant of 'Spelling' for incomplete functions.+type Spelling_M i = i -> Maybe (T.Note,T.Alteration)++-- | 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 octpc_to_pitch sp (o,pc) =     let (n,a) = sp pc     in Pitch n a (fromIntegral o) --- | Normalise 'OctPC' value, ie. ensure 'PitchClass' is in (0,11).+-- | Midi note number to 'Pitch'. ----- > octpc_nrm (4,16) == (5,4)-octpc_nrm :: Integral i => Octave_PitchClass i -> Octave_PitchClass i-octpc_nrm (o,pc) =-    if pc > 11-    then octpc_nrm (o+1,pc-12)-    else if pc < 0-         then octpc_nrm (o-1,pc+12)-         else (o,pc)+-- > import Music.Theory.Pitch.Spelling.Table as T+-- > let r = ["C4","E♭4","F♯4"]+-- > 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 --- | Transpose 'OctPC' value.+{- | Fractional midi note number to 'Pitch'.++> 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' = 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+         Nothing -> Nothing+         Just a' -> Just (Pitch n a' o)++-- | Erroring variant. ----- > octpc_trs 7 (4,9) == (5,4)--- > octpc_trs (-11) (4,9) == (3,10)-octpc_trs :: Integral i => i -> Octave_PitchClass i -> Octave_PitchClass i-octpc_trs n (o,pc) =-    let pc' = fromIntegral pc-        k = pc' + n-        (i,j) = k `divMod` 12-    in (fromIntegral o + fromIntegral i,fromIntegral j)+-- > 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) --- | 'OctPC' value to integral /midi/ note number.+-- | Composition of 'pitch_to_fmidi' and then 'fmidi_to_pitch'. ----- > octpc_to_midi (4,9) == 69-octpc_to_midi :: Integral i => Octave_PitchClass i -> i-octpc_to_midi (o,pc) = 60 + ((fromIntegral o - 4) * 12) + pc+-- > import Music.Theory.Pitch.Name as T+-- > import Music.Theory.Pitch.Spelling as T+-- > 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) --- | 'fromIntegral' of 'octpc_to_midi'.-octpc_to_fmidi :: (Integral i,Num n) => Octave_PitchClass i -> n-octpc_to_fmidi = fromIntegral . octpc_to_midi+-- | Displacement of /q/ into octave of /p/.+fmidi_in_octave_of :: RealFrac f => f -> f -> f+fmidi_in_octave_of p = fmidi_in_octave (fmidi_octave p) --- | Inverse of 'octpc_to_midi'.+-- | Octave displacement of /m2/ that is nearest /m1/. ----- > midi_to_octpc 69 == (4,9)-midi_to_octpc :: Integral i => i -> Octave_PitchClass i-midi_to_octpc n = (n - 12) `divMod` 12+-- > 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+        m2'' = [m2' - 12,m2',m2' + 12]+        d = map (abs . (m1 -)) m2''+        z = sortOn snd (zip m2'' d)+    in fst (head z) --- | Enumerate range, inclusive.+-- | Displacement of /q/ into octave above /p/. ----- > 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 (l,r) =-    let (l',r') = (octpc_to_midi l,octpc_to_midi r)-    in map midi_to_octpc [l' .. r']+-- > fmidi_in_octave_of 69 51 == 63+-- > fmidi_in_octave_nearest 69 51 == 63+-- > fmidi_in_octave_above 69 51 == 75+fmidi_in_octave_above :: RealFrac a => a -> a -> a+fmidi_in_octave_above p q = let r = fmidi_in_octave_nearest p q in if r < p then r + 12 else r --- | Midi note number to 'Pitch'.+-- | Displacement of /q/ into octave below /p/. ----- > 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-midi_to_pitch sp = octpc_to_pitch sp . midi_to_octpc+-- > fmidi_in_octave_of 69 85 == 61+-- > fmidi_in_octave_nearest 69 85 == 73+-- > fmidi_in_octave_below 69 85 == 61+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 --- | Fractional midi note number to 'Pitch'.+-- | 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'. ----- > import Music.Theory.Pitch.Spelling--- > pitch_pp (fmidi_to_pitch pc_spell_ks 65.5) == "F𝄲4"--- > pitch_pp (fmidi_to_pitch pc_spell_ks 66.5) == "F𝄰4"--- > pitch_pp (fmidi_to_pitch pc_spell_ks 67.5) == "A𝄭4"--- > pitch_pp (fmidi_to_pitch pc_spell_ks 69.5) == "B𝄭4"-fmidi_to_pitch :: RealFrac n => Spelling Int -> n -> Pitch-fmidi_to_pitch sp m =-    let m' = round m-        (Pitch n a o) = midi_to_pitch sp m'-        q = m - fromIntegral m'-    in case alteration_edit_quarter_tone q a of-         Nothing -> error "fmidi_to_pitch"-         Just a' -> Pitch n a' o+-- > 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 = lift_fmidi_binop_to_cps fmidi_in_octave_nearest --- | Composition of 'pitch_to_fmidi' and then 'fmidi_to_pitch'.+-- | CPS form of 'fmidi_in_octave_above'. ----- > import Music.Theory.Pitch.Name as T--- > import Music.Theory.Pitch.Spelling as T+-- > 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 = 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/. ----- > pitch_tranpose T.pc_spell_ks 2 T.ees5 == T.f5-pitch_tranpose :: RealFrac n => Spelling Int -> n -> Pitch -> Pitch-pitch_tranpose sp n p =-    let m = pitch_to_fmidi p-    in fmidi_to_pitch sp (m + n)+-- > 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 o1 = octave p1-        p2' = map (\n -> p2 {octave = n}) [o1 - 1,o1,o1 + 1]-        m1 = pitch_to_fmidi p1 :: Double-        m2 = map (pitch_to_fmidi) p2'-        d = map (abs . (m1 -)) m2-        z = sortBy (compare `on` snd) (zip p2' d)-    in fst (head z)+    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@@ -207,7 +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@@ -219,145 +409,327 @@ -- | 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-      ThreeQuarterToneFlat -> pitch_note_lower (Pitch n QuarterToneSharp o)-      ThreeQuarterToneSharp -> pitch_note_raise (Pitch n QuarterToneFlat o)+      T.ThreeQuarterToneFlat -> pitch_note_lower (Pitch n T.QuarterToneSharp o)+      T.ThreeQuarterToneSharp -> pitch_note_raise (Pitch n T.QuarterToneFlat o)       _ -> Pitch n a o  -- | 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.------ > map midi_to_cps [60,69] == [261.6255653005986,440.0]-midi_to_cps :: (Integral i,Floating f) => i -> f-midi_to_cps = fmidi_to_cps . fromIntegral+-- | '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 --- | Fractional /midi/ note number to cycles per second.------ > map fmidi_to_cps [69,69.1] == [440.0,442.5488940698553]-fmidi_to_cps :: Floating a => a -> a-fmidi_to_cps i = 440 * (2 ** ((i - 69) * (1 / 12)))+-- | '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 = pitch_to_cps_k0 (69,f0) --- | 'fmidi_to_cps' of 'pitch_to_fmidi'.+-- | 'pitch_to_cps_k0' (60,440). pitch_to_cps :: Floating n => Pitch -> n-pitch_to_cps = fmidi_to_cps . pitch_to_fmidi+pitch_to_cps = pitch_to_cps_k0 (69,440) --- | Frequency (cycles per second) to /midi/ note number, ie. 'round'--- of 'cps_to_fmidi'.+-- | Frequency (cps = cycles per second) to fractional /midi/ note+-- number, given frequency of ISO A4 (mnn = 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_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_k0 (69,440)++-- | 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 --- | Frequency (cycles per second) to fractional /midi/ note number.+-- | '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_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_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 . T.real_round_int . cps_to_fmidi++cps_octave :: (Floating f,RealFrac f) => f -> Octave+cps_octave = fst . cps_to_octpc++-- * MIDI detune (cents)++-- | Is cents in (-50,+50]. ----- > 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 a = (logBase 2 (a * (1 / 440)) * 12) + 69+-- > map cents_is_normal [-250,-75,75,250] == replicate 4 False+cents_is_normal :: (Num c, Ord c) => c -> Bool+cents_is_normal c = c > (-50) && c <= 50 --- | Midi note number with cents detune.-type Midi_Detune = (Int,Double)+-- | 'cents_is_normal' of 'snd'.+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 :: (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 :: (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 :: (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 :: (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 = 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,Double)++-- | Fractional midi note number to 'Midi_Detune'.+--+-- > fmidi_to_midi_detune 60.50 == (60,50.0)+fmidi_to_midi_detune :: Double -> Midi_Detune+fmidi_to_midi_detune mnn =+    let (n,c) = T.integral_and_fractional_parts mnn+    in (n,c * 100)+ -- | Frequency (in hertz) to 'Midi_Detune'. -- -- > map (fmap round . cps_to_midi_detune) [440.00,508.35] == [(69,0),(71,50)] cps_to_midi_detune :: Double -> Midi_Detune-cps_to_midi_detune f =-    let (n,c) = T.integral_and_fractional_parts (cps_to_fmidi f)-    in (n,c * 100)+cps_to_midi_detune = fmidi_to_midi_detune . cps_to_fmidi --- | Inverse of 'cps_to_midi_detune'.-midi_detune_to_cps :: Midi_Detune -> Double-midi_detune_to_cps (m,c) = fmidi_to_cps (fromIntegral m + (c / 100))+-- | Round /detune/ value to nearest multiple of @50@, normalised.+--+-- > map midi_detune_nearest_24et [(59,70),(59,80)] == [(59,50),(60,00)]+midi_detune_nearest_24et :: Midi_Detune -> Midi_Detune+midi_detune_nearest_24et (m,dt) = midi_detune_normalise (m,T.round_to 50 dt) --- | 'midi_to_cps' of 'octpc_to_midi'.+-- * MIDI cents++-- | Midi note number with integral cents detune.+type Midi_Cents = (Midi,Int)++midi_detune_to_midi_cents :: Midi_Detune -> Midi_Cents+midi_detune_to_midi_cents (m,c) = (m,round c)++-- | Printed as /fmidi/ value with cents to two places.  Must be normal. ----- > octpc_to_cps (4,9) == 440-octpc_to_cps :: (Integral i,Floating n) => Octave_PitchClass i -> n-octpc_to_cps = midi_to_cps . octpc_to_midi+-- > map midi_cents_pp [(60,0),(60,25)] == ["60.00","60.25"]+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" --- | '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_octpc . cps_to_midi+-- * 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 --- | Slight generalisation of ISO pitch representation.  Allows octave+-- | 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"] == [2,4,2,1]x+parse_octave :: Octave -> String -> Octave+parse_octave def_o = T.run_parser_error (p_octave_iso_opt def_o)++-- | 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 nte n = let tb = zip "cdefgab" [C,D,E,F,G,A,B]-                in lookup (toLower n) tb-        oct o = case o of-                  [] -> Just def_o-                  [n] -> if isDigit n-                         then Just (fromIntegral (digitToInt n))-                         else Nothing-                  _ -> Nothing-        mk n a o = case nte n of-                   Nothing -> Nothing-                   Just n' -> fmap (Pitch n' a) (oct o)-    in case s of-         [] -> Nothing-         n:'b':'b':o -> mk n DoubleFlat o-         n:'#':'#':o -> mk n DoubleSharp o-         n:'x':o -> mk n DoubleSharp o-         n:'b':o -> mk n Flat o-         n:'#':o -> mk n Sharp o-         n:o -> mk n 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 parse_iso_pitch = parse_iso_pitch_oct (error "parse_iso_pitch: no octave") +-- | 'error' variant.+parse_iso_pitch_err :: String -> Pitch+parse_iso_pitch_err = fromMaybe (error "parse_iso_pitch") . parse_iso_pitch+ -- * Pretty printers  -- | Pretty printer for 'Pitch' (unicode, see 'alteration_symbol').+-- Option selects if 'Natural's are printed. ----- > pitch_pp (Pitch E Flat 4) == "E♭4"--- > pitch_pp (Pitch F QuarterToneSharp 3) == "F𝄲3"+-- > pitch_pp_opt (True,True) (Pitch T.E T.Natural 4) == "E♮4"+pitch_pp_opt :: (Bool,Bool) -> Pitch -> String+pitch_pp_opt (show_nat,show_oct) (Pitch n a o) =+    let a' = if a == T.Natural && not show_nat then "" else [T.alteration_symbol a]+        rem_oct_f c = isDigit c || c == '-' -- negative octave values...+        rem_oct = if show_oct then id else T.dropWhileRight rem_oct_f+    in rem_oct (show n ++ a' ++ show o)++-- | 'pitch_pp_opt' with default options, ie. (False,True).+--+-- > pitch_pp (Pitch T.E T.Natural 4) == "E4"+-- > pitch_pp (Pitch T.E T.Flat 4) == "E♭4"+-- > pitch_pp (Pitch T.F T.QuarterToneSharp 3) == "F𝄲3" pitch_pp :: Pitch -> String-pitch_pp (Pitch n a o) =-    let a' = if a == Natural then "" else [alteration_symbol a]-    in show n ++ a' ++ show o+pitch_pp = pitch_pp_opt (False,True) --- | 'Pitch' printed without octave.+-- | 'pitch_pp_opt' with options (False,False).+--+-- > pitch_class_pp (Pitch T.C T.ThreeQuarterToneSharp 0) == "C𝄰" pitch_class_pp :: Pitch -> String-pitch_class_pp = T.dropWhileRight isDigit . pitch_pp+pitch_class_pp = pitch_pp_opt (False,False)  -- | Sequential list of /n/ pitch class names starting from /k/. ----- > pitch_class_names_12et 11 2 == ["B","C"]-pitch_class_names_12et :: Integral n => n -> n -> [String]-pitch_class_names_12et k n =-    let f = pitch_class_pp . midi_to_pitch pc_spell_ks+-- > 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 . T.from_integral_to_int     in map f [60 + k .. 60 + k + n - 1]  -- | Pretty printer for 'Pitch' (ISO, ASCII, see 'alteration_iso'). -- -- > pitch_pp_iso (Pitch E Flat 4) == "Eb4" -- > pitch_pp_iso (Pitch F DoubleSharp 3) == "Fx3"+-- > pitch_pp_iso (Pitch C ThreeQuarterToneSharp 4) -- error pitch_pp_iso :: Pitch -> String-pitch_pp_iso (Pitch n a o) = show n ++ alteration_iso a ++ show o+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"@@ -366,7 +738,7 @@ pitch_pp_hly :: Pitch -> String pitch_pp_hly (Pitch n a o) =     let n' = map toLower (show n)-    in n' ++ alteration_tonh a ++ show o+    in n' ++ T.alteration_tonh a ++ show o  -- | Pretty printer for 'Pitch' (Tonhöhe, see 'alteration_tonh'). --@@ -377,9 +749,41 @@ pitch_pp_tonh (Pitch n a o) =     let o' = show o     in case (n,a) of-         (B,Natural) -> "H" ++ o'-         (B,Flat) -> "B" ++ o'-         (B,DoubleFlat) -> "Heses" ++ o'-         (A,Flat) -> "As" ++ o'-         (E,Flat) -> "Es" ++ o'-         _ -> show n ++ alteration_tonh a ++ o'+         (T.B,T.Natural) -> "H" ++ o'+         (T.B,T.Flat) -> "B" ++ o'+         (T.B,T.DoubleFlat) -> "Heses" ++ o'+         (T.A,T.Flat) -> "As" ++ o'+         (T.E,T.Flat) -> "Es" ++ o'+         _ -> show n ++ T.alteration_tonh a ++ o'++-- * Parsers++p_octave_ly :: T.P Octave+p_octave_ly =+    fmap+    (fromMaybe (error "p_octave_ly") . octave_parse_ly)+    (P.many1 (P.oneOf ",'"))++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))++-- | Run 'p_pitch_ly'.+--+-- > 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++-- | 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
@@ -0,0 +1,148 @@+module Music.Theory.Pitch.Chord where++import Data.List {- base -}+import Data.Maybe {- base -}++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.Alteration)++pc_pp :: Pc -> [Char]+pc_pp (n,a) = T.note_pp n : T.alteration_iso a++-- | D = dominant, M = major+data Extension = D7 | M7 deriving (Eq,Show)++extension_tbl :: Num n => [(Extension, (String,n))]+extension_tbl = [(D7,("7",10)),(M7,("M7",11))]++extension_dat :: Num n => Extension -> (String,n)+extension_dat = flip T.lookup_err extension_tbl++extension_pp :: Extension -> String+extension_pp = fst . (extension_dat :: Extension -> (String,Int))++extension_to_pc :: Num n => Extension -> n+extension_to_pc = snd . extension_dat++data Chord_Type = Major | Minor+                | Augmented | Diminished+                | Diminished_7 | Half_Diminished+                | Suspended_2 | Suspended_4+                  deriving (Eq,Show)++is_suspended :: Chord_Type -> Bool+is_suspended ty = ty `elem` [Suspended_2,Suspended_4]++-- | Names and pc-sets for chord types.+-- The name used here is in the first position, alternates follow.+chord_type_tbl :: Num n => [(Chord_Type,([String],[n]))]+chord_type_tbl =+    [(Major,(["","M","maj"],[0,4,7]))+    ,(Minor,(["m","min"],[0,3,7]))+    ,(Augmented,(["+","aug"],[0,4,8]))+    ,(Diminished,(["o","dim"],[0,3,6]))+    ,(Diminished_7,(["o7","dim7"],[0,3,6,9]))+    ,(Half_Diminished,(["Ø","halfdim","m7(b5)"],[0,3,6,10]))+    ,(Suspended_2,(["sus2"],[0,2,7]))+    ,(Suspended_4,(["sus4"],[0,5,7]))]++chord_type_dat :: Num n => Chord_Type -> ([String],[n])+chord_type_dat = flip T.lookup_err chord_type_tbl++chord_type_pp :: Chord_Type -> String+chord_type_pp = head . fst . (chord_type_dat :: Chord_Type -> ([String],[Int]))++chord_type_pcset :: Num n => Chord_Type -> [n]+chord_type_pcset = snd . chord_type_dat++-- (root,mode,extensions,bass)+data Chord = Chord Pc Chord_Type (Maybe Extension) (Maybe Pc)+             deriving (Show)++chord_pcset :: Chord -> (Maybe Int,[Int])+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 (`delete` ch) bs'+    in (bs',ch')++bass_pp :: Pc -> String+bass_pp = ('/' :) . pc_pp++chord_pp :: Chord -> String+chord_pp (Chord pc ty ex bs) =+    let (pre_ty,post_ty) = if is_suspended ty+                           then (Nothing,Just ty)+                           else (Just ty,Nothing)+    in concat [pc_pp pc+              ,maybe "" chord_type_pp pre_ty+              ,maybe "" extension_pp ex+              ,maybe "" chord_type_pp post_ty+              ,maybe "" bass_pp bs]++m_error :: String -> Maybe a -> a+m_error txt = fromMaybe (error txt)++p_pc :: T.P Pc+p_pc = do+  n <- T.p_note_t+  a <- P.optionMaybe (T.p_alteration_t_iso True)+  return (n,fromMaybe T.Natural a)++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 :: T.P Chord_Type+p_chord_type =+    let m = P.char 'm' >> return Minor+        au = P.char '+' >> return Augmented+        dm = P.char 'o' >> return Diminished+        dm7 = P.try (P.string "o7" >> return Diminished_7)+        hdm = P.char 'Ø' >> return Half_Diminished+        sus2 = P.try (P.string "sus2" >> return Suspended_2)+        sus4 = P.try (P.string "sus4" >> return Suspended_4)+    in P.option Major (P.choice [dm7,dm,hdm,au,sus2,sus4,m])++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 :: T.P (Maybe Pc)+p_bass = P.optionMaybe (P.char '/' >> p_pc)++p_chord :: T.P Chord+p_chord = do+  pc <- p_pc+  ty <- p_chord_type+  ex <- P.optionMaybe p_extension+  b <- p_bass+  ty' <- p_chord_type+  let ty'' = case (ty,ty') of+               (Major,Suspended_2) -> Suspended_2+               (Major,Suspended_4) -> Suspended_4+               (_,Major) -> ty -- ie. nothing+               _ -> error ("trailing type not sus2 or sus4: " ++ show ty')+  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+-- > map chord_pcset c+parse_chord :: String -> Chord+parse_chord =+    either (\e -> error ("parse_chord failed\n" ++ show e)) id .+    P.parse p_chord ""
Music/Theory/Pitch/Note.hs view
@@ -1,49 +1,95 @@ -- | Common music notation note and alteration values. module Music.Theory.Pitch.Note where +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  -- | Enumeration of common music notation note names (@C@ to @B@).-data Note_T = C | D | E | F | G | A | B-              deriving (Eq,Enum,Bounded,Ord,Show)+data Note = C | D | E | F | G | A | B+              deriving (Eq,Enum,Bounded,Ord,Read,Show) --- | Transform 'Note_T' to pitch-class number.+-- | Note sequence as usually understood, ie. 'C' - 'B'.+note_seq :: [Note]+note_seq = [C .. B]++-- | Char variant of 'show'.+note_pp :: Note -> Char+note_pp = head . show++-- | 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' to pitch-class number. -- -- > map note_to_pc [C,E,G] == [0,4,7]-note_to_pc :: Integral i => Note_T -> i-note_to_pc n =-    case n of-      C -> 0-      D -> 2-      E -> 4-      F -> 5-      G -> 7-      A -> 9-      B -> 11+note_to_pc :: Num i => Note -> i+note_to_pc n = T.lookup_err_msg "note_to_pc" n note_pc_tbl --- | Modal transposition of 'Note_T' value.+-- | 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+pc_to_note i = T.reverse_lookup i note_pc_tbl++-- | 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+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++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 -> Note -> [Note]+note_span n1 n2 =+    let fn x = toEnum (x `mod` 7)+        n1' = fromEnum n1+        n2' = fromEnum n2+        n2'' = if n1' > n2' then n2' + 7 else n2'+    in map fn [n1' .. n2'']+ -- * Alteration  -- | Enumeration of common music notation note alterations.-data Alteration_T = DoubleFlat-                  | ThreeQuarterToneFlat | Flat | QuarterToneFlat-                  | Natural-                  | QuarterToneSharp | Sharp | ThreeQuarterToneSharp-                  | DoubleSharp-                    deriving (Eq,Enum,Bounded,Ord,Show)+data Alteration =+    DoubleFlat+  | ThreeQuarterToneFlat | Flat | QuarterToneFlat+  | Natural+  | QuarterToneSharp | Sharp | ThreeQuarterToneSharp+  | DoubleSharp+    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)@@ -53,30 +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@@ -85,12 +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@@ -104,29 +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@@ -134,10 +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@@ -146,79 +192,184 @@       ThreeQuarterToneSharp -> Sharp       _ -> x +-- | Table of Unicode characters for alterations.+alteration_symbol_tbl :: [(Alteration,Char)]+alteration_symbol_tbl =+    [(DoubleFlat,'𝄫')+    ,(ThreeQuarterToneFlat,'𝄭')+    ,(Flat,'♭')+    ,(QuarterToneFlat,'𝄳')+    ,(Natural,'♮')+    ,(QuarterToneSharp,'𝄲')+    ,(Sharp,'♯')+    ,(ThreeQuarterToneSharp,'𝄰')+    ,(DoubleSharp,'𝄪')]+ -- | Unicode has entries for /Musical Symbols/ in the range @U+1D100@ -- through @U+1D1FF@.  The @3/4@ symbols are non-standard, here they -- correspond to @MUSICAL SYMBOL FLAT DOWN@ and @MUSICAL SYMBOL SHARP -- UP@. -- -- > map alteration_symbol [minBound .. maxBound] == "𝄫𝄭♭𝄳♮𝄲♯𝄰𝄪"-alteration_symbol :: Alteration_T -> Char-alteration_symbol a =    case a of-      DoubleFlat -> '𝄫'-      ThreeQuarterToneFlat -> '𝄭'-      Flat -> '♭'-      QuarterToneFlat -> '𝄳'-      Natural -> '♮'-      QuarterToneSharp -> '𝄲'-      Sharp -> '♯'-      ThreeQuarterToneSharp -> '𝄰'-      DoubleSharp -> '𝄪'+alteration_symbol :: Alteration -> Char+alteration_symbol a = fromMaybe (error "alteration_symbol") (lookup a alteration_symbol_tbl) --- | The @ISO@ ASCII spellings for alterations.  Naturals as written+-- | Inverse of 'alteration_symbol'.+--+-- > mapMaybe symbol_to_alteration "♭♮♯" == [Flat,Natural,Sharp]+symbol_to_alteration :: Char -> Maybe Alteration+symbol_to_alteration c = T.reverse_lookup c alteration_symbol_tbl++-- | 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++-- | ISO alteration table, strings not characters because of double flat.+alteration_iso_tbl :: [(Alteration,String)]+alteration_iso_tbl =+    [(DoubleFlat,"bb")+    ,(Flat,"b")+    ,(Natural,"")+    ,(Sharp,"#")+    ,(DoubleSharp,"x")]++-- | The @ISO@ ASCII spellings for alterations.  Naturals are written -- as the empty string. -- -- > mapMaybe alteration_iso_m [Flat .. Sharp] == ["b","","#"]-alteration_iso_m :: Alteration_T -> Maybe String-alteration_iso_m a =-    case a of-      DoubleFlat -> Just "bb"-      ThreeQuarterToneFlat -> Nothing-      Flat -> Just "b"-      QuarterToneFlat -> Nothing-      Natural -> Just ""-      QuarterToneSharp -> Nothing-      Sharp -> Just "#"-      ThreeQuarterToneSharp -> Nothing-      DoubleSharp -> Just "x"+-- > mapMaybe alteration_iso_m [DoubleFlat,DoubleSharp] == ["bb","x"]+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 --- * Generalised Alteration+-- | 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 --- | Generalised alteration, given as a rational semitone difference+tonh_to_alteration_err :: String -> Alteration+tonh_to_alteration_err = fromMaybe (error "tonh_to_alteration") . tonh_to_alteration++-- * 12-ET++-- | 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, 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, 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,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,Alteration)+pc_to_note_alteration_ks i = T.reverse_lookup i pc_note_alteration_ks_tbl++-- * Rational Alteration++-- | Alteration given as a rational semitone difference -- and a string representation of the alteration.-type Alteration_T' = (Rational,String)+type Alteration_R = (Rational,String) --- | Transform 'Alteration_T' to 'Alteration_T''.+-- | Transform 'Alteration' to 'Alteration_R'. -- -- > let r = [(-1,"♭"),(0,"♮"),(1,"♯")]--- > in map alteration_t' [Flat,Natural,Sharp] == r-alteration_t' :: Alteration_T -> Alteration_T'-alteration_t' a = (alteration_to_fdiff a,[alteration_symbol a])+-- > map alteration_r [Flat,Natural,Sharp] == r+alteration_r :: Alteration -> Alteration_R+alteration_r a = (alteration_to_fdiff a,[alteration_symbol a]) --- | Function to spell a 'PitchClass'.-type Spelling n = n -> (Note_T,Alteration_T)+-- * 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
@@ -0,0 +1,88 @@+-- | Constants names for notes.  /eses/ indicates double+-- flat, /eseh/ three quarter tone flat, /es/ flat, /eh/ quarter tone+-- flat, /ih/ quarter tone sharp, /is/ sharp, /isih/ three quarter+-- tone sharp and /isis/ double sharp.+module Music.Theory.Pitch.Note.Name where++import Music.Theory.Pitch.Note++ceses,deses,eeses,feses,geses,aeses,beses :: (Note,Alteration)+ceses = (C,DoubleFlat)+deses = (D,DoubleFlat)+eeses = (E,DoubleFlat)+feses = (F,DoubleFlat)+geses = (G,DoubleFlat)+aeses = (A,DoubleFlat)+beses = (B,DoubleFlat)++ceseh,deseh,eeseh,feseh,geseh,aeseh,beseh :: (Note,Alteration)+ceseh = (C,ThreeQuarterToneFlat)+deseh = (D,ThreeQuarterToneFlat)+eeseh = (E,ThreeQuarterToneFlat)+feseh = (F,ThreeQuarterToneFlat)+geseh = (G,ThreeQuarterToneFlat)+aeseh = (A,ThreeQuarterToneFlat)+beseh = (B,ThreeQuarterToneFlat)++ces,des,ees,fes,ges,aes,bes :: (Note,Alteration)+ces = (C,Flat)+des = (D,Flat)+ees = (E,Flat)+fes = (F,Flat)+ges = (G,Flat)+aes = (A,Flat)+bes = (B,Flat)++ceh,deh,eeh,feh,geh,aeh,beh :: (Note,Alteration)+ceh = (C,QuarterToneFlat)+deh = (D,QuarterToneFlat)+eeh = (E,QuarterToneFlat)+feh = (F,QuarterToneFlat)+geh = (G,QuarterToneFlat)+aeh = (A,QuarterToneFlat)+beh = (B,QuarterToneFlat)++c,d,e,f,g,a,b :: (Note,Alteration)+c = (C,Natural)+d = (D,Natural)+e = (E,Natural)+f = (F,Natural)+g = (G,Natural)+a = (A,Natural)+b = (B,Natural)++cih,dih,eih,fih,gih,aih,bih :: (Note,Alteration)+cih = (C,QuarterToneSharp)+dih = (D,QuarterToneSharp)+eih = (E,QuarterToneSharp)+fih = (F,QuarterToneSharp)+gih = (G,QuarterToneSharp)+aih = (A,QuarterToneSharp)+bih = (B,QuarterToneSharp)++cis,dis,eis,fis,gis,ais,bis :: (Note,Alteration)+cis = (C,Sharp)+dis = (D,Sharp)+eis = (E,Sharp)+fis = (F,Sharp)+gis = (G,Sharp)+ais = (A,Sharp)+bis = (B,Sharp)++cisih,disih,eisih,fisih,gisih,aisih,bisih :: (Note,Alteration)+cisih = (C,ThreeQuarterToneSharp)+disih = (D,ThreeQuarterToneSharp)+eisih = (E,ThreeQuarterToneSharp)+fisih = (F,ThreeQuarterToneSharp)+gisih = (G,ThreeQuarterToneSharp)+aisih = (A,ThreeQuarterToneSharp)+bisih = (B,ThreeQuarterToneSharp)++cisis,disis,eisis,fisis,gisis,aisis,bisis :: (Note,Alteration)+cisis = (C,DoubleSharp)+disis = (D,DoubleSharp)+eisis = (E,DoubleSharp)+fisis = (F,DoubleSharp)+gisis = (G,DoubleSharp)+aisis = (A,DoubleSharp)+bisis = (B,DoubleSharp)
Music/Theory/Pitch/Spelling.hs view
@@ -1,75 +1,19 @@ -- | Spelling rules for common music notation. module Music.Theory.Pitch.Spelling where -import Music.Theory.Pitch.Note (Note_T(..),Alteration_T(..),Spelling)---- | Variant of 'Spelling' for incomplete functions.-type Spelling_M i = i -> Maybe (Note_T, Alteration_T)---- | 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 pc =-    case pc of-      0 -> Just (C,Natural)-      2 -> Just (D,Natural)-      4 -> Just (E,Natural)-      5 -> Just (F,Natural)-      7 -> Just (G,Natural)-      9 -> Just (A,Natural)-      11 -> Just (B,Natural)-      _ -> Nothing---- | 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 pc =-    case pc_spell_natural_m pc of-      Just p -> p-      _ -> error "pc_spell_natural"---- | Use spelling from simplest key-signature.  Note that this is--- ambiguous for @8@, which could be either G Sharp (♯) in /A Major/--- or A Flat (♭) in /E Flat (♭) Major/.------ > map pc_spell_ks [6,8] == [(F,Sharp),(A,Flat)]-pc_spell_ks :: Integral i => Spelling i-pc_spell_ks pc =-    case pc of-      1 -> (C,Sharp) -- 2#-      3 -> (E,Flat) -- 3b-      6 -> (F,Sharp) -- 1#-      8 -> (A,Flat) -- 3b/3#-      10 -> (B,Flat) -- 1b-      _ -> pc_spell_natural pc+import qualified Music.Theory.Pitch as T {- hmt -}+import qualified Music.Theory.Pitch.Spelling.Cluster as T {- hmt -}+import qualified Music.Theory.Pitch.Spelling.Key as T {- hmt -}+import qualified Music.Theory.Pitch.Spelling.Table as T {- hmt -} --- | 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]--- > octpc_to_pitch pc_spell_sharp (4,6) == Pitch F Sharp 4-pc_spell_sharp :: Integral i => Spelling i-pc_spell_sharp pc =-    case pc of-      1 -> (C,Sharp)-      3 -> (D,Sharp)-      6 -> (F,Sharp)-      8 -> (G,Sharp)-      10 -> (A,Sharp)-      _ -> pc_spell_natural pc+spell_octpc_set :: [T.OctPc] -> [T.Pitch]+spell_octpc_set o =+  case T.octpc_spell_implied_key o of+    Just r -> r+    Nothing ->+      case T.spell_cluster_octpc o of+        Just r -> r+        Nothing -> map T.octpc_to_pitch_ks o --- | 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 pc =-    case pc of-      1 -> (D,Flat)-      3 -> (E,Flat)-      6 -> (G,Flat)-      8 -> (A,Flat)-      10 -> (B,Flat)-      _ -> pc_spell_natural pc+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
@@ -1,128 +1,175 @@ -- | Spelling for chromatic clusters. module Music.Theory.Pitch.Spelling.Cluster where -import Data.List-import Music.Theory.Pitch-import Music.Theory.Pitch.Name+import Data.List {- base -} --- | Spelling table for chromatic clusters.+import qualified Music.Theory.List as T {- hmt -}+import qualified Music.Theory.Pitch as T {- hmt -}+import qualified Music.Theory.Pitch.Note as T {- hmt -}+import           Music.Theory.Pitch.Note.Name {- hmt -}++-- | Form of cluster with smallest outer boundary interval. ----- > let f (p,q) = p == sort (map (snd . pitch_to_octpc) q)--- > in all f spell_cluster_c4_table == True-spell_cluster_c4_table :: [([PitchClass],[Pitch])]-spell_cluster_c4_table =-    [([0],[c4])-    ,([0,1],[c4,des4])-    ,([0,1,2],[bis3,cis4,d4])-    ,([0,1,2,3],[bis3,cis4,d4,ees4])-    ,([0,1,2,3,10,11],[ais3,b3,c4,cis4,d4,ees4]) -- overlap...-    ,([0,1,2,10],[ais3,bis3,cis4,d4])-    ,([0,1,2,11],[aisis3,bis3,cis4,d4])-    ,([0,1,3],[c4,des4,ees4])-    ,([0,1,3,10],[bes3,c4,des4,ees4])-    ,([0,1,3,11],[b3,c4,des4,ees4])-    ,([0,1,10],[bes3,c4,des4])-    ,([0,1,10,11],[ais3,b3,c4,des4])-    ,([0,1,11],[b3,c4,des4])-    ,([0,2],[c4,d4])-    ,([0,2,3],[c4,d4,ees4])-    ,([0,2,3,10],[bes3,c4,d4,ees4])-    ,([0,2,3,11],[b3,c4,d4,ees4])-    ,([0,2,11],[b3,c4,d4])-    ,([0,2,10],[bes3,c4,d4])-    ,([0,2,10,11],[ais3,b3,c4,d4])-    ,([0,3,10,11],[ais3,b3,c4,dis4])-    ,([0,3,11],[b3,c4,dis4])-    ,([0,10,11],[ais3,b3,c4])-    ,([0,11],[b3,c4])-    ,([1],[cis4])-    ,([1,2],[cis4,d4])-    ,([1,2,3],[cis4,d4,ees4])-    ,([1,2,3,10],[bes3,cis4,d4,ees4])-    ,([1,2,3,11],[b3,cis4,d4,ees4])-    ,([1,2,10],[ais3,cis4,d4])-    ,([1,2,10,11],[ais3,b3,cis4,d4])-    ,([1,2,11],[b3,cis4,d4])-    ,([1,3,11],[b3,cis4,dis4])-    ,([1,3,10,11],[ais3,b3,cis4,dis4])-    ,([1,10,11],[ais3,b3,cis4])-    ,([1,11],[b3,cis4])-    ,([2],[d4])-    ,([2,3],[d4,ees4])-    ,([2,3,4],[d4,ees4,fes4])-    ,([2,3,5],[d4,ees4,f4])-    ,([2,3,4,5],[d4,ees4,fes4,geses4])-    ,([2,3,10,11],[bes3,ces4,d4,ees4])-    ,([2,3,11],[b3,d4,ees4])-    ,([2,4],[d4,e4])-    ,([2,4,5],[d4,e4,f4])-    ,([2,5],[d4,f4])-    ,([2,10,11],[ais3,b3,d4])-    ,([2,11],[b3,d4])-    ,([3],[ees4])-    ,([3,4],[dis4,e4])-    ,([3,4,5],[dis4,e4,f4])-    ,([3,5],[ees4,f4])-    ,([4],[e4])-    ,([4,5],[e4,f4])-    ,([5],[f4])-    ,([5,6],[f4,ges4])-    ,([5,6,7],[eis4,fis4,g4])-    ,([5,6,8],[f4,ges4,aes4])-    ,([5,6,9],[f4,ges4,a4])-    ,([5,6,7,8],[eis4,fis4,g4,aes4])-    ,([5,6,7,8,9],[eis4,fis4,g4,aes4,beses4])-    ,([5,6,7,9],[eis4,fis4,g4,a4])-    ,([5,6,8,9],[eis4,fis4,gis4,a4])-    ,([5,7],[f4,g4])-    ,([5,7,8],[f4,g4,aes4])-    ,([5,7,8,9],[f4,g4,aes4,beses4])-    ,([5,7,9],[f4,g4,a4])-    ,([5,8],[f4,aes4])-    ,([5,8,9],[f4,gis4,a4])-    ,([5,9],[f4,a4])-    ,([6],[fis4])-    ,([6,7],[fis4,g4])-    ,([6,7,8],[fis4,g4,aes4])-    ,([6,7,8,9],[fis4,g4,aes4,beses4])-    ,([6,7,9],[fis4,g4,a4])-    ,([6,8],[fis4,gis4])-    ,([6,8,9],[fis4,gis4,a4])-    ,([6,9],[fis4,a4])-    ,([7],[g4])-    ,([7,8],[g4,aes4])-    ,([7,8,9],[fisis4,gis4,a4])-    ,([7,9],[g4,a4])-    ,([8],[aes4])-    ,([8,9],[gis4,a4])-    ,([8,9,10],[gis4,a4,bes4])-    ,([8,10],[aes4,bes4])-    ,([9],[a4])-    ,([9,10],[a4,bes4])-    ,([10],[bes4])-    ,([10,11],[ais4,b4])-    ,([11],[b4])]+-- > cluster_normal_order [0,1,11] == [11,0,1]+cluster_normal_order :: [T.PitchClass] -> [T.PitchClass]+cluster_normal_order =+    let with_bounds x = ((last x - head x) `mod` 12,x)+    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 o pc =+    let pc_n = cluster_normal_order pc+        pc_0 = head pc_n+    in map (\x -> (if x >= pc_0 then o else o + 1,x)) pc_n++-- | True if 'sort' of cluster is not equal to 'cluster_normal_order'.+--+-- > map cluster_is_multiple_octave [[0,1,11],[1,2,3],[1,2,11]] == [True,False,True]+cluster_is_multiple_octave :: [T.PitchClass] -> Bool+cluster_is_multiple_octave x = sort x /= cluster_normal_order x++-- | Spelling table for chromatic and near-chromatic clusters,+-- pitch-classes are in cluster order.+--+-- > 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.Alteration)])]+spell_cluster_table =+    [([0,1,2,3],[bis,cis,d,ees])+    ,([0,1,2],[bis,cis,d])+    ,([0,1,3],[c,des,ees])+    ,([0,1],[c,des])+    ,([0,2,3],[c,d,ees])+    ,([0,2],[c,d])+    ,([0],[c])+    ,([1,2,3],[cis,d,ees])+    ,([1,2],[cis,d])+    ,([10,0,1,2],[ais,bis,cis,d])+    ,([10,0,1,3],[bes,c,des,ees])+    ,([10,0,1],[bes,c,des])+    ,([10,0,2,3],[bes,c,d,ees])+    ,([10,0,2],[bes,c,d])+    ,([10,1,2,3],[bes,cis,d,ees])+    ,([10,1,2],[ais,cis,d])+    ,([10,11,0,1,2,3],[ais,b,c,cis,d,ees]) -- overlap...+    ,([10,11,0,1],[ais,b,c,des])+    ,([10,11,0,2],[ais,b,c,d])+    ,([10,11,0,3],[ais,b,c,dis])+    ,([10,11,0],[ais,b,c])+    ,([10,11,1,2],[ais,b,cis,d])+    ,([10,11,1,3],[ais,b,cis,dis])+    ,([10,11,1],[ais,b,cis])+    ,([10,11,2,3],[bes,ces,d,ees])+    ,([10,11,2],[ais,b,d])+    ,([10,11],[ais,b])+    ,([10],[bes])+    ,([11,0,1,2],[aisis,bis,cis,d])+    ,([11,0,1,3],[b,c,des,ees])+    ,([11,0,1],[b,c,des])+    ,([11,0,2,3],[b,c,d,ees])+    ,([11,0,2],[b,c,d])+    ,([11,0,3],[b,c,dis])+    ,([11,0],[b,c])+    ,([11,1,2,3],[b,cis,d,ees])+    ,([11,1,2],[b,cis,d])+    ,([11,1,3],[b,cis,dis])+    ,([11,1],[b,cis])+    ,([11,2,3],[b,d,ees])+    ,([11,2],[b,d])+    ,([11],[b])+    ,([1],[cis])+    ,([2,3,4,5],[d,ees,fes,geses])+    ,([2,3,4],[d,ees,fes])+    ,([2,3,5],[d,ees,f])+    ,([2,3],[d,ees])+    ,([2,4,5],[d,e,f])+    ,([2,4],[d,e])+    ,([2,5],[d,f])+    ,([2],[d])+    ,([3,4,5],[dis,e,f])+    ,([3,4],[dis,e])+    ,([3,5],[ees,f])+    ,([3],[ees])+    ,([4,5],[e,f])+    ,([4],[e])+    ,([5,6,7,8,9],[eis,fis,g,aes,beses])+    ,([5,6,7,8],[eis,fis,g,aes])+    ,([5,6,7,9],[eis,fis,g,a])+    ,([5,6,7],[eis,fis,g])+    ,([5,6,8,9],[eis,fis,gis,a])+    ,([5,6,8],[f,ges,aes])+    ,([5,6,9],[f,ges,a])+    ,([5,6],[f,ges])+    ,([5,7,8,9],[f,g,aes,beses])+    ,([5,7,8],[f,g,aes])+    ,([5,7,9],[f,g,a])+    ,([5,7],[f,g])+    ,([5,8,9],[f,gis,a])+    ,([5,8],[f,aes])+    ,([5,9],[f,a])+    ,([5],[f])+    ,([6,7,8,9],[fis,g,aes,beses])+    ,([6,7,8],[fis,g,aes])+    ,([6,7,9],[fis,g,a])+    ,([6,7],[fis,g])+    ,([6,8,9],[fis,gis,a])+    ,([6,8],[fis,gis])+    ,([6,9],[fis,a])+    ,([6],[fis])+    ,([7,8,9],[fisis,gis,a])+    ,([7,8],[g,aes])+    ,([7,9],[g,a])+    ,([7],[g])+    ,([8,10],[aes,bes])+    ,([8,9,10],[gis,a,bes])+    ,([8,9],[gis,a])+    ,([8],[aes])+    ,([9,10],[a,bes])+    ,([9],[a])]++spell_cluster :: [T.PitchClass] -> Maybe [(T.Note,T.Alteration)]+spell_cluster = flip lookup spell_cluster_table++-- | 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 o =+    let p = cluster_normal_order (sort (nub (map snd o)))+        na_f na =+            let na_tbl = map (\x -> (T.note_alteration_to_pc_err x,x)) na+                o_f (oct,pc) = let (n,alt) = T.lookup_err pc na_tbl in T.Pitch n alt oct+            in map o_f o+    in fmap na_f (spell_cluster p)+ -- | Spelling for chromatic clusters.  Sequence must be ascending. -- Pitch class @0@ maps to 'c4', if there is no @0@ then all notes are -- in octave @4@. ----- > let f = fmap (map pitch_pp) . spell_cluster_c4--- > in map f [[11,0],[11]] == [Just ["B3","C4"],Just ["B4"]]+-- > let f = (fmap (map T.pitch_pp) . spell_cluster_c4)+-- > map f [[11,0],[11],[0,11]] == [Just ["B3","C4"],Just ["B4"],Nothing] ----- > fmap (map pitch_pp) (spell_cluster_c4 [10,11]) == Just ["A♯4","B4"]-spell_cluster_c4 :: [PitchClass] -> Maybe [Pitch]-spell_cluster_c4 p = lookup (sort p) spell_cluster_c4_table+-- > fmap (map T.pitch_pp) (spell_cluster_c4 [10,11]) == Just ["A♯4","B4"]+spell_cluster_c4 :: [T.PitchClass] -> Maybe [T.Pitch]+spell_cluster_c4 p =+    let o_0 = if cluster_is_multiple_octave p then 3 else 4+        oct = map fst (cluster_normal_order_octpc o_0 p)+    in case spell_cluster p of+         Nothing -> Nothing+         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 -- above. ----- > fmap (map pitch_pp) (spell_cluster_c 3 [11,0]) == Just ["B2","C3"]--- > fmap (map pitch_pp) (spell_cluster_c 3 [10,11]) == Just ["A♯3","B3"]-spell_cluster_c :: Octave -> [PitchClass] -> Maybe [Pitch]+-- > fmap (map T.pitch_pp) (spell_cluster_c 3 [11,0]) == Just ["B2","C3"]+-- > fmap (map T.pitch_pp) (spell_cluster_c 3 [10,11]) == Just ["A♯3","B3"]+spell_cluster_c :: T.Octave -> [T.PitchClass] -> Maybe [T.Pitch] spell_cluster_c o =-    fmap (map (pitch_edit_octave (+ (o - 4)))) .+    fmap (map (T.pitch_edit_octave (+ (o - 4)))) .     spell_cluster_c4  -- | Variant of 'spell_cluster_c4' that runs 'pitch_edit_octave' so@@ -130,28 +177,30 @@ -- -- > import Data.Maybe ----- > let {f n = if n >= 11 then 3 else 4--- >     ;g = map 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-spell_cluster_f :: (PitchClass -> Octave) -> [PitchClass] -> Maybe [Pitch]+-- > 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) = pitch_to_octpc l-                           f = (+ (o_f n - o))-                       in (map (pitch_edit_octave f) r)+                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 fmap fn (spell_cluster_c4 p)  -- | Variant of 'spell_cluster_c4' that runs 'pitch_edit_octave' so -- that the left-most note is in octave /o/. ----- > fmap (map pitch_pp) (spell_cluster_left 3 [11,0]) == Just ["B3","C4"]--- > fmap (map pitch_pp) (spell_cluster_left 3 [10,11]) == Just ["A♯3","B3"]-spell_cluster_left :: Octave -> [PitchClass] -> Maybe [Pitch]+-- > fmap (map T.pitch_pp) (spell_cluster_left 3 [11,0]) == Just ["B3","C4"]+-- > fmap (map T.pitch_pp) (spell_cluster_left 3 [10,11]) == Just ["A♯3","B3"]+spell_cluster_left :: T.Octave -> [T.PitchClass] -> Maybe [T.Pitch] spell_cluster_left o p =     let fn r = case r of                 [] -> []-                l:_ -> let f = (+ (o - octave l))-                       in map (pitch_edit_octave f) r+                l:_ -> let oct_f = (+ (o - T.octave l))+                       in map (T.pitch_edit_octave oct_f) r     in fmap fn (spell_cluster_c4 p)
+ Music/Theory/Pitch/Spelling/Key.hs view
@@ -0,0 +1,33 @@+module Music.Theory.Pitch.Spelling.Key where++import qualified Music.Theory.Key as T {- hmt -}+import qualified Music.Theory.Pitch as T {- hmt -}+import qualified Music.Theory.Pitch.Note as T {- hmt -}+import qualified Music.Theory.Pitch.Spelling.Table as T {- hmt -}++pcset_spell_implied_key_f :: Integral i => [i] -> Maybe (T.Spelling i)+pcset_spell_implied_key_f x =+    case T.implied_fifths T.Major_Mode x of+      Nothing -> Nothing+      Just n -> if n == 0+                then Just T.pc_spell_natural+                else if n < 0+                     then Just T.pc_spell_flat+                     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.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 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))++-- > map (fmap (map T.pitch_pp_iso) . midi_spell_implied_key) [[59,61],[59,70]]+midi_spell_implied_key :: [T.Midi] -> Maybe [T.Pitch]+midi_spell_implied_key = octpc_spell_implied_key . map T.midi_to_octpc
+ Music/Theory/Pitch/Spelling/Table.hs view
@@ -0,0 +1,105 @@+-- | Simple table based spelling rules for common music notation.+module Music.Theory.Pitch.Spelling.Table where++import Data.Maybe {- base -}++import qualified Music.Theory.Pitch as T {- hmt -}+import Music.Theory.Pitch.Note {- hmt -}++type Spelling_Table i = [(i,(Note,Alteration))]++-- | Spelling table for natural (♮) notes only.+pc_spell_natural_tbl :: Integral i => Spelling_Table i+pc_spell_natural_tbl =+    [(0,(C,Natural))+    ,(2,(D,Natural))+    ,(4,(E,Natural))+    ,(5,(F,Natural))+    ,(7,(G,Natural))+    ,(9,(A,Natural))+    ,(11,(B,Natural))]++-- | Spelling table for sharp (♯) notes only.+pc_spell_sharp_tbl :: Integral i => Spelling_Table i+pc_spell_sharp_tbl =+    [(1,(C,Sharp))+    ,(3,(D,Sharp))+    ,(6,(F,Sharp))+    ,(8,(G,Sharp))+    ,(10,(A,Sharp))]++-- | Spelling table for flat (♭) notes only.+pc_spell_flat_tbl :: Integral i => Spelling_Table i+pc_spell_flat_tbl =+    [(1,(D,Flat))+    ,(3,(E,Flat))+    ,(6,(G,Flat))+    ,(8,(A,Flat))+    ,(10,(B,Flat))]++-- | Spelling table from simplest key-signature.  Note that this is+-- ambiguous for @8@, which could be either G Sharp (♯) in /A Major/+-- or A Flat (♭) in /E Flat (♭) Major/.+pc_spell_ks_tbl :: Integral i => Spelling_Table i+pc_spell_ks_tbl =+      [(1,(C,Sharp)) -- 2♯+      ,(3,(E,Flat)) -- 3♭+      ,(6,(F,Sharp)) -- 1♯+      ,(8,(A,Flat)) -- 3♭/3♯+      ,(10,(B,Flat))] -- 1♭++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 -> 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 => 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 => 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 => 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 => 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 => T.Spelling i+pc_spell_flat = pc_spell_tbl (pc_spell_flat_tbl ++ pc_spell_natural_tbl)++octpc_to_pitch_ks :: Integral i => T.Octave_PitchClass i -> T.Pitch+octpc_to_pitch_ks = T.octpc_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 -> T.Pitch+fmidi_to_pitch_ks = T.fmidi_to_pitch_err 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
@@ -0,0 +1,219 @@+-- | 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-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)++{-| (sum={6,7,8,9},+     (yarrow probablity={1,3,5,7}/16,+      three-coin probablity={2,6}/16,+      name,signification,symbol))+-}+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---"))]++-- | 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 = 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+line_is_moving n = n `elem` [L6,L9]++-- | Old yin (L6) becomes yang (L7), and old yang (L9) becomes yin (L8).+line_complement :: Line -> Maybe Line+line_complement n =+    case n of+      L6 -> Just L7+      L9 -> Just L8+      _ -> Nothing++{- | 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 four_coin_sequence)++-}+four_coin_sequence :: [Line]+four_coin_sequence =+    [L6,L9,L9,L9+    ,L7,L7,L7,L7+    ,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+four_coin_gen_hexagram :: IO Hexagram+four_coin_gen_hexagram = fmap (map (four_coin_sequence !!)) (replicateM 6 (randomRIO (0,15)))++-- | 'any' of 'line_is_moving'.+hexagram_has_complement :: Hexagram -> Bool+hexagram_has_complement = any line_is_moving++-- | If 'hexagram_has_complement' then derive it.+--+-- > h <- four_coin_gen_hexagram+-- > putStrLn (hexagram_pp h)+-- > maybe (return ()) (putStrLn . hexagram_pp) (hexagram_complement h)+hexagram_complement :: Hexagram -> Maybe Hexagram+hexagram_complement h =+    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 (see also data/csv/combinatorics/yijing.csv)+--+-- > length hexagram_names == 64+hexagram_names :: [(String,String)]+hexagram_names =+    [("乾","qián")+    ,("坤","kūn")+    ,("屯","zhūn")+    ,("蒙","méng")+    ,("需","xū")+    ,("訟","sòng")+    ,("師","shī")+    ,("比","bǐ")+    ,("小畜","xiǎo chù")+    ,("履","lǚ")+    ,("泰","tài")+    ,("否","pǐ")+    ,("同人","tóng rén")+    ,("大有","dà yǒu")+    ,("謙","qiān")+    ,("豫","yù")+    ,("隨","suí")+    ,("蠱","gŭ")+    ,("臨","lín")+    ,("觀","guān")+    ,("噬嗑","shì kè")+    ,("賁","bì")+    ,("剝","bō")+    ,("復","fù")+    ,("無妄","wú wàng")+    ,("大畜","dà chù")+    ,("頤","yí")+    ,("大過","dà guò")+    ,("坎","kǎn")+    ,("離","lí")+    ,("咸","xián")+    ,("恆","héng")+    ,("遯","dùn")+    ,("大壯","dà zhuàng")+    ,("晉","jìn")+    ,("明夷","míng yí")+    ,("家人","jiā rén")+    ,("睽","kuí")+    ,("蹇","jiǎn")+    ,("解","xiè")+    ,("損","sǔn")+    ,("益","yì")+    ,("夬","guài")+    ,("姤","gòu")+    ,("萃","cuì")+    ,("升","shēng")+    ,("困","kùn")+    ,("井","jǐng")+    ,("革","gé")+    ,("鼎","dǐng")+    ,("震","zhèn")+    ,("艮","gèn")+    ,("漸","jiàn")+    ,("歸妹","guī mèi")+    ,("豐","fēng")+    ,("旅","lǚ")+    ,("巽","xùn")+    ,("兌","duì")+    ,("渙","huàn")+    ,("節","jié")+    ,("中孚","zhōng fú")+    ,("小過","xiǎo guò")+    ,("既濟","jì jì")+    ,("未濟","wèi jì")]++-- | Unicode hexagram characters, in King Wen order.+--+-- > import Data.List.Split {- split -}+-- > mapM_ putStrLn (chunksOf 8 hexagram_unicode_sequence)+hexagram_unicode_sequence :: [Char]+hexagram_unicode_sequence = map (toEnum . fst) T.yijing_tbl++-- | Binary form of 'Hexagram'.+hexagram_to_binary :: Hexagram -> Int8+hexagram_to_binary = T.pack_bitseq . map line_unbroken++-- | 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 . fst) T.bagua_tbl++-- | (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,'☰',"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/Set/List.hs view
@@ -1,15 +1,18 @@ -- | Set operations on lists. module Music.Theory.Set.List where -import Control.Monad-import Data.List+import Control.Monad {- base -}+import Data.List {- base -}+ import qualified Math.Combinatorics.Multiset as M {- multiset-comb -} --- | Remove duplicate elements with 'nub' and then 'sort'.+import qualified Music.Theory.List as T {- hmt-base -}++-- | 'sort' then 'nub'. ----- > set_l [3,3,3,2,2,1] == [1,2,3]+-- > set [3,3,3,2,2,1] == [1,2,3] set :: (Ord a) => [a] -> [a]-set = sort . nub+set = nub . sort  -- | Size of powerset of set of cardinality /n/, ie. @2@ '^' /n/. --@@ -24,6 +27,12 @@ powerset :: [a] -> [[a]] powerset = filterM (const [True,False]) +-- | Variant where result is sorted and the empty set is not given.+--+-- > 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. -- -- > pairs [1,2,3] == [(1,2),(1,3),(2,3)]@@ -33,12 +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@@ -54,19 +65,37 @@     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 of two sets.++> 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]++-- | List form of n-fold cartesian product.+--+-- > length (nfold_cartesian_product [[1..13],[1..4]]) == 52+-- > length (nfold_cartesian_product ["abc","de","fgh"]) == 3 * 2 * 3+nfold_cartesian_product :: [[a]] -> [[a]]+nfold_cartesian_product l =+    case l of+      [] -> []+      [_] -> []+      [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/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@@ -79,7 +79,7 @@ -- | Lookup metronome mark in table. -- -- > mm_name metronome_table_nikko 72 == Just "Andante"-mm_name :: (Num a, Ord a) => [(String,(a,a))] -> a -> Maybe String+mm_name :: Ord a => [(String,(a,a))] -> a -> Maybe String mm_name tbl x =     let f (_,(p,q)) = x >= p && x < q     in fmap fst (find f tbl)
Music/Theory/Tiling/Canon.hs view
@@ -1,11 +1,14 @@ module Music.Theory.Tiling.Canon where -import Control.Monad.Logic {- logict -}-import Data.Function {- base -}+import Control.Monad {- base -} import Data.List {- base -} import Data.List.Split {- split -} import Text.Printf {- base -} +import qualified Control.Monad.Logic as L {- logict -}++import qualified Music.Theory.List as T {- hmt -}+ -- | Sequence. type S = [Int] @@ -35,16 +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) @@ -61,7 +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)@@ -70,28 +74,29 @@ -- | 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)-    in map f (groupBy ((==) `on` t3_1) e)+        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]+-- > L.observeAll (fromList [1..7]) == [1..7] fromList :: MonadPlus m => [a] -> m a fromList = msum . map return @@ -113,37 +118,37 @@                     rec (m':p) (s'':q)     in rec [] [] --- | 't_normal' of 'observeAll' of 'perfect_tilings_m'.------ > 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------ > 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],[4,9],[6,8]]--- >         ,[[0,1],[2,7],[3,5],[4,8],[6,9]]--- >         ,[[0,2],[1,4],[3,8],[5,9],[6,7]]--- >         ,[[0,2],[1,5],[3,6],[4,9],[7,8]]--- >         ,[[0,3],[1,6],[2,4],[5,9],[7,8]]]--- > in perfect_tilings [[0,1]] [1..5] 10 5 == r------ 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]------ > 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]+{- | 't_normal' of 'L.observeAll' of 'perfect_tilings_m'.++> 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]]]+> 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]]]+> 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]]+>         ,[[0,2],[1,4],[3,8],[5,9],[6,7]]+>         ,[[0,2],[1,5],[3,6],[4,9],[7,8]]+>         ,[[0,3],[1,6],[2,4],[5,9],[7,8]]]+> in perfect_tilings [[0,1]] [1..5] 10 5 == r++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]]+> 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]]+> perfect_tilings [[0,1,2]] [1,2,4,5,7,8,10] 21 7 == [t_retrograde r]++-} perfect_tilings :: [S] -> [Int] -> Int -> Int -> [T] perfect_tilings s m n =-    nub . sort . map t_normal . observeAll . perfect_tilings_m s m n+    nub . sort . map t_normal . L.observeAll . perfect_tilings_m s m n  -- * Display
Music/Theory/Time/Bel1990/R.hs view
@@ -11,184 +11,7 @@   Centre National de la Recherche Scientifique, 1992. /GRTC 458/   (<http://www.lpl.univ-aix.fr/~belbernard/music/2algorithms.pdf>) -For patterns without tempo indications, the two notations should give-equivalent phase diagrams, for instance (Bel 1990, §11, p.24):--> > bel_ascii_pp "ab{ab,cde}cd"->-> Bel(R): "ab{ab,cde}cd", Dur: 7->-> a _ b _ a _ _ b _ _ c _ d _->         c _ d _ e _        --and:--> > bel_ascii_pp "{a{bc,def},ghijk}"->-> Bel(R): "{a{bc,def},ghijk}", Dur: 5->-> a _ _ _ _ _ _ _ _ _ b _ _ _ _ _ _ _ _ _ _ _ _ _ _ c _ _ _ _ _ _ _ _ _ _ _ _ _ _->                     d _ _ _ _ _ _ _ _ _ e _ _ _ _ _ _ _ _ _ f _ _ _ _ _ _ _ _ _-> g _ _ _ _ _ _ _ h _ _ _ _ _ _ _ i _ _ _ _ _ _ _ j _ _ _ _ _ _ _ k _ _ _ _ _ _ _--The /Bel/ notation allows /n/-ary parallel structures,-ie. @{a_bcd_e,a_f_gh_,ji_a_i_}@ (Bel 1992, p.29), however /Bel(R)/-allows only binary structures.  The parallel interpretation rules are-associative:--> > bel_ascii_pp "{a_bcd_e,{a_f_gh_,ji_a_i_}}"->-> Bel(R): "{a_bcd_e,{a_f_gh_,ji_a_i_}}", Dur: 7->-> a _ b c d _ e-> a _ f _ g h _-> j i _ a _ i _--/Bel(R)/ does allow unary parallel structures (see 'Iso'), which can-be used to /isolate/ tempo changes:--> > bel_ascii_pp "ab{*2cd}ef{*2/3gh}ij"->-> Bel(R): "ab{*2cd}ef{*2/3gh}ij", Dur: 10->-> a _ b _ c d e _ f _ g _ _ h _ _ i _ j _--Patterns with tempo indications have completely different meanings in-/Bel/ and /Bel(R)/, though in both cases parallel nodes delimit the-scope of tempo markings.--/Bel(R)/ replaces the @\/n@ notation for explicit tempo marks with a-@*n@ notation to indicate a tempo multiplier, and a set of bracketing-notations to specify interpretation rules for parallel (concurrent)-temporal structures.--The tempo indication @\/1@ in the expression @ab{\/1ab,cde}cd@-(Bel 1990, p.24) requires that the inner @ab@ have the same tempo as-the outer @ab@, which is implicitly @\/1@.  Setting the tempo of one-part of a parallel structure requires assigning a tempo to the other-part in order that the two parts have equal duration.  Here the tempo-assigned to @cde@ is @\/1.5@, but since fractional tempi are not-allowed the expression is re-written as @\/2ab{\/2ab,\/3cde}\/2cd@.--Importantly the explicit tempo indications make it possible to write-syntactically correct expressions in /Bel/ that do not have a coherent-interpretation, ie. @{\/1ab,\/1cde}@.  Determining if a coherent set-of tempos can be assigned, and assigning these tempos, is the object-of the interpretation system.--In comparison, all syntactically valid /Bel(R)/ strings have an-interpretation.  The expression @{*1ab,*1cde}@ is trivially equal to-@{ab,cde}@, and tempo marks in parallel parts do not interact:--> > bel_ascii_pp "{a*2b,*3c/2d/3e}"->-> Bel(R): "{a*2b,*3c*1/2d*1/3e}", Dur: 3->-> a _ _ _ _ _ b _ _-> c d _ e _ _ _ _ _--Here @a@ is twice the duration of @b@, and @e@ is three times the-duration of @d@, which is twice the duration of @c@ (in /Bel(R)/ @\/n@-is equivalent to @*1\/n@).  The duration of any /Bel(R)/ expression-can be calculated directly, given an initial 'Tempo':--> bel_dur 1 (bel_char_parse "a*2b") == 3/2-> bel_dur 1 (bel_char_parse "*3c/2d/3e") == 3--Therefore in the composite expression the left part is slowed by a-factor of two to align with the right part.--The /Bel/ string @ab{\/1ab,cde}cd@ can be re-written in /Bel(R)/ as-either @ab~{ab,cde}cd@ or @ab(ab,cde)cd@.  The absolute tempo-indication is replaced by notations giving alternate modes of-interpretation for the parallel structure.--In the first case the @~@ indicates the /opposite/ of the normal rule-for parallel nodes.  The normal rule is the same as for /Bel/ and is-that the duration of the whole is equal to duration of the longer of-the two parts.  The @~@ inverts this so that the whole has the-duration of the shorter of the two parts, and the longer part is-scaled to have equal duration.--In the second case the parentheses @()@ replacing the braces @{}@-indicates that the duration of the whole is equal to the duration of-the left side, and that the right is to be scaled.  Similarly, a @~@-preceding parentheses indicates the duration of the whole should be-the duration of the right side, and the left scaled.--> > bel_ascii_pp "ab~{ab,cde}cd"->-> Bel(R): "ab~{ab,cde}cd", Dur: 6->-> a _ _ b _ _ a _ _ b _ _ c _ _ d _ _->             c _ d _ e _            --There is one other parallel mode that has no equivalent in /Bel/-notation.  It is a mode that does not scale either part, leaving a-/hole/ at the end of the shorter part, and is indicated by square-brackets:--> > bel_ascii_pp "ab[ab,cde]cd"->-> Bel(R): "ab[ab,cde]cd", Dur: 7->-> a b a b   c d->     c d e    --The /Bel/ string @\/2abc\/3de@ (Bel 1992, p.53) can be written as-@*2abc*1/2*3de@, or equivalently as @*2abc*3/2de@:--> > bel_ascii_pp "*2abc*3/2de"->-> Bel(R): "*2abc*3/2de", Dur: 13/6->-> a _ _ b _ _ c _ _ d _ e _--It can also be written using the shorthand notation for rest-sequences, where an integer /n/ indicates a sequence of /n/ rests, as:--> > bel_ascii_pp "(9,abc)(4,de)"->-> Bel(R): "(---------,abc)(----,de)", Dur: 13->-> - - - - - - - - - - - - --> a _ _ b _ _ c _ _ d _ e _--In the /Bel/ string @{ab{/3abc,de},fghijk}@ (Bel 1992, p.20) the tempo-indication does not change the inter-relation of the parts but rather-scales the parallel node altogether, and can be re-written in /Bel(R)/-notation as:--> > bel_ascii_pp "{ab*3{abc,de},fghijk}"->-> Bel(R): "{ab*3{abc,de},fghijk}", Dur: 6->-> a _ _ _ _ _ b _ _ _ _ _ a _ b _ c _->                         d _ _ e _ _-> f _ _ g _ _ h _ _ i _ _ j _ _ k _ _--Curiously the following example (Bel 1990, p. 24) does not correspond-to the phase diagram given:--> > bel_ascii_pp "{i{ab,cde},jk}"->-> Bel(R): "{i{ab,cde},jk}", Dur: 4->-> i _ a _ _ b _ _->     c _ d _ e _-> j _ _ _ k _ _ _--The paper assigns tempi of @\/6@ to both @i@ and @ab@, which in-/Bel(R)/ could be written:--> > bel_ascii_pp "{i~{ab,cde},jk}"->-> Bel(R): "{i~{ab,cde},jk}", Dur: 3->-> i _ _ _ _ _ a _ _ _ _ _ b _ _ _ _ _->             c _ _ _ d _ _ _ e _ _ _-> j _ _ _ _ _ _ _ _ k _ _ _ _ _ _ _ _-+For details see <http://rohandrape.net/?t=hmt-texts>. -}  module Music.Theory.Time.Bel1990.R where@@ -197,18 +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)@@ -220,6 +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@@ -228,25 +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@@ -264,13 +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@@ -310,14 +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)@@ -334,6 +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] @@ -359,7 +227,7 @@  -- | Merge two ascending 'L_Bel'. lbel_merge :: L_Bel a -> L_Bel a -> L_Bel a-lbel_merge = T.merge_by (compare `on` lterm_time)+lbel_merge = T.merge_on lterm_time  -- | Set of unique 'Tempo' at 'L_Bel'. lbel_tempi :: L_Bel a -> [Tempo]@@ -369,18 +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') @@ -391,14 +266,14 @@ -- | Unique 'Voice's at 'L_Bel'. lbel_voices :: L_Bel a -> [Voice] lbel_voices =-    sortBy (compare `on` reverse) .+    sortOn reverse .     nub .     map (\((_,_,v),_) -> voice_normalise v)  -- | The duration of 'L_Bel'. lbel_duration :: L_Bel a -> Time lbel_duration b =-    let l = last (groupBy ((==) `on` lterm_time) b)+    let l = last (T.group_on lterm_time b)     in maximum (map (\((st,tm,_),_) -> st + recip tm) l)  -- | Locate an 'L_Term' that is active at the indicated 'Time' and in@@ -448,10 +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 @@ -488,9 +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@@ -499,87 +376,85 @@  -- * 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_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 positive 'Integer'.+-- | Parse non-negative 'Integer'. ----- > P.parse p_integer "" "3"-p_integer :: P Integer-p_integer = liftM read (P.many1 P.digit)+-- > P.parse p_non_negative_integer "" "3"+p_non_negative_integer :: T.P Integer+p_non_negative_integer = fmap read (P.many1 P.digit) --- | Parse positive 'Rational'.+-- | Parse non-negative 'Rational'. ----- > P.parse (p_rational `P.sepBy` (P.char ',')) "" "3%5,2/3"-p_rational :: P Rational-p_rational = do-  n <- p_integer+-- > P.parse (p_non_negative_rational `P.sepBy` (P.char ',')) "" "3%5,2/3"+p_non_negative_rational :: T.P Rational+p_non_negative_rational = do+  n <- p_non_negative_integer   _ <- P.oneOf "%/"-  d <- p_integer+  d <- p_non_negative_integer   return (n % d) --- | Parse positive 'Double'.+-- | Parse non-negative 'Double'. ----- > P.parse p_double "" "3.5"--- > P.parse (p_double `P.sepBy` (P.char ',')) "" "3.5,7.2,1.0"-p_double :: P Double-p_double = do+-- > 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 :: T.P Double+p_non_negative_double = do   a <- P.many1 P.digit   _ <- P.char '.'   b <- P.many1 P.digit   return (read (a ++ "." ++ b)) --- | Parse positive number as 'Rational'.+-- | Parse non-negative number as 'Rational'. ----- > P.parse (p_number `P.sepBy` (P.char ',')) "" "7%2,3.5,3"-p_number :: P Rational-p_number = P.choice [P.try p_rational-                    ,P.try (liftM toRational p_double)-                    ,P.try (liftM toRational p_integer)]+-- > P.parse (p_non_negative_number `P.sepBy` (P.char ',')) "" "7%2,3.5,3"+p_non_negative_number :: T.P Rational+p_non_negative_number =+    P.choice [P.try p_non_negative_rational+             ,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_number+  n <- p_non_negative_number   let n' = case op of              '*' -> n              '/' -> recip n@@ -587,50 +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 
@@ -1,43 +0,0 @@-module Music.Theory.Time.Notation where--import Text.Printf {- base -}---- | Fractional seconds.-type FSEC = Double---- | Minutes, seconds as @(min,sec)@-type MINSEC = (Int,Int)---- | Minutes, seconds, centi-seconds as @(min,sec,csec)@-type MINCSEC = (Int,Int,Int)---- | 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 tm = round tm `divMod` 60---- | '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---- | Fractional seconds to @(min,sec,csec)@.------ > 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) = tm' `divMod` 60-        cs = round ((tm - fromIntegral tm') * 100)-    in (m,s,cs)---- | 'MINCSEC' pretty printer.------ > map (mincsec_pp . fsec_to_mincsec) [1,4/3] == ["00:01.00","00:01.33"]-mincsec_pp :: MINCSEC -> String-mincsec_pp (m,s,cs) = printf "%02d:%02d.%02d" m s cs--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.Monoid {- 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.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--- an /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 a /empty/--- value.  To indicate the duration of the final value /a/ must have--- an /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)@@ -63,30 +77,49 @@     (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 (+)) +-- | Start time of sequence.+--+-- > wseq_start [((1,2),'a')] == 1+-- > wseq_start [] == 0+wseq_start :: Num t => Wseq t a -> t+wseq_start = fst . wseq_tspan++-- | End time of sequence.+--+-- > wseq_end [((1,2),'a')] == 3+-- > wseq_end (useq_to_wseq 0 (1,"linear")) == 6+wseq_end :: Num t => Wseq t a -> t+wseq_end = snd . wseq_tspan+ -- * 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@@ -94,23 +127,62 @@  -- * Window --- | Keep only elements in the indicated temporal window.+-- | 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)++-- | Keep only elements that are entirely contained within the indicated+-- temporal window, which is inclusive at the left & right+-- 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..10] (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 wseq_twindow (w0,w1) =     let f (st,du) = w0 <= st && (st + du) <= w1-    in wseq_tfilter f+    in wseq_tfilter f . wseq_until w1 +-- | Select nodes that are active at indicated time, comparison is+-- inclusive at left and exclusive at right.  Halts processing at end+-- of window.+--+-- > let sq = [((1,1),'a'),((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+wseq_at sq tm =+    let sel ((t0,t1),_) = t0 <= tm && tm < (t0 + t1)+        end ((t0,_),_) = t0 <= tm+    in filter sel (takeWhile end sq)++-- | Select nodes that are active within the indicated window, comparison is+-- inclusive at left and exclusive at right.  Halts processing at end+-- of window.+--+-- > let sq = [((0,2),'a'),((0,4),'b'),((2,4),'c')]+-- > 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+wseq_at_window sq (w0,w1) =+    let f (t0,t1) t = t0 <= t && t < t1+        g (st,du) = let w = (st,st + du) in f w w0 || f w w1+    in wseq_tfilter g (wseq_until w1 sq)+ -- * 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 = (++) @@ -140,11 +212,28 @@         g (t,p) (_,q) = (t,f p q)     in T.merge_by_resolve g cmp +-- | Compare first by start time, then by duration.+w_compare :: Ord t => ((t,t),a) -> ((t,t),a) -> Ordering+w_compare ((t1,d1),_) ((t2,d2),_) =+    case compare t1 t2 of+      EQ -> compare d1 d2+      r -> r++-- | Merge considering only start times. wseq_merge :: Ord t => Wseq t a -> Wseq t a -> Wseq t a wseq_merge = O.mergeBy (compare `on` (fst . fst)) +-- | Merge set considering both start times & durations.+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. tseq_lookup_window_by :: (t -> t -> Ordering) -> Tseq t e -> t -> (Maybe (t,e),Maybe (t,e)) tseq_lookup_window_by cmp =     let recur l sq t =@@ -173,13 +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@@ -208,41 +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 =@@ -256,6 +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 (==) @@ -263,11 +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 @@ -275,21 +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-        from_map = sortBy (compare `on` fst) .-                   map (\(v,l) -> (v,reverse l)) .-                   M.toList-    in from_map (foldl assign M.empty sq)+    let assign m (t,a) = Map.insertWith (++) (voice a) [(t,a)] m+        from_map = sortOn fst .+                   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 @@ -317,16 +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@@ -336,12 +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@@ -358,6 +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 @@ -366,7 +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@@ -378,23 +481,27 @@ -- | 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")] tseq_group :: (Eq t,Num t) => Tseq t a -> Tseq t [a] tseq_group = group_f (==)  -- | 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)@@ -412,6 +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@@ -430,127 +541,284 @@                                    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 --- | Transform 'Wseq' to 'Tseq' by discaring durations.+-- | Sort 'Wseq' by start time, 'Wseq' ought never to be out of+-- order.+--+-- > wseq_sort [((3,1),'a'),((1,3),'b')] == [((1,3),'b'),((3,1),'a')]+wseq_sort :: Ord t => Wseq t a -> Wseq t a+wseq_sort = sortBy (compare `on` (fst . fst))++-- | 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 --- | Edit durations to ensure that notes don't overlap.  If the same--- note is played simultaneously delete shorter note.  If a note--- extends into a later note shorten duration (apply /d_fn/ to iot).-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 d_fn =-    let go sq =-            case sq of-              [] -> []-              ((t,d),a):sq' ->-                  case find (eq_fn a . snd) sq' of-                      Nothing -> ((t,d),a) : go sq'-                      Just ((t',d'),a') ->-                          if t == t'-                          then if d <= d'-                               then -- delete LHS-                                   go sq'-                               else -- delete RHS-                                   ((t,d),a) :-                                   go (delete ((t',d'),a') sq')-                          else if t' < t + d-                               then ((t,d_fn (t' - t)),a) : go sq'-                               else ((t,d),a) : go sq'-    in go+-- | 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))) +-- | 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+          e0:sq' -> wseq_find_overlap_1 eq_fn e0 sq' || recur sq'+  in recur++{- | Remove overlaps by deleting any overlapping nodes.++> 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')]+> wseq_has_overlaps (==) sq == True+> 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_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_remove_overlap_rw_1 eq_f dur_fn h sq' of+              Nothing -> h : recur sq'+              Just sq'' -> recur sq''+    in recur+ -- | Unjoin elements (assign equal time stamps to all elements). 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 --- * On/Off+-- | Shift (displace) onset times by /i/.+--+-- > wseq_shift 3 [((1,2),'a')] == [((4,2),'a')]+wseq_shift :: Num t => t -> Wseq t a -> Wseq t a+wseq_shift i = wseq_tmap_st (+ i) --- | Container for values that have /on/ and /off/ modes.-data On_Off a = On a | Off a deriving (Eq,Show)+-- | Shift q to end of p and append.+--+-- > wseq_append [((1,2),'a')] [((1,2),'b')] == [((1,2),'a'),((4,2),'b')]+wseq_append :: Num t => Wseq t a -> Wseq t a -> Wseq t a+wseq_append p q = p ++ wseq_shift (wseq_end p) q --- | Structural comparison at 'On_Off', 'On' compares less than 'Off'.-cmp_on_off :: On_Off a -> On_Off b -> Ordering-cmp_on_off p q =+-- | 'foldl1' of 'wseq_append'+--+-- > wseq_concat [[((1,2),'a')],[((1,2),'b')]] == [((1,2),'a'),((4,2),'b')]+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.+data Begin_End a = Begin a | End a deriving (Eq,Show)++-- | Functor instance.+begin_end_map :: (t -> u) -> Begin_End t -> Begin_End u+begin_end_map f x =+    case x of+      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 =     case (p,q) of-      (On _,Off _) -> LT-      (On _,On _) -> EQ-      (Off _,Off _) -> EQ-      (Off _,On _) -> GT+      (Begin _,End _) -> LT+      (Begin _,Begin _) -> EQ+      (End _,End _) -> EQ+      (End _,Begin _) -> GT +--instance Eq t => Ord (Begin_End t) where compare = cmp_begin_end+ -- | Translate container types.-either_to_on_off :: Either a a -> On_Off a-either_to_on_off p =+either_to_begin_end :: Either a a -> Begin_End a+either_to_begin_end p =     case p of-      Left a -> On a-      Right a -> Off a+      Left a -> Begin a+      Right a -> End a  -- | Translate container types.-on_off_to_either :: On_Off a -> Either a a-on_off_to_either p =+begin_end_to_either :: Begin_End a -> Either a a+begin_end_to_either p =     case p of-      On a -> Left a-      Off a -> Right a+      Begin a -> Left a+      End a -> Right a --- | Convert 'Wseq' to 'Tseq' transforming elements to 'On' and 'Off'--- parts.  When merging, /off/ elements precede /on/ elements at equal--- times.------ > let {sq = [((0,5),'a'),((2,2),'b')]--- >     ;r = [(0,On 'a'),(2,On 'b'),(4,Off 'b'),(5,Off 'a')]}--- > in wseq_on_off sq == r------ > let {sq = [((0,1),'a'),((1,1),'b'),((2,1),'c')]--- >     ;r = [(0,On 'a'),(1,Off 'a')--- >          ,(1,On 'b'),(2,Off 'b')--- >          ,(2,On 'c'),(3,Off 'c')]}--- > in wseq_on_off sq == r-wseq_on_off :: (Num t, Ord t) => Wseq t a -> Tseq t (On_Off a)-wseq_on_off sq =-    let f ((t,d),a) = [(t,On a),(t + d,Off a)]+-- | Equivalent to 'partitionEithers'.+begin_end_partition :: [Begin_End a] -> ([a],[a])+begin_end_partition =+  let f e (p,q) = case e of+                    Begin x -> (x:p,q)+                    End x -> (p,x:q)+  in foldr f ([],[])++-- | 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 -> deleteBy eq_f x st++-- | '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.ordering_invert .: cmp_on_off) e (g l')+              e:l' -> tseq_merge_by (\x -> T.ord_invert . cmp_begin_end x) e (g l')     in g (map f sq) --- | 'on_off_to_either' of 'wseq_on_off'.-wseq_on_off_either :: (Num t, Ord t) => Wseq t a -> Tseq t (Either a a)-wseq_on_off_either = tseq_map on_off_to_either . wseq_on_off+-- | 'begin_end_to_either' of 'wseq_begin_end'.+wseq_begin_end_either :: (Num t, Ord t) => Wseq t a -> Tseq t (Either a a)+wseq_begin_end_either = tseq_map begin_end_to_either . wseq_begin_end --- | Variant that applies /on/ and /off/ functions to nodes.+-- | 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_on_off_f Data.Char.toUpper id sq == r-wseq_on_off_f :: (Ord t,Num t) => (a -> b) -> (a -> b) -> Wseq t a -> Tseq t b-wseq_on_off_f f g = tseq_map (either f g) . wseq_on_off_either+-- > 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 --- | Inverse of 'wseq_on_off' given a predicate function for locating--- the /off/ node of an /on/ node.+-- | 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 =+  let f st (t,x) =+            let (b,e) = begin_end_partition x+                st' = foldl begin_end_track st x+            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) =+            let g st' = (st',(t,st'))+            in g (foldl begin_end_track st e)+    in snd . mapAccumL f []++-- | The transition sequence of /active/ elements. ----- > let {sq = [(0,On 'a'),(2,On 'b'),(4,Off 'b'),(5,Off 'a')]--- >     ;r = [((0,5),'a'),((2,2),'b')]}--- > in tseq_on_off_to_wseq (==) sq == r-tseq_on_off_to_wseq :: Num t => (a -> a -> Bool) -> Tseq t (On_Off a) -> Wseq t a-tseq_on_off_to_wseq cmp =+-- > let w = [((0,3),'a'),((1,2),'b'),((2,1),'c'),((3,3),'d')]+-- > wseq_accumulate w == [(0,"a"),(1,"ba"),(2,"cba"),(3,"d"),(6,"")]+wseq_accumulate :: (Eq a,Ord t,Num t) => Wseq t a -> Tseq t [a]+wseq_accumulate = tseq_accumulate . tseq_group . wseq_begin_end++-- | 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')]+-- > 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 =             case e of-              Off x' -> cmp x x'+              End x' -> cmp x x'               _ -> False         f e r = case seq_find (cmp' e) r of-                        Nothing -> error "tseq_on_off_to_wseq: no matching off?"+                        Nothing -> error "tseq_begin_end_to_wseq: no matching end?"                         Just (t,_) -> t         go sq = case sq of                   [] -> []-                  (_,Off _) : sq' -> go sq'-                  (t,On e) : sq' -> let t' = f e sq' in ((t,t' - t),e) : go sq'+                  (_,End _) : sq' -> go sq'+                  (t,Begin e) : sq' -> let t' = f e sq' in ((t,t' - t),e) : go sq'     in go  -- * Interop@@ -558,35 +826,48 @@ useq_to_dseq :: Useq t a -> Dseq t a useq_to_dseq (t,e) = zip (repeat t) e +useq_to_wseq :: Num t => t -> Useq t a -> Wseq t a+useq_to_wseq t0 = dseq_to_wseq t0 . useq_to_dseq+ -- | The conversion requires a start time and a /nil/ value used as an -- /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/ is take as the last element of the--- sequence.+-- | 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@@ -595,13 +876,14 @@     in wseq_zip t d a  -- | The last element of 'Tseq' is required to be an /eof/ marker that--- has no duration and is not represented in the 'Dseq'.+-- has no duration and is not represented in the 'Dseq'.  A 'nil'+-- 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@@ -610,16 +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@@ -628,7 +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@@ -639,7 +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@@ -651,16 +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,_),_)) =@@ -675,13 +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 =@@ -690,8 +1010,33 @@             in (z',zip r el)     in mapAccumL f --- * Type specialised map+-- * Cycle +-- | 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 (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_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_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 maps+ dseq_tmap :: (t -> t') -> Dseq t a -> Dseq t' a dseq_tmap = seq_tmap @@ -758,3 +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
@@ -1,11 +1,12 @@ -- | Time Signatures. module Music.Theory.Time_Signature where +import Data.Function {- base -} import Data.Ratio {- base -}  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.@@ -37,6 +38,7 @@       (1,1) -> [whole_note]       (2,2) -> [whole_note]       (4,4) -> [whole_note]+      (8,8) -> [whole_note]       (5,4) -> [whole_note,quarter_note]       (3,2) -> [dotted_whole_note]       (6,4) -> [dotted_whole_note]@@ -47,22 +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 --- | 'Time_Signature' derived from whole note duration in 'RQ' form.+-- | '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. -- -- > map rq_to_ts [4,3/2,7/4,6] == [(4,4),(3,8),(7,16),(6,4)]-rq_to_ts :: Rational -> Time_Signature+rq_to_ts :: Rq -> Time_Signature rq_to_ts rq =     let n = numerator rq         d = denominator rq * 4@@ -74,7 +80,8 @@ -- > ts_divisions (3,8) == [1/2,1/2,1/2] -- > ts_divisions (2,2) == [2,2] -- > ts_divisions (1,1) == [4]-ts_divisions :: Time_Signature -> [RQ]+-- > ts_divisions (7,4) == [1,1,1,1,1,1,1]+ts_divisions :: Time_Signature -> [Rq] ts_divisions (i,j) =     let k = fromIntegral i     in replicate k (recip (j % 4))@@ -116,23 +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)@@ -142,7 +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@@ -151,11 +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@@ -164,7 +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)@@ -174,14 +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)@@ -191,5 +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
@@ -1,304 +1,206 @@ -- | Tuning theory module Music.Theory.Tuning where -import Data.Fixed {- base -}-import Data.List {- base -}-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.Pitch as T {- hmt -}---- * Types---- | An approximation of a ratio.-type Approximate_Ratio = Double---- | A real valued division of a semi-tone into one hundred parts, and--- hence of the octave into @1200@ parts.-type Cents = Double+import qualified Music.Theory.Math as T {- hmt -}+import qualified Music.Theory.Ord as T {- hmt -} --- | A tuning specified 'Either' as a sequence of exact ratios, or as--- a sequence of possibly inexact 'Cents'.-data Tuning = Tuning {ratios_or_cents :: Either [Rational] [Cents]-                     ,octave_ratio :: Rational}-              deriving (Eq,Show)+-- * Math/Floating --- | Divisions of octave.+-- | Fractional /midi/ note number to cycles per second, given (k0,f0) pair. ----- > divisions ditone == 12-divisions :: Tuning -> Int-divisions = either length length . ratios_or_cents---- | 'Maybe' exact ratios of 'Tuning'.-ratios :: Tuning -> Maybe [Rational]-ratios = T.fromLeft . ratios_or_cents---- | 'error'ing variant.-ratios_err :: Tuning -> [Rational]-ratios_err = fromMaybe (error "ratios") . ratios---- | Possibly inexact 'Cents' of tuning.-cents :: Tuning -> [Cents]-cents = either (map ratio_to_cents) id . ratios_or_cents---- | 'map' 'round' '.' 'cents'.-cents_i :: Integral i => Tuning -> [i]-cents_i = map round . cents+-- > 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))) --- | Variant of 'cents' that includes octave at right.-cents_octave :: Tuning -> [Cents]-cents_octave t = cents t ++ [ratio_to_cents (octave_ratio t)]+-- | 'fmidi_to_cps_k0' with k0 of 69.+--+-- > 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) --- | Convert from interval in cents to frequency ratio.+-- | 'fmidi_to_cps_k0' (69,440) ----- > 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 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) --- | Possibly inexact 'Approximate_Ratio's of tuning.-approximate_ratios :: Tuning -> [Approximate_Ratio]-approximate_ratios =-    either (map approximate_ratio) (map cents_to_ratio) .-    ratios_or_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 --- | Cyclic form, taking into consideration 'octave_ratio'.-approximate_ratios_cyclic :: Tuning -> [Approximate_Ratio]-approximate_ratios_cyclic t =-    let r = approximate_ratios t-        m = realToFrac (octave_ratio t)-        g = iterate (* m) 1-        f n = map (* n) r-    in concatMap f g+-- | '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) --- | 'Maybe' exact ratios reconstructed from possibly inexact 'Cents'--- of 'Tuning'.+-- | Convert from interval in cents to frequency ratio. ----- > 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]--- > in reconstructed_ratios 1e-2 werckmeister_iii == Just r-reconstructed_ratios :: Double -> Tuning -> Maybe [Rational]-reconstructed_ratios epsilon =-    fmap (map (reconstructed_ratio epsilon)) .-    T.fromRight .-    ratios_or_cents+-- > 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)  -- | Convert from a 'Floating' ratio to /cents/. -- -- > let r = [0,498,702,1200]--- > in map (round . fratio_to_cents) [1,4/3,3/2,2] == r+-- > 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 --- | Type specialised 'fratio_to_cents'.-approximate_ratio_to_cents :: Approximate_Ratio -> Cents-approximate_ratio_to_cents = fratio_to_cents---- | Type specialised 'fromRational'.-approximate_ratio :: Rational -> Approximate_Ratio-approximate_ratio = fromRational---- | 'approximate_ratio_to_cents' '.' 'approximate_ratio'.-ratio_to_cents :: Rational -> Cents-ratio_to_cents = approximate_ratio_to_cents . approximate_ratio---- | Construct an exact 'Rational' that approximates 'Cents' to within--- /epsilon/.------ > map (reconstructed_ratio 1e-5) [0,700,1200] == [1,442/295,2]------ > ratio_to_cents (442/295) == 699.9976981706734-reconstructed_ratio :: Double -> Cents -> Rational-reconstructed_ratio epsilon c = approxRational (cents_to_ratio c) epsilon- -- | Frequency /n/ cents from /f/. ----- > import Music.Theory.Pitch+-- > 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_ratio+cps_shift_cents f = (* f) . cents_to_fratio --- | Interval in /cents/ from /p/ to /q/, ie. 'ratio_to_cents' of /p/--- '/' /q/.+-- | Interval in /cents/ from /p/ to /q/, ie. 'ratio_to_cents' of /p/ '/' /q/. ----- > cps_difference_cents 440 (octpc_to_cps (5,2)) == 500+-- > map (round . cps_difference_cents 440) [412,415,octpc_to_cps (5,2)] == [-114,-101,500] -- -- > 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 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) --- * Commas+-- * Math/Ratio --- | The Syntonic comma.+-- | Convert a (signed) number of octaves difference of given ratio to a ratio. ----- > syntonic_comma == 81/80-syntonic_comma :: Rational-syntonic_comma = 81 % 80+-- > 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 T.recur_n n (* r) 1 else T.recur_n (negate n) (/ r) 1 --- | The Pythagorean comma.+-- | 'ratio_to_cents' rounded to nearest multiple of 100, modulo 12. ----- > pythagorean_comma == 3^12 / 2^19-pythagorean_comma :: Rational-pythagorean_comma = 531441 / 524288+-- > 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 --- | Mercators comma.+-- | 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. ----- > mercators_comma == 3^53 / 2^84-mercators_comma :: Rational-mercators_comma = 19383245667680019896796723 / 19342813113834066795298816+-- > 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" --- | Calculate /n/th root of /x/.+-- | Fold ratio until within an octave, ie. @1@ '<' /n/ '<=' @2@.+--   It is an error if /n/ is less than or equal to zero. ----- > 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))+-- > 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 --- | 12-tone equal temperament comma (ie. 12th root of 2).+-- | In /n/ is greater than zero, 'fold_ratio_to_octave_err', else 'Nothing'. ----- > 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+-- > 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) --- | 12-tone equal temperament.+-- | 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/. ----- > 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)+-- > 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)) --- | 72-tone equal temperament.+-- | 'ratio_interval_class_by' 'ratio_nd_sum' ----- > 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)+-- > 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 --- * Harmonic series+-- * Types --- | Raise or lower the frequency /q/ by octaves until it is in the--- octave starting at /p/.------ > fold_cps_to_octave_of 55 392 == 98-fold_cps_to_octave_of :: (Ord a, Fractional a) => a -> a -> a-fold_cps_to_octave_of p =-    let f q = if q > p * 2 then f (q / 2) else if q < p then f (q * 2) else q-    in f+-- | An approximation of a ratio.+type Approximate_Ratio = Double --- | Harmonic series on /n/.-harmonic_series_cps :: (Num t, Enum t) => t -> [t]-harmonic_series_cps n = [n,n * 2 ..]+-- | Type specialised 'fromRational'.+approximate_ratio :: Rational -> Approximate_Ratio+approximate_ratio = fromRational --- | /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+-- | A real valued division of a semi-tone into one hundred parts, and+-- hence of the octave into @1200@ parts.+type Cents = Double --- | Sub-harmonic series on /n/.-subharmonic_series_cps :: (Fractional t,Enum t) => t -> [t]-subharmonic_series_cps n = map (* n) (map recip [1..])+-- | Integral cents value.+type Cents_I = Int --- | /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+-- | Type specialised 'fratio_to_cents'.+approximate_ratio_to_cents :: Approximate_Ratio -> Cents+approximate_ratio_to_cents = fratio_to_cents --- | /n/th partial of /f1/, ie. one indexed.+-- | 'approximate_ratio_to_cents' '.' 'approximate_ratio'. ----- > 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)+-- > 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 --- | Fold ratio until within an octave, ie. @1@ '<' /n/ '<=' @2@.+-- | Construct an exact 'Rational' that approximates 'Cents' to within /epsilon/. ----- > map fold_ratio_to_octave [2/3,3/4] == [4/3,3/2]-fold_ratio_to_octave :: Integral i => Ratio i -> Ratio i-fold_ratio_to_octave n =-    if n >= 2-    then fold_ratio_to_octave (n / 2)-    else if n < 1-         then fold_ratio_to_octave (n * 2)-         else n---- | 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 (reconstructed_ratio 1e-5) [0,700,1200,1800] == [1,442/295,2,577/204] ----- > map ratio_interval_class [2/3,3/2,3/4,4/3] == [3/2,3/2,3/2,3/2]-ratio_interval_class :: Integral i => Ratio i -> Ratio i-ratio_interval_class i =-    let f = fold_ratio_to_octave-    in max (f i) (f (recip i))+-- > ratio_to_cents (442/295) == 699.9976981706735+reconstructed_ratio :: Double -> Cents -> Rational+reconstructed_ratio epsilon c = approxRational (cents_to_fratio c) epsilon --- | 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 = fold_cps_to_octave_of f1 (partial f1 k)-    in harmonic_series_cps f0+-- * Commas --- | Harmonic series to /n/th harmonic (folded).+-- | The Syntonic comma. ----- > harmonic_series_folded 17 == [1,17/16,9/8,5/4,11/8,3/2,13/8,7/4,15/8]+-- > syntonic_comma == 81/80+syntonic_comma :: Rational+syntonic_comma = 81 % 80++-- | The Pythagorean comma. ----- > let r = [0,105,204,386,551,702,841,969,1088]--- > in map (round . ratio_to_cents) (harmonic_series_folded 17) == r-harmonic_series_folded :: Integer -> [Rational]-harmonic_series_folded n =-    nub (sort (map fold_ratio_to_octave [1 .. n%1]))+-- > pythagorean_comma == 3^12 / 2^19+pythagorean_comma :: Rational+pythagorean_comma = 531441 / 524288 --- | 'ratio_to_cents' variant of 'harmonic_series_folded'.+-- | Mercators comma. ----- > map round (harmonic_series_folded_c 21) == [0,105,204,298,386,471,551,702,841,969,1088]-harmonic_series_folded_c :: Integer -> [Cents]-harmonic_series_folded_c = map ratio_to_cents . harmonic_series_folded+-- > mercators_comma == 3^53 / 2^84+mercators_comma :: Rational+mercators_comma = 19383245667680019896796723 / 19342813113834066795298816 --- | @12@-tone tuning of first @21@ elements of the harmonic series.+-- | 12-tone equal temperament comma (ie. 12th root of 2). ----- > 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 = Tuning (Left (harmonic_series_folded 21)) 2+-- > twelve_tone_equal_temperament_comma == 1.0594630943592953+twelve_tone_equal_temperament_comma :: (Floating a,Eq a) => a+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@@ -307,7 +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)@.@@ -315,7 +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@@ -324,7 +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@.@@ -355,41 +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+-- * Savart --- | (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)+-- | Felix Savart (1791-1841), the ratio of 10:1 is assigned a value of 1000 savarts.+type Savarts = Double --- | 'Midi_Tuning_F' for 'D12_Midi_Tuning'.+-- | Ratio to savarts. ----- > import Music.Theory.Tuning.Gann--- > let f = d12_midi_tuning_f (la_monte_young,-74.7,-3)--- > octpc_to_midi (-1,11) == 11--- > map (round . midi_detune_to_cps . f) [62,63,69] == [293,298,440]-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 (-) (cents t) [0,100 .. 1200]-    in (n,(dt `at` pc) + c_diff)+-- > 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 --- | (t,f0,k) where t=tuning, f0=fundamental frequency, k=midi note--- number for f0, n=gamut-type CPS_Midi_Tuning = (Tuning,Double,Int,Int)+-- | Savarts to ratio.+--+-- > 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) --- | 'Midi_Tuning_F' for 'CPS_Midi_Tuning'.-cps_midi_tuning_f :: CPS_Midi_Tuning -> Midi_Tuning_F-cps_midi_tuning_f (t,f0,k,g) n =-    let r = approximate_ratios_cyclic t-        m = take g (map (T.cps_to_midi_detune . (* f0)) r)-    in m `at` (n - k)+-- | Savarts to cents.+--+-- > savarts_to_cents 1 == 3.9863137138648352+savarts_to_cents :: Floating a => a -> a+savarts_to_cents s = s * (6 / (5 * logBase 10 2)) --- Local Variables:--- truncate-lines:t--- End:+-- | Cents to savarts.+--+-- > 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.hs 
@@ -1,25 +0,0 @@--- | Bill Alves.-module Music.Theory.Tuning.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>------ > 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/Alves_1997.hs view
@@ -3,48 +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]+{- | 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]+{- | 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 2,3,4,6,7/ tuning.+-- | 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 barang/ tuning.+-- | 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 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 
@@ -1,248 +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 Music.Theory.List {- hmt -}-import Music.Theory.Pitch {- hmt -}-import Music.Theory.Pitch.Note {- hmt -}-import Music.Theory.Pitch.Spelling {- hmt -}-import Music.Theory.Tuning {- hmt -}---- | 'octpc_to_pitch' and 'octpc_to_cps'.-octpc_to_pitch_cps :: (Floating n) => OctPC -> (Pitch,n)-octpc_to_pitch_cps x = (octpc_to_pitch pc_spell_ks x,octpc_to_cps x)---- | 12-tone equal temperament table equating 'Pitch' and frequency--- over range of human hearing, where @A4@ = @440@hz.------ > length tbl_12et == 132--- > let min_max l = (minimum l,maximum l)--- > min_max (map (round . snd) tbl_12et) == (16,31609)-tbl_12et :: [(Pitch,Double)]-tbl_12et =-    let z = [(o,pc) | o <- [0..10], pc <- [0..11]]-    in map octpc_to_pitch_cps z---- | 24-tone equal temperament variant of 'tbl_12et'.------ > length tbl_24et == 264--- > min_max (map (round . snd) tbl_24et) == (16,32535)-tbl_24et :: [(Pitch,Double)]-tbl_24et =-    let f x = let p = fmidi_to_pitch pc_spell_ks x-                  p' = pitch_rewrite_threequarter_alteration p-              in (p',fmidi_to_cps x)-    in map f [12,12.5 .. 143.5]---- | Given an @ET@ table (or like) find bounds of frequency.------ > let r = Just (at_pair 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 tbl =-    let f (_,p) = compare p-    in find_bounds True f tbl---- | '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'.-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',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' 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',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'-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)---- | Exract '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) =-    let p2' = pitch_in_octave_nearest p1 p2-    in (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/Gann.hs 
@@ -1,141 +0,0 @@--- | Kyle Gann.-module Music.Theory.Tuning.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-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]-pietro_aaron_1523 :: Tuning-pietro_aaron_1523 = Tuning (Right pietro_aaron_1523_c) 2---- | Andreas Werckmeister (1645-1706), <http://www.kylegann.com/histune.html>.-werckmeister_iii_c :: [Cents]-werckmeister_iii_c =-    [0,90.225-    ,192.18,294.135-    ,390.225-    ,498.045,588.27-    ,696.09,792.18-    ,888.27,996.09-    ,1092.18]---- | 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]-thomas_young_1799 :: Tuning-thomas_young_1799 = Tuning (Right thomas_young_1799_c) 2---- | Ratios for 'zarlino'.-zarlino_r :: [Rational]-zarlino_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 == 16--- > cents_i zarlino == [0,71,182,204,294,316,386,498,569,590,702,773,884,996,1018,1088]-zarlino :: Tuning-zarlino = Tuning (Left zarlino_r) 2---- * 20th Century---- | Ratios for 'la_monte_young'.------ > let c = [0,177,204,240,471,444,675,702,738,969,942,1173]--- > in map (round . ratio_to_cents) la_monte_young_r == c-la_monte_young_r :: [Rational]-la_monte_young_r =-    [1,567/512-    ,9/8,147/128-    ,21/16-    ,1323/1024,189/128-    ,3/2,49/32-    ,7/4,441/256-    ,63/32]---- | La Monte Young's \"The Well-Tuned Piano\", see--- <http://www.kylegann.com/wtp.html>.------ > cents_i la_monte_young == [0,177,204,240,471,444,675,702,738,969,942,1173]-la_monte_young :: Tuning-la_monte_young = Tuning (Left la_monte_young_r) 2---- | Ratios for 'ben_johnston'.------ > let c = [0,105,204,298,386,471,551,702,841,906,969,1088]--- > in map (round . ratio_to_cents) ben_johnston_r == c-ben_johnston_r :: [Rational]-ben_johnston_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 == [0,105,204,298,386,471,551,702,841,906,969,1088]-ben_johnston :: Tuning-ben_johnston = Tuning (Left ben_johnston_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-gann_superparticular :: Tuning-gann_superparticular = Tuning (Left gann_superparticular_r) 2
+ Music/Theory/Tuning/Gann_1993.hs view
@@ -0,0 +1,141 @@+-- | Kyle Gann. "La Monte Young's The Well-Tuned Piano".+-- /Perspectives of New Music/, 31(1):134--162, Winter 1993.+module Music.Theory.Tuning.Gann_1993 where++import Data.List {- base -}+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.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.++> let c = [0,177,204,240,471,444,675,702,738,969,942,1173]+> in map (round . T.ratio_to_cents) lmy_wtp_r == c++-}+lmy_wtp_r :: [Rational]+lmy_wtp_r =+    [1,567/512+    ,9/8,147/128+    ,21/16+    ,1323/1024,189/128+    ,3/2,49/32+    ,7/4,441/256+    ,63/32]++-- | The pitch-class of the key associated with each ratio of the tuning.+--+-- > mapMaybe lmy_wtp_ratio_to_pc [1,1323/1024,7/4] == [3,8,0]+lmy_wtp_ratio_to_pc :: Rational -> Maybe T.PitchClass+lmy_wtp_ratio_to_pc r = fmap (T.mod12 . (+ 3)) (elemIndex r lmy_wtp_r)++lmy_wtp_ratio_to_pc_err :: Rational -> T.PitchClass+lmy_wtp_ratio_to_pc_err = fromMaybe (error "lmy_wtp_ratio_to_pc") . lmy_wtp_ratio_to_pc++-- | The list of all non-unison ascending intervals possible in 'lmy_wtp_r'.+--+-- > length lmy_wtp_univ == 66+lmy_wtp_univ :: [(Rational,(T.PitchClass,T.PitchClass))]+lmy_wtp_univ =+    let f (p,q) = if p < q+                  then Just (T.ratio_interval_class (p/q)+                            ,(lmy_wtp_ratio_to_pc_err p+                             ,lmy_wtp_ratio_to_pc_err q))+                  else Nothing+    in mapMaybe f (T.all_pairs lmy_wtp_r lmy_wtp_r)++{- | Collated and sorted 'lmy_wtp_univ'.++> let r_cents_pp = show . round . T.ratio_to_cents++> import qualified Music.Theory.Math as T {- hmt -}++> let f (r,i) = concat [T.ratio_pp r," = "+>                      ,r_cents_pp r," = #"+>                      ,show (length i)," = "+>                      ,unwords (map show i)]++> putStrLn $ unlines $ map f lmy_wtp_uniq++3:2 = 702 = #9 = (3,10) (4,9) (5,10) (6,11) (6,1) (7,0) (7,2) (8,1) (9,2)+7:4 = 969 = #7 = (3,0) (5,2) (6,7) (7,10) (8,9) (11,0) (1,2)+7:6 = 267 = #6 = (4,8) (5,7) (6,2) (7,11) (9,1) (10,0)+9:7 = 435 = #4 = (4,1) (5,0) (6,9) (11,2)+9:8 = 204 = #6 = (3,5) (4,2) (6,8) (7,9) (11,1) (0,2)+21:16 = 471 = #6 = (3,7) (5,9) (6,0) (7,1) (8,2) (10,2)+27:14 = 1137 = #2 = (4,6) (9,11)+27:16 = 906 = #3 = (4,7) (8,11) (9,0)+49:32 = 738 = #3 = (3,11) (5,1) (6,10)+49:36 = 534 = #1 = (5,11)+63:32 = 1173 = #5 = (3,2) (4,5) (8,7) (9,10) (1,0)+49:48 = 36 = #2 = (5,6) (10,11)+81:56 = 639 = #1 = (4,11)+81:64 = 408 = #1 = (4,0)+147:128 = 240 = #3 = (3,6) (5,8) (10,1)+189:128 = 675 = #3 = (3,9) (4,10) (8,0)+441:256 = 942 = #2 = (3,1) (8,10)+567:512 = 177 = #1 = (3,4)+1323:1024 = 444 = #1 = (3,8)++-}+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)++{- | Gann, 1993, p.137.++> cents_i lmy_wtp == [0,177,204,240,471,444,675,702,738,969,942,1173]++> import Data.List {- base -}+> import Music.Theory.Tuning.Scala {- hmt -}+> scl <- scl_load "young-lm_piano"+> cents_i (scale_to_tuning 0.01 scl) == cents_i lmy_wtp++> let f = d12_midi_tuning_f (lmy_wtp,-74.7,-3)+> import qualified Music.Theory.Pitch as T+> T.octpc_to_midi (-1,11) == 11+> map (round . T.midi_detune_to_cps . f) [62,63,69] == [293,298,440]+> map (fmap round . T.midi_detune_normalise . f) [0 .. 127]++-}+lmy_wtp :: T.Tuning+lmy_wtp = T.Tuning (Left lmy_wtp_r) Nothing++-- | Ratios for 'lmy_wtp_1964.+lmy_wtp_1964_r :: [Rational]+lmy_wtp_1964_r =+    let n = [1,279,9,147,21,93,189,3,49,7,31,63]+        d = [1,256,8,128,16,64,128,2,32,4,16,32]+    in zipWith (/) n d++{- | La Monte Young's initial 1964 tuning for \"The Well-Tuned Piano\" (Gann, 1993, p.141).++> cents_i lmy_wtp_1964 == [0,149,204,240,471,647,675,702,738,969,1145,1173]++> import Music.Theory.Tuning.Scala+> let nm = ("young-lm_piano_1964","LaMonte Young's Well-Tuned Piano (1964)")+> let scl = tuning_to_scale nm lmy_wtp_1964+> putStr $ unlines $ scale_pp scl++-}+lmy_wtp_1964 :: T.Tuning+lmy_wtp_1964 = T.Tuning (Left lmy_wtp_1964_r) Nothing++{- | Euler diagram for 'lmy_wtp'.++let dir = "/home/rohan/sw/hmt/data/dot/"+let f = unlines . T.euler_plane_to_dot_rat (3,True)+writeFile (dir ++ "euler-wtp.dot") (f lmy_wtp_euler)++-}+lmy_wtp_euler :: T.Euler_Plane Rational+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+        ;(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
@@ -0,0 +1,85 @@+-- | Functions to load a tuning definition and transform it into a sparse tuning function.+module Music.Theory.Tuning.Load where++import System.Random {- random -}++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.+--+-- > load_cps_tbl "/home/rohan/dr.csv"+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+              [p,q] -> (read p,read q)+              _ -> error "load_cps_tbl"+  return (map f tbl)++-- | Load scala scl file as 'T.Tuning'.+load_tuning_scl :: String -> IO T.Tuning+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 :: 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 - 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 :: 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 :: 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)+    in fmap f (load_cps_tbl nm)++type Choose_f st t = [t] -> st-> (t,st)++-- | Randomly choose from elements in table, equal weighting.+default_choose_f :: RandomGen g => Choose_f g t+default_choose_f l g =+    let (i,g') = randomR (0,length l - 1) g+    in (l !! i,g')++-- | Load tuning table with stateful selection function for one-to-many entries.+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+                        [] -> (g,Nothing)+                        l -> let ((_,e),g') = choose_f l g+                             in (g',Just (from_cps e))+    in fmap f (load_cps_tbl nm)++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+      "d12" -> load_tuning_d12 opt+      "tbl" -> load_tuning_tbl opt+      _ -> error "cps|d12|tbl"++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)+      "d12" -> fmap T.lift_sparse_tuning_f (load_tuning_d12 opt)+      "tbl" -> load_tuning_tbl_st default_choose_f opt+      _ -> error "cps|d12|tbl"
Music/Theory/Tuning/Meyer_1929.hs view
@@ -3,8 +3,9 @@ -- University of Missouri, 1929.  p.22 module Music.Theory.Tuning.Meyer_1929 where -import Data.List-import Data.Ratio+import Data.List {- base -}+import Data.Ratio {- base -}+ import qualified Music.Theory.Tuning as T  -- | Odd numbers to /n/.@@ -17,17 +18,17 @@ -- -- > row 7 == [1,5/4,3/2,7/4] row :: Integral i => i -> [Ratio i]-row = sort . map T.fold_ratio_to_octave . odd_to . (% 1)+row = sort . map T.fold_ratio_to_octave_err . odd_to . (% 1)  -- | Generate initial column for /n/. -- -- > column 7 == [1,8/5,4/3,8/7] column :: Integral i => i -> [Ratio i]-column = map (T.fold_ratio_to_octave . recip) . row+column = map (T.fold_ratio_to_octave_err . recip) . row  -- | 'T.fold_to_octave' '.' '*'. in_oct_mul :: Integral i => Ratio i -> Ratio i -> Ratio i-in_oct_mul i j = T.fold_ratio_to_octave (i * j)+in_oct_mul i j = T.fold_ratio_to_octave_err (i * j)  -- | Given /row/ and /column/ generate matrix value at /(i,j)/. --@@ -94,13 +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/Microtonal_Synthesis.hs 
@@ -1,205 +0,0 @@--- | <http://www.microtonal-synthesis.com/scales.html>-module Music.Theory.Tuning.Microtonal_Synthesis where--import Music.Theory.Tuning {- hmt -}---- | Ratios for 'pythagorean'.------ > let c = [0,90,204,294,408,498,612,702,792,906,996,1110]--- > in map (round . ratio_to_cents) pythagorean_r == c-pythagorean_r :: [Rational]-pythagorean_r =-    [1,256/243 {- 2187/2048 -}-    ,9/8,32/27-    ,81/64-    ,4/3,729/512-    ,3/2,128/81 {- 6561/4096 -}-    ,27/16,16/9-    ,243/128]---- | Pythagorean tuning, <http://www.microtonal-synthesis.com/scale_pythagorean.html>.------ > divisions pythagorean == 12--- > cents_i pythagorean == [0,90,204,294,408,498,612,702,792,906,996,1110]-pythagorean :: Tuning-pythagorean = Tuning (Left pythagorean_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).------ > cents_i five_limit_tuning == [0,112,204,316,386,498,590,702,814,884,996,1088]-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>------ > cents_i septimal_tritone_just_intonation == [0,112,204,316,386,498,583,702,814,884,1018,1088]-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]-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]-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_reinhard == c-mayumi_reinhard_r :: [Rational]-mayumi_reinhard_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 Reinhard 13-limit Just Intonation scale,--- <http://www.microtonal-synthesis.com/scale_reinhard.html>.------ > cents_i mayumi_reinhard == [0,128,139,359,454,563,637,746,841,911,1072,1183]-mayumi_reinhard :: Tuning-mayumi_reinhard = Tuning (Left mayumi_reinhard_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-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]-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>-ben_johnston_25 :: Tuning-ben_johnston_25 = Tuning (Left ben_johnston_25_r) 2
+ 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
@@ -1,30 +1,47 @@--- | Larry Polansky. \"Psaltery (for Lou Harrison)\". Frog Peak Music,--- 1978.+-- | Larry Polansky. \"Psaltery (for Lou Harrison)\".+-- Frog Peak Music, 1978. module Music.Theory.Tuning.Polansky_1978 where -import Data.List-import qualified Music.Theory.Tuning as T+import Data.List {- base -} --- | Three interlocking harmonic series on 1:5:3, by Larry Polansky in--- \"Psaltery\".------ > import qualified Music.Theory.Tuning.Scala as T--- > let fn = "/home/rohan/opt/scala/scl/polansky_ps.scl"--- > s <- T.load fn--- > T.scale_pitch_representations s == (0,50)--- > 1 : Data.Either.rights (T.scale_pitches s) == psaltery-psaltery :: [Rational]-psaltery = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,5/4,5/2,15/4,5,25/4,15/2,35/4,10,45/4,25/2,55/4,15,65/4,35/2,75/4,20,85/4,3/2,3,9/2,6,15/2,9,21/2,12,27/2,15,33/2,18,39/2,21,45/2,24,51/2]+import qualified Music.Theory.Tuning as T {- hmt -}+import qualified Music.Theory.Tuning.Type as T {- hmt -} --- | 'T.fold_ratio_to_octave' of 'psaltery'.------ > length psaltery == 51 && length psaltery_o == 21--- > psaltery_o == [1,65/64,33/32,17/16,35/32,9/8,75/64,39/32--- >               ,5/4,21/16,85/64,11/8,45/32--- >               ,3/2,25/16,51/32,13/8,27/16,55/32,7/4,15/8]-psaltery_o :: [Rational]-psaltery_o = nub (sort (map T.fold_ratio_to_octave psaltery))+{- | Three interlocking harmonic series on 1:5:3, by Larry Polansky in \"Psaltery\". --- Local Variables:--- truncate-lines:t--- End:+> import qualified Music.Theory.Tuning.Scala as T+> scl <- T.scl_load "polansky_ps"+> T.pitch_representations (T.scale_pitches scl) == (0,50)+> 1 : Data.Either.rights (T.scale_pitches scl) == psaltery_r++-}+psaltery_r :: [Rational]+psaltery_r =+    let sq_at n = map (* n) [1..17]+    in concat [sq_at 1,sq_at (5/4),sq_at (3/2)]++{- | 'T.fold_ratio_to_octave'' of 'psaltery'.++> length psaltery_r == 51 && length psaltery_o_r == 21++> psaltery_o_r == [1,65/64,33/32,17/16,35/32,9/8,75/64,39/32+>                 ,5/4,21/16,85/64,11/8,45/32+>                 ,3/2,25/16,51/32,13/8,27/16,55/32,7/4,15/8]++-}+psaltery_o_r :: [Rational]+psaltery_o_r = nub (sort (map T.fold_ratio_to_octave_err psaltery_r))++{- | 'Tuning' derived from 'psaltery_o' with 'octave_ratio' of @2@.++> cents_i psaltery_o == [0,27,53,105,155,204,275,342,386,471,491,551,590+                        ,702,773,807,841,906,938,969,1088]++> let r = [0,1200,1902,2400,2786,3102,3369,3600,3804,3986,4151,4302,4441,4569,4688,4800,4905+          ,386,1586,2288,2786,3173,3488,3755,3986,4190,4373,4538,4688,4827,4955,5075,5186,5291+          ,702,1902,2604,3102,3488,3804,4071,4302,4506,4688,4853,5004,5142,5271,5390,5502]+> in cents_i (T.scale_tuning 0.01 scl) == r++-}+psaltery_o :: T.Tuning+psaltery_o = T.Tuning (Left psaltery_o_r) Nothing
Music/Theory/Tuning/Polansky_1984.hs view
@@ -2,9 +2,11 @@ -- Interval Sizes in Javanese Slendro\". /Balungan/, 1(2):9-11, 1984 module Music.Theory.Tuning.Polansky_1984 where -import Data.List-import Music.Theory.Tuning+import Data.List {- base -} +import qualified Music.Theory.List as T+import qualified Music.Theory.Tuning as T+ k_manisrenga :: Fractional n => [n] k_manisrenga = [219.5,266.5,227,233.5,258.5] @@ -100,12 +102,6 @@     let f n (i,j) = i <= n && n < j     in maybe "U" snd (find (f x . fst) i_categories) --- | Pad 'String' to right with spaces until at least /n/ characters.------ > map (pad 3) ["S","E-L"] == ["S  ","E-L"]-pad :: Int -> String -> String-pad n s = s ++ replicate (n - length s) ' '- -- | Pretty interval category table (pp. 10-11). -- -- > i_category_table k_set ==@@ -128,7 +124,7 @@ -- >  ,"S-E  S    L    E    L  " -- >  ,"S    S    E-L  L    L  "] i_category_table :: (Ord a, Num a) => [[a]] -> [String]-i_category_table = map (intercalate "  " .  map (pad 3 . i_category))+i_category_table = map (intercalate "  " .  map (T.pad_right ' ' 3 . i_category))  -- | Rational tuning derived from 'gm_averages', p.11. --@@ -148,5 +144,5 @@ -- -- > import Music.Theory.List -- > map round (d_dx polansky_1984_c) == [231,240,223,240,231]-polansky_1984_c :: [Cents]-polansky_1984_c = map ratio_to_cents polansky_1984_r+polansky_1984_c :: [T.Cents]+polansky_1984_c = map T.ratio_to_cents polansky_1984_r
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/Riley.hs 
@@ -1,18 +0,0 @@--- | Terry Riley.-module Music.Theory.Tuning.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]-riley_albion :: Tuning-riley_albion = Tuning (Left riley_albion_r) 2
+ Music/Theory/Tuning/Rosenboom_1979.hs view
@@ -0,0 +1,143 @@+-- | David Rosenboom, "In the Beginning: Etude I (Trombones)", 1979+--   <http://davidrosenboom.com/media/beginning-etude-i-trombones>+--+-- kw: subharmonics, difference tones+module Music.Theory.Tuning.Rosenboom_1979 where++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.Scala as Scala+import qualified Music.Theory.Tuple as T++t2_to_ratio :: (Integer,Integer) -> Rational+t2_to_ratio (n,d) = n % d++-- | Tuning, ratios for each octave.+--+-- > length (concat dr_tuning_oct) == 19+-- > import qualified Music.Theory.Tuning as T+-- > map (map (T.ratio_to_cents . t2_to_ratio)) dr_tuning_oct+dr_tuning_oct :: Num n => [[(n,n)]]+dr_tuning_oct =+    [[(1,1),(4,3),(16,11),(8,5),(16,9)]+    ,[(1,1),(8,7),(4,3),(3,2),(8,5),(16,9)]+    ,[(1,1),(9,8),(5,4),(4,3),(11,8),(3,2),(8,5),(7,4)]]++-- | Tuning, actual ratios.+dr_tuning :: [Rational]+dr_tuning = concat (zipWith (\o -> map ((* o) . t2_to_ratio)) [1,2,4] dr_tuning_oct)++-- | 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]+-- > map round dr_scale == r+dr_scale :: [Double]+dr_scale =+    let f0 = T.octpc_to_cps (1::Int,8)+        f = (* f0) . fromRational+    in map f dr_tuning++-- > 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_k0 (69,440)) dr_scale++-- > Scala.scale_verify dr_scale_scala+-- > putStrLn $ unlines $ Scala.scale_pp dr_scale_scala+dr_scale_scala :: Scala.Scale+dr_scale_scala =+    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))+        r_seq = snd (mapAccumL g 1 [33 .. 32 + 12 * 3 - 1]) ++ [(68,8)]+    in ("dr_itb_etude_1","...",3 * 12,map (Right . snd) r_seq)++-- > 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_k0 (69,440)) dr_scale++dr_chords :: [[T.Pitch]]+dr_chords =+    [[T.aes1,T.bes2,T.des3,T.ees4] -- S1+    ,[T.aes1,T.aes2,T.fes3,T.ees4]+    ,[T.aes1,T.bes2,T.des3,T.ees4]+    ,[T.aes1,T.bes2,T.des3,T.ees4] -- S2+    ,[T.aes1,T.ges2,T.aes3,T.ees4]+    ,[T.aes1,T.bes2,T.des3,T.ees4]+    ,[T.aes1,T.bes2,T.des3,T.ees4] -- S3+    ,[T.aes1,T.ges2,T.aes3,T.ees4]+    ,[T.aes1,T.ges2,T.aes3,T.ees4] -- S4+    ,[T.aes1,T.aes2,T.fes3,T.ees4]+    ,[T.aes1,T.fes2,T.des4,T.ees4] -- S5+    ,[T.ges2,T.aes2,T.aes3,T.d4]+    ,[T.aes1,T.d2,T.aes3,T.ees4]+    ,[T.aes2,T.fes3,T.d4] -- S6+    ,[T.aes1,T.fes2,T.des4,T.ees4]+    ,[T.aes1,T.fes2,T.des4,T.ees4] -- S7+    ,[T.aes1,T.ges2,T.aes3,T.ees4]+    ,[T.aes1,T.ges2,T.aes3,T.ees4] -- S8+    ,[T.aes1,T.d2,T.aes3,T.ees4]+    ]++-- > sum (map snd (concat dr_ratio_seq)) == 20 * 11+-- > map (sum . map snd) dr_ratio_seq == replicate 20 11+dr_ratio_seq :: Num n => [[(n,n)]]+dr_ratio_seq =+    [[(11,3),(2,2),(6,6)]+    ,[(7,2),(7,7),(6,2)]+    ,[(6,9),(2,2)]+    ,[(2,9),(11,2)]+    ,[(10,5),(10,3),(10,3)]+    ,[(10,10),(5,1)]+    ,[(5,7),(11,4)]+    ,[(11,3),(8,8)]+    ,[(8,8),(10,3)] -- p2+    ,[(10,7),(10,4)]+    ,[(10,4),(3,3),(4,4)]+    ,[(4,3),(9,7),(5,1)]+    ,[(7,7),(7,4)]+    ,[(9,9),(9,2)]+    ,[(9,7),(7,4)]+    ,[(7,3),(9,4),(7,4)]+    ,[(5,3),(4,4),(6,1),(4,3)]+    ,[(4,4),(7,7)]+    ,[(7,2),(5,8),(8,1)]+    ,[(8,1),(1,10)]+    ]++-- > 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)++dr_nt :: Integral i => [([i],[i])]+dr_nt =+    [([1,7,8,17],[12,13,15,17])+    ,([1,6,10,17],[6,10,9])]++-- > map (T.bimap1 (map T.pitch_pp) . dr_nt_pitch) dr_nt+dr_nt_pitch :: ([Int], [Int]) -> ([T.Pitch], [T.Pitch])+dr_nt_pitch =+    let f k = T.p5_snd (dr_scale_tbl_24et !! (k - 1))+    in T.bimap1 (map f)++{-++-- from harmonic series+hs :: Num n => [(n,n)]+hs = [(1,1),(9,8),(5,4),(11,8),(3,2),(7,4)]++-- from subharmonic series+shs :: Num n => [(n,n)]+shs = [(8,7),(16,11),(8,5),(16,9)]++-}
Music/Theory/Tuning/Scala.hs view
@@ -1,196 +1,504 @@--- | Parser for the Scala scale file format.  See--- <http://www.huygens-fokker.org/scala/scl_format.html> for details.--- This module succesfully parses all 4496 scales in v.81 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 qualified Codec.Binary.UTF8.String as U {- utf8-string -}-import qualified Data.ByteString as B {- bytestring -}-import Data.List-import Data.Ratio-import qualified Music.Theory.Tuning as T+import Control.Monad {- base -}+import Data.Either {- base -}+import Data.List {- base -}+import Data.Maybe {- base -}+import Data.Ratio {- base -} import System.Directory {- directory -}+import System.Environment {- base -} import System.FilePath {- filepath -} --- | A @.scl@ pitch is either in 'Cents' or is a 'Ratio'.-type Pitch i = Either T.Cents (Ratio i)---- | A scale has a description, a degree, and a list of 'Pitch'es.-type Scale i = (String,i,[Pitch i])---- | Text description of scale.-scale_description :: Scale i -> String-scale_description (d,_,_) = d+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 -} --- | The degree of the scale (number of 'Pitch'es).-scale_degree :: Scale i -> i-scale_degree (_,n,_) = n+-- * Pitch --- | The 'Pitch'es at 'Scale'.-scale_pitches :: Scale i -> [Pitch i]-scale_pitches (_,_,p) = p+-- | A @.scl@ pitch is either in 'Cents' or is a 'Ratio'.+type Pitch = Either T.Cents Rational --- | The last 'Pitch' element of the scale (ie. the /ocatve/).-scale_octave :: Scale i -> Maybe (Pitch i)-scale_octave (_,_,s) =-    case s of-      [] -> Nothing-      _ -> Just (last s)+-- | An enumeration type for @.scl@ pitch classification.+data Pitch_Type = Pitch_Cents | Pitch_Ratio deriving (Eq,Show) --- | 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)]+-- | A nearness value for deriving approximate rationals.+type Epsilon = Double --- | A pair giving the number of 'Cents' and number of 'Ratio' pitches--- at 'Scale'.-scale_pitch_representations :: (Integral t) => Scale i -> (t,t)-scale_pitch_representations s =-    let f (l,r) p = case p of-                      Left _ -> (l + 1,r)-                      Right _ -> (l,r + 1)-    in foldl f (0,0) (scale_pitches s)+-- | Derive 'Pitch_Type' from 'Pitch'.+pitch_type :: Pitch -> Pitch_Type+pitch_type = either (const Pitch_Cents) (const Pitch_Ratio) --- | Pitch as 'T.Cents', conversion by 'T.to_cents_r' if necessary.-pitch_cents :: Pitch Integer -> T.Cents+-- | Pitch as 'T.Cents', conversion by 'T.ratio_to_cents' if necessary.+pitch_cents :: Pitch -> T.Cents pitch_cents p =     case p of       Left c -> c       Right r -> T.ratio_to_cents r -type Epsilon = Double- -- | 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 --- | Make scale pitches uniform, conforming to the most promininent--- pitch type.-scale_uniform :: Epsilon -> Scale Integer -> Scale Integer-scale_uniform epsilon s =-    let (d,n,p) = s-        (c,r) = scale_pitch_representations s :: (Int,Int)-    in if c >= r-       then (d,n,map (Left . pitch_cents) p)-       else (d,n,map (Right . pitch_ratio epsilon) p)+-- | A pair giving the number of 'Cents' and number of 'Ratio' pitches.+pitch_representations :: [Pitch] -> (Int,Int)+pitch_representations =+    let f (l,r) p = case p of+                      Left _ -> (l + 1,r)+                      Right _ -> (l,r + 1)+    in foldl f (0,0) +-- | If scale is uniform, give type.+uniform_pitch_type :: [Pitch] -> Maybe Pitch_Type+uniform_pitch_type p =+    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] -> Pitch_Type+pitch_type_predominant p =+    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 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 -> String+scale_name (nm,_,_,_) = nm++-- | Text description of a scale.+scale_description :: Scale -> String+scale_description (_,d,_,_) = d++-- | The degree of the scale (number of 'Pitch'es).+scale_degree :: Scale -> Int+scale_degree (_,_,n,_) = n++-- | The 'Pitch'es at 'Scale'.+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 -> Bool+scale_verify (_,_,n,p) = n == length p++-- | Raise error if scale doesn't verify, else 'id'.+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 /octave/).  For empty scales give 'Nothing'.+scale_octave :: Scale -> Maybe Pitch+scale_octave (_,_,_,s) =+    case s of+      [] -> Nothing+      _ -> Just (last s)++-- | 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 -> Bool+is_scale_uniform = isJust . uniform_pitch_type . scale_pitches++-- | 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 :: Scale Integer -> [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 :: 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) --- | Comment lines being with @!@.-comment_p :: String -> Bool-comment_p x =+-- | 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++-- | 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 ("","",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 0.00001 ("","",length c,map Left c)) db+> scale_name py' == "pyth_12"++-}+scale_eq :: Scale -> Scale -> Bool+scale_eq (_,_,d0,p0) (_,_,d1,p1) = d0 == d1 && p0 == 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 @!@.+is_comment :: String -> Bool+is_comment x =     case x of       '!':_ -> True       _ -> False --- | Remove @\r@.-filter_cr :: String -> String-filter_cr = filter (not . (==) '\r')---- | Logical /or/ of list of predicates.-p_or :: [a -> Bool] -> a -> Bool-p_or p x =-    case p of-      [] -> False-      f:p' -> f x || p_or p' x- -- | Remove to end of line @!@ comments.+--+-- > remove_eol_comments " 1 ! comment" == " 1 " remove_eol_comments :: String -> String remove_eol_comments = takeWhile (/= '!') --- | Remove comments and null lines.+-- | Remove comments and trailing comments (the description may be empty, keep nulls) ----- > filter_comments ["!a","b","","c"] == ["b","c"]+-- > filter_comments ["!a","b","","c","d!e"] == ["b","","c","d"] filter_comments :: [String] -> [String]-filter_comments = map remove_eol_comments .-                  filter (not . p_or [comment_p,null])---- | Delete trailing @.@, 'read' fails for @700.@.-delete_trailing_point :: String -> String-delete_trailing_point s =-    case reverse s of-      '.':s' -> reverse s'-      _ -> s+filter_comments =+    map remove_eol_comments .+    filter (not . Function.predicate_any [is_comment]) --- | Pitches are either cents (with decimal point) or ratios (with @/@).+-- | Pitches are either cents (with decimal point, possibly trailing) or ratios (with @/@). ----- > map pitch ["700.0","3/2","2"] == [Left 700,Right (3/2),Right 2]-pitch :: (Read i,Integral i) => String -> Pitch i-pitch p =+-- > 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 (read (delete_trailing_point p))-    else case break (== '/') p of-             (n,'/':d) -> Right (read n % read d)-             _ -> Right (read p % 1)+    then Left (T.read_fractional_allow_trailing_point_err p)+    else Right (T.read_ratio_with_div_err p)  -- | Pitch lines may contain commentary.-pitch_ln :: (Read i, Integral i) => String -> Pitch i-pitch_ln x =+parse_pitch_ln :: String -> Pitch+parse_pitch_ln x =     case words x of-      p:_ -> pitch p-      _ -> error (show ("pitch",words x))+      p:_ -> parse_pitch p+      _ -> error (show ("parse_pitch_ln",words x))  -- | Parse @.scl@ file.-parse :: (Read i, Integral i) => String -> Scale i-parse s =-    case filter_comments (lines (filter_cr s)) of-      t:n:p -> (t,read n,map pitch_ln p)+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_msg "degree" n+                         ,map parse_pitch_ln p)+               in scale_verify_err scl       _ -> error "parse" --- | Load @.scl@ file.+-- * Io++-- | Read the environment variable @SCALA_SCL_DIR@, which is a+-- sequence of directories used to locate scala files on. ----- > s <- load "/home/rohan/data/scala/81/scl/xenakis_chrom.scl"--- > scale_pitch_representations s == (6,1)+-- > 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.+-- It is an error if the name has a file extension.+--+-- > mapM scl_derive_filename ["young-lm_piano","et12"]+scl_derive_filename :: FilePath -> IO FilePath+scl_derive_filename nm = do+  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")+  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/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"+    in if isAbsolute nm && takeExtension nm == ".scl"+       then doesFileExist nm >>= ex_f+       else scl_derive_filename nm++-- | Load @.scl@ file, runs 'resolve_scl'.+--+-- > 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]-load :: (Read i, Integral i) => FilePath -> IO (Scale i)-load fn = do-  b <- B.readFile fn-  let s = U.decode (B.unpack b)-  return (parse s)+scl_load :: String -> IO Scale+scl_load nm = do+  fn <- scl_resolve_name nm+  s <- Io.read_file_iso_8859_1 fn+  return (parse_scl (takeBaseName nm) s) --- | 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)))+{- | Load all @.scl@ files at /dir/, associate with file-name. --- | Load all @.scl@ files at /dir/.+> 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_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 <- load_dir "/home/rohan/data/scala/81/scl"--- > length db == 4496--- > length (filter ((== 0) . scale_degree) db) == 0--- > length (filter (== Just (Right 2)) (map scale_octave db)) == 3855+-- > db <- scl_load_db+-- > 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++-- | <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. ----- > let r = [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24--- >         ,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44--- >         ,45,46,47,48,49,50,51,53,54,55,56,57,58,59,60,61,62,63,64--- >         ,65,66,67,68,69,70,71,72,74,75,77,78,79,80,81,84,87,88--- >         ,90,91,92,95,96,99,100,101,105,110,112,117,118,130,140,171--- >         ,180,271,311,342,366,441,612]--- > in nub (sort (map scale_degree db)) == r+-- > 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. ----- > 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+-- > db <- scl_load_db+-- > writeFile "/tmp/scl.txt" (unlines (intercalate [""] (map scale_stat db)))+scale_stat :: Scale -> [String]+scale_stat 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 :: Pitch -> String+pitch_pp p =+    case p of+      Left c -> show c+      Right r -> show (numerator r) ++ "/" ++ show (denominator r)++-- | Pretty print 'Scale' in @Scala@ format. ----- > length (filter (not . perfect_octave) db) == 544+-- > 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"+    ,"!"+    ,dsc+    ,show k+    ,"!"] ++ map pitch_pp p++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@. ----- > mapM_ (putStrLn.scale_description) (filter (not . perfect_octave) db)-load_dir :: (Read i, Integral i) => FilePath -> IO [Scale i]-load_dir d = dir_subset [".scl"] d >>= mapM load+-- > setEnv "SCALA_DIST_DIR" "/home/rohan/opt/build/scala-22"+dist_get_dir :: IO String+dist_get_dir = getEnv "SCALA_DIST_DIR" --- Local Variables:--- truncate-lines:t--- End:+-- | Load file from 'dist_get_dir'.+load_dist_file :: FilePath -> IO String+load_dist_file nm = do+  d <- dist_get_dir+  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
@@ -0,0 +1,86 @@+-- | 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 Read {- hmt -}+import qualified Music.Theory.Tuning.Scala as Scala {- hmt -}++-- | Interval and name, ie. (3/2,"perfect fifth")+type INTERVAL = (Rational,String)++-- | 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")+> 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" == [(81/80,"syntonic comma, Didymus comma")]+intnam_search_description_ci :: INTNAM -> String -> [INTERVAL]+intnam_search_description_ci (_,i) x =+    let downcase = map toLower+        x' = downcase x+    in filter (isInfixOf x' . downcase . snd) i++-- * Parser++-- | 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 i+               in if n' == length i' then (n',i') else error "parse_intnam"+      _ -> error "parse_intnam"++-- * IO++{- | '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 <- 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
@@ -0,0 +1,179 @@+{- | 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 Function {- hmt -}+import qualified Music.Theory.List as List {- hmt -}+import qualified Music.Theory.Tuning.Scala as Scala {- hmt -}++-- | (mode-start-degree,mode-intervals,mode-description)+type Mode = (Int,[Int],String)++-- | 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++-- | Intervals (in steps) between adjacent elements of the mode.+mode_intervals :: Mode -> [Int]+mode_intervals (_,i,_) = i++-- | 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++-- | 'length' (or degree) of 'mode_intervals' (ie. number of notes in mode)+mode_length :: Mode -> Int+mode_length = length . mode_intervals++-- | 'sum' of 'mode_intervals' (ie. number of notes in tuning system)+mode_univ :: Mode -> Int+mode_univ = sum . mode_intervals++-- | '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 (_,_,m) x = filter ((== x) . mode_intervals) m++-- | Expect /one/ result.+--+-- > mn <- load_modenam+-- > let sq = putStrLn . unlines . mode_stat . fromJust . modenam_search_seq1 mn+-- > sq [2,2,1,2,2,2,1]+-- > sq [2,1,2,2,1,2,2]+-- > sq [2,1,2,2,1,3,1]+-- > sq (replicate 6 2)+-- > 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 = 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 (_,_,m) x = filter (isInfixOf x . mode_description) m++-- | 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.+--+-- > map non_implicit_degree ["4","[4]"] == [Nothing,Just 4]+non_implicit_degree :: String -> Maybe Int+non_implicit_degree 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 w =+    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 List.separate_last' p of+                  (p',Just '\\') -> join_long_lines ((p' ++ q) : l')+                  _ -> p : join_long_lines (q : l')+      _ -> l++-- | Parse joined non-comment lines of modenam file.+parse_modenam :: [String] -> ModeNam+parse_modenam l =+    case l of+      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++{- | '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 <- Scala.load_dist_file_ln "modenam.par"+  return (parse_modenam (Scala.filter_comments (join_long_lines l)))
+ Music/Theory/Tuning/Sethares_1994.hs view
@@ -0,0 +1,85 @@+-- | William A. Sethares.+-- "Adaptive Tunings for Musical Scales".+-- /Journal of the Acoustical Society of America/, 96(1), July 1994.+module Music.Theory.Tuning.Sethares_1994 where++import Data.Maybe {- base -}++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+        c1 = 5+        c2 = -5+        a1 = -3.51+        a2 = -5.75+        s = d_star / (s1 * min f1 f2 + s2)+        f_dif = abs (f2 - f1)+        e1 = c1 * exp (a1 * s * f_dif)+        e2 = c2 * exp (a2 * s * f_dif)+    in v1 * v2 * (e1 + e2)++-- | 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_fratio [0 .. 1200]+    in map (\f -> map (\r -> pl_dissonance (f,1) (f * r,1)) r_seq) f0++-- > 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/Werckmeister.hs 
@@ -1,105 +0,0 @@--- | Andreas Werckmeister (1645-1706).-module Music.Theory.Tuning.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]-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]-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]-werckmeister_v :: Tuning-werckmeister_v = Tuning (Right werckmeister_v_c) 2---- | Ratios for 'werckmeister_vi'.------ > let c = [0,91,196,298,395,498,595,698,793,893,1000,1097]--- > in map (round . ratio_to_cents) werckmeister_vi_r == c-werckmeister_vi_r :: [Rational]-werckmeister_vi_r =-    [1,98/93-    ,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 == [0,91,196,298,395,498,595,698,793,893,1000,1097]-werckmeister_vi :: Tuning-werckmeister_vi = Tuning (Left werckmeister_vi_r) 2-
+ 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 
@@ -1,258 +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--import Data.Monoid {- base -}---- * 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 :: [t] -> T2 t-t2 l = case l of {[p,q] -> (p,q);_ -> error "t2"}--t2_list :: T2 a -> [a]-t2_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 :: [t] -> T3 t-t3 l = case l of {[p,q,r] -> (p,q,r);_ -> error "t3"}--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_list :: T3 a -> [a]-t3_list (i,j,k) = [i,j,k]--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 :: [t] -> T4 t-t4 l = case l of {[p,q,r,s] -> (p,q,r,s); _ -> error "t4"}--t4_list :: T4 t -> [t]-t4_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---- * T5 (5-tuple, regular)--type T5 a = (a,a,a,a,a)--t5 :: [t] -> T5 t-t5 l = case l of {[p,q,r,s,t] -> (p,q,r,s,t); _ -> error "t5"}--t5_list :: T5 t -> [t]-t5_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 :: [t] -> T6 t-t6 l = case l of {[p,q,r,s,t,u] -> (p,q,r,s,t,u);_ -> error "t6"}--t6_list :: T6 t -> [t]-t6_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_list :: T7 t -> [t]-t7_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_list :: T8 t -> [t]-t8_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)---- * T9 (9-tuple, regular)--type T9 a = (a,a,a,a,a,a,a,a,a)--t9_list :: T9 t -> [t]-t9_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)
− Music/Theory/Unicode.hs 
@@ -1,56 +0,0 @@--- | <http://www.unicode.org/charts/PDF/U1D100.pdf>-module Music.Theory.Unicode where--type Unicode_Table = [(Int,String)]---- > putStrLn (map (toEnum . fst) (concat unicode))-unicode :: [Unicode_Table]-unicode = [accidentals,notes,rests,clefs]--accidentals :: Unicode_Table-accidentals =-    [(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")]--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")]--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")]--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")]
+ Music/Theory/Wyschnegradsky.hs view
@@ -0,0 +1,332 @@+-- | <http://www.ivan-wyschnegradsky.fr/en/chromatic-drawings/>+module Music.Theory.Wyschnegradsky where++import Data.Char {- base -}+import Data.List {- list -}+import Data.Maybe {- base -}++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.+--+-- > map (normalise_step 6) [-5,-1,1,5] == [1,-1,1,-1]+normalise_step :: (Eq n,Num n) => n -> n -> n+normalise_step m n+    | n == 1 = 1+    | n == -1 = -1+    | n == m - 1 = -1+    | n == 1 - m = 1+    | otherwise = error "normalise_step"++-- | Wyschnegradsky writes the direction sign at the end of the number.+--+-- > map parse_num_sign ["2+","4-"] == [2,-4]+parse_num_sign :: (Num n, Read n) => String -> n+parse_num_sign s =+    case List.separate_last s of+      (n,'+') -> read n+      (n,'-') -> negate (read n)+      _ -> error "parse_num_sign"++-- | Expand a chromatic (step-wise) sequence, sign indicates direction.+--+-- > map vec_expand [2,-4] == [[1,1],[-1,-1,-1,-1]]+vec_expand :: Num n => Int -> [n]+vec_expand n = if n > 0 then replicate n 1 else replicate (abs n) (-1)++-- | Parse the vector notation used in some drawings, a comma+-- separated list of chromatic sequences.+--+-- > parse_vec Nothing 0 "4-,4+,4-,4+,4-,4+,4-,4+,4-"+-- > parse_vec Nothing 0 "2+,2-,2+,2-,2+,2-,2+,2-,2+,18+"+parse_vec :: Num n => Maybe Int -> n -> String -> [n]+parse_vec n m =+    let f = case n of+              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+add_m n p q = (p + q) `mod` n++-- | Parse hex colour string, as standard in HTML5.+--+-- > parse_hex_clr "#e14630" == (225,70,48)+parse_hex_clr :: (Read n,Num n) => String -> (n,n,n)+parse_hex_clr clr =+    let f p q = read ("0x" ++ [p,q])+    in case clr of+         ['#',p,q,r,s,t,u] -> (f p q,f r s,f t u)+         _ -> error "parse_hex"++-- | Type specialised.+parse_hex_clr_int :: String -> (Int,Int,Int)+parse_hex_clr_int = parse_hex_clr++-- | Normalise colour by dividing each component by /m/.+--+-- > clr_normalise 255 (parse_hex_clr "#ff0066") == (1,0,0.4)+clr_normalise :: (Real r,Fractional f) => f -> (r,r,r) -> (f,f,f)+clr_normalise m (r,g,b) = let f x = realToFrac x / m in (f r,f g,f b)++-- | Sequences are either in 'Radial' or 'Circumferential' order.+data Seq a = Radial [a] | Circumferential [a]++-- | Group sequence into normal (ie. 'Circumferential') order given+-- drawing dimensions.+seq_group :: Int -> Int -> Seq a -> [[a]]+seq_group c_div r_div s =+    case s of+      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.pitch_pp_opt (False,False) . Pitch.octpc_to_pitch Spelling.pc_spell_ks . (,) 4+    in putStrLn . intercalate sep . map (unwords . map f)++-- * U3++-- | Index to colour name abbreviation.+--+-- > map u3_ix_ch [0..5] == "ROYGBV"+u3_ix_ch :: Integral i => i -> Char+u3_ix_ch = genericIndex "ROYGBV" . (`mod` 6)++-- | Inverse of 'u3_ix_ch'.+--+-- > map u3_ch_ix "ROYGBV" == [0..5]+u3_ch_ix :: Char -> Int+u3_ch_ix = fromMaybe (error "u3_ch_ix") . flip elemIndex "ROYGBV"++-- | Drawing definition, as written by Wyschnegradsky.+--+-- > mapM_ (\(c,r) -> putStrLn (unlines ["C: " ++ c,"R: " ++ r])) u3_vec_text_iw+u3_vec_text_iw :: [(String, String)]+u3_vec_text_iw =+    [("4+,4-,4+,4-,2+"+     ,"4-,4+,4-,4+,4-,4+,4-,4+,4-")+    ,("9+,2+,2-,2+,2-,2+"+     ,"2+,2-,2+,2-,2+,2-,2+,2-,2+,18+")+    ,("12-,12+,12-"+     ,"18+,18-")+    ,("3+,3-,3+,3-,3+,3-"+     ,"18+,18-")+    ,("9+,9-"+     ,"3+,3-,3+,3-,3+,3-,3+,3-,3+,3-,3+,3-")+    ,("2+,2-,2+,2-,2+,2-"+     ,"6-,6+,6-,6+,6-,6+")+    ,("2+,2-,2+,2-,2+,2-"+     ,"6+,6-,6+,6-,6+,6-")+    ,("6+,6-"+     ,"2+,2-,2+,2-,2+,2-,2+,2-,2+,2-,2+,2-,2+,2-,2+,2-,2+,2-")]++-- | Re-written for local parser and to correct ambiguities and errors+-- (to align with actual drawing).+--+-- > 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])+-- > 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+"+     ,"4-,3+,5-,3+,5-,3+,5-,3+,5-") -- 1+    ,("9+,2+,1-,3+,1-,2+"+     ,"2+,1-,3+,1-,3+,1-,3+,1-,3+,1-,3+,1-,3+,1-,3+,1-,3+,2-") -- 2+    ,("12-,12+,12-"+     ,"18+,18-")+    ,("3+,2-,4+,2-,4+,3-"+     ,"18+,18-")+    ,("9+,9-"+     ,"3+,2-,4+,1-,1+,1-,3+,1-,1+,1-,3+,2-,4+,1-,1+,1-,3+,1-,1+,1-") -- 5+    ,("2+,1-,3+,1-,3+,2-"+     ,"6-,6+,6-,6+,6-,6+") -- 6+    ,("2+,1-,3+,1-,3+,2-"+     ,"6+,6-,6+,6-,6+,6-") -- 7+    ,("6+,6-"+     ,"2+,1-,3+,1-,3+,1-,3+,1-,3+,1-,3+,1-,3+,1-,3+,1-,3+,2-")] -- 8++-- | Parse of 'u3_vec_text_rw'.+--+-- > let {(c,r) = u3_vec_ix ; c' = map length c}+-- > in (length c,c',sum c',length r,map length r)+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) = List.firstSecond (transpose (map f u3_vec_text_rw))+    in (c,r)++-- | Radial indices (ie. each /ray/ as an index sequence).+--+-- > putStrLn $ unlines $ map (map u3_ix_ch) u3_ix_radial+u3_ix_radial :: Integral n => [[n]]+u3_ix_radial =+    let (c,r) = u3_vec_ix+        r' = zipWith replicate (map length c) r+    in zipWith (map . add_m 6) (concat c) (concat r')++-- | Colour names in index sequence.+u3_clr_nm :: [String]+u3_clr_nm = words "red orange yellow green blue violet"++-- | Colour values (hex strings) in index sequence.+u3_clr_hex :: [String]+u3_clr_hex = words "#e14630 #e06e30 #e2c48e #498b43 #2a5a64 #cb7b74"++-- | RGB form of 'u3_clr_hex'.+u3_clr_rgb :: Fractional n => [(n,n,n)]+u3_clr_rgb = map (clr_normalise 256 . parse_hex_clr_int) u3_clr_hex++-- | Notated radial color sequence, transcribed from drawing.+--+-- > map (\(n,c) -> let v = u3_ch_seq_to_vec c in (n,sum v,v)) u3_radial_ch+u3_radial_ch :: [(Int,[Char])]+u3_radial_ch =+    [(1,"RVBGY GBV BGYOR OYG YORVB VRO RVBGY GBVBGYO")+    ,(5,"ROYG YO YGBV BV BVRO RO ROYG YO YGBV BV BVR OR O")]++-- | Notated circumferenctial color sequence, transcribed from drawing.+--+-- > map (\(n,c) -> (n,u3_ch_seq_to_vec c)) u3_circ_ch+u3_circ_ch :: [(Int,[Char])]+u3_circ_ch =+    [(6,"ROYOYGBGBVRV")+    ,(7,"ROYOYGBGBVRV")+    ,(8,"ROYGBVRVBGYO")]++-- | Translate notated sequence to "re-written" vector notation.+u3_ch_seq_to_vec :: [Char] -> [Int]+u3_ch_seq_to_vec =+    map length .+    group .+    map (normalise_step 6) .+    List.d_dx .+    map u3_ch_ix .+    filter (not . isSpace)++-- * DC9++{- | Circumference pitch classes, C = 0.++> let c' = map length dc9_circ in (sum c',c') == (72,[5,6,7,2,3,4,4,3,2,7,7,4,4,3,2,2,3,4])++> iw_pc_pp " | " dc9_circ++-}+dc9_circ :: Num n => [[n]]+dc9_circ =+    [[6,5,4,3,2]+    ,[3,2,1,0,11,10]+    ,[11,10,9,8,7,6,5]+    ,[6,5]+    ,[6,5,4]+    ,[5,4,3,2]+    ,[3,2,1,0]+    ,[1,0,11]+    ,[0,11]+    ,[0,1,2,3,4,5,6]+    ,[5,6,7,8,9,10,9]+    ,[10,11,0,1]+    ,[0,1,2,3]+    ,[2,3,4]+    ,[3,4]+    ,[3,4]+    ,[3,4,5]+    ,[4,5,6,7]]++-- | Rayon pitch classes, C = 0.+--+-- > length dc9_rad == 18+-- > putStrLn $ unwords $ map f dc9_rad+dc9_rad :: Num n => [n]+dc9_rad = [0,10,8,6,4,2,0,10,8,6,4,2,0,10,8,6,4,2]++-- | Radial indices.+--+-- > map length dc9_ix == replicate 72 18+dc9_ix :: Integral n => [[n]]+dc9_ix = map (\n -> map (add_m 12 n) dc9_rad) (concat dc9_circ)++-- | Approximate colours, hex strings.+dc9_clr_hex :: [String]+dc9_clr_hex =+    let c = ["#e96d61","#e6572b"+            ,"#e07122","#e39e36"+            ,"#e8b623","#e5c928"+            ,"#c2ba3d","#a2a367"+            ,"#537a77","#203342"+            ,"#84525e","#bc6460"]+        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.+dc9_clr_rgb :: Fractional n => [(n,n,n)]+dc9_clr_rgb = map (clr_normalise 255 . parse_hex_clr_int) dc9_clr_hex++-- * U11++-- > 18 * 4 == 72+-- > let c' = map length u11_circ in (sum c',length c',c')+--+-- > iw_pc_pp "\n- " u11_circ+u11_circ :: Num n => [[n]]+u11_circ =+    [[7,8,9,10,11,0,1,2,3]+    ,[10,11,0,1,2,3,4,5,6]+    ,[0,1,2,3,4,5]+    ,[0,1,2]+    ,[10,11]+    ,[6,7]+    ,[2]+    ,[9]+    ,[4]+    ,[11]+    ,[6,7]+    ,[2]+    ,[9]+    ,[2]+    ,[11]+    ,[6,7]+    ,[2,3]+    ,[10,11,0]+    ,[7,8,9,10,11,0]+    ,[7,8,9,10,11,0,1,2,3]+    ,[10,11,0,1,2,3,4,5,6]]++-- > 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 . 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)++-- > ull_rad_text == "012588---------885210"+ull_rad_text :: [Char]+ull_rad_text =+    let x = "012588----"+        y = "-"+    in x ++ y ++ reverse x++-- > iw_pc_pp "\n- " u11_rad+u11_rad :: Integral n => [[n]]+u11_rad =+    let f c = if c == '-' then Nothing else Just (read [c])+    in map (u11_seq_rule . f) ull_rad_text++u11_clr_hex :: [String]+u11_clr_hex =+    let c = ["#dbb56a","#ffb05c","#ea7c3f","#f93829","#ee6054","#d18d9c"+            ,"#a94c79","#215272","#628b7d","#9dbc90","#ecdfaa","#fbeaa5"]+        n = reverse ([4..11] ++ [0..3]) :: [Int]+    in map snd (sort (zip n c))++u11_clr_rgb :: Fractional n => [(n,n,n)]+u11_clr_rgb = map (clr_normalise 256 . parse_hex_clr_int) u11_clr_hex
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@@ -49,12 +49,12 @@     case sort x of       [1,2,3,4] -> x       [5,6,7,8] -> complement x-      _ -> error "lower"+      _ -> error (show ("lower",x))  -- | Application of 'Label' /p/ on /q/. -- -- > l_on Q1 I == Q1--- > l_on D A == G+-- > l_on D Q12 == Q4 -- > [l_on L L,l_on E D,l_on D E] == [L2,C,B] l_on :: Label -> Label -> Label l_on p q =@@ -63,6 +63,47 @@         r = map (\i -> q' !! (i - 1)) p'     in label_of r +{- | Generalisation of Fibonnaci process, /f/ is the binary operator+giving the next element, /p/ and /q/ are the initial elements.++See discussion in: Carlos Agon, Moreno Andreatta, Gérard Assayag, and+Stéphan Schaub. _Formal Aspects of Iannis Xenakis' "Symbolic Music": A+Computer-Aided Exploration of Compositional Processes_. Journal of New+Music Research, 33(2):145-159, 2004.++Note that the article has an error, printing Q4 for Q11 in the sequence below.++> 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]+> (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]+> (take 16 (fib_proc l_on E G2) == r,T.duplicates r == [B,C,D2,E,G,L2])++> 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]+> 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]+> take 24 (fib_proc (\p q -> (p * q) `mod` 18) 11 13) == r++-}+fib_proc :: (a -> a -> a) -> a -> a -> [a]+fib_proc f p q = let r = f p q in p : fib_proc f q r+ -- | 'Seq' of 'Label', inverse of 'label_of'. -- -- > seq_of Q1 == [8,7,5,6,4,3,1,2]@@ -81,15 +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@@ -97,7 +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'. --@@ -111,12 +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@@ -125,7 +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) @@ -135,14 +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@@ -170,11 +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)@@ -186,42 +216,56 @@  -- * Figures --- | Fig. VIII-6. Hexahedral (Octahedral) Group (p. 220)+-- | Label sequence of Fig. VIII-6. Hexahedral (Octahedral) Group (p. 220) ----- > length viii_6_l == 24--- > take 7 viii_6_l == [L2,L,A,Q1,Q7,Q3,Q9]-viii_6_l :: [Label]-viii_6_l =+-- > let r = [I,A,B,C,D,D2,E,E2,G,G2,L,L2,Q1,Q2,Q3,Q4,Q5,Q6,Q7,Q8,Q9,Q10,Q11,Q12]+-- > in viii_6_lseq == r+viii_6_lseq :: [Label]+viii_6_lseq =     [L2,L,A,Q1,Q7,Q3,Q9     ,G2,G,C,Q8,Q5,Q10,Q2     ,E,E2,B,Q4,Q11,Q12,Q6     ,D,D2,I] +-- | Label sequence of Fig. VIII-7 (p.221)+--+-- > let r = [I,A,B,C,D,D2,E,E2,G,G2,L,L2,Q1,Q2,Q3,Q4,Q5,Q6,Q7,Q8,Q9,Q10,Q11,Q12]+-- > in viii_7_lseq == r+viii_7_lseq :: [Label]+viii_7_lseq =+    [I,A,B,C+    ,D,D2,E,E2+    ,G,G2,L,L2+    ,Q1,Q2,Q3,Q4+    ,Q5,Q6,Q7,Q8+    ,Q9,Q10,Q11,Q12]+ -- | Fig. VIII-7 (p.221) -- -- > map (take 4) (take 4 viii_7) == [[I,A,B,C] -- >                                 ,[A,I,C,B] -- >                                 ,[B,C,I,A] -- >                                 ,[C,B,A,I]]+--+-- > import Music.Theory.Array.MD+--+-- > let t = md_matrix_opt show (\x -> "_" ++ x ++ "_") (head viii_7,head viii_7) viii_7+-- > putStrLn $ unlines $ md_table' t viii_7 :: [[Label]]-viii_7 =-    let o = [I,A,B,C-            ,D,D2,E,E2-            ,G,G2,L,L2-            ,Q1,Q2,Q3,Q4-            ,Q5,Q6,Q7,Q8-            ,Q9,Q10,Q11,Q12]-    in map (\i -> map (`l_on` i) o) o+viii_7 = map (\i -> map (`l_on` i) viii_7_lseq) viii_7_lseq --- | Fig. VIII-6/b 'Labels' (p.221)+-- | Label sequence of Fig. VIII-6/b (p.221) -- -- > length viii_6b_l == length viii_6_l -- > take 8 viii_6b_l == [I,A,B,C,D2,D,E2,E]-viii_6b_l :: [Label]-viii_6b_l =-    [I,A,B,C,D2,D,E2,E-    ,G2,G,L2,L,Q7,Q2,Q3,Q11-    ,Q8,Q6,Q1,Q5,Q9,Q10,Q4,Q12]+viii_6b_lseq :: [Label]+viii_6b_lseq =+    [I,A,B,C+    ,D2,D,E2,E+    ,G2,G,L2,L+    ,Q7,Q2,Q3,Q11+    ,Q8,Q6,Q1,Q5+    ,Q9,Q10,Q4,Q12]  -- | Fig. VIII-6/b 'Half_Seq'. --@@ -258,7 +302,7 @@  -- | Variant of 'viii_6b' with 'Half_Seq'. viii_6b' :: [(Label,Half_Seq)]-viii_6b' = zip viii_6b_l viii_6b_p'+viii_6b' = zip viii_6b_lseq viii_6b_p'  -- | Fig. VIII-6/b. --@@ -266,19 +310,19 @@ -- >                              ,(G2,[3,2,4,1,7,6,8,5]) -- >                              ,(Q8,[6,8,5,7,2,4,1,3])] viii_6b :: [(Label,Seq)]-viii_6b = zip viii_6b_l (map full_seq viii_6b_p')+viii_6b = zip viii_6b_lseq (map full_seq viii_6b_p')  -- | The sequence of 'Rel' to give 'viii_6_l' from 'L2'. -- -- > apply_relations_l viii_6_relations L2 == viii_6_l -- > length (nub viii_6_relations) == 14 viii_6_relations :: [Rel]-viii_6_relations = relations (map half_seq_of viii_6_l)+viii_6_relations = relations (map half_seq_of viii_6_lseq)  -- | The sequence of 'Rel' to give 'viii_6b_l' from 'I'. -- -- > apply_relations_l viii_6b_relations I == viii_6b_l -- > length (nub viii_6b_relations) == 10 viii_6b_relations :: [Rel]-viii_6b_relations = relations (map half_seq_of viii_6b_l)+viii_6b_relations = relations (map half_seq_of viii_6b_lseq)
Music/Theory/Xenakis/Sieve.hs view
@@ -6,14 +6,12 @@ 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'              deriving (Eq,Show)  -- | The 'Union' of a list of 'Sieve's, ie. 'foldl1' 'Union'.@@ -32,23 +30,39 @@ (∩) :: Sieve -> Sieve -> Sieve (∩) = Intersection +-- | Synonym for 'Complement'.+c :: Sieve -> Sieve+c = Complement++-- | Pretty-print sieve.  Fully parenthesised.+sieve_pp :: Sieve -> String+sieve_pp s =+    case s of+      Empty -> "∅"+      L (p,q) -> concat [show p,".",show q]+      Union p q -> concat ["(",sieve_pp p," ∪ ",sieve_pp q,")"]+      Intersection p q -> concat ["(",sieve_pp p," ∩ ",sieve_pp q,")"]+      Complement p -> concat ["(∁ ",sieve_pp p,")"]+ -- | 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)+{- | 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@@ -56,33 +70,53 @@       L (m,i) -> L (m,i `mod` m)       Union s0 s1 -> Union (normalise s0) (normalise s1)       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+{- | 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       L (m,i) -> n `mod` m == i `mod` m && n >= i       Union s0 s1 -> element s0 n || element s1 n       Intersection s0 s1 -> element s0 n && element s1 n+      Complement s' -> not (element s' n) --- | 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]+{- | '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 ..]+                e:s' -> case compare x e of+                          LT -> x : f (x + 1) s+                          EQ -> f (x + 1) s'+                          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]+> 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]@@ -93,9 +127,9 @@          L (m,i) -> [i, i+m ..]          Union s0 s1 -> u_f (merge (build s0) (build s1))          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]@@ -106,46 +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)+> 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 {- hmt -}++> 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]+> 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]+> 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)+> 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)+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@@ -153,12 +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@@ -173,18 +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)------ > 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 =@@ -202,3 +298,44 @@          Intersection s1 Empty -> s1          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
@@ -1,94 +1,146 @@--- | Generalised Z-/n/ functions.+-- | Z-/n/ functions module Music.Theory.Z where -{---From GHC 7.6 onwards there is the modular-arithmetic package, which subsumes this work.--{-# Language DataKinds #-}--import Data.Modular {- modular-arithmetic -}-import GHC.TypeLits {- base -}+import Data.Char {- base -}+import Data.List {- base -} -type Z n = Mod Integer n+import qualified Music.Theory.List as T {- hmt -} --- > map negate [0::Z12 .. 11] == [0,11,10,9,8,7,6,5,4,3,2,1]--- > map (+ 5) [0::Z12 .. 11] == [5,6,7,8,9,10,11,0,1,2,3,4]-type Z12 = Mod Integer 12+-- | Z type.+--+-- > map z_modulus [z7,z12] == [7,12]+newtype Z i = Z {z_modulus :: i} --- > map invert [0::Z12 .. 11] == [0,11,10,9,8,7,6,5,4,3,2,1]-invert :: KnownNat n => Z n -> Z n-invert = negate+-- | '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 -import Data.List {- base -}+-- | 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 -lift_unary_Z :: Integral a => a -> (t -> a) -> t -> a-lift_unary_Z z f n = mod (f n) z+lift_unary_Z :: Integral i => Z i -> (t -> i) -> t -> i+lift_unary_Z z f = z_mod z . f -lift_binary_Z :: Integral a => a -> (s -> t -> a) -> s -> t -> a-lift_binary_Z z f n1 n2 = mod (n1 `f` n2) z+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_mod 12 (6::Z12.Z12) 12--- > z_add 12 (1::Z12.Z12) 5--- > (1::Z12.Z12) + 5--- > map (z_add 12 4) [1,5,6] == [5,9,10]-z_add :: Integral a => a -> a -> a -> a+-- | 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 (+) -z_sub :: Integral a => a -> a -> a -> a+-- | The underlying type /i/ is presumed to be signed...+--+-- > z_sub z12 0 8 == 4+--+-- > 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 (-) -z_mul :: Integral a => a -> a -> a -> a+-- | 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_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 :: Integral a => a -> a -> a-z_negate z = lift_unary_Z z negate+-- > 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 a => a -> Integer -> a-z_fromInteger z i = fromInteger i `mod` z+z_fromInteger :: Integral i => Z i -> Integer -> i+z_fromInteger z i = z_mod z (fromInteger i) -z_signum :: t -> t1 -> t2+z_signum :: t -> u -> v z_signum _ _ = error "Z numbers are not signed" -z_abs :: t -> t1 -> t2+z_abs :: t -> u -> v z_abs _ _ = error "Z numbers are not signed" --- > map (to_Z 12) [-9,-3,0] == [3,9,0]-to_Z :: Integral i => i -> i -> i+-- > 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 --- | Z not in set.+-- | Universe of 'Z'. ----- > z_complement 5 [0,2,3] == [1,4]--- > z_complement 12 [0,2,4,5,7,9,11] == [1,3,6,8,10]-z_complement :: (Enum a, Eq a, Num a) => a -> [a] -> [a]-z_complement z = (\\) [0 .. z - 1]+-- > z_univ z12 == [0..11]+z_univ :: Integral i => Z i -> [i]+z_univ (Z z) = [0 .. z - 1] -z_quot :: Integral i => i -> i -> i -> i+-- | Z of 'z_univ' not in given set.+--+-- > 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)++z_quot :: Integral i => Z i -> i -> i -> i z_quot z p = to_Z z . quot p -z_rem :: Integral c => c -> c -> c -> c+z_rem :: Integral i => Z i -> i -> i -> i z_rem z p = to_Z z . rem p -z_div :: Integral c => c -> c -> c -> c-z_div z p = to_Z z . div p+div_err :: Integral i => String -> i -> i -> i+div_err s p q = if q == 0 then error ("div_err: zero" ++ s) else p `div` q --- > z_mod 12 6 12-z_mod :: Integral c => c -> c -> c -> c-z_mod z p = to_Z z . mod p+z_div :: Integral i => Z i -> i -> i -> i+z_div z p = to_Z z . div_err "z_div" p -z_quotRem :: Integral t => t -> t -> t -> (t, t)+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 t => t -> t -> t -> (t, t)-z_divMod z p q = (z_div z p q,z_mod 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 (mod p q)) -z_toInteger :: Integral i => i -> i -> i-z_toInteger z = to_Z z+z_toInteger :: Integral i => Z i -> i -> i+z_toInteger = to_Z++-- * Z16++-- | 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
@@ -0,0 +1,300 @@+-- | James Boros. "Some Properties of the All-Trichord Hexachord".+-- _In Theory Only_, 11(6):19--41, 1990.+module Music.Theory.Z.Boros_1990 where++import Data.Char {- base -}+import Data.List {- base -}+import Data.Maybe {- base -}+import Numeric {- base -}++import qualified Data.Graph.Inductive.Graph as G {- fgl -}+import qualified Data.Graph.Inductive.Basic as G {- fgl -}+import qualified Data.Graph.Inductive.PatriciaTree as G {- fgl -}+import qualified Data.Graph.Inductive.Query.BFS as G {- fgl -}++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.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++-- * Util++singular :: String -> [t] -> t+singular err l =+    case l of+      [x] -> x+      _ -> error ("not singular: " ++ err)++set_eq :: Ord t => [t] -> [t] -> Bool+set_eq p q = T.set p == T.set q++elem_by :: (t -> t -> Bool) -> t -> [t] -> Bool+elem_by f e = any (f e)++-- * Tto++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.z12 n) p) [0..11]++all_tni :: Integral i => [i] -> [[i]]+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++-- > 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.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.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 = 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 . concatMap (`showHex` "")++-- * Ath++-- | Forte prime form of the all-trichord hexachord.+--+-- > T.sc_name ath == "6-Z17"+-- > T.sc "6-Z17" == ath+ath :: Pcset+ath = [0,1,2,4,7,8]++-- | Is /p/ an instance of '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 = uniq_tni ath++-- | Calculate 'T.Tto' of pcset, which must be an instance of '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 p =+    let r = ath_tni p+        h = if T.tto_I r then 'h' else 'H'+    in h : show (T.tto_T r)++-- | The twenty three-element subsets of 'ath'.+--+-- > length ath_trichords == 20+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 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 p q =+    let f z = is_ath (p ++ z)+    in filter f (uniq_tni q)++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.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.Edge Pcset] -> [T.Edge Pcset]+gr_trs n = let f (p,q) = (pcset_trs n p,pcset_trs n q) in map f++-- * Tables++-- > length table_3 == 20+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.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 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 = nub (map T.t2_sort table_3)++-- > putStrLn $ unlines $ table_4_md+table_4_md :: [String]+table_4_md =+    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 pp_tbl (hdr : map f table_4)++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 pp_tbl (["SC","#ATH"] : map f table_5)++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++-- > putStrLn $ unlines $ table_6_md+table_6_md :: [String]+table_6_md =+    let f (p,q,r) = [pcset_pp_hex p,show q,show r]+    in pp_tbl (["SC","#H0","#Hn"] : map f table_6)++-- * Figures++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 = T.g_from_edges fig_1++-- > putStrLn $ unlines $ map (unwords . map pcset_pp) fig_2+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 (\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.Edge Pcset]]+fig_3 = map (concatMap (T.adj2 1) . realise_ath_seq) fig_2++fig_3_gr :: [G.Gr Pcset ()]+fig_3_gr = map T.g_from_edges fig_3++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.Edge Pcset]]+fig_5 =+    let c = [0,4,8]+        f gr = case ath_gr_extend gr c of+                 [] -> Nothing+                 r -> Just (gr ++ r)+        g0 = concat fig_4+    in mapMaybe (\n -> f (gr_trs n g0)) [0 .. 11]++-- * Drawing++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 -> T.Dot_Attr+set_shape v = ("shape",if self_inv v then "doublecircle" else "circle")++type Gr = G.Gr Pcset ()++gr_pp' :: (Pcset -> String) -> T.Graph_Pp Pcset ()+gr_pp' f = (\(_,v) -> [set_shape v,("label",f v)],const [])++gr_pp :: T.Graph_Pp Pcset ()+gr_pp = gr_pp' pcset_pp++d_fig_1 :: [String]+d_fig_1 = T.fgl_to_udot [] gr_pp fig_1_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.fgl_to_udot [] gr_pp d_fig_3_g++d_fig_3' :: [[String]]+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 = T.g_from_edges (uedge_set (concat fig_4))++d_fig_4 :: [String]+d_fig_4 = T.fgl_to_udot [] gr_pp d_fig_4_g++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.fgl_to_udot [("edge:len","1.5")] (gr_pp' pcset_pp_hex) d_fig_5_g++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' = T.g_from_edges_l d_fig_5_e++d_fig_5' :: [String]+d_fig_5' =+    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
@@ -0,0 +1,127 @@+-- | John Clough. "Aspects of Diatonic Sets".+-- _Journal of Music Theory_, 23(1):45--61, 1979.+module Music.Theory.Z.Clough_1979 where++import Data.List {- base -}++import qualified Music.Theory.List as T {- hmt -}++-- | 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 (subtract n) p++-- | Diatonic pitch class (Z7) set to /chord/.+--+-- > map dpcset_to_chord [[0,1],[0,2,4],[2,3,4,5,6]] == [[1,6],[2,2,3],[1,1,1,1,3]]+dpcset_to_chord :: Integral n => [n] -> [n]+dpcset_to_chord = T.d_dx . (++ [7]) . transpose_to_zero . nub . sort++-- | Inverse of 'dpcset_to_chord'.+--+-- > map chord_to_dpcset [[1,6],[2,2,3]] == [[0,1],[0,2,4]]+chord_to_dpcset :: Integral n => [n] -> [n]+chord_to_dpcset = T.dropRight 1 . T.dx_d 0++-- | Complement, ie. in relation to 'z7_univ'.+--+-- > map dpcset_complement [[0,1],[0,2,4]] == [[2,3,4,5,6],[1,3,5,6]]+dpcset_complement :: Integral n => [n] -> [n]+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 = is_z4++-- | Interval to interval class.+--+-- > map i_to_ic [0..7] == [0,1,2,3,3,2,1,0]+i_to_ic :: Integral n => n -> n+i_to_ic n = if n > 3 then 7 - n else n++-- | Is /chord/, ie. is 'sum' @7@.+--+-- > is_chord [2,2,3]+is_chord :: Integral n => [n] -> Bool+is_chord = (== 7) . sum++-- | Interval vector, given list of intervals.+--+-- > iv [2,2,3] == [0,2,1]+iv :: Integral n => [n] -> [n]+iv p =+    let h = T.generic_histogram p+        f n = T.lookup_def n 0 h+    in map f [1,2,3]++-- | Comparison function for 'inv'.+inf_cmp :: Ord a => [a] -> [a] -> Ordering+inf_cmp p q =+    if null p && null q+    then EQ+    else case compare (last p) (last q) of+           EQ -> inf_cmp (T.dropRight 1 p) (T.dropRight 1 q)+           r -> r++-- | Interval normal form.+--+-- > map inf [[2,2,3],[1,2,4],[2,1,4]] == [[2,2,3],[1,2,4],[2,1,4]]+inf :: Integral n => [n] -> [n]+inf = maximumBy inf_cmp . T.rotations++-- | Inverse of chord (retrograde).+--+-- > let p = [1,2,4] in (inf p,invert p,inf (invert p)) == ([1,2,4],[4,2,1],[2,1,4])+invert :: [n] -> [n]+invert = reverse++-- | Complement of /chord/.+--+-- > let r = [[1,1,1,1,3],[1,1,1,2,2],[1,1,2,1,2],[1,1,1,4],[2,1,1,3],[1,2,1,3],[1,2,2,2]]+-- > in map complement [[1,6],[2,5],[3,4],[1,1,5],[1,2,4],[1,3,3],[2,2,3]] == r+complement :: Integral n => [n] -> [n]+complement = inf . dpcset_to_chord . dpcset_complement . chord_to_dpcset++-- | Z7 pitch sequence to Z7 interval sequence, ie. 'mod7' of 'T.d_dx'.+--+-- > map iseq (permutations [0,1,2]) == [[1,1],[6,2],[6,6],[1,5],[5,1],[2,6]]+-- > map iseq (permutations [0,1,3]) == [[1,2],[6,3],[5,6],[2,4],[4,1],[3,5]]+-- > map iseq (permutations [0,2,3]) == [[2,1],[5,3],[6,5],[1,4],[4,2],[3,6]]+-- > map iseq (permutations [0,1,4]) == [[1,3],[6,4],[4,6],[3,3],[3,1],[4,4]]+-- > map iseq (permutations [0,2,4]) == [[2,2],[5,4],[5,5],[2,3],[3,2],[4,5]]+iseq :: Integral n => [n] -> [n]+iseq = map mod7 . T.d_dx++-- * Z++-- | Is /n/ in (0,/m/ - 1).+is_z_n :: Integral n => n -> n -> Bool+is_z_n m n = n >= 0 && n < m++-- | 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
@@ -0,0 +1,578 @@+-- | 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.Forte_1973+import Music.Theory.Z.Sro+import Music.Theory.Z.Tto++-- | 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 z12 [0,1,2,3] [6,4,1,11]) == ["T1M","T4MI"]++-}+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.++>>> $ pct rsg 156 3BA+>>> T4I+>>> $ pct rsg 0123 05A3+>>> T0M+>>> $ pct rsg 0123 4B61+>>> RT1M+>>> $ pct rsg 0123 B614+>>> r3RT1M++> 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 = 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
@@ -1,91 +1,103 @@--- | 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 -} -import Music.Theory.List-import qualified Music.Theory.Set.List as S-import Music.Theory.Z-import Music.Theory.Z.SRO+import qualified Music.Theory.List as T {- hmt -}+import qualified Music.Theory.Set.List as S {- hmt -} +import Music.Theory.Unicode {- hmt -}+import Music.Theory.Z {- 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 12 [0,1,3] == [[0,1,3],[0,2,11],[0,9,10]]-t_rotations :: Integral a => a -> [a] -> [[a]]-t_rotations z p =-    let r = rotations (sort p)-    in map (tn_to z 0) r+-- > 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 12 [0,1,3] == [[0,1,3],[0,2,11],[0,9,10]--- >                            ,[0,9,11],[0,2,3],[0,1,10]]-ti_rotations :: Integral a => a -> [a] -> [[a]]-ti_rotations z p =-    let q = invert z 0 p-        r = rotations (sort p) ++ rotations (sort q)-    in map (tn_to z 0) r---- | Variant with default value for empty input list case.-minimumBy_or :: a -> (a -> a -> Ordering) -> [a] -> a-minimumBy_or p f q = if null q then p else minimumBy f q+-- > 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  -- | Prime form rule requiring comparator, considering 't_rotations'.-t_cmp_prime :: Integral a => a -> ([a] -> [a] -> Ordering) -> [a] -> [a]-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 a => a -> ([a] -> [a] -> Ordering) -> [a] -> [a]-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). -- -- > forte_cmp [0,1,3,6,8,9] [0,2,3,6,7,9] == LT forte_cmp :: (Ord t) => [t] -> [t] -> Ordering-forte_cmp [] [] = EQ forte_cmp p  q  =-    let r = compare (last p) (last q)-    in if r == EQ then compare p q else r+    case (p,q) of+      ([],[]) -> EQ+      ([],_) -> LT+      (_,[]) -> GT+      _ -> 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 12 [0,1,3,6,8,9] == [0,1,3,6,8,9]--- > forte_prime 5 [0,1,4] == [0,1,2]------ > S.set (map (forte_prime 5) (S.powerset [0..4]))-forte_prime :: Integral a => a -> [a] -> [a]-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 12 [0,2,3],t_prime 12 [0,2,3]) == ([0,1,3],[0,2,3])-t_prime :: Integral a => a -> [a] -> [a]-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 i interval /i/.+-- | Interval class of interval /i/. ----- > 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 12) [-13,-1,0,1,13] == [1,1,0,1,1]-ic :: Integral a => a -> a -> a-ic z i = if i <= (z `div` 2) then i else z_sub z 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 . uncurry (z_sub z)) (S.pairs s)-        j = map f (group (sort i))-        k = map (`lookup` j) [1 .. z `div` 2]+-- > 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_modulus z `div` 2]     in map (fromMaybe 0) k  -- * BIP Metric@@ -96,6 +108,344 @@ -- >>> 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 . to_Z z) . d_dx+-- > 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.++> 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)++-}+z_sc_univ :: Integral i => Z i -> [[i]]+z_sc_univ z =+    T.sort_by_two_stage_on length id $+    nub $+    map (z_forte_prime z) $+    S.powerset (z_univ z)++-- * Forte Names (Z12)++-- | Synonym for 'String'.+type SC_Name = String++-- | 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_Table n+sc_table =+    [("0-1",[])+    ,("1-1",[0])+    ,("2-1",[0,1])+    ,("2-2",[0,2])+    ,("2-3",[0,3])+    ,("2-4",[0,4])+    ,("2-5",[0,5])+    ,("2-6",[0,6])+    ,("3-1",[0,1,2])+    ,("3-2",[0,1,3])+    ,("3-3",[0,1,4])+    ,("3-4",[0,1,5])+    ,("3-5",[0,1,6])+    ,("3-6",[0,2,4])+    ,("3-7",[0,2,5])+    ,("3-8",[0,2,6])+    ,("3-9",[0,2,7])+    ,("3-10",[0,3,6])+    ,("3-11",[0,3,7])+    ,("3-12",[0,4,8])+    ,("4-1",[0,1,2,3])+    ,("4-2",[0,1,2,4])+    ,("4-3",[0,1,3,4])+    ,("4-4",[0,1,2,5])+    ,("4-5",[0,1,2,6])+    ,("4-6",[0,1,2,7])+    ,("4-7",[0,1,4,5])+    ,("4-8",[0,1,5,6])+    ,("4-9",[0,1,6,7])+    ,("4-10",[0,2,3,5])+    ,("4-11",[0,1,3,5])+    ,("4-12",[0,2,3,6])+    ,("4-13",[0,1,3,6])+    ,("4-14",[0,2,3,7])+    ,("4-Z15",[0,1,4,6])+    ,("4-16",[0,1,5,7])+    ,("4-17",[0,3,4,7])+    ,("4-18",[0,1,4,7])+    ,("4-19",[0,1,4,8])+    ,("4-20",[0,1,5,8])+    ,("4-21",[0,2,4,6])+    ,("4-22",[0,2,4,7])+    ,("4-23",[0,2,5,7])+    ,("4-24",[0,2,4,8])+    ,("4-25",[0,2,6,8])+    ,("4-26",[0,3,5,8])+    ,("4-27",[0,2,5,8])+    ,("4-28",[0,3,6,9])+    ,("4-Z29",[0,1,3,7])+    ,("5-1",[0,1,2,3,4])+    ,("5-2",[0,1,2,3,5])+    ,("5-3",[0,1,2,4,5])+    ,("5-4",[0,1,2,3,6])+    ,("5-5",[0,1,2,3,7])+    ,("5-6",[0,1,2,5,6])+    ,("5-7",[0,1,2,6,7])+    ,("5-8",[0,2,3,4,6])+    ,("5-9",[0,1,2,4,6])+    ,("5-10",[0,1,3,4,6])+    ,("5-11",[0,2,3,4,7])+    ,("5-Z12",[0,1,3,5,6])+    ,("5-13",[0,1,2,4,8])+    ,("5-14",[0,1,2,5,7])+    ,("5-15",[0,1,2,6,8])+    ,("5-16",[0,1,3,4,7])+    ,("5-Z17",[0,1,3,4,8])+    ,("5-Z18",[0,1,4,5,7])+    ,("5-19",[0,1,3,6,7])+    ,("5-20",[0,1,3,7,8])+    ,("5-21",[0,1,4,5,8])+    ,("5-22",[0,1,4,7,8])+    ,("5-23",[0,2,3,5,7])+    ,("5-24",[0,1,3,5,7])+    ,("5-25",[0,2,3,5,8])+    ,("5-26",[0,2,4,5,8])+    ,("5-27",[0,1,3,5,8])+    ,("5-28",[0,2,3,6,8])+    ,("5-29",[0,1,3,6,8])+    ,("5-30",[0,1,4,6,8])+    ,("5-31",[0,1,3,6,9])+    ,("5-32",[0,1,4,6,9])+    ,("5-33",[0,2,4,6,8])+    ,("5-34",[0,2,4,6,9])+    ,("5-35",[0,2,4,7,9])+    ,("5-Z36",[0,1,2,4,7])+    ,("5-Z37",[0,3,4,5,8])+    ,("5-Z38",[0,1,2,5,8])+    ,("6-1",[0,1,2,3,4,5])+    ,("6-2",[0,1,2,3,4,6])+    ,("6-Z3",[0,1,2,3,5,6])+    ,("6-Z4",[0,1,2,4,5,6])+    ,("6-5",[0,1,2,3,6,7])+    ,("6-Z6",[0,1,2,5,6,7])+    ,("6-7",[0,1,2,6,7,8])+    ,("6-8",[0,2,3,4,5,7])+    ,("6-9",[0,1,2,3,5,7])+    ,("6-Z10",[0,1,3,4,5,7])+    ,("6-Z11",[0,1,2,4,5,7])+    ,("6-Z12",[0,1,2,4,6,7])+    ,("6-Z13",[0,1,3,4,6,7])+    ,("6-14",[0,1,3,4,5,8])+    ,("6-15",[0,1,2,4,5,8])+    ,("6-16",[0,1,4,5,6,8])+    ,("6-Z17",[0,1,2,4,7,8])+    ,("6-18",[0,1,2,5,7,8])+    ,("6-Z19",[0,1,3,4,7,8])+    ,("6-20",[0,1,4,5,8,9])+    ,("6-21",[0,2,3,4,6,8])+    ,("6-22",[0,1,2,4,6,8])+    ,("6-Z23",[0,2,3,5,6,8])+    ,("6-Z24",[0,1,3,4,6,8])+    ,("6-Z25",[0,1,3,5,6,8])+    ,("6-Z26",[0,1,3,5,7,8])+    ,("6-27",[0,1,3,4,6,9])+    ,("6-Z28",[0,1,3,5,6,9])+    ,("6-Z29",[0,1,3,6,8,9])+    ,("6-30",[0,1,3,6,7,9])+    ,("6-31",[0,1,3,5,8,9])+    ,("6-32",[0,2,4,5,7,9])+    ,("6-33",[0,2,3,5,7,9])+    ,("6-34",[0,1,3,5,7,9])+    ,("6-35",[0,2,4,6,8,10])+    ,("6-Z36",[0,1,2,3,4,7])+    ,("6-Z37",[0,1,2,3,4,8])+    ,("6-Z38",[0,1,2,3,7,8])+    ,("6-Z39",[0,2,3,4,5,8])+    ,("6-Z40",[0,1,2,3,5,8])+    ,("6-Z41",[0,1,2,3,6,8])+    ,("6-Z42",[0,1,2,3,6,9])+    ,("6-Z43",[0,1,2,5,6,8])+    ,("6-Z44",[0,1,2,5,6,9])+    ,("6-Z45",[0,2,3,4,6,9])+    ,("6-Z46",[0,1,2,4,6,9])+    ,("6-Z47",[0,1,2,4,7,9])+    ,("6-Z48",[0,1,2,5,7,9])+    ,("6-Z49",[0,1,3,4,7,9])+    ,("6-Z50",[0,1,4,6,7,9])+    ,("7-1",[0,1,2,3,4,5,6])+    ,("7-2",[0,1,2,3,4,5,7])+    ,("7-3",[0,1,2,3,4,5,8])+    ,("7-4",[0,1,2,3,4,6,7])+    ,("7-5",[0,1,2,3,5,6,7])+    ,("7-6",[0,1,2,3,4,7,8])+    ,("7-7",[0,1,2,3,6,7,8])+    ,("7-8",[0,2,3,4,5,6,8])+    ,("7-9",[0,1,2,3,4,6,8])+    ,("7-10",[0,1,2,3,4,6,9])+    ,("7-11",[0,1,3,4,5,6,8])+    ,("7-Z12",[0,1,2,3,4,7,9])+    ,("7-13",[0,1,2,4,5,6,8])+    ,("7-14",[0,1,2,3,5,7,8])+    ,("7-15",[0,1,2,4,6,7,8])+    ,("7-16",[0,1,2,3,5,6,9])+    ,("7-Z17",[0,1,2,4,5,6,9])+    ,("7-Z18",[0,1,2,3,5,8,9])+    ,("7-19",[0,1,2,3,6,7,9])+    ,("7-20",[0,1,2,4,7,8,9])+    ,("7-21",[0,1,2,4,5,8,9])+    ,("7-22",[0,1,2,5,6,8,9])+    ,("7-23",[0,2,3,4,5,7,9])+    ,("7-24",[0,1,2,3,5,7,9])+    ,("7-25",[0,2,3,4,6,7,9])+    ,("7-26",[0,1,3,4,5,7,9])+    ,("7-27",[0,1,2,4,5,7,9])+    ,("7-28",[0,1,3,5,6,7,9])+    ,("7-29",[0,1,2,4,6,7,9])+    ,("7-30",[0,1,2,4,6,8,9])+    ,("7-31",[0,1,3,4,6,7,9])+    ,("7-32",[0,1,3,4,6,8,9])+    ,("7-33",[0,1,2,4,6,8,10])+    ,("7-34",[0,1,3,4,6,8,10])+    ,("7-35",[0,1,3,5,6,8,10])+    ,("7-Z36",[0,1,2,3,5,6,8])+    ,("7-Z37",[0,1,3,4,5,7,8])+    ,("7-Z38",[0,1,2,4,5,7,8])+    ,("8-1",[0,1,2,3,4,5,6,7])+    ,("8-2",[0,1,2,3,4,5,6,8])+    ,("8-3",[0,1,2,3,4,5,6,9])+    ,("8-4",[0,1,2,3,4,5,7,8])+    ,("8-5",[0,1,2,3,4,6,7,8])+    ,("8-6",[0,1,2,3,5,6,7,8])+    ,("8-7",[0,1,2,3,4,5,8,9])+    ,("8-8",[0,1,2,3,4,7,8,9])+    ,("8-9",[0,1,2,3,6,7,8,9])+    ,("8-10",[0,2,3,4,5,6,7,9])+    ,("8-11",[0,1,2,3,4,5,7,9])+    ,("8-12",[0,1,3,4,5,6,7,9])+    ,("8-13",[0,1,2,3,4,6,7,9])+    ,("8-14",[0,1,2,4,5,6,7,9])+    ,("8-Z15",[0,1,2,3,4,6,8,9])+    ,("8-16",[0,1,2,3,5,7,8,9])+    ,("8-17",[0,1,3,4,5,6,8,9])+    ,("8-18",[0,1,2,3,5,6,8,9])+    ,("8-19",[0,1,2,4,5,6,8,9])+    ,("8-20",[0,1,2,4,5,7,8,9])+    ,("8-21",[0,1,2,3,4,6,8,10])+    ,("8-22",[0,1,2,3,5,6,8,10])+    ,("8-23",[0,1,2,3,5,7,8,10])+    ,("8-24",[0,1,2,4,5,6,8,10])+    ,("8-25",[0,1,2,4,6,7,8,10])+    ,("8-26",[0,1,2,4,5,7,9,10])+    ,("8-27",[0,1,2,4,5,7,8,10])+    ,("8-28",[0,1,3,4,6,7,9,10])+    ,("8-Z29",[0,1,2,3,5,6,7,9])+    ,("9-1",[0,1,2,3,4,5,6,7,8])+    ,("9-2",[0,1,2,3,4,5,6,7,9])+    ,("9-3",[0,1,2,3,4,5,6,8,9])+    ,("9-4",[0,1,2,3,4,5,7,8,9])+    ,("9-5",[0,1,2,3,4,6,7,8,9])+    ,("9-6",[0,1,2,3,4,5,6,8,10])+    ,("9-7",[0,1,2,3,4,5,7,8,10])+    ,("9-8",[0,1,2,3,4,6,7,8,10])+    ,("9-9",[0,1,2,3,5,6,7,8,10])+    ,("9-10",[0,1,2,3,4,6,7,9,10])+    ,("9-11",[0,1,2,3,5,6,7,9,10])+    ,("9-12",[0,1,2,4,5,6,8,9,10])+    ,("10-1",[0,1,2,3,4,5,6,7,8,9])+    ,("10-2",[0,1,2,3,4,5,6,7,8,10])+    ,("10-3",[0,1,2,3,4,5,6,7,9,10])+    ,("10-4",[0,1,2,3,4,5,6,8,9,10])+    ,("10-5",[0,1,2,3,4,5,7,8,9,10])+    ,("10-6",[0,1,2,3,4,6,7,8,9,10])+    ,("11-1",[0,1,2,3,4,5,6,7,8,9,10])+    ,("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_Table n+sc_table_unicode =+    let f = map (\c -> if c == '-' then non_breaking_hypen else c)+    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.+--+-- > forte_prime_name [0,1,4,6] == ("4-Z15",[0,1,4,6])+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)++-- | 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++-- | 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++-- | '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' of 'z12' before lookup.+--+-- > 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 [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 => [i] -> SC_Name+sc_name_unicode = sc_name_tbl sc_table_unicode++-- | Lookup a set-class given a set-class name.+--+-- > sc "6-Z17" == [0,1,2,4,7,8]+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++-- | 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, Num n) => i -> [[n]]+scs_n n = filter ((== n) . genericLength) scs++-- | Vector indicating degree of intersection with inversion at each transposition.+--+-- > 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)+    in map (length . intersect p) q++-- * Z-relation++-- | Locate /Z/ relation of set class.+--+-- > 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) && (z_icv z12 x `eq_i` z_icv z12 y)+    in case filter f (scs_n n) of+         [] -> Nothing+         [r] -> Just r+         _ -> error "z_relation_of"
+ 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
@@ -5,83 +5,101 @@  import Data.Bits {- base -} import Data.Char {- base -}-import Data.Function {- base -} import Data.List {- base -} import Data.Maybe {- base -}+import Data.Word {- base -} -import qualified Music.Theory.Z.SRO as T {- hmt -}+import qualified Music.Theory.List as List {- hmt -}+import qualified Music.Theory.Z 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]--- > T.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]--- > map (set_to_code 12) (T.ti_related 12 [0,2,3,5])+-- > set_to_code 12 [0,2,3,5] == 2880+-- > 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-        z = length a-        u = maximum (map (set_to_code z) (T.ti_related z p))+-- > 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 = 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@@ -90,55 +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 . groupBy ((==) `on` fst) . sortBy (compare `on` 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 12 [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 => i -> [i] -> [i]-encode_prime z s =-    let t = map (\n -> T.tn z n s) [0..11]-        c = t ++ map (T.invert z 0) t-    in decode 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 
@@ -1,83 +0,0 @@--- | Serial (ordered) pitch-class operations on 'Z'.-module Music.Theory.Z.SRO where--import Data.List {- base -}--import Music.Theory.Z---- | Transpose /p/ by /n/.------ > tn 5 4 [0,1,4] == [4,0,3]--- > tn 12 4 [1,5,6] == [5,9,10]-tn :: (Integral i, Functor f) => i -> i -> f i -> f i-tn z n = fmap (z_add z n)---- | Invert /p/ about /n/.------ > invert 5 0 [0,1,4] == [0,4,1]--- > invert 12 6 [4,5,6] == [8,7,6]--- > invert 12 0 [0,1,3] == [0,11,9]-invert :: (Integral i, Functor f) => i -> i -> f i -> f i-invert z n = fmap (\p -> z_sub z n (z_sub z p  n))---- | Composition of 'invert' about @0@ and 'tn'.------ > tni 5 1 [0,1,3] == [1,0,3]--- > tni 12 4 [1,5,6] == [3,11,10]--- > (invert 12 0 . tn  12 4) [1,5,6] == [7,3,2]-tni :: (Integral i, Functor f) => i -> i -> f i -> f i-tni z n = tn z n . invert z 0---- | Modulo multiplication.------ > mn 12 11 [0,1,4,9] == tni 12 0 [0,1,4,9]-mn :: (Integral i, Functor f) => i -> i -> f i -> f i-mn z n = fmap (z_mul z n)---- | T-related sequences of /p/.------ > length (t_related 12 [0,3,6,9]) == 12-t_related :: (Integral i, Functor f) => i -> f i -> [f i]-t_related z p = fmap (\n -> tn z n p) [0..11]---- | T\/I-related sequences of /p/.------ > length (ti_related 12 [0,1,3]) == 24--- > length (ti_related 12 [0,3,6,9]) == 24--- > ti_related 12 [0] == map return [0..11]-ti_related :: (Eq (f i), Integral i, Functor f) => i -> f i -> [f i]-ti_related z p = nub (t_related z p ++ t_related z (invert z 0 p))---- | R\/T\/I-related sequences of /p/.------ > length (rti_related 12 [0,1,3]) == 48--- > length (rti_related 12 [0,3,6,9]) == 24-rti_related :: Integral i => i -> [i] -> [[i]]-rti_related z p = let q = ti_related z p in nub (q ++ map reverse q)---- * Sequence operations---- | Variant of 'tn', transpose /p/ so first element is /n/.------ > tn_to 12 5 [0,1,3] == [5,6,8]--- > map (tn_to 12 0) [[0,1,3],[1,3,0],[3,0,1]]-tn_to :: Integral a => a -> a -> [a] -> [a]-tn_to z n p =-    case p of-      [] -> []-      x:xs -> n : tn z (z_sub z n x) xs---- | Variant of 'invert', inverse about /n/th element.------ > map (invert_ix 12 0) [[0,1,3],[3,4,6]] == [[0,11,9],[3,2,0]]--- > map (invert_ix 12 1) [[0,1,3],[3,4,6]] == [[2,1,11],[5,4,2]]-invert_ix :: Integral i => i -> Int -> [i] -> [i]-invert_ix z n p = invert z (p !! n) p---- | The standard t-matrix of /p/.------ > tmatrix 12 [0,1,3] == [[0,1,3]--- >                       ,[11,0,2]--- >                       ,[9,10,0]]-tmatrix :: Integral i => i -> [i] -> [[i]]-tmatrix z p = map (\n -> tn z n p) (tn_to z 0 (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 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 
@@ -1,102 +0,0 @@-{-# Language GeneralizedNewtypeDeriving #-}-module Music.Theory.Z12 where--import Data.List {- base -}---- | Z12 are modulo 12 integers.------ > map signum [-1,0::Z12,1] == [1,0,1]--- > map abs [-1,0::Z12,1] == [11,0,1]-newtype Z12 = Z12 Int deriving (Eq,Ord,Integral,Real)---- | Cyclic 'Enum' instance for Z12.------ > pred (0::Z12) == 11--- > succ (11::Z12) == 0--- > [9::Z12 .. 3] == [9,10,11,0,1,2,3]--- > [9::Z12,11 .. 3] == [9,11,1,3]-instance Enum Z12 where-    pred = subtract 1-    succ = (+) 1-    toEnum = fromIntegral-    fromEnum = fromIntegral-    enumFromThenTo n m o =-        let m' = m + (m - n)-        in if m' == o then [n,m,o] else n : enumFromThenTo m m' o-    enumFromTo n m =-        let n' = succ n-        in if n' == m then [n,m] else n : enumFromTo n' m---- | 'Bounded' instance for Z12.------ > [minBound::Z12 .. maxBound] == [0::Z12 .. 11]-instance Bounded Z12 where-    minBound = Z12 0-    maxBound = Z12 11---- | The Z12 modulo (ie. @12@) as a 'Z12' value.  This is required--- when lifting generalised @Z@ functions to 'Z12'.  It is /not/ the--- same as writing @12::Z12@.------ > z12_modulo == Z12 12--- > z12_modulo /= 12--- > (12::Z12) == 0--- > show z12_modulo == "(Z12 12)"-z12_modulo :: Z12-z12_modulo = Z12 12---- | Basis for Z12 show instance.------ > map show [-1,0::Z12,1,z12_modulo] == ["11","0","1","(Z12 12)"]-z12_showsPrec :: Int -> Z12 -> ShowS-z12_showsPrec p (Z12 i) =-    let x = showsPrec p i-    in if i < 0 || i > 11-       then showString "(Z12 " . x . showString ")"-       else x--instance Show Z12 where showsPrec = z12_showsPrec---- | Lift unary function over integers to Z12.------ > lift_unary_Z12 (negate) 7 == 5-lift_unary_Z12 :: (Int -> Int) -> Z12 -> Z12-lift_unary_Z12 f (Z12 a) = Z12 (f a `mod` 12)---- | Lift unary function over integers to Z12.------ > map (lift_binary_Z12 (+) 4) [1,5,6] == [5,9,10]-lift_binary_Z12 :: (Int -> Int -> Int) -> Z12 -> Z12 -> Z12-lift_binary_Z12 f (Z12 a) (Z12 b) = Z12 (mod (a `f` b) 12)---- | Raise an error if the internal 'Z12' value is negative.-check_negative :: (Int -> Int) -> Z12 -> Z12-check_negative f (Z12 n) =-    if n < 0-    then error "check_negative: negative Z12"-    else Z12 (f n)--instance Num Z12 where-  (+) = lift_binary_Z12 (+)-  (-) = lift_binary_Z12 (-)-  (*) = lift_binary_Z12 (*)-  negate = lift_unary_Z12 negate-  fromInteger n = Z12 (fromInteger n `mod` 12)-  signum = check_negative signum-  abs = check_negative abs---- | Convert integral to 'Z12'.------ > map to_Z12 [-9,-3,0,13] == [3,9,0,1]-to_Z12 :: Integral i => i -> Z12-to_Z12 = fromIntegral---- | Convert 'Z12' to integral.-from_Z12 :: Integral i => Z12 -> i-from_Z12 = fromIntegral---- | Z12 not in set.------ > complement [0,2,4,5,7,9,11] == [1,3,6,8,10]-complement :: [Z12] -> [Z12]-complement = (\\) [0 .. 11]
− Music/Theory/Z12/Castren_1994.hs 
@@ -1,150 +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.Z12 (Z12)-import qualified Music.Theory.Z12.Forte_1973 as T-import qualified Music.Theory.Z12.TTO as T---- | Is /p/ symmetrical under inversion.------ > import Music.Theory.Z12.Forte_1973--- > map inv_sym (scs_n 2) == [True,True,True,True,True,True]--- > map (fromEnum.inv_sym) (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.tn i (T.invert 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 (T.invert 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 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 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 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) (T.t_related 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) (T.ti_related 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 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 
@@ -1,342 +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 qualified Music.Theory.List as T-import qualified Music.Theory.Set.List as T-import Music.Theory.Z12-import qualified Music.Theory.Z12.Forte_1973 as T-import qualified Music.Theory.Z12.Morris_1987 as T-import qualified Music.Theory.Z12.TTO as TTO-import qualified Music.Theory.Z12.SRO as SRO---- | 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]]-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.------ >>> 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---- | Cyclic interval segment.-ciseg :: [Z12] -> [Z12]-ciseg = T.int . cyc---- | Synonynm for 'complement'.------ >>> cmpl 02468t--- 13579B------ > cmpl [0,2,4,6,8,10] == [1,3,5,7,9,11]-cmpl :: [Z12] -> [Z12]-cmpl = complement---- | Form cycle.------ >>> cyc 056--- 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 (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.------ >>> 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.------ >>> 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 | 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 | 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 = [TTO.tn j p,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 = T.sc_name---- | p `has_ess` q is true iff p can embed q in sequence.-has_ess :: [Z12] -> [Z12] -> Bool-has_ess _ [] = True-has_ess [] _ = False-has_ess (p:ps) (q:qs) = if p == q-                        then has_ess ps qs-                        else has_ess ps (q:qs)---- | Embedded segment search.------ >>> echo 23a | ess 0164325--- 2B013A9--- 923507A------ > ess [2,3,10] [0,1,6,4,3,2,5] == [[9,2,3,5,0,7,10],[2,11,0,1,3,10,9]]-ess :: [Z12] -> [Z12] -> [[Z12]]-ess p = filter (`has_ess` p) . SRO.rtmi_related---- | 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 q `elem` map pf (cf [n] (cg p))---- | Can the set-class q be drawn from the pcset p.-has_sc :: [Z12] -> [Z12] -> Bool-has_sc = has_sc_pf T.forte_prime---- | Interval cycle filter.------ >>> echo 22341 | 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.------ >>> 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.------ >>> 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 T.ic . iseg---- | Interval segment (INT).-iseg :: [Z12] -> [Z12]-iseg = T.int---- | Imbrications.-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 concatMap (f (tails p)) cs---- | 'issb' gives the set-classes that can append to 'p' to give 'q'.------ >>> 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 -> T.forte_prime (p ++ x) == q) . TTO.ti_related-    in map T.sc_name (filter f (cf [k] T.scs))---- | Matrix search.------ >>> 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`) (SRO.rti_related p)---- | Normalize.------ >>> 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@).------ >>> pi 0236 12--- 0236--- 6320--- 532B--- B235------ > pci [0,2,3,6] [1,2] == [[0,2,3,6],[5,3,2,11],[6,3,2,0],[11,2,3,5]]-pci :: [Z12] -> [Z12] -> [[Z12]]-pci p i =-    let f q = T.set (map (q `genericIndex`) i)-    in filter (\q -> f q == f p) (SRO.rti_related p)---- | Relate sets.------ >>> rs 0123 641e--- T1M------ > import Music.Theory.Z12.Morris_1987.Parse--- > rs [0,1,2,3] [6,4,1,11] == [(rnrtnmi "T1M",[1,6,11,4])--- >                            ,(rnrtnmi "T4MI",[4,11,6,1])]-rs :: [Z12] -> [Z12] -> [(T.SRO, [Z12])]-rs x y =-    let xs = map (\o -> (o, o `T.sro` x)) T.sro_TnMI-        q = T.set y-    in filter (\(_,p) -> T.set p == q) xs---- | Relate segments.------ >>> rsg 156 3BA--- T4I------ > rsg [1,5,6] [3,11,10] == [rnrtnmi "T4I",rnrtnmi "r1RT4MI"]------ >>> rsg 0123 05t3--- T0M------ > rsg [0,1,2,3] [0,5,10,3] == [rnrtnmi "T0M",rnrtnmi "RT3MI"]------ >>> rsg 0123 4e61--- RT1M------ > rsg [0,1,2,3] [4,11,6,1] == [rnrtnmi "T4MI",rnrtnmi "RT1M"]------ >>> echo e614 | rsg 0123--- r3RT1M------ > rsg [0,1,2,3] [11,6,1,4] == [rnrtnmi "r1T4MI",rnrtnmi "r1RT1M"]----rsg :: [Z12] -> [Z12] -> [T.SRO]-rsg x y = map fst (filter (\(_,x') -> x' == y) (T.sros x))---- | Subsets.-sb :: [[Z12]] -> [[Z12]]-sb xs =-    let f p = all id (map (`has_sc` p) xs)-    in filter f T.scs---- | Super set-class.------ >>> spsc 4-11 4-12--- 5-26[02458]------ > spsc [T.sc "4-11",T.sc "4-12"] == ["5-26"]------ >>> spsc 3-11 3-8--- 4-27[0258]--- 4-Z29[0137]------ > spsc [T.sc "3-11",T.sc "3-8"] == ["4-27","4-Z29"]------ >>> spsc `fl 3`--- 6-Z17[012478]------ > spsc (cf [3] T.scs) == ["6-Z17"]-spsc :: [[Z12]] -> [String]-spsc xs =-    let f y = all (y `has_sc`) xs-        g = (==) `on` length-    in (map T.sc_name . head . groupBy g . filter f) T.scs
− Music/Theory/Z12/Forte_1973.hs 
@@ -1,554 +0,0 @@--- | Allen Forte. /The Structure of Atonal Music/. Yale University--- Press, New Haven, 1973.-module Music.Theory.Z12.Forte_1973 where--import Data.List {- base -}-import Data.Maybe {- base -}--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 z12_modulo---- | 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 z12_modulo---- | 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 :: [Z12] -> [Z12]-forte_prime = Z.forte_prime z12_modulo---- | 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 z12_modulo---- * Set Class Table---- | Synonym for 'String'.-type SC_Name = String---- | The set-class table (Forte prime forms).------ > length sc_table == 224-sc_table :: [(SC_Name,[Z12])]-sc_table =-    [("0-1",[])-    ,("1-1",[0])-    ,("2-1",[0,1])-    ,("2-2",[0,2])-    ,("2-3",[0,3])-    ,("2-4",[0,4])-    ,("2-5",[0,5])-    ,("2-6",[0,6])-    ,("3-1",[0,1,2])-    ,("3-2",[0,1,3])-    ,("3-3",[0,1,4])-    ,("3-4",[0,1,5])-    ,("3-5",[0,1,6])-    ,("3-6",[0,2,4])-    ,("3-7",[0,2,5])-    ,("3-8",[0,2,6])-    ,("3-9",[0,2,7])-    ,("3-10",[0,3,6])-    ,("3-11",[0,3,7])-    ,("3-12",[0,4,8])-    ,("4-1",[0,1,2,3])-    ,("4-2",[0,1,2,4])-    ,("4-3",[0,1,3,4])-    ,("4-4",[0,1,2,5])-    ,("4-5",[0,1,2,6])-    ,("4-6",[0,1,2,7])-    ,("4-7",[0,1,4,5])-    ,("4-8",[0,1,5,6])-    ,("4-9",[0,1,6,7])-    ,("4-10",[0,2,3,5])-    ,("4-11",[0,1,3,5])-    ,("4-12",[0,2,3,6])-    ,("4-13",[0,1,3,6])-    ,("4-14",[0,2,3,7])-    ,("4-Z15",[0,1,4,6])-    ,("4-16",[0,1,5,7])-    ,("4-17",[0,3,4,7])-    ,("4-18",[0,1,4,7])-    ,("4-19",[0,1,4,8])-    ,("4-20",[0,1,5,8])-    ,("4-21",[0,2,4,6])-    ,("4-22",[0,2,4,7])-    ,("4-23",[0,2,5,7])-    ,("4-24",[0,2,4,8])-    ,("4-25",[0,2,6,8])-    ,("4-26",[0,3,5,8])-    ,("4-27",[0,2,5,8])-    ,("4-28",[0,3,6,9])-    ,("4-Z29",[0,1,3,7])-    ,("5-1",[0,1,2,3,4])-    ,("5-2",[0,1,2,3,5])-    ,("5-3",[0,1,2,4,5])-    ,("5-4",[0,1,2,3,6])-    ,("5-5",[0,1,2,3,7])-    ,("5-6",[0,1,2,5,6])-    ,("5-7",[0,1,2,6,7])-    ,("5-8",[0,2,3,4,6])-    ,("5-9",[0,1,2,4,6])-    ,("5-10",[0,1,3,4,6])-    ,("5-11",[0,2,3,4,7])-    ,("5-Z12",[0,1,3,5,6])-    ,("5-13",[0,1,2,4,8])-    ,("5-14",[0,1,2,5,7])-    ,("5-15",[0,1,2,6,8])-    ,("5-16",[0,1,3,4,7])-    ,("5-Z17",[0,1,3,4,8])-    ,("5-Z18",[0,1,4,5,7])-    ,("5-19",[0,1,3,6,7])-    ,("5-20",[0,1,3,7,8])-    ,("5-21",[0,1,4,5,8])-    ,("5-22",[0,1,4,7,8])-    ,("5-23",[0,2,3,5,7])-    ,("5-24",[0,1,3,5,7])-    ,("5-25",[0,2,3,5,8])-    ,("5-26",[0,2,4,5,8])-    ,("5-27",[0,1,3,5,8])-    ,("5-28",[0,2,3,6,8])-    ,("5-29",[0,1,3,6,8])-    ,("5-30",[0,1,4,6,8])-    ,("5-31",[0,1,3,6,9])-    ,("5-32",[0,1,4,6,9])-    ,("5-33",[0,2,4,6,8])-    ,("5-34",[0,2,4,6,9])-    ,("5-35",[0,2,4,7,9])-    ,("5-Z36",[0,1,2,4,7])-    ,("5-Z37",[0,3,4,5,8])-    ,("5-Z38",[0,1,2,5,8])-    ,("6-1",[0,1,2,3,4,5])-    ,("6-2",[0,1,2,3,4,6])-    ,("6-Z3",[0,1,2,3,5,6])-    ,("6-Z4",[0,1,2,4,5,6])-    ,("6-5",[0,1,2,3,6,7])-    ,("6-Z6",[0,1,2,5,6,7])-    ,("6-7",[0,1,2,6,7,8])-    ,("6-8",[0,2,3,4,5,7])-    ,("6-9",[0,1,2,3,5,7])-    ,("6-Z10",[0,1,3,4,5,7])-    ,("6-Z11",[0,1,2,4,5,7])-    ,("6-Z12",[0,1,2,4,6,7])-    ,("6-Z13",[0,1,3,4,6,7])-    ,("6-14",[0,1,3,4,5,8])-    ,("6-15",[0,1,2,4,5,8])-    ,("6-16",[0,1,4,5,6,8])-    ,("6-Z17",[0,1,2,4,7,8])-    ,("6-18",[0,1,2,5,7,8])-    ,("6-Z19",[0,1,3,4,7,8])-    ,("6-20",[0,1,4,5,8,9])-    ,("6-21",[0,2,3,4,6,8])-    ,("6-22",[0,1,2,4,6,8])-    ,("6-Z23",[0,2,3,5,6,8])-    ,("6-Z24",[0,1,3,4,6,8])-    ,("6-Z25",[0,1,3,5,6,8])-    ,("6-Z26",[0,1,3,5,7,8])-    ,("6-27",[0,1,3,4,6,9])-    ,("6-Z28",[0,1,3,5,6,9])-    ,("6-Z29",[0,1,3,6,8,9])-    ,("6-30",[0,1,3,6,7,9])-    ,("6-31",[0,1,3,5,8,9])-    ,("6-32",[0,2,4,5,7,9])-    ,("6-33",[0,2,3,5,7,9])-    ,("6-34",[0,1,3,5,7,9])-    ,("6-35",[0,2,4,6,8,10])-    ,("6-Z36",[0,1,2,3,4,7])-    ,("6-Z37",[0,1,2,3,4,8])-    ,("6-Z38",[0,1,2,3,7,8])-    ,("6-Z39",[0,2,3,4,5,8])-    ,("6-Z40",[0,1,2,3,5,8])-    ,("6-Z41",[0,1,2,3,6,8])-    ,("6-Z42",[0,1,2,3,6,9])-    ,("6-Z43",[0,1,2,5,6,8])-    ,("6-Z44",[0,1,2,5,6,9])-    ,("6-Z45",[0,2,3,4,6,9])-    ,("6-Z46",[0,1,2,4,6,9])-    ,("6-Z47",[0,1,2,4,7,9])-    ,("6-Z48",[0,1,2,5,7,9])-    ,("6-Z49",[0,1,3,4,7,9])-    ,("6-Z50",[0,1,4,6,7,9])-    ,("7-1",[0,1,2,3,4,5,6])-    ,("7-2",[0,1,2,3,4,5,7])-    ,("7-3",[0,1,2,3,4,5,8])-    ,("7-4",[0,1,2,3,4,6,7])-    ,("7-5",[0,1,2,3,5,6,7])-    ,("7-6",[0,1,2,3,4,7,8])-    ,("7-7",[0,1,2,3,6,7,8])-    ,("7-8",[0,2,3,4,5,6,8])-    ,("7-9",[0,1,2,3,4,6,8])-    ,("7-10",[0,1,2,3,4,6,9])-    ,("7-11",[0,1,3,4,5,6,8])-    ,("7-Z12",[0,1,2,3,4,7,9])-    ,("7-13",[0,1,2,4,5,6,8])-    ,("7-14",[0,1,2,3,5,7,8])-    ,("7-15",[0,1,2,4,6,7,8])-    ,("7-16",[0,1,2,3,5,6,9])-    ,("7-Z17",[0,1,2,4,5,6,9])-    ,("7-Z18",[0,1,2,3,5,8,9])-    ,("7-19",[0,1,2,3,6,7,9])-    ,("7-20",[0,1,2,4,7,8,9])-    ,("7-21",[0,1,2,4,5,8,9])-    ,("7-22",[0,1,2,5,6,8,9])-    ,("7-23",[0,2,3,4,5,7,9])-    ,("7-24",[0,1,2,3,5,7,9])-    ,("7-25",[0,2,3,4,6,7,9])-    ,("7-26",[0,1,3,4,5,7,9])-    ,("7-27",[0,1,2,4,5,7,9])-    ,("7-28",[0,1,3,5,6,7,9])-    ,("7-29",[0,1,2,4,6,7,9])-    ,("7-30",[0,1,2,4,6,8,9])-    ,("7-31",[0,1,3,4,6,7,9])-    ,("7-32",[0,1,3,4,6,8,9])-    ,("7-33",[0,1,2,4,6,8,10])-    ,("7-34",[0,1,3,4,6,8,10])-    ,("7-35",[0,1,3,5,6,8,10])-    ,("7-Z36",[0,1,2,3,5,6,8])-    ,("7-Z37",[0,1,3,4,5,7,8])-    ,("7-Z38",[0,1,2,4,5,7,8])-    ,("8-1",[0,1,2,3,4,5,6,7])-    ,("8-2",[0,1,2,3,4,5,6,8])-    ,("8-3",[0,1,2,3,4,5,6,9])-    ,("8-4",[0,1,2,3,4,5,7,8])-    ,("8-5",[0,1,2,3,4,6,7,8])-    ,("8-6",[0,1,2,3,5,6,7,8])-    ,("8-7",[0,1,2,3,4,5,8,9])-    ,("8-8",[0,1,2,3,4,7,8,9])-    ,("8-9",[0,1,2,3,6,7,8,9])-    ,("8-10",[0,2,3,4,5,6,7,9])-    ,("8-11",[0,1,2,3,4,5,7,9])-    ,("8-12",[0,1,3,4,5,6,7,9])-    ,("8-13",[0,1,2,3,4,6,7,9])-    ,("8-14",[0,1,2,4,5,6,7,9])-    ,("8-Z15",[0,1,2,3,4,6,8,9])-    ,("8-16",[0,1,2,3,5,7,8,9])-    ,("8-17",[0,1,3,4,5,6,8,9])-    ,("8-18",[0,1,2,3,5,6,8,9])-    ,("8-19",[0,1,2,4,5,6,8,9])-    ,("8-20",[0,1,2,4,5,7,8,9])-    ,("8-21",[0,1,2,3,4,6,8,10])-    ,("8-22",[0,1,2,3,5,6,8,10])-    ,("8-23",[0,1,2,3,5,7,8,10])-    ,("8-24",[0,1,2,4,5,6,8,10])-    ,("8-25",[0,1,2,4,6,7,8,10])-    ,("8-26",[0,1,2,4,5,7,9,10])-    ,("8-27",[0,1,2,4,5,7,8,10])-    ,("8-28",[0,1,3,4,6,7,9,10])-    ,("8-Z29",[0,1,2,3,5,6,7,9])-    ,("9-1",[0,1,2,3,4,5,6,7,8])-    ,("9-2",[0,1,2,3,4,5,6,7,9])-    ,("9-3",[0,1,2,3,4,5,6,8,9])-    ,("9-4",[0,1,2,3,4,5,7,8,9])-    ,("9-5",[0,1,2,3,4,6,7,8,9])-    ,("9-6",[0,1,2,3,4,5,6,8,10])-    ,("9-7",[0,1,2,3,4,5,7,8,10])-    ,("9-8",[0,1,2,3,4,6,7,8,10])-    ,("9-9",[0,1,2,3,5,6,7,8,10])-    ,("9-10",[0,1,2,3,4,6,7,9,10])-    ,("9-11",[0,1,2,3,5,6,7,9,10])-    ,("9-12",[0,1,2,4,5,6,8,9,10])-    ,("10-1",[0,1,2,3,4,5,6,7,8,9])-    ,("10-2",[0,1,2,3,4,5,6,7,8,10])-    ,("10-3",[0,1,2,3,4,5,6,7,9,10])-    ,("10-4",[0,1,2,3,4,5,6,8,9,10])-    ,("10-5",[0,1,2,3,4,5,7,8,9,10])-    ,("10-6",[0,1,2,3,4,6,7,8,9,10])-    ,("11-1",[0,1,2,3,4,5,6,7,8,9,10])-    ,("12-1",[0,1,2,3,4,5,6,7,8,9,10,11])]---- | 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 p =-    let n = find (\(_,q) -> forte_prime p == q) sc_table-    in fst (fromMaybe (error "sc_name") n)---- | Lookup a set-class given a set-class name.------ > sc "6-Z17" == [0,1,2,4,7,8]-sc :: SC_Name -> [Z12]-sc n = snd (fromMaybe (error "sc") (find (\(m,_) -> n == m) sc_table))--{- | 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 = map snd sc_table---- | 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 n = filter ((== n) . genericLength) scs---- * BIP Metric---- | Basic interval pattern, see Allen Forte \"The Basic Interval Patterns\"--- /JMT/ 17/2 (1973):234-272------ >>> 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 = Z.bip z12_modulo---- * 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 = Z.ic z12_modulo---- | 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 = Z.icv z12_modulo
− Music/Theory/Z12/Lewin_1980.hs 
@@ -1,47 +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 Music.Theory.Z12-import qualified Music.Theory.Z12.Castren_1994 as C---- | 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 Control.Monad.Logic {- logict -}---- | 'msum' '.' 'map' 'return'.------ > observeAll (fromList [1..7]) == [1..7]-fromList :: MonadPlus m => [a] -> m a-fromList = msum . map return---- | 'MonadPlus' all-interval series.------ > [0,1,3,2,9,5,10,4,7,11,8,6] `elem` observeAll (all_interval_m 12)--- > length (observeAll (all_interval_m 12)) == 3856--- > map (length . observeAll . all_interval_m) [4,6,8,10] == [2,4,24,288]-all_interval_m :: MonadPlus m => Int -> m [Int]-all_interval_m n =-    let rec p q =-            if length p == n-            then return (reverse p)-            else do i <- fromList [1 .. n - 1]-                    guard (i `notElem` p)-                    let j:_ = p-                        m = abs ((i - j) `mod` n)-                    guard (m `notElem` q)-                    rec (i:p) (m:q)-    in rec [0] []---- | '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 = observeAll . all_interval_m
− Music/Theory/Z12/Morris_1987.hs 
@@ -1,99 +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 Data.List-import Music.Theory.List-import Music.Theory.Z12-import Music.Theory.Z12.SRO---- | @INT@ operator.------ > int [0,1,3,6,10] == [1,2,3,4]-int :: [Z12] -> [Z12]-int = d_dx---- * Serial operations---- | Serial Operator,of the form rRTMI.-data SRO = SRO Z12 Bool Z12 Bool Bool-           deriving (Eq,Show)---- | Serial operation.------ >>> sro T4 156--- 59A------ > sro (rnrtnmi "T4") (pco "156") == [5,9,10]------ >>> echo 024579 | sro RT4I--- 79B024------ > sro (SRO 0 True 4 False True) [0,2,4,5,7,9] == [7,9,11,0,2,4]------ >>> sro T4I 156--- 3BA------ > sro (rnrtnmi "T4I") (pco "156") == [3,11,10]--- > sro (SRO 0 False 4 False True) [1,5,6] == [3,11,10]------ >>> echo 156 | sro T4  | sro T0I--- 732------ > (sro (rnrtnmi "T0I") . sro (rnrtnmi "T4")) (pco "156") == [7,3,2]------ >>> echo 024579 | sro RT4I--- 79B024------ > sro (rnrtnmi "RT4I") (pco "024579") == [7,9,11,0,2,4]------ > sro (SRO 1 True 1 True False) [0,1,2,3] == [11,6,1,4]--- > sro (SRO 1 False 4 True True) [0,1,2,3] == [11,6,1,4]-sro :: SRO -> [Z12] -> [Z12]-sro (SRO r r' t m i) x =-    let x1 = if i then invert 0 x else x-        x2 = if m then m5 x1 else x1-        x3 = tn t x2-        x4 = if r' then reverse x3 else x3-    in genericRotate_left r x4---- | The total set of serial operations.-sros :: [Z12] -> [(SRO,[Z12])]-sros x = [let o = (SRO r r' t m i) in (o,sro o x) |-          r <- [0 .. genericLength x - 1],-          r' <- [False,True],-          t <- [0 .. 11],-          m <- [False,True],-          i <- [False,True]]---- | The set of transposition 'SRO's.-sro_Tn ::[SRO]-sro_Tn = [SRO 0 False n False False | n <- [0..11]]---- | The set of transposition and inversion 'SRO's.-sro_TnI ::[SRO]-sro_TnI = [SRO 0 False n False i |-           n <- [0..11],-           i <- [False,True]]---- | The set of retrograde and transposition and inversion 'SRO's.-sro_RTnI ::[SRO]-sro_RTnI = [SRO 0 r n False i |-            r <- [True,False],-            n <- [0..11],-            i <- [False,True]]---- | The set of transposition,@M5@ and inversion 'SRO's.-sro_TnMI ::[SRO]-sro_TnMI = [SRO 0 False n m i |-            n <- [0..11],-            m <- [True,False],-            i <- [True,False]]---- | The set of retrograde,transposition,@M5@ and inversion 'SRO's.-sro_RTnMI ::[SRO]-sro_RTnMI = [SRO 0 r n m i |-             r <- [True,False],-             n <- [0..11],-             m <- [True,False],-             i <- [True,False]]
− Music/Theory/Z12/Morris_1987/Parse.hs 
@@ -1,57 +0,0 @@--- | Parsers for pitch class sets and sequences, and for 'SRO's.-module Music.Theory.Z12.Morris_1987.Parse (rnrtnmi,pco) where--import Control.Monad {- base -}-import Data.Char {- base -}-import Text.ParserCombinators.Parsec {- parsec -}--import Music.Theory.Z12-import Music.Theory.Z12.Morris_1987---- | A 'Char' parser.-type P a = GenParser Char () a---- | Boolean 'P' for given 'Char'.-is_char :: Char -> P Bool-is_char c =-    let f '_' = False-        f _ = True-    in liftM f (option '_' (char c))---- | Parse 'Int'.-get_int :: P Z12-get_int = liftM (fromInteger . read) (many1 digit)---- | Parse a Morris format serial operator descriptor.------ > rnrtnmi "r2RT3MI" == SRO 2 True 3 True True-rnrtnmi :: String -> SRO-rnrtnmi s =-  let p = do r <- rot-             r' <- is_char 'R'-             _ <- char 'T'-             t <- get_int-             m <- is_char 'M'-             i <- is_char 'I'-             eof-             return (SRO r r' t m i)-      rot = option 0 (char 'r' >> get_int)-  in either-         (\e -> error ("rnRTnMI parse failed\n" ++ show e))-         id-         (parse p "" s)---- | 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 z12_modulo 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 z12_modulo
− Music/Theory/Z12/SRO.hs 
@@ -1,96 +0,0 @@--- | Serial (ordered) pitch-class operations on 'Z12'.-module Music.Theory.Z12.SRO where--import Data.List-import qualified Music.Theory.List as T-import qualified Music.Theory.Z.SRO as Z-import Music.Theory.Z12---- | Transpose /p/ by /n/.------ > tn 4 [1,5,6] == [5,9,10]-tn :: Z12 -> [Z12] -> [Z12]-tn = Z.tn z12_modulo---- | Invert /p/ about /n/.------ > invert 6 [4,5,6] == [8,7,6]--- > invert 0 [0,1,3] == [0,11,9]-invert :: Z12 -> [Z12] -> [Z12]-invert = Z.invert z12_modulo---- | Composition of 'invert' about @0@ and 'tn'.------ > tni 4 [1,5,6] == [3,11,10]--- > (invert 0 . tn  4) [1,5,6] == [7,3,2]-tni :: Z12 -> [Z12] -> [Z12]-tni = Z.tni z12_modulo---- | Modulo 12 multiplication------ > mn 11 [0,1,4,9] == tni 0 [0,1,4,9]-mn :: Z12 -> [Z12] -> [Z12]-mn = Z.mn z12_modulo---- | M5, ie. 'mn' @5@.------ > m5 [0,1,3] == [0,5,3]-m5 :: [Z12] -> [Z12]-m5 = mn 5---- | T-related sequences of /p/.------ > length (t_related [0,3,6,9]) == 12-t_related :: [Z12] -> [[Z12]]-t_related = Z.t_related z12_modulo---- | 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]-ti_related :: [Z12] -> [[Z12]]-ti_related = Z.ti_related z12_modulo---- | R\/T\/I-related sequences of /p/.------ > length (rti_related [0,1,3]) == 48--- > length (rti_related [0,3,6,9]) == 24-rti_related :: [Z12] -> [[Z12]]-rti_related = Z.rti_related z12_modulo---- | T\/M\/I-related sequences of /p/.-tmi_related :: [Z12] -> [[Z12]]-tmi_related p = let q = ti_related p in nub (q ++ map m5 q)---- | R\/T\/M\/I-related sequences of /p/.-rtmi_related :: [Z12] -> [[Z12]]-rtmi_related p = let q = tmi_related p in nub (q ++ map reverse q)---- | r\/R\/T\/M\/I-related sequences of /p/.-rrtmi_related :: [Z12] -> [[Z12]]-rrtmi_related p = nub (concatMap rtmi_related (T.rotations p))---- * Sequence operations---- | Variant of 'tn', transpose /p/ so first element is /n/.------ > tn_to 5 [0,1,3] == [5,6,8]--- > map (tn_to 0) [[0,1,3],[1,3,0],[3,0,1]] == [[0,1,3],[0,2,11],[0,9,10]]-tn_to :: Z12 -> [Z12] -> [Z12]-tn_to = Z.tn_to z12_modulo---- | Variant of 'invert', inverse about /n/th element.------ > map (invert_ix 0) [[0,1,3],[3,4,6]] == [[0,11,9],[3,2,0]]--- > map (invert_ix 1) [[0,1,3],[3,4,6]] == [[2,1,11],[5,4,2]]-invert_ix :: Int -> [Z12] -> [Z12]-invert_ix = Z.invert_ix z12_modulo---- | The standard t-matrix of /p/.------ > tmatrix [0,1,3] == [[0,1,3]--- >                    ,[11,0,2]--- >                    ,[9,10,0]]-tmatrix :: [Z12] -> [[Z12]]-tmatrix = Z.tmatrix z12_modulo
− Music/Theory/Z12/TTO.hs 
@@ -1,58 +0,0 @@--- | Pitch-class set (unordered) operations on 'Z12'.-module Music.Theory.Z12.TTO where--import Data.List-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.------ > tn 4 [1,5,6] == [5,9,10]--- > tn 4 [0,4,8] == [0,4,8]-tn :: Z12 -> [Z12] -> [Z12]-tn n = sort . map (+ n)---- | Invert about n.------ > invert 6 [4,5,6] == [6,7,8]--- > invert 0 [0,1,3] == [0,9,11]-invert :: Z12 -> [Z12] -> [Z12]-invert n = sort . map (\p -> n - (p - n))---- | Composition of 'invert' about @0@ and 'tn'.------ > tni 4 [1,5,6] == [3,10,11]--- > (invert 0 . tn  4) [1,5,6] == [2,3,7]-tni :: Z12 -> [Z12] -> [Z12]-tni n = tn n . invert 0---- | Modulo 12 multiplication------ > mn 11 [0,1,4,9] == invert 0 [0,1,4,9]-mn :: Z12 -> [Z12] -> [Z12]-mn n = sort . map (* n)---- | M5, ie. 'mn' @5@.------ > m5 [0,1,3] == [0,3,5]-m5 :: [Z12] -> [Z12]-m5 = mn 5---- | T-related sets of /p/.------ > length (t_related [0,1,3]) == 12--- > t_related [0,3,6,9] == [[0,3,6,9],[1,4,7,10],[2,5,8,11]]-t_related :: [Z12] -> [[Z12]]-t_related p = nub (map (`tn` p) [0..11])---- | T\/I-related set of /p/.------ > length (ti_related [0,1,3]) == 24--- > ti_related [0,3,6,9] == [[0,3,6,9],[1,4,7,10],[2,5,8,11]]-ti_related :: [Z12] -> [[Z12]]-ti_related p = nub (t_related p ++ t_related (invert 0 p))
− README 
@@ -1,15 +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]--[hs]: http://haskell.org/-[hmt-diagrams]:  http://rd.slavepianos.org/?t=hmt-diagrams--© [rohan drape][rd], 2006-2014, [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/1080-C01.csv view
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+ 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/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/scl/et12.scl view
@@ -0,0 +1,17 @@+! et12.scl+!+12 tone equal temperament+12+!+100.0+200.0+300.0+400.0+500.0+600.0+700.0+800.0+900.0+1000.0+1100.0+2/1
+ data/scl/et19.scl view
@@ -0,0 +1,24 @@+! et19.scl+!+19 tone equal temperament+19+!+63.1578947368421+126.3157894736842+189.4736842105263+252.63157894736838+315.78947368421046+378.94736842105254+442.1052631578946+505.2631578947367+568.4210526315787+631.5789473684208+694.7368421052629+757.894736842105+821.0526315789471+884.2105263157891+947.3684210526312+1010.5263157894733+1073.6842105263154+1136.8421052631575+2/1
+ data/scl/et31.scl view
@@ -0,0 +1,36 @@+! et31.scl+!+31 tone equal temperament+31+!+38.70967741935484+77.41935483870968+116.12903225806451+154.83870967741933+193.54838709677415+232.25806451612897+270.9677419354838+309.6774193548386+348.3870967741934+387.09677419354824+425.80645161290306+464.5161290322579+503.2258064516127+541.9354838709676+580.6451612903224+619.3548387096773+658.0645161290322+696.7741935483871+735.483870967742+774.1935483870968+812.9032258064517+851.6129032258066+890.3225806451615+929.0322580645163+967.7419354838712+1006.4516129032261+1045.161290322581+1083.8709677419358+1122.5806451612907+1161.2903225806456+2/1
+ data/scl/et53.scl view
@@ -0,0 +1,58 @@+! et53.scl+!+53 tone equal temperament+53+!+22.641509433962263+45.283018867924525+67.9245283018868+90.56603773584906+113.20754716981133+135.8490566037736+158.49056603773585+181.1320754716981+203.77358490566036+226.4150943396226+249.05660377358487+271.6981132075471+294.3396226415094+316.98113207547163+339.6226415094339+362.26415094339615+384.9056603773584+407.54716981132066+430.1886792452829+452.83018867924517+475.4716981132074+498.1132075471697+520.7547169811319+543.3962264150941+566.0377358490564+588.6792452830186+611.3207547169809+633.9622641509432+656.6037735849054+679.2452830188677+701.8867924528299+724.5283018867922+747.1698113207544+769.8113207547167+792.452830188679+815.0943396226412+837.7358490566035+860.3773584905657+883.018867924528+905.6603773584902+928.3018867924525+950.9433962264147+973.584905660377+996.2264150943392+1018.8679245283015+1041.5094339622638+1064.150943396226+1086.7924528301883+1109.4339622641505+1132.0754716981128+1154.716981132075+1177.3584905660373+2/1
+ data/scl/et72.scl view
@@ -0,0 +1,77 @@+! et72.scl+!+72 tone equal temperament+72+!+16.666666666666668+33.333333333333336+50.0+66.66666666666666+83.33333333333331+99.99999999999997+116.66666666666663+133.3333333333333+149.99999999999994+166.6666666666666+183.33333333333326+199.99999999999991+216.66666666666657+233.33333333333323+249.9999999999999+266.6666666666665+283.33333333333314+299.9999999999998+316.6666666666664+333.33333333333303+349.99999999999966+366.6666666666663+383.3333333333329+399.99999999999955+416.6666666666662+433.3333333333328+449.99999999999943+466.66666666666606+483.3333333333327+499.9999999999993+516.666666666666+533.3333333333326+549.9999999999992+566.6666666666658+583.3333333333325+599.9999999999991+616.6666666666657+633.3333333333323+649.999999999999+666.6666666666656+683.3333333333322+699.9999999999989+716.6666666666655+733.3333333333321+749.9999999999987+766.6666666666654+783.333333333332+799.9999999999986+816.6666666666653+833.3333333333319+849.9999999999985+866.6666666666652+883.3333333333318+899.9999999999984+916.666666666665+933.3333333333317+949.9999999999983+966.6666666666649+983.3333333333316+999.9999999999982+1016.6666666666648+1033.3333333333314+1049.9999999999982+1066.666666666665+1083.3333333333317+1099.9999999999984+1116.6666666666652+1133.333333333332+1149.9999999999986+1166.6666666666654+1183.3333333333321+2/1
+ data/scl/et96.scl view
@@ -0,0 +1,101 @@+! et96.scl+!+96 tone equal temperament+96+!+12.5+25.0+37.5+50.0+62.5+75.0+87.5+100.0+112.5+125.0+137.5+150.0+162.5+175.0+187.5+200.0+212.5+225.0+237.5+250.0+262.5+275.0+287.5+300.0+312.5+325.0+337.5+350.0+362.5+375.0+387.5+400.0+412.5+425.0+437.5+450.0+462.5+475.0+487.5+500.0+512.5+525.0+537.5+550.0+562.5+575.0+587.5+600.0+612.5+625.0+637.5+650.0+662.5+675.0+687.5+700.0+712.5+725.0+737.5+750.0+762.5+775.0+787.5+800.0+812.5+825.0+837.5+850.0+862.5+875.0+887.5+900.0+912.5+925.0+937.5+950.0+962.5+975.0+987.5+1000.0+1012.5+1025.0+1037.5+1050.0+1062.5+1075.0+1087.5+1100.0+1112.5+1125.0+1137.5+1150.0+1162.5+1175.0+1187.5+2/1
+ 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/young-lm_piano_1964.scl view
@@ -0,0 +1,17 @@+! young-lm_piano_1964.scl+!+LaMonte Young's Well-Tuned Piano (1964)+12+!+279/256+9/8+147/128+21/16+93/64+189/128+3/2+49/32+7/4+31/16+63/32+2/1
hmt.cabal view
@@ -1,81 +1,110 @@+cabal-version:     2.4 Name:              hmt-Version:           0.15+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, 2006-2014+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 == 7.8.2+Homepage:          http://rohandrape.net/t/hmt+Tested-With:       GHC == 9.2.4 Build-Type:        Simple-Cabal-Version:     >= 1.8 -Data-files:        README-                   Help/hmt.help.lhs+Data-files:        README.md+                   data/csv/mnd/*.csv+                   data/dot/euler/*.dot+                   data/scl/*.scl  Library   Build-Depends:   array,-                   base == 4.*,+                   base >= 4.9 && < 5,                    bytestring,                    colour,                    containers,+                   data-memocombinators,                    data-ordlist,                    directory,+                   fgl,                    filepath,+                   hmt-base == 0.20.*,                    lazy-csv,                    logict,                    multiset-comb,                    parsec,-                   permutation,                    primes,+                   process,+                   random,                    safe,                    split,-                   utf8-string+                   strict,+                   text,+                   time+  Default-Language:Haskell2010   GHC-Options:     -Wall -fwarn-tabs-  Exposed-modules: Music.Theory.Array.CSV-                   Music.Theory.Array.CSV.Midi-                   Music.Theory.Array.MD+  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.Square                    Music.Theory.Bjorklund                    Music.Theory.Block_Design.Johnson_2007+                   Music.Theory.Braille                    Music.Theory.Clef-                   Music.Theory.Combinations                    Music.Theory.Contour.Polansky_1992+                   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.Function+                   Music.Theory.Gamelan+                   Music.Theory.Graph.Deacon_1934+                   Music.Theory.Graph.Dot+                   Music.Theory.Graph.Fgl+                   Music.Theory.Graph.Johnson_2014                    Music.Theory.Instrument.Choir+                   Music.Theory.Instrument.Names                    Music.Theory.Interval                    Music.Theory.Interval.Barlow_1987                    Music.Theory.Interval.Name                    Music.Theory.Interval.Spelling                    Music.Theory.Key-                   Music.Theory.List-                   Music.Theory.Math-                   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.Permutations+                   Music.Theory.Parse                    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+                   Music.Theory.Pitch.Note.Name                    Music.Theory.Pitch.Spelling                    Music.Theory.Pitch.Spelling.Cluster+                   Music.Theory.Pitch.Spelling.Key+                   Music.Theory.Pitch.Spelling.Table+                   Music.Theory.Random.I_Ching+                   Music.Theory.Random.Jones_1981                    Music.Theory.Set.List                    Music.Theory.Set.Set                    Music.Theory.Tempo_Marking@@ -83,47 +112,66 @@                    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                    Music.Theory.Tuning.Alves_1997-                   Music.Theory.Tuning.ET-                   Music.Theory.Tuning.Gann+                   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.Microtonal_Synthesis+                   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.Riley+                   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.Tuning.Werckmeister-                   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.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