diff --git a/Music/Theory/Array.hs b/Music/Theory/Array.hs
deleted file mode 100644
--- a/Music/Theory/Array.hs
+++ /dev/null
@@ -1,119 +0,0 @@
--- | Array & table functions
-module Music.Theory.Array where
-
-import Data.List {- base -}
-import qualified Data.Array as A {- array -}
-
-import qualified Music.Theory.List as T {- hmt -}
-
--- * Association List (List Array)
-
--- | 'T.minmax' of /k/.
-larray_bounds :: Ord k => [(k,v)] -> (k,k)
-larray_bounds = T.minmax . map fst
-
--- | 'A.array' of association list.
-larray :: A.Ix k => [(k,v)] -> A.Array k v
-larray a = A.array (larray_bounds a) a
-
--- * List Table
-
--- | 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]]
-
--- | Table row count.
-tbl_rows :: Table t -> Int
-tbl_rows = length
-
--- | Table column count, assumes table is regular.
-tbl_columns :: Table t -> Int
-tbl_columns tbl =
-  case tbl of
-    [] -> 0
-    r0:_ -> length r0
-
--- | Determine is table is regular, ie. all rows have the same number of columns.
---
--- > tbl_is_regular [[0..3],[4..7],[8..11]] == True
-tbl_is_regular :: Table t -> Bool
-tbl_is_regular = (== 1) . length . nub . map length
-
--- | Map /f/ at table, padding short rows with /k/.
-tbl_make_regular :: (t -> u,u) -> Table t -> Table u
-tbl_make_regular (f,k) tbl =
-    let z = maximum (map length tbl)
-    in map (T.pad_right k z) (map (map f) tbl)
-
--- | Append a sequence of /nil/ (or default) values to each row of /tbl/
--- so to make it regular (ie. all rows of equal length).
-tbl_make_regular_nil :: t -> Table t -> Table t
-tbl_make_regular_nil k = tbl_make_regular (id,k)
-
--- * Matrix Indices
-
--- | Matrix dimensions are written (rows,columns).
-type Dimensions i = (i,i)
-
--- | Matrix indices are written (row,column) & are here _zero_ indexed.
-type Ix i = (i,i)
-
--- | Translate 'Ix' by row and column delta.
---
--- > ix_translate (1,2) (3,4) == (4,6)
-ix_translate :: Num t => (t,t) -> Ix t -> Ix t
-ix_translate (dr,dc) (r,c) = (r + dr,c + dc)
-
--- | Modulo 'Ix' by 'Dimensions'.
---
--- > ix_modulo (4,4) (3,7) == (3,3)
-ix_modulo :: Integral t => Dimensions t -> Ix t -> Ix t
-ix_modulo (nr,nc) (r,c) = (r `mod` nr,c `mod` nc)
-
--- | Given number of columns and row index, list row indices.
---
--- > row_indices 3 1 == [(1,0),(1,1),(1,2)]
-row_indices :: (Enum t, Num t) => t -> t -> [Ix t]
-row_indices nc r = map (\c -> (r,c)) [0 .. nc - 1]
-
--- | Given number of rows and column index, list column indices.
---
--- > column_indices 3 1 == [(0,1),(1,1),(2,1)]
-column_indices :: (Enum t, Num t) => t -> t -> [Ix t]
-column_indices nr c = map (\r -> (r,c)) [0 .. nr - 1]
-
--- | All zero-indexed matrix indices, in row order.  This is the order
--- given by 'sort'.
---
--- > matrix_indices (2,3) == [(0,0),(0,1),(0,2),(1,0),(1,1),(1,2)]
--- > sort (matrix_indices (2,3)) == matrix_indices (2,3)
-matrix_indices :: (Enum t, Num t) => Dimensions t -> [Ix t]
-matrix_indices (nr,nc) = concatMap (row_indices nc) [0 .. nr - 1 ]
-
--- | Corner indices of given 'Dimensions', in row order.
---
--- > matrix_corner_indices (2,3) == [(0,0),(0,2),(1,0),(1,2)]
-matrix_corner_indices :: Num t => Dimensions t -> [Ix t]
-matrix_corner_indices (nr,nc) = [(0,0),(0,nc - 1),(nr - 1,0),(nr - 1,nc - 1)]
-
--- | Parallelogram corner indices, given as rectangular 'Dimensions' with an
--- offset for the lower indices.
---
--- > parallelogram_corner_indices ((2,3),2) == [(0,0),(0,2),(1,2),(1,4)]
-parallelogram_corner_indices :: Num t => (Dimensions t,t) -> [Ix t]
-parallelogram_corner_indices ((nr,nc),o) = [(0,0),(0,nc - 1),(nr - 1,o),(nr - 1,nc + o - 1)]
-
--- | Apply 'ix_modulo' and 'ix_translate' for all 'matrix_indices',
--- ie. all translations of a 'shape' in row order.  The resulting 'Ix'
--- sets are not sorted and may have duplicates.
---
--- > concat (all_ix_translations (2,3) [(0,0)]) == matrix_indices (2,3)
-all_ix_translations :: Integral t => Dimensions t -> [Ix t] -> [[Ix t]]
-all_ix_translations dm ix =
-    let f z = ix_modulo dm . ix_translate z
-    in map (\dx -> map (f dx) ix) (matrix_indices dm)
-
--- | Sort sets into row order and remove duplicates.
-all_ix_translations_uniq :: Integral t => Dimensions t -> [Ix t] -> [[Ix t]]
-all_ix_translations_uniq dm = nub . map sort . all_ix_translations dm
diff --git a/Music/Theory/Array/CSV.hs b/Music/Theory/Array/CSV.hs
deleted file mode 100644
--- a/Music/Theory/Array/CSV.hs
+++ /dev/null
@@ -1,222 +0,0 @@
--- | Regular matrix array data, CSV, column & row indexing.
-module Music.Theory.Array.CSV where
-
-import Data.List {- base -}
-
-import qualified Data.Array as A {- array -}
-import qualified Safe {- safe -}
-import qualified Text.CSV.Lazy.String as C {- lazy-csv -}
-
-import qualified Music.Theory.Array as T {- hmt -}
-import qualified Music.Theory.Array.Cell_Ref as R {- hmt -}
-import qualified Music.Theory.IO as T {- hmt -}
-import qualified Music.Theory.List as T {- hmt -}
-import qualified Music.Theory.Tuple as T {- hmt -}
-
--- * FIELD / QUOTE
-
--- | Quoting is required is the string has a double-quote, comma newline or carriage-return.
-csv_requires_quote :: String -> Bool
-csv_requires_quote = any (`elem` "\",\n\r")
-
--- | Quoting places double-quotes at the start and end and escapes double-quotes.
-csv_quote :: String -> String
-csv_quote fld =
-  let esc s =
-        case s of
-          [] -> []
-          '"':s' -> '"' : '"' : esc s'
-          c:s' -> c : esc s'
-  in '"' : esc fld ++ "\""
-
--- | Quote field if required.
-csv_quote_if_req :: String -> String
-csv_quote_if_req fld = if csv_requires_quote fld then csv_quote fld else fld
-
--- * TABLE
-
--- | When reading a CSV file is the first row a header?
-type CSV_Has_Header = Bool
-
--- | Alias for 'Char', allow characters other than @,@ as delimiter.
-type CSV_Delimiter = Char
-
--- | Alias for 'Bool', allow linebreaks in fields.
-type CSV_Allow_Linebreaks = Bool
-
--- | When writing a CSV file should the delimiters be aligned,
--- ie. should columns be padded with spaces, and if so at which side
--- of the data?
-data CSV_Align_Columns = CSV_No_Align | CSV_Align_Left | CSV_Align_Right
-
--- | CSV options.
-type CSV_Opt = (CSV_Has_Header,CSV_Delimiter,CSV_Allow_Linebreaks,CSV_Align_Columns)
-
--- | Default CSV options, no header, comma delimiter, no linebreaks, no alignment.
-def_csv_opt :: CSV_Opt
-def_csv_opt = (False,',',False,CSV_No_Align)
-
--- | CSV table, ie. a 'Table' with 'Maybe' a header.
-type CSV_Table a = (Maybe [String],T.Table a)
-
--- | Read 'CSV_Table' from @CSV@ file.
-csv_table_read :: CSV_Opt -> (String -> a) -> FilePath -> IO (CSV_Table a)
-csv_table_read (hdr,delim,brk,_) f fn = do
-  s <- T.read_file_utf8 fn
-  let t = C.csvTable (C.parseDSV brk delim s)
-      p = C.fromCSVTable t
-      (h,d) = if hdr then (Just (head p),tail p) else (Nothing,p)
-  return (h,map (map f) d)
-
--- | Read 'T.Table' only with 'def_csv_opt'.
-csv_table_read_def :: (String -> a) -> FilePath -> IO (T.Table a)
-csv_table_read_def f = fmap snd . csv_table_read def_csv_opt f
-
--- | Read plain CSV 'T.Table'.
-csv_table_read_plain :: FilePath -> IO (T.Table String)
-csv_table_read_plain = csv_table_read_def id
-
--- | Read and process @CSV@ 'CSV_Table'.
-csv_table_with :: CSV_Opt -> (String -> a) -> FilePath -> (CSV_Table a -> b) -> IO b
-csv_table_with opt f fn g = fmap g (csv_table_read opt f fn)
-
--- | Align table according to 'CSV_Align_Columns'.
---
--- > csv_table_align CSV_No_Align [["a","row","and"],["then","another","one"]]
-csv_table_align :: CSV_Align_Columns -> T.Table String -> T.Table String
-csv_table_align align tbl =
-    let c = transpose tbl
-        n = map (maximum . map length) c
-        ext k s = let pd = replicate (k - length s) ' '
-                  in case align of
-                       CSV_No_Align -> s
-                       CSV_Align_Left -> pd ++ s
-                       CSV_Align_Right -> s ++ pd
-    in transpose (zipWith (map . ext) n c)
-
--- | Pretty-print 'CSV_Table'.
-csv_table_pp :: (a -> String) -> CSV_Opt -> CSV_Table a -> String
-csv_table_pp f (_,delim,brk,align) (hdr,tbl) =
-  let tbl' = csv_table_align align (T.mcons hdr (map (map f) tbl))
-      (_,t) = C.toCSVTable tbl'
-  in C.ppDSVTable brk delim t
-
--- | 'T.write_file_utf8' of 'csv_table_pp'.
-csv_table_write :: (a -> String) -> CSV_Opt -> FilePath -> CSV_Table a -> IO ()
-csv_table_write f opt fn csv = T.write_file_utf8 fn (csv_table_pp f opt csv)
-
--- | Write 'Table' only (no header) with 'def_csv_opt'.
-csv_table_write_def :: (a -> String) -> FilePath -> T.Table a -> IO ()
-csv_table_write_def f fn tbl = csv_table_write f def_csv_opt fn (Nothing,tbl)
-
--- | Write plain CSV 'Table'.
-csv_table_write_plain :: FilePath -> T.Table String -> IO ()
-csv_table_write_plain = csv_table_write_def id
-
--- | @0@-indexed (row,column) cell lookup.
-table_lookup :: T.Table a -> (Int,Int) -> a
-table_lookup t (r,c) = let ix = Safe.atNote "table_lookup" in (t `ix` r) `ix` c
-
--- | Row data.
-table_row :: T.Table a -> R.Row_Ref -> [a]
-table_row t r = Safe.atNote "table_row" t (R.row_index r)
-
--- | Column data.
-table_column :: T.Table a -> R.Column_Ref -> [a]
-table_column t c = Safe.atNote "table_column" (transpose t) (R.column_index c)
-
--- | Lookup value across columns.
-table_column_lookup :: Eq a => T.Table a -> (R.Column_Ref,R.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 :: T.Table a -> R.Cell_Ref -> a
-table_cell t (c,r) =
-    let (r',c') = (R.row_index r,R.column_index c)
-    in table_lookup t (r',c')
-
--- | @0@-indexed (row,column) cell lookup over column range.
-table_lookup_row_segment :: T.Table a -> (Int,(Int,Int)) -> [a]
-table_lookup_row_segment t (r,(c0,c1)) =
-    let r' = Safe.atNote "table_lookup_row_segment" t r
-    in take (c1 - c0 + 1) (drop c0 r')
-
--- | Range of cells from row.
-table_row_segment :: T.Table a -> (R.Row_Ref,R.Column_Range) -> [a]
-table_row_segment t (r,c) =
-    let (r',c') = (R.row_index r,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 :: T.Table a -> A.Array R.Cell_Ref a
-table_to_array t =
-    let nr = length t
-        nc = length (Safe.atNote "table_to_array" t 0)
-        bnd = (R.cell_ref_minima,(toEnum (nc - 1),nr))
-        asc = zip (R.cell_range_row_order bnd) (concat t)
-    in A.array bnd asc
-
--- | 'table_to_array' of 'csv_table_read'.
-csv_array_read :: CSV_Opt -> (String -> a) -> FilePath -> IO (A.Array R.Cell_Ref a)
-csv_array_read opt f fn = fmap (table_to_array . snd) (csv_table_read opt f fn)
-
--- * Irregular
-
-csv_field_str :: C.CSVField -> String
-csv_field_str f =
-    case f of
-      C.CSVField _ _ _ _ s _ -> s
-      C.CSVFieldError _ _ _ _ _ -> error "csv_field_str"
-
-csv_error_recover :: C.CSVError -> C.CSVRow
-csv_error_recover e =
-    case e of
-      C.IncorrectRow _ _ _ f -> f
-      C.BlankLine _ _ _ _ -> []
-      _ -> error "csv_error_recover: not recoverable"
-
-csv_row_recover :: Either [C.CSVError] C.CSVRow -> C.CSVRow
-csv_row_recover r =
-    case r of
-      Left [e] -> csv_error_recover e
-      Left _ -> error "csv_row_recover: multiple errors"
-      Right r' -> r'
-
--- | Read irregular @CSV@ file, ie. rows may have any number of columns, including no columns.
-csv_load_irregular :: (String -> a) -> FilePath -> IO [[a]]
-csv_load_irregular f fn = do
-  s <- T.read_file_utf8 fn
-  return (map (map (f . csv_field_str) . csv_row_recover) (C.parseCSV s))
-
-csv_write_irregular :: (a -> String) -> CSV_Opt -> FilePath -> CSV_Table a -> IO ()
-csv_write_irregular f opt fn (hdr,tbl) =
-  let tbl' = T.tbl_make_regular_nil "" (map (map f) tbl)
-  in T.write_file_utf8 fn (csv_table_pp id opt (hdr,tbl'))
-
-csv_write_irregular_def :: (a -> String) -> FilePath -> T.Table a -> IO ()
-csv_write_irregular_def f fn tbl = csv_write_irregular f def_csv_opt fn (Nothing,tbl)
-
--- * Tuples
-
-type P5_Parser t1 t2 t3 t4 t5 = (String -> t1,String -> t2,String -> t3,String -> t4,String -> t5)
-type P5_Writer t1 t2 t3 t4 t5 = (t1 -> String,t2 -> String,t3 -> String,t4 -> String,t5 -> String)
-
-csv_table_read_p5 :: P5_Parser t1 t2 t3 t4 t5 -> CSV_Opt -> FilePath -> IO (Maybe [String],[(t1,t2,t3,t4,t5)])
-csv_table_read_p5 f opt fn = do
-  (hdr,dat) <- csv_table_read opt id fn
-  return (hdr,map (T.p5_from_list f) dat)
-
-csv_table_write_p5 :: P5_Writer t1 t2 t3 t4 t5 -> CSV_Opt -> FilePath -> (Maybe [String],[(t1,t2,t3,t4,t5)]) -> IO ()
-csv_table_write_p5 f opt fn (hdr,dat) = csv_table_write id opt fn (hdr,map (T.p5_to_list f) dat)
diff --git a/Music/Theory/Array/CSV/Midi/MND.hs b/Music/Theory/Array/CSV/Midi/MND.hs
deleted file mode 100644
--- a/Music/Theory/Array/CSV/Midi/MND.hs
+++ /dev/null
@@ -1,241 +0,0 @@
--- | Functions for reading midi note data (MND) from CSV files.
--- This is /not/ a generic text midi notation.
--- The defined commands are @on@ and @off@, but others may be present.
--- Non-integral note number and key velocity data are allowed.
-module Music.Theory.Array.CSV.Midi.MND where
-
-import Data.Function {- base -}
-import Data.Maybe {- base -}
-import Data.Word {- base -}
-
-import Sound.SC3.Server.Param {- hsc3 -}
-
-import qualified Music.Theory.Array.CSV as T {- hmt -}
-import qualified Music.Theory.Math as T {- hmt -}
-import qualified Music.Theory.Read as T {- hmt -}
-import qualified Music.Theory.Show as T {- hmt -}
-import qualified Music.Theory.Time.Seq as T {- hmt -}
-
--- | If /r/ is whole to /k/ places then show as integer, else as float to /k/ places.
-data_value_pp :: Real t => Int -> t -> String
-data_value_pp k r =
-    if T.whole_to_precision k r
-    then show (T.real_floor_int r)
-    else T.real_pp k r
-
--- | Channel values are 4-bit (0-15).
-type Channel = Word8
-
--- | The required header field.
-csv_mnd_hdr :: [String]
-csv_mnd_hdr = ["time","on/off","note","velocity","channel","param"]
-
--- | Midi note data, the type parameters are to allow for fractional note & velocity values.
--- The command is a string, @on@ and @off@ are standard, other commands may be present.
---
--- > unwords csv_mnd_hdr == "time on/off note velocity channel param"
---
--- > 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 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
diff --git a/Music/Theory/Array/CSV/Midi/SKINI.hs b/Music/Theory/Array/CSV/Midi/SKINI.hs
deleted file mode 100644
--- a/Music/Theory/Array/CSV/Midi/SKINI.hs
+++ /dev/null
@@ -1,57 +0,0 @@
--- | 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)
diff --git a/Music/Theory/Array/Cell_Ref.hs b/Music/Theory/Array/Cell_Ref.hs
deleted file mode 100644
--- a/Music/Theory/Array/Cell_Ref.hs
+++ /dev/null
@@ -1,228 +0,0 @@
--- | Cell references & indexing.
-module Music.Theory.Array.Cell_Ref where
-
-import qualified Data.Array as A {- array -}
-import Data.Char {- base -}
-import Data.Function {- base -}
-import Data.Maybe {- base -}
-import Data.String {- base -}
-
--- | @A@ indexed case-insensitive column references.  The column
--- following @Z@ is @AA@.
-data Column_Ref = Column_Ref {column_ref_string :: String}
-
-instance IsString Column_Ref where fromString = Column_Ref
-instance Read Column_Ref where readsPrec _ s = [(Column_Ref s,[])]
-instance Show Column_Ref where show = column_ref_string
-instance Eq Column_Ref where (==) = (==) `on` column_index
-instance Ord Column_Ref where compare = compare `on` column_index
-
-instance Enum Column_Ref where
-    fromEnum = column_index
-    toEnum = column_ref
-
-instance A.Ix Column_Ref where
-    range = column_range
-    index = interior_column_index
-    inRange = column_in_range
-    rangeSize = column_range_size
-
--- | Inclusive range of column references.
-type Column_Range = (Column_Ref,Column_Ref)
-
--- | @1@-indexed row reference.
-type Row_Ref = Int
-
--- | Zero index of 'Row_Ref'.
-row_index :: Row_Ref -> Int
-row_index r = r - 1
-
--- | Inclusive range of row references.
-type Row_Range = (Row_Ref,Row_Ref)
-
--- | Cell reference, column then row.
-type Cell_Ref = (Column_Ref,Row_Ref)
-
--- | Inclusive range of cell references.
-type Cell_Range = (Cell_Ref,Cell_Ref)
-
--- | Case folding letter to index function.  Only valid for ASCII letters.
---
--- > map letter_index ['A' .. 'Z'] == [0 .. 25]
--- > map letter_index ['a','d' .. 'm'] == [0,3 .. 12]
-letter_index :: Char -> Int
-letter_index c = fromEnum (toUpper c) - fromEnum 'A'
-
--- | Inverse of 'letter_index'.
---
--- > map index_letter [0,3 .. 12] == ['A','D' .. 'M']
-index_letter :: Int -> Char
-index_letter i = toEnum (i + fromEnum 'A')
-
--- | Translate column reference to @0@-index.
---
--- > :set -XOverloadedStrings
--- > map column_index ["A","c","z","ac","XYZ"] == [0,2,25,28,17575]
-column_index :: Column_Ref -> Int
-column_index (Column_Ref c) =
-    let m = iterate (* 26) 1
-        i = reverse (map letter_index c)
-    in sum (zipWith (*) m (zipWith (+) [0..] i))
-
--- | Column reference to interior index within specified range.  Type
--- specialised 'Data.Ix.index'.
---
--- > map (Data.Ix.index ('A','Z')) ['A','C','Z'] == [0,2,25]
--- > map (interior_column_index ("A","Z")) ["A","C","Z"] == [0,2,25]
---
--- > map (Data.Ix.index ('B','C')) ['B','C'] == [0,1]
--- > map (interior_column_index ("B","C")) ["B","C"] == [0,1]
-interior_column_index :: Column_Range -> Column_Ref -> Int
-interior_column_index (l,r) c =
-    let n = column_index c
-        l' = column_index l
-        r' = column_index r
-    in if n > r'
-       then error (show ("interior_column_index",l,r,c))
-       else n - l'
-
--- | Inverse of 'column_index'.
---
--- > let c = ["A","Z","AA","AZ","BA","BZ","CA"]
--- > in map column_ref [0,25,26,51,52,77,78] == c
---
--- > column_ref (0+25+1+25+1+25+1) == "CA"
-column_ref :: Int -> Column_Ref
-column_ref =
-    let rec n = case n `quotRem` 26 of
-                  (0,r) -> [index_letter r]
-                  (q,r) -> index_letter (q - 1) : rec r
-    in Column_Ref . rec
-
--- | Type specialised 'pred'.
---
--- > column_ref_pred "DF" == "DE"
-column_ref_pred :: Column_Ref -> Column_Ref
-column_ref_pred = pred
-
--- | Type specialised 'succ'.
---
--- > column_ref_succ "DE" == "DF"
-column_ref_succ :: Column_Ref -> Column_Ref
-column_ref_succ = succ
-
--- | Bimap of 'column_index'.
---
--- > column_indices ("b","p") == (1,15)
--- > column_indices ("B","IT") == (1,253)
-column_indices :: Column_Range -> (Int,Int)
-column_indices =
-    let bimap f (i,j) = (f i,f j)
-    in bimap column_index
-
--- | Type specialised 'Data.Ix.range'.
---
--- > column_range ("L","R") == ["L","M","N","O","P","Q","R"]
--- > Data.Ix.range ('L','R') == "LMNOPQR"
-column_range :: Column_Range -> [Column_Ref]
-column_range rng =
-    let (l,r) = column_indices rng
-    in map column_ref [l .. r]
-
--- | Type specialised 'Data.Ix.inRange'.
---
--- > map (column_in_range ("L","R")) ["A","N","Z"] == [False,True,False]
--- > map (column_in_range ("L","R")) ["L","N","R"] == [True,True,True]
---
--- > map (Data.Ix.inRange ('L','R')) ['A','N','Z'] == [False,True,False]
--- > map (Data.Ix.inRange ('L','R')) ['L','N','R'] == [True,True,True]
-column_in_range :: Column_Range -> Column_Ref -> Bool
-column_in_range rng c =
-    let (l,r) = column_indices rng
-        k = column_index c
-    in k >= l && k <= r
-
--- | Type specialised 'Data.Ix.rangeSize'.
---
--- > map column_range_size [("A","Z"),("AA","ZZ")] == [26,26 * 26]
--- > Data.Ix.rangeSize ('A','Z') == 26
-column_range_size :: Column_Range -> Int
-column_range_size = (+ 1) . negate . uncurry (-) . column_indices
-
--- | Type specialised 'Data.Ix.range'.
-row_range :: Row_Range -> [Row_Ref]
-row_range = A.range
-
--- | The standard uppermost leftmost cell reference, @A1@.
---
--- > Just cell_ref_minima == parse_cell_ref "A1"
-cell_ref_minima :: Cell_Ref
-cell_ref_minima = (Column_Ref "A",1)
-
--- | Cell reference parser for standard notation of (column,row).
---
--- > parse_cell_ref "CC348" == Just ("CC",348)
-parse_cell_ref :: String -> Maybe Cell_Ref
-parse_cell_ref s =
-    case span isUpper s of
-      ([],_) -> Nothing
-      (c,r) -> case span isDigit r of
-                 (n,[]) -> Just (Column_Ref c,read n)
-                 _ -> Nothing
-
-is_cell_ref :: String -> Bool
-is_cell_ref = isJust . parse_cell_ref
-
-parse_cell_ref_err :: String -> Cell_Ref
-parse_cell_ref_err = fromMaybe (error "parse_cell_ref") . parse_cell_ref
-
--- | Cell reference pretty printer.
---
--- > cell_ref_pp ("CC",348) == "CC348"
-cell_ref_pp :: Cell_Ref -> String
-cell_ref_pp (Column_Ref c,r) = c ++ show r
-
--- | Translate cell reference to @0@-indexed pair.
---
--- > cell_index ("CC",348) == (80,347)
--- > Data.Ix.index (("AA",1),("ZZ",999)) ("CC",348) == 54293
-cell_index :: Cell_Ref -> (Int,Int)
-cell_index (c,r) = (column_index c,row_index r)
-
--- | Inverse of cell_index.
---
--- > index_to_cell (80,347) == (Column_Ref "CC",348)
--- > index_to_cell (4,5) == (Column_Ref "E",6)
-index_to_cell :: (Int,Int) -> Cell_Ref
-index_to_cell (c,r) = (column_ref c,r + 1)
-
-parse_cell_index :: String -> (Int,Int)
-parse_cell_index = cell_index . parse_cell_ref_err
-
--- | Type specialised 'Data.Ix.range', cells are in column-order.
---
--- > cell_range (("AA",1),("AC",1)) == [("AA",1),("AB",1),("AC",1)]
---
--- > let r = [("AA",1),("AA",2),("AB",1),("AB",2),("AC",1),("AC",2)]
--- > in cell_range (("AA",1),("AC",2)) == r
---
--- > Data.Ix.range (('A',1),('C',1)) == [('A',1),('B',1),('C',1)]
---
--- > let r = [('A',1),('A',2),('B',1),('B',2),('C',1),('C',2)]
--- > in Data.Ix.range (('A',1),('C',2)) == r
-cell_range :: Cell_Range -> [Cell_Ref]
-cell_range ((c1,r1),(c2,r2)) =
-    [(c,r) |
-     c <- column_range (c1,c2)
-    ,r <- row_range (r1,r2)]
-
--- | Variant of 'cell_range' in row-order.
---
--- > let r = [(AA,1),(AB,1),(AC,1),(AA,2),(AB,2),(AC,2)]
--- > in cell_range_row_order (("AA",1),("AC",2)) == r
-cell_range_row_order ::  Cell_Range -> [Cell_Ref]
-cell_range_row_order ((c1,r1),(c2,r2)) =
-    [(c,r) |
-     r <- row_range (r1,r2)
-    ,c <- column_range (c1,c2)]
-
diff --git a/Music/Theory/Array/Csv/Midi/Cli.hs b/Music/Theory/Array/Csv/Midi/Cli.hs
new file mode 100644
--- /dev/null
+++ b/Music/Theory/Array/Csv/Midi/Cli.hs
@@ -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"
+-}
+
diff --git a/Music/Theory/Array/Csv/Midi/Mnd.hs b/Music/Theory/Array/Csv/Midi/Mnd.hs
new file mode 100644
--- /dev/null
+++ b/Music/Theory/Array/Csv/Midi/Mnd.hs
@@ -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
diff --git a/Music/Theory/Array/Csv/Midi/Skini.hs b/Music/Theory/Array/Csv/Midi/Skini.hs
new file mode 100644
--- /dev/null
+++ b/Music/Theory/Array/Csv/Midi/Skini.hs
@@ -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)
diff --git a/Music/Theory/Array/Direction.hs b/Music/Theory/Array/Direction.hs
--- a/Music/Theory/Array/Direction.hs
+++ b/Music/Theory/Array/Direction.hs
@@ -41,7 +41,7 @@
 derive_vec (c1,r1) (c2,r2) = (c2 - c1,r2 - r1)
 
 unfold_path :: Num n => LOC n -> [VEC n] -> [LOC n]
-unfold_path l p = scanl apply_vec l p
+unfold_path = scanl apply_vec
 
 -- * DIRECTION (non-diagonal)
 
diff --git a/Music/Theory/Array/Square.hs b/Music/Theory/Array/Square.hs
new file mode 100644
--- /dev/null
+++ b/Music/Theory/Array/Square.hs
@@ -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
+
diff --git a/Music/Theory/Array/Text.hs b/Music/Theory/Array/Text.hs
deleted file mode 100644
--- a/Music/Theory/Array/Text.hs
+++ /dev/null
@@ -1,123 +0,0 @@
--- | Regular array data as plain text tables.
-module Music.Theory.Array.Text where
-
-import Data.List {- base -}
-
-import qualified Data.List.Split as Split {- split -}
-
-import qualified Music.Theory.Array as T {- hmt -}
-import qualified Music.Theory.Function as T {- hmt -}
-import qualified Music.Theory.List as T {- hmt -}
-import qualified Music.Theory.String as T {- hmt -}
-
--- | Tabular text.
-type TABLE = [[String]]
-
--- | Split table at indicated places.
---
--- > let tbl = [["1","2","3","4"],["A","B","E","F"],["C","D","G","H"]]
--- > table_split [2,2] tbl
-table_split :: [Int] -> TABLE -> [TABLE]
-table_split pl dat = transpose (map (Split.splitPlaces pl) dat)
-
--- | Join tables left to right.
---
--- > table_concat [[["1","2"],["A","B"],["C","D"]],[["3","4"],["E","F"],["G","H"]]]
-table_concat :: [TABLE] -> TABLE
-table_concat sq = map concat (transpose sq)
-
--- | Add a row number column at the front of the table.
---
--- > table_number_rows 0 tbl
-table_number_rows :: Int -> TABLE -> TABLE
-table_number_rows k dat = map (\(i,r) -> show i : r) (zip [k ..] dat)
-
-{- | (HEADER,PAD-LEFT,EQ-WIDTH,COL-SEP,TBL-DELIM).
-
-Options are:
- has header
- pad text with space to left instead of right,
- make all columns equal width,
- column separator string,
- print table delimiters
--}
-type TABLE_OPT = (Bool,Bool,Bool,String,Bool)
-
--- | Options for @simple@ layout.
-table_opt_simple :: TABLE_OPT
-table_opt_simple = (True,True,False," ",True)
-
--- | Options for @pipe@ layout.
-table_opt_pipe :: TABLE_OPT
-table_opt_pipe = (True,True,False," | ",False)
-
--- | Pretty-print table.  Table is in row order.
---
--- > let tbl = [["1","2","3","4"],["a","bc","def"],["ghij","klm","no","p"]]
--- > putStrLn$unlines$"": table_pp (True,True,True," ",True) tbl
--- > putStrLn$unlines$"": table_pp (False,False,True," ",False) tbl
-table_pp :: TABLE_OPT -> TABLE -> [String]
-table_pp (has_hdr,pad_left,eq_width,col_sep,print_eot) dat =
-    let c = transpose (T.tbl_make_regular_nil "" dat)
-        nc = length c
-        n = let k = map (maximum . map length) c
-            in if eq_width then replicate nc (maximum k) else k
-        ext k s = if pad_left then T.pad_left ' ' k s else T.pad_right ' ' k s
-        jn = intercalate col_sep
-        m = jn (map (flip replicate '-') n)
-        w = map jn (transpose (zipWith (map . ext) n c))
-        d = map T.delete_trailing_whitespace w
-        pr x = if print_eot then T.bracket (m,m) x else x
-    in case d of
-         [] -> error "table_pp"
-         d0:dr -> if has_hdr then d0 : pr dr else pr d
-
--- | Variant relying on 'Show' instances.
---
--- > table_pp_show table_opt_simple [[1..4],[5..8],[9..12]]
-table_pp_show :: Show t => TABLE_OPT -> T.Table t -> [String]
-table_pp_show opt = table_pp opt . map (map show)
-
--- | Variant in column order (ie. 'transpose').
---
--- > table_pp_column_order table_opt_simple [["a","bc","def"],["ghij","klm","no"]]
-table_pp_column_order :: TABLE_OPT -> TABLE -> [String]
-table_pp_column_order opt = table_pp opt . transpose
-
-{- | Matrix form, ie. header in both first row and first column, in
-each case displaced by one location which is empty.
-
-> let h = (map return "abc",map return "efgh")
-> let t = table_matrix h (map (map show) [[1,2,3,4],[2,3,4,1],[3,4,1,2]])
-
->>> putStrLn $ unlines $ table_pp table_opt_simple t
-- - - - -
-  e f g h
-a 1 2 3 4
-b 2 3 4 1
-c 3 4 1 2
-- - - - -
-
--}
-table_matrix :: ([String],[String]) -> TABLE -> TABLE
-table_matrix (r,c) t = table_concat [[""] : map return r,c : t]
-
--- | Variant that takes a 'show' function and a /header decoration/ function.
---
--- > table_matrix_opt show id ([1,2,3],[4,5,6]) [[7,8,9],[10,11,12],[13,14,15]]
-table_matrix_opt :: (a -> String) -> (String -> String) -> ([a],[a]) -> T.Table a -> TABLE
-table_matrix_opt show_f hd_f nm t =
-    let nm' = T.bimap1 (map (hd_f . show_f)) nm
-        t' = map (map show_f) t
-    in table_matrix nm' t'
-
-{-
--- | Two-tuple 'show' variant.
-table_table_p2 :: (Show a,Show b) => TABLE_Opt -> Maybe [String] -> ([a],[b]) -> [String]
-table_table_p2 opt hdr (p,q) = table_table' opt hdr [map show p,map show q]
-
--- | Three-tuple 'show' variant.
-table_table_p3 :: (Show a,Show b,Show c) => TABLE_Opt -> Maybe [String] -> ([a],[b],[c]) -> [String]
-table_table_p3 opt hdr (p,q,r) = table_table' opt hdr [map show p,map show q,map show r]
-
--}
diff --git a/Music/Theory/Bits.hs b/Music/Theory/Bits.hs
deleted file mode 100644
--- a/Music/Theory/Bits.hs
+++ /dev/null
@@ -1,38 +0,0 @@
--- | Bits functions.
-module Music.Theory.Bits where
-
-import Data.Bits {- base -}
-
-bit_pp :: Bool -> Char
-bit_pp b = if b then '1' else '0'
-
-bits_pp :: [Bool] -> String
-bits_pp = map bit_pp
-
--- | Generate /n/ place bit sequence for /x/.
-gen_bitseq :: FiniteBits b => Int -> b -> [Bool]
-gen_bitseq n x =
-    if finiteBitSize x < n
-    then error "gen_bitseq"
-    else map (testBit x) (reverse [0 .. n - 1])
-
--- | Given bit sequence (most to least significant) generate 'Bits' value.
---
--- > :set -XBinaryLiterals
--- > pack_bitseq [True,False,True,False] == 0b1010
--- > pack_bitseq [True,False,False,True,False,False] == 0b100100
--- > 0b100100 == 36
-pack_bitseq :: Bits i => [Bool] -> i
-pack_bitseq =
-    last .
-    scanl (\n (k,b) -> if b then setBit n k else n) zeroBits .
-    zip [0..] .
-    reverse
-
--- | 'bits_pp' of 'gen_bitseq'.
---
--- > :set -XBinaryLiterals
--- > 0xF0 == 0b11110000
--- > gen_bitseq_pp 8 (0xF0::Int) == "11110000"
-gen_bitseq_pp :: FiniteBits b => Int -> b -> String
-gen_bitseq_pp n = bits_pp . gen_bitseq n
diff --git a/Music/Theory/Bjorklund.hs b/Music/Theory/Bjorklund.hs
--- a/Music/Theory/Bjorklund.hs
+++ b/Music/Theory/Bjorklund.hs
@@ -9,37 +9,39 @@
 
 import qualified Music.Theory.List as T
 
-type STEP a = ((Int,Int),([[a]],[[a]]))
+-- | Bjorklund state
+type BJORKLUND_ST a = ((Int,Int),([[a]],[[a]]))
 
-left :: STEP a -> STEP a
-left ((i,j),(xs,ys)) =
+-- | Bjorklund left process
+bjorklund_left_f :: BJORKLUND_ST a -> BJORKLUND_ST a
+bjorklund_left_f ((i,j),(xs,ys)) =
     let (xs',xs'') = splitAt j xs
     in ((j,i-j),(zipWith (++) xs' ys,xs''))
 
-right :: STEP a -> STEP a
-right ((i,j),(xs,ys)) =
+-- | Bjorklund right process
+bjorklund_right_f :: BJORKLUND_ST a -> BJORKLUND_ST a
+bjorklund_right_f ((i,j),(xs,ys)) =
     let (ys',ys'') = splitAt i ys
     in ((i,j-i),(zipWith (++) xs ys',ys''))
 
-bjorklund' :: STEP a -> STEP a
-bjorklund' (n,x) =
+-- | Bjorklund process, left & recur or right & recur or halt.
+bjorklund_f :: BJORKLUND_ST a -> BJORKLUND_ST a
+bjorklund_f (n,x) =
     let (i,j) = n
     in if min i j <= 1
        then (n,x)
-       else bjorklund' (if i > j then left (n,x) else right (n,x))
+       else bjorklund_f (if i > j then bjorklund_left_f (n,x) else bjorklund_right_f (n,x))
 
 {- | Bjorklund's algorithm to construct a binary sequence of /n/ bits
 with /k/ ones such that the /k/ ones are distributed as evenly as
 possible among the (/n/ - /k/) zeroes.
 
 > bjorklund (5,9) == [True,False,True,False,True,False,True,False,True]
-> map xdot (bjorklund (5,9)) == "x.x.x.x.x"
+> map xdot_ascii (bjorklund (5,9)) == "x.x.x.x.x"
 
-> let {es = [(2,[3,5]),(3,[4,5,8]),(4,[7,9,12,15]),(5,[6,7,8,9,11,12,13,16])
->           ,(6,[7,13]),(7,[8,9,10,12,15,16,17,18]),(8,[17,19])
->           ,(9,[14,16,22,23]),(11,[12,24]),(13,[24]),(15,[34])]
->     ;es' = concatMap (\(i,j) -> map ((,) i) j) es}
-> in mapM_ (putStrLn . euler_pp') es'
+> let es = [(2,[3,5]),(3,[4,5,8]),(4,[7,9,12,15]),(5,[6,7,8,9,11,12,13,16]),(6,[7,13]),(7,[8,9,10,12,15,16,17,18]),(8,[17,19]),(9,[14,16,22,23]),(11,[12,24]),(13,[24]),(15,[34])]
+> let es' = concatMap (\(i,j) -> map ((,) i) j) es
+> mapM_ (putStrLn . euler_pp_unicode) es'
 
 > > E(2,3) [××·] (12)
 > > E(2,5) [×·×··] (23)
@@ -85,12 +87,12 @@
     let j = j' - i
         x = replicate i [True]
         y = replicate j [False]
-        (_,(x',y')) = bjorklund' ((i,j),(x,y))
+        (_,(x',y')) = bjorklund_f ((i,j),(x,y))
     in concat x' ++ concat y'
 
 -- | 'T.rotate_right' of 'bjorklund'.
 --
--- > map xdot' (bjorklund_r 2 (5,16)) == "··×··×··×··×··×·"
+-- > map xdot_unicode (bjorklund_r 2 (5,16)) == "··×··×··×··×··×·"
 bjorklund_r :: Int -> (Int, Int) -> [Bool]
 bjorklund_r n = T.rotate_right n . bjorklund
 
@@ -102,40 +104,37 @@
 
 -- | Unicode form, ie. @×·@.
 --
--- > euler_pp' (7,12) == "E(7,12) [×·××·×·××·×·] (2122122)"
-euler_pp' :: (Int, Int) -> String
-euler_pp' = euler_pp_f xdot'
+-- > euler_pp_unicode (7,12) == "E(7,12) [×·××·×·××·×·] (2122122)"
+euler_pp_unicode :: (Int, Int) -> String
+euler_pp_unicode = euler_pp_f xdot_unicode
 
 -- | ASCII form, ie. @x.@.
 --
--- > euler_pp (7,12) == "E(7,12) [x.xx.x.xx.x.] (2122122)"
-euler_pp :: (Int, Int) -> String
-euler_pp = euler_pp_f xdot
+-- > euler_pp_ascii (7,12) == "E(7,12) [x.xx.x.xx.x.] (2122122)"
+euler_pp_ascii :: (Int, Int) -> String
+euler_pp_ascii = euler_pp_f xdot_ascii
 
 -- | /xdot/ notation for pattern.
 --
--- > map xdot (bjorklund (5,9)) == "x.x.x.x.x"
-xdot :: Bool -> Char
-xdot x = if x then 'x' else '.'
+-- > map xdot_ascii (bjorklund (5,9)) == "x.x.x.x.x"
+xdot_ascii :: Bool -> Char
+xdot_ascii x = if x then 'x' else '.'
 
 -- | Unicode variant.
 --
--- > map xdot' (bjorklund (5,12)) == "×··×·×··×·×·"
--- > map xdot' (bjorklund (5,16)) == "×··×··×··×··×···"
-xdot' :: Bool -> Char
-xdot' x = if x then '×' else '·'
+-- > map xdot_unicode (bjorklund (5,12)) == "×··×·×··×·×·"
+-- > map xdot_unicode (bjorklund (5,16)) == "×··×··×··×··×···"
+xdot_unicode :: Bool -> Char
+xdot_unicode x = if x then '×' else '·'
 
 -- | The 'iseq' of a pattern is the distance between 'True' values.
 --
 -- > iseq (bjorklund (5,9)) == [2,2,2,2,1]
 iseq :: [Bool] -> [Int]
-iseq =
-    let f = split . keepDelimsL . whenElt
-    in tail . map length . f (== True)
+iseq = let f = split . keepDelimsL . whenElt in tail . map length . f (== True)
 
 -- | 'iseq' of pattern as compact string.
 --
 -- > iseq_str (bjorklund (5,9)) == "(22221)"
 iseq_str :: [Bool] -> String
-iseq_str = let f xs = "(" ++ concatMap show xs ++ ")"
-           in f . iseq
+iseq_str = let f xs = "(" ++ concatMap show xs ++ ")" in f . iseq
diff --git a/Music/Theory/Braille.hs b/Music/Theory/Braille.hs
--- a/Music/Theory/Braille.hs
+++ b/Music/Theory/Braille.hs
@@ -103,7 +103,7 @@
 --
 -- > braille_lookup_ascii 'N' == Just (0x4E,'N',[1,3,4,5],'⠝',"n")
 braille_lookup_ascii :: Char -> Maybe BRAILLE
-braille_lookup_ascii c = find ((== (toUpper c)) . braille_ascii) braille_table
+braille_lookup_ascii c = find ((== toUpper c) . braille_ascii) braille_table
 
 -- | The arrangement of the 6-dot patterns into /decades/, sequences
 -- of (1,10,3) cells.  The cell to the left of the decade is the empty
@@ -160,6 +160,7 @@
     let f n = if n `elem` d then b else w
     in map (map f) [[1,4],[2,5],[3,6]]
 
+-- | 'lines' as rows and 'Char' as cells in HTML table.
 string_html_table :: String -> String
 string_html_table s =
     let f x = "<td>" ++ [x] ++ "</td>"
diff --git a/Music/Theory/Byte.hs b/Music/Theory/Byte.hs
deleted file mode 100644
--- a/Music/Theory/Byte.hs
+++ /dev/null
@@ -1,145 +0,0 @@
--- | Byte functions.
-module Music.Theory.Byte where
-
-import Data.Char {- base -}
-import Data.Maybe {- base -}
-import Data.Word {- base -}
-import Numeric {- base -}
-
-import qualified Data.ByteString as B {- bytestring -}
-import qualified Data.List.Split as Split {- split -}
-import qualified Safe {- safe -}
-
-import qualified Music.Theory.Math.Convert as T {- hmt -}
-import qualified Music.Theory.Read as T {- hmt -}
-
-{-
-import Data.Int {- base -}
-import qualified Data.ByteString.Lazy as L {- bytestring -}
-
--- * LBS
-
--- | Section function for 'L.ByteString', ie. from (n,m).
---
--- > lbs_slice 4 5 (L.pack [1..10]) == L.pack [5,6,7,8,9]
-lbs_slice :: Int64 -> Int64 -> L.ByteString -> L.ByteString
-lbs_slice n m = L.take m . L.drop n
-
--- | Variant of slice with start and end indices (zero-indexed).
---
--- > lbs_section 4 8 (L.pack [1..]) == L.pack [5,6,7,8,9]
-lbs_section :: Int64 -> Int64 -> L.ByteString -> L.ByteString
-lbs_section l r = L.take (r - l + 1) . L.drop l
--}
-
--- * Enumerations & Char
-
--- | 'toEnum' of 'T.word8_to_int'
-word8_to_enum :: Enum e => Word8 -> e
-word8_to_enum = toEnum . T.word8_to_int
-
--- | 'T.int_to_word8_maybe' of 'fromEnum'
-enum_to_word8 :: Enum e => e -> Maybe Word8
-enum_to_word8 = T.int_to_word8_maybe . fromEnum
-
--- | Type-specialised 'word8_to_enum'
---
--- > map word8_to_char [60,62] == "<>"
-word8_to_char :: Word8 -> Char
-word8_to_char = word8_to_enum
-
--- | 'T.int_to_word8' of 'fromEnum'
-char_to_word8 :: Char -> Word8
-char_to_word8 = T.int_to_word8 . fromEnum
-
--- | 'T.int_to_word8' of 'digitToInt'
-digit_to_word8 :: Char -> Word8
-digit_to_word8 = T.int_to_word8 . digitToInt
-
--- | 'intToDigit' of 'T.word8_to_int'
-word8_to_digit :: Word8 -> Char
-word8_to_digit = intToDigit . T.word8_to_int
-
--- * Indexing
-
--- | 'Safe.at' of 'T.word8_to_int'
-word8_at :: [t] -> Word8 -> t
-word8_at l = Safe.at l . T.word8_to_int
-
--- * Text
-
--- | Given /n/ in (0,255) make two character hex string.
---
--- > mapMaybe byte_hex_pp [0x0F,0xF0,0xF0F] == ["0F","F0"]
-byte_hex_pp :: (Integral i, Show i) => i -> Maybe String
-byte_hex_pp n =
-    case showHex n "" of
-      [c] -> Just ['0',toUpper c]
-      [c,d] -> Just (map toUpper [c,d])
-      _ -> Nothing
-
--- | Erroring variant.
-byte_hex_pp_err :: (Integral i, Show i) => i -> String
-byte_hex_pp_err = fromMaybe (error "byte_hex_pp") . byte_hex_pp
-
--- | 'byte_hex_pp_err' either plain (ws = False) or with spaces (ws = True).
---   Plain is the same format written by xxd -p and read by xxd -r -p.
---
--- > byte_seq_hex_pp True [0x0F,0xF0] == "0F F0"
-byte_seq_hex_pp :: (Integral i, Show i) => Bool -> [i] -> String
-byte_seq_hex_pp ws = (if ws then unwords else concat) . map byte_hex_pp_err
-
--- | Read two character hexadecimal string.
---
--- > mapMaybe read_hex_byte (Split.chunksOf 2 "0FF0F") == [0x0F,0xF0]
-read_hex_byte :: (Eq t,Num t) => String -> Maybe t
-read_hex_byte s =
-    case s of
-      [_,_] -> T.reads_to_read_precise readHex s
-      _ -> Nothing
-
--- | Erroring variant.
-read_hex_byte_err :: (Eq t,Num t) => String -> t
-read_hex_byte_err = fromMaybe (error "read_hex_byte") . read_hex_byte
-
--- | Sequence of 'read_hex_byte_err'
---
--- > read_hex_byte_seq "000FF0FF" == [0x00,0x0F,0xF0,0xFF]
-read_hex_byte_seq :: (Eq t,Num t) => String -> [t]
-read_hex_byte_seq = map read_hex_byte_err . Split.chunksOf 2
-
--- | Variant that filters white space.
---
--- > read_hex_byte_seq_ws "00 0F F0 FF" == [0x00,0x0F,0xF0,0xFF]
-read_hex_byte_seq_ws :: (Eq t,Num t) => String -> [t]
-read_hex_byte_seq_ws = read_hex_byte_seq . filter (not . isSpace)
-
--- * IO
-
--- | Load binary 'U8' sequence from file.
-load_byte_seq :: Integral i => FilePath -> IO [i]
-load_byte_seq = fmap (map fromIntegral . B.unpack) . B.readFile
-
--- | Store binary 'U8' sequence to file.
-store_byte_seq :: Integral i => FilePath -> [i] -> IO ()
-store_byte_seq fn = B.writeFile fn . B.pack . map fromIntegral
-
--- | Load hexadecimal text 'U8' sequences from file.
-load_hex_byte_seq :: Integral i => FilePath -> IO [[i]]
-load_hex_byte_seq = fmap (map read_hex_byte_seq . lines) . readFile
-
--- | Store 'U8' sequences as hexadecimal text, one sequence per line.
-store_hex_byte_seq :: (Integral i,Show i) => FilePath -> [[i]] -> IO ()
-store_hex_byte_seq fn = writeFile fn . unlines . map (byte_seq_hex_pp False)
-
-{-
-
-import qualified Data.ByteString.Base64 as Base64 {- base64-bytestring -}
-let fn = "/home/rohan/sw/hsc3-data/data/yamaha/dx7/rom/ROM1A.syx"
-b <- load_byte_seq fn :: IO [Word8]
-let e = B.unpack (Base64.encode (B.pack b))
-let r = B.unpack (Base64.decodeLenient (B.pack e))
-(length b,length e,length r,b == r) == (4104,5472,4104,True)
-map word8_to_char e
-
--}
diff --git a/Music/Theory/Clef.hs b/Music/Theory/Clef.hs
--- a/Music/Theory/Clef.hs
+++ b/Music/Theory/Clef.hs
@@ -5,11 +5,11 @@
 import Music.Theory.Pitch.Name {- hmt -}
 
 -- | Clef enumeration type.
-data Clef_T = Bass | Tenor | Alto | Treble | Percussion
+data Clef_Type = Bass | Tenor | Alto | Treble | Percussion
               deriving (Eq,Ord,Show)
 
 -- | Clef with octave offset.
-data Clef i = Clef {clef_t :: Clef_T
+data Clef i = Clef {clef_t :: Clef_Type
                    ,clef_octave :: i}
               deriving (Eq,Ord,Show)
 
@@ -18,7 +18,7 @@
 --
 -- > map clef_range [Treble,Bass] == [Just (d4,g5),Just (f2,b3)]
 -- > clef_range Percussion == Nothing
-clef_range :: Clef_T -> Maybe (Pitch,Pitch)
+clef_range :: Clef_Type -> Maybe (Pitch,Pitch)
 clef_range c =
     case c of
       Bass -> Just (f2,b3)
diff --git a/Music/Theory/Combinations.hs b/Music/Theory/Combinations.hs
deleted file mode 100644
--- a/Music/Theory/Combinations.hs
+++ /dev/null
@@ -1,22 +0,0 @@
--- | Combination functions.
-module Music.Theory.Combinations where
-
-import qualified Music.Theory.Permutations as T
-
--- | Number of /k/ element combinations of a set of /n/ elements.
---
--- > map (uncurry nk_combinations) [(4,2),(5,3),(6,3),(13,3)] == [6,10,20,286]
-nk_combinations :: Integral a => a -> a -> a
-nk_combinations n k = T.nk_permutations n k `div` T.factorial k
-
--- | /k/ element subsets of /s/.
---
--- > combinations 3 [1..4] == [[1,2,3],[1,2,4],[1,3,4],[2,3,4]]
--- > length (combinations 3 [1..5]) == nk_combinations 5 3
--- > combinations 3 "xyzw" == ["xyz","xyw","xzw","yzw"]
-combinations :: Int -> [a] -> [[a]]
-combinations k s =
-    case (k,s) of
-      (0,_) -> [[]]
-      (_,[]) -> []
-      (_,e:s') -> map (e :) (combinations (k - 1) s') ++ combinations k s'
diff --git a/Music/Theory/Contour/Polansky_1992.hs b/Music/Theory/Contour/Polansky_1992.hs
--- a/Music/Theory/Contour/Polansky_1992.hs
+++ b/Music/Theory/Contour/Polansky_1992.hs
@@ -10,10 +10,11 @@
 import Data.Maybe {- base -}
 import Data.Ratio {- base -}
 
-import qualified Music.Theory.List as T
-import qualified Music.Theory.Ord as T
-import qualified Music.Theory.Permutations.List as T
-import qualified Music.Theory.Set.List as T
+import qualified Music.Theory.List as T {- hmt-base -}
+import qualified Music.Theory.Ord as T {- hmt-base -}
+
+import qualified Music.Theory.Permutations.List as T {- hmt -}
+import qualified Music.Theory.Set.List as T {- hmt -}
 
 -- * Indices
 
diff --git a/Music/Theory/DB/CSV.hs b/Music/Theory/DB/CSV.hs
deleted file mode 100644
--- a/Music/Theory/DB/CSV.hs
+++ /dev/null
@@ -1,24 +0,0 @@
--- | Keys are given in the header, empty fields are omitted from records.
-module Music.Theory.DB.CSV where
-
-import Data.Maybe {- base -}
-import qualified Text.CSV.Lazy.String as C {- lazy-csv -}
-
-import Music.Theory.DB.Common {- hmt -}
-import qualified Music.Theory.IO as T {- hmt -}
-
--- | Load 'DB' from 'FilePath'.
-db_load_utf8 :: FilePath -> IO DB'
-db_load_utf8 fn = do
-  s <- T.read_file_utf8 fn
-  let p = C.fromCSVTable (C.csvTable (C.parseCSV s))
-      (h,d) = (head p,tail p)
-      f k v = if null v then Nothing else Just (k,v)
-  return (map (catMaybes . zipWith f h) d)
-
-db_store_utf8 :: FilePath -> DB' -> IO ()
-db_store_utf8 fn db = do
-  let (hdr,tbl) = db_to_table (fromMaybe "") db
-      (_,tbl') = C.toCSVTable (hdr : tbl)
-      str = C.ppCSVTable tbl'
-  T.write_file_utf8 fn str
diff --git a/Music/Theory/DB/Common.hs b/Music/Theory/DB/Common.hs
deleted file mode 100644
--- a/Music/Theory/DB/Common.hs
+++ /dev/null
@@ -1,130 +0,0 @@
-module Music.Theory.DB.Common where
-
-import Data.List {- base -}
-import Data.Maybe {- base -}
-import Safe {- safe -}
-
-import qualified Music.Theory.List as T {- base -}
-import qualified Music.Theory.Maybe as T {- base -}
-
--- * Type
-
-type Entry k v = (k,v)
-type Record k v = [Entry k v]
-type DB k v = [Record k v]
-
-type Key = String
-type Value = String
-type Entry' = Entry Key Value
-type Record' = Record Key Value
-type DB' = DB Key Value
-
--- * Record
-
--- | The sequence of keys at 'Record'.
-record_key_seq :: Record k v -> [k]
-record_key_seq = map fst
-
--- | 'True' if 'Key' is present in 'Entity'.
-record_has_key :: Eq k => k -> Record k v -> Bool
-record_has_key k = elem k . record_key_seq
-
--- | 'T.histogram' of 'record_key_seq'.
-record_key_histogram :: Ord k => Record k v -> [(k,Int)]
-record_key_histogram = T.histogram . record_key_seq
-
--- | Duplicate keys predicate.
-record_has_duplicate_keys :: Ord k => Record k v -> Bool
-record_has_duplicate_keys = any (> 0) . map snd . record_key_histogram
-
--- | Find all associations for key using given equality function.
-record_lookup_by :: (k -> k -> Bool) -> k -> Record k v -> [v]
-record_lookup_by f k = map snd . filter (f k . fst)
-
--- | 'record_lookup_by' of '=='.
-record_lookup :: Eq k => k -> Record k v -> [v]
-record_lookup = record_lookup_by (==)
-
--- | /n/th element of 'record_lookup'.
-record_lookup_at :: Eq k => (k,Int) -> Record k v -> Maybe v
-record_lookup_at (c,n) = flip atMay n . record_lookup c
-
--- | Variant of 'record_lookup' requiring a unique key.  'Nothing' indicates
--- there is no entry, it is an 'error' if duplicate keys are present.
-record_lookup_uniq :: Eq k => k -> Record k v -> Maybe v
-record_lookup_uniq k r =
-    case record_lookup k r of
-      [] -> Nothing
-      [v] -> Just v
-      _ -> error "record_lookup_uniq: non uniq"
-
--- | 'True' if key exists and is unique.
-record_has_key_uniq :: Eq k => k -> Record k v -> Bool
-record_has_key_uniq k = isJust . record_lookup_uniq k
-
--- | Error variant.
-record_lookup_uniq_err :: Eq k => k -> Record k v -> v
-record_lookup_uniq_err k = T.from_just "record_lookup_uniq: none" . record_lookup_uniq k
-
--- | Default value variant.
-record_lookup_uniq_def :: Eq k => v -> k -> Record k v -> v
-record_lookup_uniq_def v k = fromMaybe v . record_lookup_uniq k
-
--- | Remove all associations for key using given equality function.
-record_delete_by :: (k -> k -> Bool) -> k -> Record k v -> Record k v
-record_delete_by f k = filter (not . f k . fst)
-
--- | 'record_delete_by' of '=='.
-record_delete :: Eq k => k -> Record k v -> Record k v
-record_delete = record_delete_by (==)
-
--- * DB
-
--- | Preserves order of occurence.
-db_key_set :: Ord k => DB k v -> [k]
-db_key_set = nub . map fst . concat
-
-db_lookup_by :: (k -> k -> Bool) -> (v -> v -> Bool) -> k -> v -> DB k v -> [Record k v]
-db_lookup_by k_cmp v_cmp k v =
-    let f = any (v_cmp v) . record_lookup_by k_cmp k
-    in filter f
-
-db_lookup :: (Eq k,Eq v) => k -> v -> DB k v -> [Record k v]
-db_lookup = db_lookup_by (==) (==)
-
-db_has_duplicate_keys :: Ord k => DB k v -> Bool
-db_has_duplicate_keys = any id . map record_has_duplicate_keys
-
-db_key_histogram :: Ord k => DB k v -> [(k,Int)]
-db_key_histogram db =
-    let h = concatMap record_key_histogram db
-        f k = (k,maximum (record_lookup k h))
-    in map f (db_key_set db)
-
-db_to_table :: Ord k => (Maybe v -> e) -> DB k v -> ([k],[[e]])
-db_to_table f db =
-    let kh = db_key_histogram db
-        hdr = concatMap (\(k,n) -> replicate n k) kh
-        ix = concatMap (\(k,n) -> zip (repeat k) [0 .. n - 1]) kh
-    in (hdr,map (\r -> map (\i -> f (record_lookup_at i r)) ix) db)
-
--- * Collating duplicate keys.
-
-record_collate' :: Eq k => (k,[v]) -> Record k v -> Record k [v]
-record_collate' (k,v) r =
-    case r of
-      [] -> [(k,reverse v)]
-      (k',v'):r' ->
-          if k == k'
-          then record_collate' (k,v' : v) r'
-          else (k,reverse v) : record_collate' (k',[v']) r'
-
--- | Collate adjacent entries of existing sequence with equal key.
-record_collate :: Eq k => Record k v -> Record k [v]
-record_collate r =
-    case r of
-      [] -> error "record_collate: nil"
-      (k,v):r' -> record_collate' (k,[v]) r'
-
-record_uncollate :: Record k [v] -> Record k v
-record_uncollate = concatMap (\(k,v) -> zip (repeat k) v)
diff --git a/Music/Theory/DB/JSON.hs b/Music/Theory/DB/JSON.hs
deleted file mode 100644
--- a/Music/Theory/DB/JSON.hs
+++ /dev/null
@@ -1,67 +0,0 @@
--- | JSON string association database.
--- JSON objects do no allow multiple keys.
--- Here multiple keys are read & written as arrays.
-module Music.Theory.DB.JSON where
-
-import qualified Data.Aeson as A {- aeson -}
-import qualified Data.ByteString.Lazy as B {- bytestring -}
-import qualified Data.Map as M {- containers -}
-
-import qualified Music.Theory.DB.Common as DB
-
--- | Load 'DB' from 'FilePath'.
-db_load_utf8 :: FilePath -> IO DB.DB'
-db_load_utf8 fn = do
-  b <- B.readFile fn
-  case A.decode b of
-    Just m ->
-        let f = DB.record_uncollate .
-                map (fmap maybe_list_to_list) .
-                M.toList
-        in return (map f m)
-    Nothing -> return []
-
--- | Store 'DB' to 'FilePath'.
---
--- > let fn = "/home/rohan/ut/www-spr/data/db.js"
--- > db <- db_load_utf8 fn
--- > length db == 1334
--- > db_store_utf8 "/tmp/sp.js" db
-db_store_utf8 :: FilePath -> DB.DB' -> IO ()
-db_store_utf8 fn db = do
-  let db' = let f = map (fmap list_to_maybe_list) . DB.record_collate
-            in map f db
-      b = A.encode (map M.fromList db')
-  B.writeFile fn b
-
--- * Maybe List of String
-
-data Maybe_List_Of_String = S String | L [String] deriving (Eq,Show)
-
-maybe_list_to_list :: Maybe_List_Of_String -> [String]
-maybe_list_to_list m =
-    case m of
-      S s -> [s]
-      L l -> l
-
-list_to_maybe_list :: [String] -> Maybe_List_Of_String
-list_to_maybe_list l =
-    case l of
-      [s] -> S s
-      _ -> L l
-
--- > A.toJSON (S "x")
--- > A.toJSON (L ["x","y"])
-instance A.ToJSON Maybe_List_Of_String where
-    toJSON (S s) = A.toJSON s
-    toJSON (L l) = A.toJSON l
-
--- > :set -XOverloadedStrings
--- > A.decode "\"x\"" :: Maybe Maybe_List_Of_String
--- > A.decode "[\"x\",\"y\"]" :: Maybe Maybe_List_Of_String
-instance A.FromJSON Maybe_List_Of_String where
-    parseJSON v =
-        case v of
-          A.String _ -> fmap S (A.parseJSON v)
-          A.Array _ -> fmap L (A.parseJSON v)
-          _ -> error "parseJSON: Maybe_List_String"
diff --git a/Music/Theory/DB/Plain.hs b/Music/Theory/DB/Plain.hs
deleted file mode 100644
--- a/Music/Theory/DB/Plain.hs
+++ /dev/null
@@ -1,60 +0,0 @@
--- | @key: value@ database, allows duplicate @key@s.
-module Music.Theory.DB.Plain where
-
-import Data.List {- base -}
-import qualified Data.List.Split as Split {- split -}
-import Data.Maybe {- base -}
-import qualified Safe as Safe {- safe -}
-
-import qualified Music.Theory.IO as IO {- hmt -}
-import qualified Music.Theory.List as T {- hmt -}
-
--- | (RECORD-SEPARATOR,FIELD-SEPARATOR,ENTRY-SEPARATOR)
-type SEP = (String,String,String)
-
-type Key = String
-type Value = String
-type Entry = (Key,[Value])
-type Record = [Entry]
-type DB = [Record]
-
-sep_plain :: SEP
-sep_plain = (['\n','\n'],['\n'],": ")
-
--- > record_parse (";","=") "F=f/rec;E=au;C=A;K=P;K=Q"
-record_parse :: (String,String) -> String -> Record
-record_parse (fs,es) = T.collate_adjacent . mapMaybe (T.separate_at es) . Split.splitOn fs
-
-record_lookup :: Key -> Record -> [Value]
-record_lookup k = fromMaybe [] . lookup k
-
-record_lookup_at :: (Key,Int) -> Record -> Maybe Value
-record_lookup_at (k,n) = flip Safe.atMay n . record_lookup k
-
-record_has_key :: Key -> Record -> Bool
-record_has_key k = isJust . lookup k
-
-record_lookup_uniq :: Key -> Record -> Maybe Value
-record_lookup_uniq k r =
-    case record_lookup k r of
-      [] -> Nothing
-      [v] -> Just v
-      _ -> error "record_lookup_uniq: non uniq"
-
-db_parse :: SEP -> String -> [Record]
-db_parse (rs,fs,es) s =
-    let r = Split.splitOn rs s
-    in map (record_parse (fs,es)) r
-
-db_sort :: [(Key,Int)] -> [Record] -> [Record]
-db_sort k = T.sort_by_n_stage_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))
diff --git a/Music/Theory/Db/Cli.hs b/Music/Theory/Db/Cli.hs
new file mode 100644
--- /dev/null
+++ b/Music/Theory/Db/Cli.hs
@@ -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)
diff --git a/Music/Theory/Db/Common.hs b/Music/Theory/Db/Common.hs
new file mode 100644
--- /dev/null
+++ b/Music/Theory/Db/Common.hs
@@ -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)
diff --git a/Music/Theory/Db/Csv.hs b/Music/Theory/Db/Csv.hs
new file mode 100644
--- /dev/null
+++ b/Music/Theory/Db/Csv.hs
@@ -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
diff --git a/Music/Theory/Db/Plain.hs b/Music/Theory/Db/Plain.hs
new file mode 100644
--- /dev/null
+++ b/Music/Theory/Db/Plain.hs
@@ -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))
diff --git a/Music/Theory/Directory.hs b/Music/Theory/Directory.hs
deleted file mode 100644
--- a/Music/Theory/Directory.hs
+++ /dev/null
@@ -1,118 +0,0 @@
--- | Directory functions.
-module Music.Theory.Directory where
-
-import Data.List {- base -}
-import Data.Maybe {- base -}
-import System.Directory {- directory -}
-import System.FilePath {- filepath -}
-import System.Process {- process -}
-
-import qualified Music.Theory.Monad as T {- hmt -}
-
-{- | 'takeDirectory' gives different answers depending on whether there is a trailing separator.
-
-> x = ["x/y","x/y/","x","/"]
-> map parent_dir x == ["x","x",".","/"]
-> map takeDirectory x == ["x","x/y",".","/"]
--}
-parent_dir :: FilePath -> FilePath
-parent_dir = takeDirectory . dropTrailingPathSeparator
-
--- | Scan a list of directories until a file is located, or not.
---   This does not traverse any sub-directory structure.
---
--- > mapM (path_scan ["/sbin","/usr/bin"]) ["fsck","ghc"]
-path_scan :: [FilePath] -> FilePath -> IO (Maybe FilePath)
-path_scan p fn =
-    case p of
-      [] -> return Nothing
-      dir:p' -> let nm = dir </> fn
-                    f x = if x then return (Just nm) else path_scan p' fn
-                in doesFileExist nm >>= f
-
--- | Erroring variant.
-path_scan_err :: [FilePath] -> FilePath -> IO FilePath
-path_scan_err p x =
-    let err = error (concat ["path_scan: ",show p,": ",x])
-    in fmap (fromMaybe err) (path_scan p x)
-
--- | Get list of files at dir with ext, ie. ls dir/*.ext
---
--- > dir_list_ext "/home/rohan/rd/j/" ".hs"
-dir_list_ext :: FilePath -> String -> IO [FilePath]
-dir_list_ext dir ext = do
-  l <- listDirectory dir
-  let fn = filter ((==) ext . takeExtension) l
-  return (sort fn)
-
--- | Post-process 'dir_list_ext' to gives file-names with /dir/ prefix.
---
--- > dir_list_ext_path "/home/rohan/rd/j/" ".hs"
-dir_list_ext_path :: FilePath -> String -> IO [FilePath]
-dir_list_ext_path dir ext = dir_list_ext dir ext >>= return . map ((</>) dir)
-
--- | Find files having indicated filename.
---   This runs the system utility /find/, so is UNIX only.
---
--- > dir_find "DX7-ROM1A.syx" "/home/rohan/sw/hsc3-data/data/yamaha/"
-dir_find :: FilePath -> FilePath -> IO [FilePath]
-dir_find fn dir = fmap lines (readProcess "find" [dir,"-name",fn] "")
-
--- | Require that exactly one file is located, else error.
---
--- > dir_find_1 "DX7-ROM1A.syx" "/home/rohan/sw/hsc3-data/data/yamaha/"
-dir_find_1 :: FilePath -> FilePath -> IO FilePath
-dir_find_1 fn dir = do
-  r <- dir_find fn dir
-  case r of
-    [x] -> return x
-    _ -> error "dir_find_1?"
-
--- | Recursively find files having case-insensitive filename extension.
---   This runs the system utility /find/, so is UNIX only.
---
--- > dir_find_ext ".syx" "/home/rohan/sw/hsc3-data/data/yamaha/"
-dir_find_ext :: String -> FilePath -> IO [FilePath]
-dir_find_ext ext dir = fmap lines (readProcess "find" [dir,"-iname",'*' : ext] "")
-
--- | Post-process 'dir_find_ext' to delete starting directory.
---
--- > dir_find_ext_rel ".syx" "/home/rohan/sw/hsc3-data/data/yamaha/"
-dir_find_ext_rel :: String -> FilePath -> IO [FilePath]
-dir_find_ext_rel ext dir =
-  let f = fromMaybe (error "dir_find_ext_rel?") . stripPrefix dir
-  in fmap (map f) (dir_find_ext ext dir)
-
--- | Subset of files in /dir/ with an extension in /ext/.
---   Extensions include the leading dot and are case-sensitive.
---
--- > dir_subset [".hs"] "/home/rohan/sw/hmt/cmd"
-dir_subset :: [String] -> FilePath -> IO [FilePath]
-dir_subset ext dir = do
-  let f nm = takeExtension nm `elem` ext
-  c <- getDirectoryContents dir
-  return (map (dir </>) (sort (filter f c)))
-
--- | If path is not absolute, prepend current working directory.
---
--- > to_absolute_cwd "x"
-to_absolute_cwd :: FilePath -> IO FilePath
-to_absolute_cwd x =
-    if isAbsolute x
-    then return x
-    else fmap (</> x) getCurrentDirectory
-
--- | If /i/ is an existing file then /j/ else /k/.
-if_file_exists :: (FilePath,IO t,IO t) -> IO t
-if_file_exists (i,j,k) = T.m_if (doesFileExist i,j,k)
-
--- | 'createDirectoryIfMissing' (including parents) and then 'writeFile'
-writeFile_mkdir :: FilePath -> String -> IO ()
-writeFile_mkdir fn s = do
-  let dir = takeDirectory fn
-  createDirectoryIfMissing True dir
-  writeFile fn s
-
--- | 'writeFile_mkdir' only if file does not exist.
-writeFile_mkdir_x :: FilePath -> String -> IO ()
-writeFile_mkdir_x fn txt = if_file_exists (fn,return (),writeFile_mkdir fn txt)
diff --git a/Music/Theory/Duration.hs b/Music/Theory/Duration.hs
--- a/Music/Theory/Duration.hs
+++ b/Music/Theory/Duration.hs
@@ -1,7 +1,6 @@
 -- | Common music notation duration model.
 module Music.Theory.Duration where
 
-import Control.Monad {- base -}
 import Data.List {- base -}
 import Data.Maybe {- base -}
 import Data.Ratio {- base -}
@@ -13,11 +12,12 @@
 type Dots = Int
 
 -- | Common music notation durational model
-data Duration = Duration {division :: Division -- ^ division of whole note
-                         ,dots :: Int -- ^ 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
@@ -55,48 +55,54 @@
 no_dots (x0,x1) = dots x0 == 0 && dots x1 == 0
 
 -- | Sum undotted divisions, input is required to be sorted.
-sum_dur_undotted :: (Division, Division) -> 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 :: (Division,Dots,Division,Dots) -> Maybe Duration
-sum_dur_dotted (x0, n0, x1, n1)
+{- | Sum dotted divisions, input is required to be sorted.
+
+> sum_dur_dotted 1 (4,1,4,1) == Just (Duration 2 1 1)
+> sum_dur_dotted 1 (4,0,2,1) == Just (Duration 1 0 1)
+> sum_dur_dotted 1 (8,1,4,0) == Just (Duration 4 2 1)
+> sum_dur_dotted 1 (16,0,4,2) == Just (Duration 2 0 1)
+-}
+sum_dur_dotted :: Rational -> (Division,Dots,Division,Dots) -> Maybe Duration
+sum_dur_dotted m (x0, n0, x1, n1)
     | x0 == x1 &&
       n0 == 1 &&
-      n1 == 1 = Just (Duration (x1 `div` 2) 1 1)
+      n1 == 1 = Just (Duration (x1 `div` 2) 1 m)
     | x0 == x1 * 2 &&
       n0 == 0 &&
-      n1 == 1 = Just (Duration (x1 `div` 2) 0 1)
+      n1 == 1 = Just (Duration (x1 `div` 2) 0 m)
     | x0 == x1 * 4 &&
       n0 == 0 &&
-      n1 == 2 = Just (Duration (x1 `div` 2) 0 1)
+      n1 == 2 = Just (Duration (x1 `div` 2) 0 m)
     | x0 == x1 * 2 &&
       n0 == 1 &&
-      n1 == 0 = Just (Duration x1 2 1)
+      n1 == 0 = Just (Duration x1 2 m)
     | otherwise = Nothing
 
--- | Sum durations.  Not all durations can be summed, and the present
---   algorithm is not exhaustive.
---
--- > import Music.Theory.Duration.Name
--- > sum_dur quarter_note eighth_note == Just dotted_quarter_note
--- > sum_dur dotted_quarter_note eighth_note == Just half_note
--- > sum_dur quarter_note dotted_eighth_note == Just double_dotted_quarter_note
+{- | Sum durations.  Not all durations can be summed, and the present
+     algorithm is not exhaustive.
+
+> import Music.Theory.Duration
+> import Music.Theory.Duration.Name
+> sum_dur quarter_note eighth_note == Just dotted_quarter_note
+> sum_dur dotted_quarter_note eighth_note == Just half_note
+> sum_dur quarter_note dotted_eighth_note == Just double_dotted_quarter_note
+-}
 sum_dur :: Duration -> Duration -> Maybe Duration
 sum_dur y0 y1 =
-    let f (x0,x1) = if no_dots (x0,x1)
-                    then sum_dur_undotted (division x0, division x1)
-                    else sum_dur_dotted (division x0, dots x0
-                                        ,division x1, dots x1)
-    in join (fmap f (T.sort_pair_m duration_compare_meq (y0,y1)))
+    let (m0,m1) = (multiplier y0,multiplier y1)
+        f (x0,x1) = if m0 /= m1
+                    then Nothing -- cannot sum durations with non-equal multipliers
+                    else if no_dots (x0,x1)
+                         then sum_dur_undotted m0 (division x0, division x1)
+                         else sum_dur_dotted m0 (division x0, dots x0
+                                                ,division x1, dots x1)
+    in T.sort_pair_m duration_compare_meq (y0,y1) >>= f
 
 -- | Erroring variant of 'sum_dur'.
 sum_dur_err :: Duration -> Duration -> Duration
@@ -105,17 +111,23 @@
         err = error ("sum_dur': " ++ show (y0,y1))
     in fromMaybe err y2
 
--- | Standard divisions (from 0 to 256).  MusicXML allows @-1@ as a division (for @long@).
-divisions_set :: [Division]
-divisions_set = [0,1,2,4,8,16,32,64,128,256]
+{- | Standard divisions (from 1 to 256).
+MusicXml allows 0 for breve and -1 for long.
+Negative divisors can represent any number of longer durations, -2 be a breve, -4 a long, -8 a maximus, &etc.
+-}
+divisions_std_set :: [Division]
+divisions_std_set = [1,2,4,8,16,32,64,128,256]
 
--- | Durations set derived from 'divisions_set' with up to /k/ dots.  Multiplier of @1@.
+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_set, dt <- [0..k]]
+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 (-1 : divisions_set) [0,0,0,0,0,1,2,3,4,5,6]
+beam_count_tbl = zip divisions_musicxml_set [0,0,0,0,0,1,2,3,4,5,6]
 
 -- | Lookup 'beam_count_tbl'.
 --
@@ -132,14 +144,14 @@
         bc = whole_note_division_to_beam_count x
     in fromMaybe err bc
 
--- * MusicXML
+-- * MusicXml
 
--- | Table giving @MusicXML@ types for divisions.
+-- | Table giving MusicXml types for divisions.
 division_musicxml_tbl :: [(Division,String)]
 division_musicxml_tbl =
     let nm = ["long","breve","whole","half","quarter","eighth"
              ,"16th","32nd","64th","128th","256th"]
-    in zip (-1 : divisions_set) nm
+    in zip divisions_musicxml_set nm
 
 -- | Lookup 'division_musicxml_tbl'.
 --
@@ -194,11 +206,10 @@
 <http://humdrum.org/Humdrum/representations/recip.rep.html>
 
 > let d = map (\z -> Duration z 0 1) [0,1,2,4,8,16,32]
-> in map duration_recip_pp d == ["0","1","2","4","8","16","32"]
+> map duration_recip_pp d == ["0","1","2","4","8","16","32"]
 
 > let d = [Duration 1 1 (1/3),Duration 4 1 1,Duration 4 1 (2/3)]
-> in map duration_recip_pp d == ["3.","4.","6."]
-
+> map duration_recip_pp d == ["3.","4.","6."]
 -}
 duration_recip_pp :: Duration -> String
 duration_recip_pp (Duration x d m) =
@@ -210,20 +221,40 @@
 
 -- * 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 x =
-    let t = [(16,'s'),(8,'e'),(4,'q'),(2,'h'),(1,'w')]
-    in lookup x t
+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''"]
--- > duration_letter_pp
+-- > mapMaybe duration_letter_pp [Duration 4 0 1,Duration 2 1 1,Duration 8 2 1] == ["q","h.","e.."]
+-- > mapMaybe duration_letter_pp [Duration 4 1 (2/3)] == ["q./2:3"]
 duration_letter_pp :: Duration -> Maybe String
 duration_letter_pp (Duration x d m) =
-    let d' = genericReplicate d '\''
+    let d' = genericReplicate d '.'
         m' = case (numerator m,denominator m) of
                (1,1) -> ""
-               (1,i) -> '/' : show i
-               (i,j) -> '*' : show i ++ "/" ++ show j
+               (i,j) -> '/' : show i ++ ":" ++ show j
     in case whole_note_division_letter_pp x of
          Just x' -> Just (x' : d' ++ m')
          _ -> Nothing
diff --git a/Music/Theory/Duration/Annotation.hs b/Music/Theory/Duration/Annotation.hs
--- a/Music/Theory/Duration/Annotation.hs
+++ b/Music/Theory/Duration/Annotation.hs
@@ -5,9 +5,10 @@
 import Data.Ratio {- base -}
 import Data.Tree {- containers -}
 
+import qualified Music.Theory.List as L {- hmt-base -}
+
 import Music.Theory.Duration
-import Music.Theory.Duration.RQ
-import qualified Music.Theory.List as L {- hmt -}
+import Music.Theory.Duration.Rq
 
 -- | Standard music notation durational model annotations
 data D_Annotation = Tie_Right
@@ -57,7 +58,7 @@
 da_tuplet (d,n) x =
     let fn (p,q) = (p {multiplier = n%d},q)
         k = sum (map (duration_to_rq . fst) x) / (d%1)
-        ty = rq_to_duration_err (show ("da_tuplet",d,n,x,k)) k
+        ty = rq_to_duration_err (show ("da_tuplet",d,n,x,k)) 2 k
         t0 = [Begin_Tuplet (d,n,ty)]
         ts = [t0] ++ replicate (length x - 2) [] ++ [[End_Tuplet]]
         jn (p,q) z = (p,q++z)
diff --git a/Music/Theory/Duration/CT.hs b/Music/Theory/Duration/CT.hs
deleted file mode 100644
--- a/Music/Theory/Duration/CT.hs
+++ /dev/null
@@ -1,195 +0,0 @@
--- | Functions to generate a click track from a metric structure.
-module Music.Theory.Duration.CT where
-
-import Data.Function {- base -}
-import Data.List {- base -}
-import Data.Maybe {- base -}
-
-import qualified Music.Theory.Duration.RQ as T {- hmt -}
-import qualified Music.Theory.List as T {- hmt -}
-import qualified Music.Theory.Time_Signature as T {- hmt -}
-import qualified Music.Theory.Time.Seq as T {- hmt -}
-
--- | 1-indexed.
-type Measure = Int
-
--- | 1-indexed.
-type Pulse = Int
-
--- | Transform measures given as 'T.RQ' divisions to absolute 'T.RQ'
--- locations.  /mdv/ abbreviates measure divisions.
---
--- > mdv_to_mrq [[1,2,1],[3,2,1]] == [[0,1,3],[4,7,9]]
-mdv_to_mrq :: [[T.RQ]] -> [[T.RQ]]
-mdv_to_mrq = snd . mapAccumL T.dx_d' 0
-
--- | Lookup function for ('Measure','Pulse') indexed structure.
-mp_lookup_err :: [[a]] -> (Measure,Pulse) -> a
-mp_lookup_err sq (m,p) =
-    if m < 1 || p < 1
-    then error (show ("mp_lookup_err: one indexed?",m,p))
-    else (sq !! (m - 1)) !! (p - 1)
-
--- | Comparison for ('Measure','Pulse') indices.
-mp_compare :: (Measure,Pulse) -> (Measure,Pulse) -> Ordering
-mp_compare = T.two_stage_compare (compare `on` fst) (compare `on` snd)
-
--- * CT
-
--- | Latch measures (ie. make measures contiguous, hold previous value).
---
--- > unzip (ct_ext 10 'a' [(3,'b'),(8,'c')]) == ([1..10],"aabbbbbccc")
-ct_ext :: Int -> a -> [(Measure,a)] -> [(Measure,a)]
-ct_ext n def sq = T.tseq_latch def sq [1 .. n]
-
--- | Variant that requires a value at measure one (first measure).
-ct_ext1 :: Int -> [(Measure,a)] -> [(Measure,a)]
-ct_ext1 n sq =
-    case sq of
-      (1,e) : sq' -> ct_ext n e sq'
-      _ -> error "ct_ext1"
-
--- | 'T.rts_divisions' of 'ct_ext1'.
-ct_dv_seq :: Int -> T.Tseq Measure T.Rational_Time_Signature -> [(Measure,[[T.RQ]])]
-ct_dv_seq n ts = map (fmap T.rts_divisions) (ct_ext1 n ts)
-
--- | 'ct_dv_seq' without measures numbers.
-ct_mdv_seq :: Int -> T.Tseq Measure T.Rational_Time_Signature -> [[T.RQ]]
-ct_mdv_seq n = map (concat . snd) . ct_dv_seq n
-
--- | 'mdv_to_mrq' of 'ct_mdv_seq'.
-ct_rq :: Int -> T.Tseq Measure T.Rational_Time_Signature -> [[T.RQ]]
-ct_rq n ts = mdv_to_mrq (ct_mdv_seq n ts)
-
-ct_mp_lookup :: [[T.RQ]] -> (Measure,Pulse) -> T.RQ
-ct_mp_lookup = mp_lookup_err . mdv_to_mrq
-
-ct_m_to_rq :: [[T.RQ]] -> [(Measure,t)] -> [(T.RQ,t)]
-ct_m_to_rq sq = map (\(m,c) -> (ct_mp_lookup sq (m,1),c))
-
--- | Latch rehearsal mark sequence, only indicating marks.  Initial mark is @.@.
---
--- > ct_mark_seq 2 [] == [(1,Just '.'),(2,Nothing)]
---
--- > let r = [(1,Just '.'),(3,Just 'A'),(8,Just 'B')]
--- > in filter (isJust . snd) (ct_mark_seq 10 [(3,'A'),(8,'B')]) == r
-ct_mark_seq :: Int -> T.Tseq Measure Char -> T.Tseq Measure (Maybe Char)
-ct_mark_seq n mk = T.seq_changed (ct_ext n '.' mk)
-
--- | Indicate measures prior to marks.
---
--- > ct_pre_mark [] == []
--- > ct_pre_mark [(1,'A')] == []
--- > ct_pre_mark [(3,'A'),(8,'B')] == [(2,Just ()),(7,Just ())]
-ct_pre_mark :: [(Measure,a)] -> [(Measure,Maybe ())]
-ct_pre_mark = mapMaybe (\(m,_) -> if m <= 1 then Nothing else Just (m - 1,Just ()))
-
--- | Contiguous pre-mark sequence.
---
--- > ct_pre_mark_seq 1 [(1,'A')] == [(1,Nothing)]
--- > ct_pre_mark_seq 10 [(3,'A'),(8,'B')]
-ct_pre_mark_seq :: Measure -> T.Tseq Measure Char -> T.Tseq Measure (Maybe ())
-ct_pre_mark_seq n mk =
-    let pre = ct_pre_mark mk
-    in T.tseq_merge_resolve const pre (zip [1 .. n] (repeat Nothing))
-
-ct_tempo_lseq_rq :: [[T.RQ]] -> T.Lseq (Measure,Pulse) T.RQ -> T.Lseq T.RQ T.RQ
-ct_tempo_lseq_rq sq = T.lseq_tmap (ct_mp_lookup sq)
-
--- | Interpolating lookup of tempo sequence ('T.lseq_lookup_err').
-ct_tempo_at :: T.Lseq T.RQ T.RQ -> T.RQ -> Rational
-ct_tempo_at = T.lseq_lookup_err compare
-
--- | Types of nodes.
-data CT_Node = CT_Mark T.RQ -- ^ The start of a measure with a rehearsal mark.
-             | CT_Start T.RQ -- ^ The start of a regular measure.
-             | CT_Normal T.RQ -- ^ A regular pulse.
-             | CT_Edge T.RQ -- ^ The start of a pulse group within a measure.
-             | CT_Pre T.RQ -- ^ A regular pulse in a measure prior to a rehearsal mark.
-             | CT_End -- ^ The end of the track.
-               deriving (Eq,Show)
-
--- | Lead-in of @(pulse,tempo,count)@.
-ct_leadin :: (T.RQ,Double,Int) -> T.Dseq Double CT_Node
-ct_leadin (du,tm,n) = replicate n (realToFrac du * (60 / tm),CT_Normal du)
-
--- | Prepend initial element to start of list.
---
--- > delay1 "abc" == "aabc"
-delay1 :: [a] -> [a]
-delay1 l =
-    case l of
-      [] -> error "delay1: []"
-      e:_ -> e : l
-
-ct_measure:: T.Lseq T.RQ T.RQ -> ([T.RQ],Maybe Char,Maybe (),[[T.RQ]]) -> [(Rational,CT_Node)]
-ct_measure sq (mrq,mk,pr,dv) =
-    let dv' = concatMap (zip [1::Int ..]) dv
-        f (p,rq,(g,du)) =
-            let nm = if p == 1
-                     then case mk of
-                            Nothing -> CT_Start du
-                            Just _ -> CT_Mark du
-                     else if pr == Just ()
-                          then CT_Pre du
-                          else if g == 1 then CT_Edge du else CT_Normal du
-            in (du * (60 / ct_tempo_at sq rq),nm)
-    in map f (zip3 [1::Int ..] mrq dv')
-
--- | Click track definition.
-data CT = CT {ct_len :: Int
-             ,ct_ts :: [(Measure,T.Rational_Time_Signature)]
-             ,ct_mark :: [(Measure,Char)]
-             ,ct_tempo :: T.Lseq (Measure,Pulse) T.RQ
-             ,ct_count :: (T.RQ,Int)}
-          deriving Show
-
--- | Initial tempo, if given.
-ct_tempo0 :: CT -> Maybe T.RQ
-ct_tempo0 ct =
-    case ct_tempo ct of
-      (((1,1),_),n):_ -> Just n
-      _ -> Nothing
-
--- | Erroring variant.
-ct_tempo0_err :: CT -> T.RQ
-ct_tempo0_err = fromMaybe (error "ct_tempo0") . ct_tempo0
-
--- > import Music.Theory.Duration.CT
--- > import Music.Theory.Time.Seq
--- > let ct = CT 2 [(1,[(3,8),(2,4)])] [(1,'a')] [(((1,0),T.None),60)] undefined
--- > ct_measures ct
-ct_measures :: CT -> [T.Dseq Rational CT_Node]
-ct_measures (CT n ts mk tm _) =
-    let f msg sq = let (m,v) = unzip sq
-                   in if m == [1 .. n]
-                      then v
-                      else error (show ("ct_measures",msg,sq,m,v,n))
-        msr = zip4
-              (f "ts" (zip [1..] (ct_rq n ts)))
-              (f "mk" (ct_mark_seq n mk))
-              (f "pre-mk" (ct_pre_mark_seq n mk))
-              (f "dv" (ct_dv_seq n ts))
-    in map (ct_measure (ct_tempo_lseq_rq (ct_mdv_seq n ts) tm)) msr
-
-ct_dseq' :: CT -> T.Dseq Rational CT_Node
-ct_dseq' = concat . ct_measures
-
-ct_dseq :: CT -> T.Dseq Double CT_Node
-ct_dseq = T.dseq_tmap fromRational . ct_dseq'
-
--- * Indirect
-
-ct_rq_measure :: [[T.RQ]] -> T.RQ -> Maybe Measure
-ct_rq_measure sq rq = fmap fst (find ((rq `elem`) . snd) (zip [1..] sq))
-
-ct_rq_mp :: [[T.RQ]] -> T.RQ -> Maybe (Measure,Pulse)
-ct_rq_mp sq rq =
-    let f (m,l) = (m,fromMaybe (error "ct_rq_mp: ix") (findIndex (== rq) l) + 1)
-    in fmap f (find ((rq `elem`) . snd) (zip [1..] sq))
-
-ct_rq_mp_err :: [[T.RQ]] -> T.RQ -> (Measure, Pulse)
-ct_rq_mp_err sq = fromMaybe (error "ct_rq_mp") . ct_rq_mp sq
-
-ct_mp_to_rq :: [[T.RQ]] -> [((Measure,Pulse),t)] -> [(T.RQ,t)]
-ct_mp_to_rq sq = map (\(mp,c) -> (ct_mp_lookup sq mp,c))
diff --git a/Music/Theory/Duration/ClickTrack.hs b/Music/Theory/Duration/ClickTrack.hs
new file mode 100644
--- /dev/null
+++ b/Music/Theory/Duration/ClickTrack.hs
@@ -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))
diff --git a/Music/Theory/Duration/Hollos2014.hs b/Music/Theory/Duration/Hollos2014.hs
new file mode 100644
--- /dev/null
+++ b/Music/Theory/Duration/Hollos2014.hs
@@ -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
diff --git a/Music/Theory/Duration/Name.hs b/Music/Theory/Duration/Name.hs
--- a/Music/Theory/Duration/Name.hs
+++ b/Music/Theory/Duration/Name.hs
@@ -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
 
diff --git a/Music/Theory/Duration/Name/Abbreviation.hs b/Music/Theory/Duration/Name/Abbreviation.hs
--- a/Music/Theory/Duration/Name/Abbreviation.hs
+++ b/Music/Theory/Duration/Name/Abbreviation.hs
@@ -1,4 +1,4 @@
--- | Abbreviated names for 'Duration' values when written as literals.
+-- | Abbreviated names for 'Duration' values when written as Haskell literals.
 -- There are /letter/ names where 'w' is 'whole_note' and so on, and
 -- /numerical/ names where '_4' is 'quarter_note' and so on.  In both
 -- cases a @'@ extension means a @dot@ so that 'e''' is a double
diff --git a/Music/Theory/Duration/RQ.hs b/Music/Theory/Duration/RQ.hs
deleted file mode 100644
--- a/Music/Theory/Duration/RQ.hs
+++ /dev/null
@@ -1,193 +0,0 @@
--- | Rational quarter-note notation for durations.
-module Music.Theory.Duration.RQ where
-
-import Data.Function {- base -}
-import Data.List {- base -}
-import Data.Maybe {- base -}
-import Data.Ratio {- base -}
-
-import Music.Theory.Duration {- hmt -}
-
--- | Rational Quarter-Note
-type RQ = Rational
-
--- > rq_duration_tbl 2
-rq_duration_tbl :: Dots -> [(Rational,Duration)]
-rq_duration_tbl k = map (\d -> (duration_to_rq d,d)) (duration_set k)
-
--- | Rational quarter note to duration value.  It is a mistake to hope
--- this could handle tuplets directly since, for instance, a @3:2@
--- dotted note will be of the same duration as a plain undotted note.
---
--- > rq_to_duration (3/4) == Just dotted_eighth_note
-rq_to_duration :: RQ -> Maybe Duration
-rq_to_duration x = lookup x (rq_duration_tbl 2)
-
--- | Is 'RQ' a /cmn/ duration.
---
--- > map rq_is_cmn [1/4,1/5,1/8,3/32] == [True,False,True,False]
-rq_is_cmn :: RQ -> Bool
-rq_is_cmn = isJust . rq_to_duration
-
--- | Variant of 'rq_to_duration' with error message.
-rq_to_duration_err :: Show a => a -> RQ -> Duration
-rq_to_duration_err msg n =
-    let err = error ("rq_to_duration:" ++ show (msg,n))
-    in fromMaybe err (rq_to_duration n)
-
--- | Convert a whole note division integer to an 'RQ' value.
---
--- > map whole_note_division_to_rq [1,2,4,8] == [4,2,1,1/2]
-whole_note_division_to_rq :: 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 = [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'
-
--- * TIME
-
--- | Duration in seconds of RQ given ppm
---
---   ppm = pulses-per-minute, rq = rational-quarter-note
---
--- > map (\sd -> rq_to_seconds_ppm (90 * sd) 1) [1,2,4,8,16] == [2/3,1/3,1/6,1/12,1/24]
--- > map (rq_to_seconds_ppm 90) [1,2,3,4] == [2/3,1 + 1/3,2,2 + 2/3]
--- > map (rq_to_seconds_ppm 90) [0::RQ,1,1 + 1/2,1 + 3/4,1 + 7/8,2]
-rq_to_seconds_ppm :: Fractional a => a -> a -> a
-rq_to_seconds_ppm ppm rq = rq * (60 / ppm)
-
--- | PPM given that /rq/ has duration /x/, ie. inverse of 'rq_to_seconds'
---
--- > map (rq_to_ppm 1) [0.4,0.5,0.8,1,1.5,2] == [150,120,75,60,40,30]
--- > map (\ppm -> rq_to_seconds ppm 1) [150,120,75,60,40,30] == [0.4,0.5,0.8,1,1.5,2]
-rq_to_ppm :: Fractional a => a -> a -> a
-rq_to_ppm rq x = (rq / x) * 60
-
diff --git a/Music/Theory/Duration/RQ/Division.hs b/Music/Theory/Duration/RQ/Division.hs
deleted file mode 100644
--- a/Music/Theory/Duration/RQ/Division.hs
+++ /dev/null
@@ -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)
diff --git a/Music/Theory/Duration/RQ/Tied.hs b/Music/Theory/Duration/RQ/Tied.hs
deleted file mode 100644
--- a/Music/Theory/Duration/RQ/Tied.hs
+++ /dev/null
@@ -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
diff --git a/Music/Theory/Duration/Rq.hs b/Music/Theory/Duration/Rq.hs
new file mode 100644
--- /dev/null
+++ b/Music/Theory/Duration/Rq.hs
@@ -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
+
diff --git a/Music/Theory/Duration/Rq/Division.hs b/Music/Theory/Duration/Rq/Division.hs
new file mode 100644
--- /dev/null
+++ b/Music/Theory/Duration/Rq/Division.hs
@@ -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)
diff --git a/Music/Theory/Duration/Rq/Tied.hs b/Music/Theory/Duration/Rq/Tied.hs
new file mode 100644
--- /dev/null
+++ b/Music/Theory/Duration/Rq/Tied.hs
@@ -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
diff --git a/Music/Theory/Duration/Sequence/Notate.hs b/Music/Theory/Duration/Sequence/Notate.hs
--- a/Music/Theory/Duration/Sequence/Notate.hs
+++ b/Music/Theory/Duration/Sequence/Notate.hs
@@ -1,7 +1,7 @@
--- | Notation of a sequence of 'RQ' values as annotated 'Duration' values.
+-- | Notation of a sequence of 'Rq' values as annotated 'Duration' values.
 --
 -- 1. Separate input sequence into measures, adding tie annotations as
--- required (see 'to_measures_ts').  Ensure all 'RQ_T' values can be
+-- required (see 'to_measures_ts').  Ensure all 'Rq_Tied' values can be
 -- notated as /common music notation/ durations.
 --
 -- 2. Separate each measure into pulses (see 'm_divisions_ts').
@@ -17,53 +17,31 @@
 -- 5. Ascribe values to notated durations, see 'ascribe'.
 module Music.Theory.Duration.Sequence.Notate where
 
-import Control.Monad {- base -}
 import Data.List {- base -}
 import Data.List.Split {- split -}
 import Data.Maybe {- base -}
 import Data.Ratio {- base -}
 
+import Music.Theory.Either {- hmt-base -}
+import Music.Theory.Function {- hmt-base -}
+import Music.Theory.List {- hmt-base -}
+
 import Music.Theory.Duration {- hmt -}
 import Music.Theory.Duration.Annotation {- hmt -}
-import Music.Theory.Function {- hmt -}
-import Music.Theory.Duration.RQ {- hmt -}
-import Music.Theory.Duration.RQ.Tied {- hmt -}
-import Music.Theory.List {- hmt -}
+import Music.Theory.Duration.Rq {- hmt -}
+import Music.Theory.Duration.Rq.Tied {- hmt -}
 import Music.Theory.Time_Signature {- hmt -}
 
 -- * Lists
 
--- | Variant of 'catMaybes'.  If all elements of the list are @Just
--- a@, then gives @Just [a]@ else gives 'Nothing'.
---
--- > all_just (map Just [1..3]) == Just [1..3]
--- > all_just [Just 1,Nothing,Just 3] == Nothing
-all_just :: [Maybe a] -> Maybe [a]
-all_just x =
-    case x of
-      [] -> Just []
-      Just i:x' -> fmap (i :) (all_just x')
-      Nothing:_ -> Nothing
+{- | Applies a /join/ function to the first two elements of the list.
+     If the /join/ function succeeds the joined element is considered for further coalescing.
 
--- | Variant of 'Data.Either.rights' that preserves first 'Left'.
---
--- > all_right (map Right [1..3]) == Right [1..3]
--- > all_right [Right 1,Left 'a',Left 'b'] == Left 'a'
-all_right :: [Either a b] -> Either a [b]
-all_right x =
-    case x of
-      [] -> Right []
-      Right i:x' -> fmap (i :) (all_right x')
-      Left i:_ -> Left i
+> coalesce (\p q -> Just (p + q)) [1..5] == [15]
 
--- | Applies a /join/ function to the first two elements of the list.
--- If the /join/ function succeeds the joined element is considered
--- for further coalescing.
---
--- > coalesce (\p q -> Just (p + q)) [1..5] == [15]
---
--- > let jn p q = if even p then Just (p + q) else Nothing
--- > in coalesce jn [1..5] == map sum [[1],[2,3],[4,5]]
+> let jn p q = if even p then Just (p + q) else Nothing
+> coalesce jn [1..5] == map sum [[1],[2,3],[4,5]]
+-}
 coalesce :: (a -> a -> Maybe a) -> [a] -> [a]
 coalesce f x =
     case x of
@@ -75,13 +53,13 @@
 
 -- | Variant of 'coalesce' with accumulation parameter.
 --
--- > coalesce_accum (\i p q -> Left (p + q)) 0 [1..5] == [(0,15)]
+-- > coalesce_accum (\_ p q -> Left (p + q)) 0 [1..5] == [(0,15)]
 --
 -- > let jn i p q = if even p then Left (p + q) else Right (p + i)
--- > in coalesce_accum jn 0 [1..7] == [(0,1),(1,5),(6,9),(15,13)]
+-- > coalesce_accum jn 0 [1..7] == [(0,1),(1,5),(6,9),(15,13)]
 --
 -- > let jn i p q = if even p then Left (p + q) else Right [p,q]
--- > in coalesce_accum jn [] [1..5] == [([],1),([1,2],5),([5,4],9)]
+-- > coalesce_accum jn [] [1..5] == [([],1),([1,2],5),([5,4],9)]
 coalesce_accum :: (b -> a -> a -> Either a b) -> b -> [a] -> [(b,a)]
 coalesce_accum f i x =
     case x of
@@ -95,7 +73,7 @@
 -- | Variant of 'coalesce_accum' that accumulates running sum.
 --
 -- > let f i p q = if i == 1 then Just (p + q) else Nothing
--- > in coalesce_sum (+) 0 f [1,1/2,1/4,1/4] == [1,1]
+-- > coalesce_sum (+) 0 f [1,1/2,1/4,1/4] == [1,1]
 coalesce_sum :: (b -> a -> b) -> b -> (b -> a -> a -> Maybe a) -> [a] -> [a]
 coalesce_sum add zero f =
     let g i p q = case f i p q of
@@ -103,12 +81,6 @@
                     Nothing -> Right (i `add` p)
     in map snd . coalesce_accum g zero
 
--- * Either
-
--- | Lower 'Either' to 'Maybe' by discarding 'Left'.
-either_to_maybe :: Either a b -> Maybe b
-either_to_maybe = either (const Nothing) Just
-
 -- * Separate
 
 -- | Take elements while the sum of the prefix is less than or equal
@@ -160,21 +132,21 @@
                      Nothing -> Nothing
       _ -> Nothing
 
--- | Split sequence such that the prefix sums to precisely /m/.  The
--- third element of the result indicates if it was required to divide
--- an element.  Note that zero elements are kept left.  If the required
--- sum is non positive, or the input list does not sum to at least the
--- required sum, gives nothing.
---
--- > split_sum 5 [2,3,1] == Just ([2,3],[1],Nothing)
--- > split_sum 5 [2,1,3] == Just ([2,1,2],[1],Just (2,1))
--- > split_sum 2 [3/2,3/2,3/2] == Just ([3/2,1/2],[1,3/2],Just (1/2,1))
--- > split_sum 6 [1..10] == Just ([1..3],[4..10],Nothing)
--- > fmap (\(a,_,c)->(a,c)) (split_sum 5 [1..]) == Just ([1,2,2],Just (2,1))
--- > split_sum 0 [1..] == Nothing
--- > split_sum 3 [1,1] == Nothing
--- > split_sum 3 [2,1,0] == Just ([2,1,0],[],Nothing)
--- > split_sum 3 [2,1,0,1] == Just ([2,1,0],[1],Nothing)
+{- | Split sequence /l/ such that the prefix sums to precisely /m/.
+     The third element of the result indicates if it was required to divide an element.
+     Note that zero elements are kept left.
+     If the required sum is non positive, or the input list does not sum to at least the required sum, gives nothing.
+
+> split_sum 5 [2,3,1] == Just ([2,3],[1],Nothing)
+> split_sum 5 [2,1,3] == Just ([2,1,2],[1],Just (2,1))
+> split_sum 2 [3/2,3/2,3/2] == Just ([3/2,1/2],[1,3/2],Just (1/2,1))
+> split_sum 6 [1..10] == Just ([1..3],[4..10],Nothing)
+> fmap (\(a,_,c)->(a,c)) (split_sum 5 [1..]) == Just ([1,2,2],Just (2,1))
+> split_sum 0 [1..] == Nothing
+> split_sum 3 [1,1] == Nothing
+> split_sum 3 [2,1,0] == Just ([2,1,0],[],Nothing)
+> split_sum 3 [2,1,0,1] == Just ([2,1,0],[1],Nothing)
+-}
 split_sum :: (Ord a, Num a) => a -> [a] -> Maybe ([a],[a],Maybe (a,a))
 split_sum m l =
     let (p,n,q) = take_sum m l
@@ -186,24 +158,20 @@
               [] -> Nothing
               z:q' -> Just (p++[n],z-n:q',Just (n,z-n))
 
--- | Alias for 'True', used locally for documentation.
-_t :: Bool
-_t = True
+{- | Variant of 'split_sum' that operates at 'Rq_Tied' sequences.
 
--- | Alias for 'False', used locally for documentation.
-_f :: Bool
-_f = False
+> t = True
+> f = False
 
--- | Variant of 'split_sum' that operates at 'RQ_T' sequences.
---
--- > let r = Just ([(3,_f),(2,_t)],[(1,_f)])
--- > in rqt_split_sum 5 [(3,_f),(2,_t),(1,_f)] == r
---
--- > let r = Just ([(3,_f),(1,_t)],[(1,_t),(1,_f)])
--- > in rqt_split_sum 4 [(3,_f),(2,_t),(1,_f)] == r
---
--- > rqt_split_sum 4 [(5/2,False)] == Nothing
-rqt_split_sum :: RQ -> [RQ_T] -> Maybe ([RQ_T],[RQ_T])
+> r = Just ([(3,f),(2,t)],[(1,f)])
+> rqt_split_sum 5 [(3,f),(2,t),(1,f)] == r
+
+> r = Just ([(3,f),(1,t)],[(1,t),(1,f)])
+> rqt_split_sum 4 [(3,f),(2,t),(1,f)] == r
+
+> rqt_split_sum 4 [(5/2,False)] == Nothing
+-}
+rqt_split_sum :: Rq -> [Rq_Tied] -> Maybe ([Rq_Tied],[Rq_Tied])
 rqt_split_sum d x =
     case split_sum d (map rqt_rq x) of
       Just (i,_,k) ->
@@ -214,57 +182,61 @@
                                   ,(q,z) : t)
       Nothing -> Nothing
 
--- | Separate 'RQ_T' values in sequences summing to 'RQ' values.  This
--- is a recursive variant of 'rqt_split_sum'.  Note that is does not
--- ensure /cmn/ notation of values.
---
--- > let d = [(2,_f),(2,_f),(2,_f)]
--- > in rqt_separate [3,3] d == Right [[(2,_f),(1,_t)]
--- >                                  ,[(1,_f),(2,_f)]]
---
--- > let d = [(5/8,_f),(1,_f),(3/8,_f)]
--- > in rqt_separate [1,1] d == Right [[(5/8,_f),(3/8,_t)]
--- >                                  ,[(5/8,_f),(3/8,_f)]]
---
--- > let d = [(4/7,_t),(1/7,_f),(1,_f),(6/7,_f),(3/7,_f)]
--- > in rqt_separate [1,1,1] d == Right [[(4/7,_t),(1/7,_f),(2/7,_t)]
--- >                                    ,[(5/7,_f),(2/7,_t)]
--- >                                    ,[(4/7,_f),(3/7,_f)]]
-rqt_separate :: [RQ] -> [RQ_T] -> Either String [[RQ_T]]
+{- | Separate 'Rq_Tied' values in sequences summing to 'Rq' values.
+    This is a recursive variant of 'rqt_split_sum'.
+    Note that is does not ensure /cmn/ notation of values.
+
+> t = True
+> f = False
+
+> d = [(2,f),(2,f),(2,f)]
+> r = [[(2,f),(1,t)],[(1,f),(2,f)]]
+> rqt_separate [3,3] d == Right r
+
+> d = [(5/8,f),(1,f),(3/8,f)]
+> r = [[(5/8,f),(3/8,t)],[(5/8,f),(3/8,f)]]
+> rqt_separate [1,1] d == Right r
+
+> d = [(4/7,t),(1/7,f),(1,f),(6/7,f),(3/7,f)]
+> r = [[(4/7,t),(1/7,f),(2/7,t)],[(5/7,f),(2/7,t)],[(4/7,f),(3/7,f)]]
+> rqt_separate [1,1,1] d == Right r
+-}
+rqt_separate :: [Rq] -> [Rq_Tied] -> Either String [[Rq_Tied]]
 rqt_separate m x =
     case (m,x) of
       ([],[]) -> Right []
-      ([],_) -> Left (show ("rqt_separate",x))
+      ([],_) -> Left (show ("rqt_separate: lhs empty, rhs non-empty",x))
       (i:m',_) ->
           case rqt_split_sum i x of
             Just (r,x') -> fmap (r :) (rqt_separate m' x')
-            Nothing -> Left (show ("rqt_separate",i,m',x))
+            Nothing -> Left (show ("rqt_separate: rqt_split_sum failed",(i,x),m'))
 
-rqt_separate_m :: [RQ] -> [RQ_T] -> Maybe [[RQ_T]]
+-- | Maybe form ot 'rqt_separate'
+rqt_separate_m :: [Rq] -> [Rq_Tied] -> Maybe [[Rq_Tied]]
 rqt_separate_m m = either_to_maybe . rqt_separate m
 
--- | If the input 'RQ_T' sequence cannot be notated (see
+-- | If the input 'Rq_Tied' sequence cannot be notated (see
 -- 'rqt_can_notate') separate into equal parts, so long as each part
 -- is not less than /i/.
 --
--- > rqt_separate_tuplet undefined [(1/3,_f),(1/6,_f)]
--- > rqt_separate_tuplet undefined [(4/7,_t),(1/7,_f),(2/7,_f)]
+-- > rqt_separate_tuplet undefined [(1/3,f),(1/6,f)]
+-- > rqt_separate_tuplet undefined [(4/7,t),(1/7,f),(2/7,f)]
 --
 -- > let d = map rq_rqt [1/3,1/6,2/5,1/10]
--- > in rqt_separate_tuplet (1/8) d == Right [[(1/3,_f),(1/6,_f)]
--- >                                         ,[(2/5,_f),(1/10,_f)]]
+-- > in rqt_separate_tuplet (1/8) d == Right [[(1/3,f),(1/6,f)]
+-- >                                         ,[(2/5,f),(1/10,f)]]
 --
 -- > let d = [(1/5,True),(1/20,False),(1/2,False),(1/4,True)]
 -- > in rqt_separate_tuplet (1/16) d
 --
--- > let d = [(2/5,_f),(1/5,_f),(1/5,_f),(1/5,_t),(1/2,_f),(1/2,_f)]
+-- > let d = [(2/5,f),(1/5,f),(1/5,f),(1/5,t),(1/2,f),(1/2,f)]
 -- > in rqt_separate_tuplet (1/2) d
 --
 -- > let d = [(4/10,True),(1/10,False),(1/2,True)]
 -- > in rqt_separate_tuplet (1/2) d
-rqt_separate_tuplet :: RQ -> [RQ_T] -> Either String [[RQ_T]]
+rqt_separate_tuplet :: Rq -> [Rq_Tied] -> Either String [[Rq_Tied]]
 rqt_separate_tuplet i x =
-    if rqt_can_notate x
+    if rqt_can_notate 2 x
     then Left (show ("rqt_separate_tuplet: separation not required",x))
     else let j = sum (map rqt_rq x) / 2
          in if j < i
@@ -274,10 +246,10 @@
 -- | Recursive variant of 'rqt_separate_tuplet'.
 --
 -- > let d = map rq_rqt [1,1/3,1/6,2/5,1/10]
--- > in rqt_tuplet_subdivide (1/8) d == [[(1/1,_f)]
--- >                                    ,[(1/3,_f),(1/6,_f)]
--- >                                    ,[(2/5,_f),(1/10,_f)]]
-rqt_tuplet_subdivide :: RQ -> [RQ_T] -> [[RQ_T]]
+-- > in rqt_tuplet_subdivide (1/8) d == [[(1/1,f)]
+-- >                                    ,[(1/3,f),(1/6,f)]
+-- >                                    ,[(2/5,f),(1/10,f)]]
+rqt_tuplet_subdivide :: Rq -> [Rq_Tied] -> [[Rq_Tied]]
 rqt_tuplet_subdivide i x =
     case rqt_separate_tuplet i x of
       Left _ -> [x]
@@ -287,13 +259,13 @@
 --
 -- > let d = [(1/5,True),(1/20,False),(1/2,False),(1/4,True)]
 -- > in rqt_tuplet_subdivide_seq (1/2) [d]
-rqt_tuplet_subdivide_seq :: RQ -> [[RQ_T]] -> [[RQ_T]]
+rqt_tuplet_subdivide_seq :: Rq -> [[Rq_Tied]] -> [[Rq_Tied]]
 rqt_tuplet_subdivide_seq i = concatMap (rqt_tuplet_subdivide i)
 
 -- | If a tuplet is all tied, it ought to be a plain value?!
 --
--- > rqt_tuplet_sanity_ [(4/10,_t),(1/10,_f)] == [(1/2,_f)]
-rqt_tuplet_sanity_ :: [RQ_T] -> [RQ_T]
+-- > rqt_tuplet_sanity_ [(4/10,t),(1/10,f)] == [(1/2,f)]
+rqt_tuplet_sanity_ :: [Rq_Tied] -> [Rq_Tied]
 rqt_tuplet_sanity_ t =
     let last_tied = rqt_tied (last t)
         all_tied = all rqt_tied (dropRight 1 t)
@@ -301,82 +273,86 @@
        then [(sum (map rqt_rq t),last_tied)]
        else t
 
-rqt_tuplet_subdivide_seq_sanity_ :: RQ -> [[RQ_T]] -> [[RQ_T]]
+rqt_tuplet_subdivide_seq_sanity_ :: Rq -> [[Rq_Tied]] -> [[Rq_Tied]]
 rqt_tuplet_subdivide_seq_sanity_ i =
     map rqt_tuplet_sanity_ .
     rqt_tuplet_subdivide_seq i
 
 -- * Divisions
 
--- | Separate 'RQ' sequence into measures given by 'RQ' length.
+-- | Separate 'Rq' sequence into measures given by 'Rq' length.
 --
--- > to_measures_rq [3,3] [2,2,2] == Right [[(2,_f),(1,_t)],[(1,_f),(2,_f)]]
--- > to_measures_rq [3,3] [6] == Right [[(3,_t)],[(3,_f)]]
--- > to_measures_rq [1,1,1] [3] == Right [[(1,_t)],[(1,_t)],[(1,_f)]]
+-- > to_measures_rq [3,3] [2,2,2] == Right [[(2,f),(1,t)],[(1,f),(2,f)]]
+-- > to_measures_rq [3,3] [6] == Right [[(3,t)],[(3,f)]]
+-- > to_measures_rq [1,1,1] [3] == Right [[(1,t)],[(1,t)],[(1,f)]]
 -- > to_measures_rq [3,3] [2,2,1]
 -- > to_measures_rq [3,2] [2,2,2]
 --
 -- > let d = [4/7,33/28,9/20,4/5]
--- > in to_measures_rq [3] d == Right [[(4/7,_f),(33/28,_f),(9/20,_f),(4/5,_f)]]
-to_measures_rq :: [RQ] -> [RQ] -> Either String [[RQ_T]]
+-- > in to_measures_rq [3] d == Right [[(4/7,f),(33/28,f),(9/20,f),(4/5,f)]]
+to_measures_rq :: [Rq] -> [Rq] -> Either String [[Rq_Tied]]
 to_measures_rq m = rqt_separate m . map rq_rqt
 
--- | Variant of 'to_measures_rq' that ensures 'RQ_T' are /cmn/
+-- | Variant that is applicable only at sequence that do not require splitting and ties, else error.
+to_measures_rq_untied_err :: [Rq] -> [Rq] -> [[Rq]]
+to_measures_rq_untied_err m = either (error "to_measures_rq_untied") (map (map rqt_to_rq_err)) . to_measures_rq m
+
+-- | Variant of 'to_measures_rq' that ensures 'Rq_Tied' are /cmn/
 -- durations.  This is not a good composition.
 --
--- > to_measures_rq_cmn [6,6] [5,5,2] == Right [[(4,_t),(1,_f),(1,_t)]
--- >                                           ,[(4,_f),(2,_f)]]
+-- > to_measures_rq_cmn [6,6] [5,5,2] == Right [[(4,t),(1,f),(1,t)]
+-- >                                           ,[(4,f),(2,f)]]
 --
--- > let r = [[(4/7,_t),(1/7,_f),(1,_f),(6/7,_f),(3/7,_f)]]
+-- > let r = [[(4/7,t),(1/7,f),(1,f),(6/7,f),(3/7,f)]]
 -- > in to_measures_rq_cmn [3] [5/7,1,6/7,3/7] == Right r
 --
--- > to_measures_rq_cmn [1,1,1] [5/7,1,6/7,3/7] == Right [[(4/7,_t),(1/7,_f),(2/7,_t)]
--- >                                                     ,[(4/7,_t),(1/7,_f),(2/7,_t)]
--- >                                                     ,[(4/7,_f),(3/7,_f)]]
-to_measures_rq_cmn :: [RQ] -> [RQ] -> Either String [[RQ_T]]
+-- > to_measures_rq_cmn [1,1,1] [5/7,1,6/7,3/7] == Right [[(4/7,t),(1/7,f),(2/7,t)]
+-- >                                                     ,[(4/7,t),(1/7,f),(2/7,t)]
+-- >                                                     ,[(4/7,f),(3/7,f)]]
+to_measures_rq_cmn :: [Rq] -> [Rq] -> Either String [[Rq_Tied]]
 to_measures_rq_cmn m = fmap (map rqt_set_to_cmn) . to_measures_rq m
 
 -- | Variant of 'to_measures_rq' with measures given by
--- 'Time_Signature' values.  Does not ensure 'RQ_T' are /cmn/
+-- 'Time_Signature' values.  Does not ensure 'Rq_Tied' are /cmn/
 -- durations.
 --
--- > to_measures_ts [(1,4)] [5/8,3/8] /= Right [[(1/2,_t),(1/8,_f),(3/8,_f)]]
--- > to_measures_ts [(1,4)] [5/7,2/7] /= Right [[(4/7,_t),(1/7,_f),(2/7,_f)]]
+-- > to_measures_ts [(1,4)] [5/8,3/8] /= Right [[(1/2,t),(1/8,f),(3/8,f)]]
+-- > to_measures_ts [(1,4)] [5/7,2/7] /= Right [[(4/7,t),(1/7,f),(2/7,f)]]
 --
 -- > let {m = replicate 18 (1,4)
 -- >     ;x = [3/4,2,5/4,9/4,1/4,3/2,1/2,7/4,1,5/2,11/4,3/2]}
--- > in to_measures_ts m x == Right [[(3/4,_f),(1/4,_t)],[(1/1,_t)]
--- >                                ,[(3/4,_f),(1/4,_t)],[(1/1,_f)]
--- >                                ,[(1/1,_t)],[(1/1,_t)]
--- >                                ,[(1/4,_f),(1/4,_f),(1/2,_t)],[(1/1,_f)]
--- >                                ,[(1/2,_f),(1/2,_t)],[(1/1,_t)]
--- >                                ,[(1/4,_f),(3/4,_t)],[(1/4,_f),(3/4,_t)]
--- >                                ,[(1/1,_t)],[(3/4,_f),(1/4,_t)]
--- >                                ,[(1/1,_t)],[(1/1,_t)]
--- >                                ,[(1/2,_f),(1/2,_t)],[(1/1,_f)]]
+-- > in to_measures_ts m x == Right [[(3/4,f),(1/4,t)],[(1/1,t)]
+-- >                                ,[(3/4,f),(1/4,t)],[(1/1,f)]
+-- >                                ,[(1/1,t)],[(1/1,t)]
+-- >                                ,[(1/4,f),(1/4,f),(1/2,t)],[(1/1,f)]
+-- >                                ,[(1/2,f),(1/2,t)],[(1/1,t)]
+-- >                                ,[(1/4,f),(3/4,t)],[(1/4,f),(3/4,t)]
+-- >                                ,[(1/1,t)],[(3/4,f),(1/4,t)]
+-- >                                ,[(1/1,t)],[(1/1,t)]
+-- >                                ,[(1/2,f),(1/2,t)],[(1/1,f)]]
 --
 -- > to_measures_ts [(3,4)] [4/7,33/28,9/20,4/5]
 -- > to_measures_ts (replicate 3 (1,4)) [4/7,33/28,9/20,4/5]
-to_measures_ts :: [Time_Signature] -> [RQ] -> Either String [[RQ_T]]
+to_measures_ts :: [Time_Signature] -> [Rq] -> Either String [[Rq_Tied]]
 to_measures_ts m = to_measures_rq (map ts_rq m)
 
 -- | Variant of 'to_measures_ts' that allows for duration field
 -- operation but requires that measures be well formed.  This is
 -- useful for re-grouping measures after notation and ascription.
-to_measures_ts_by_eq :: (a -> RQ) -> [Time_Signature] -> [a] -> Maybe [[a]]
+to_measures_ts_by_eq :: (a -> Rq) -> [Time_Signature] -> [a] -> Maybe [[a]]
 to_measures_ts_by_eq f m = split_sum_by_eq f (map ts_rq m)
 
--- | Divide measure into pulses of indicated 'RQ' durations.  Measure
+-- | Divide measure into pulses of indicated 'Rq' durations.  Measure
 -- must be of correct length but need not contain only /cmn/
 -- durations.  Pulses are further subdivided if required to notate
 -- tuplets correctly, see 'rqt_tuplet_subdivide_seq'.
 --
--- > let d = [(1/4,_f),(1/4,_f),(2/3,_t),(1/6,_f),(16/15,_f),(1/5,_f)
--- >         ,(1/5,_f),(2/5,_t),(1/20,_f),(1/2,_f),(1/4,_t)]
+-- > let d = [(1/4,f),(1/4,f),(2/3,t),(1/6,f),(16/15,f),(1/5,f)
+-- >         ,(1/5,f),(2/5,t),(1/20,f),(1/2,f),(1/4,t)]
 -- > in m_divisions_rq [1,1,1,1] d
 --
--- > m_divisions_rq [1,1,1] [(4/7,_f),(33/28,_f),(9/20,_f),(4/5,_f)]
-m_divisions_rq :: [RQ] -> [RQ_T] -> Either String [[RQ_T]]
+-- > m_divisions_rq [1,1,1] [(4/7,f),(33/28,f),(9/20,f),(4/5,f)]
+m_divisions_rq :: [Rq] -> [Rq_Tied] -> Either String [[Rq_Tied]]
 m_divisions_rq z =
     fmap (rqt_tuplet_subdivide_seq_sanity_ (1/16) .
           map rqt_set_to_cmn) .
@@ -385,59 +361,59 @@
 -- | Variant of 'm_divisions_rq' that determines pulse divisions from
 -- 'Time_Signature'.
 --
--- > let d = [(4/7,_t),(1/7,_f),(2/7,_f)]
+-- > let d = [(4/7,t),(1/7,f),(2/7,f)]
 -- > in m_divisions_ts (1,4) d == Just [d]
 --
 -- > let d = map rq_rqt [1/3,1/6,2/5,1/10]
--- > in m_divisions_ts (1,4) d == Just [[(1/3,_f),(1/6,_f)]
--- >                                   ,[(2/5,_f),(1/10,_f)]]
+-- > in m_divisions_ts (1,4) d == Just [[(1/3,f),(1/6,f)]
+-- >                                   ,[(2/5,f),(1/10,f)]]
 --
 -- > let d = map rq_rqt [4/7,33/28,9/20,4/5]
--- > in m_divisions_ts (3,4) d == Just [[(4/7,_f),(3/7,_t)]
--- >                                   ,[(3/4,_f),(1/4,_t)]
--- >                                   ,[(1/5,_f),(4/5,_f)]]
-m_divisions_ts :: Time_Signature -> [RQ_T] -> Either String [[RQ_T]]
+-- > in m_divisions_ts (3,4) d == Just [[(4/7,f),(3/7,t)]
+-- >                                   ,[(3/4,f),(1/4,t)]
+-- >                                   ,[(1/5,f),(4/5,f)]]
+m_divisions_ts :: Time_Signature -> [Rq_Tied] -> Either String [[Rq_Tied]]
 m_divisions_ts ts = m_divisions_rq (ts_divisions ts)
 
 {-| Composition of 'to_measures_rq' and 'm_divisions_rq', where
 measures are initially given as sets of divisions.
 
 > let m = [[1,1,1],[1,1,1]]
-> in to_divisions_rq m [2,2,2] == Right [[[(1,_t)],[(1,_f)],[(1,_t)]]
->                                      ,[[(1,_f)],[(1,_t)],[(1,_f)]]]
+> in to_divisions_rq m [2,2,2] == Right [[[(1,t)],[(1,f)],[(1,t)]]
+>                                      ,[[(1,f)],[(1,t)],[(1,f)]]]
 
 > let d = [2/7,1/7,4/7,5/7,8/7,1,1/7]
-> in to_divisions_rq [[1,1,1,1]] d == Right [[[(2/7,_f),(1/7,_f),(4/7,_f)]
->                                           ,[(4/7,_t),(1/7,_f),(2/7,_t)]
->                                           ,[(6/7,_f),(1/7,_t)]
->                                           ,[(6/7,_f),(1/7,_f)]]]
+> in to_divisions_rq [[1,1,1,1]] d == Right [[[(2/7,f),(1/7,f),(4/7,f)]
+>                                           ,[(4/7,t),(1/7,f),(2/7,t)]
+>                                           ,[(6/7,f),(1/7,t)]
+>                                           ,[(6/7,f),(1/7,f)]]]
 
 > let d = [5/7,1,6/7,3/7]
-> in to_divisions_rq [[1,1,1]] d == Right [[[(4/7,_t),(1/7,_f),(2/7,_t)]
->                                         ,[(4/7,_t),(1/7,_f),(2/7,_t)]
->                                         ,[(4/7,_f),(3/7,_f)]]]
+> in to_divisions_rq [[1,1,1]] d == Right [[[(4/7,t),(1/7,f),(2/7,t)]
+>                                         ,[(4/7,t),(1/7,f),(2/7,t)]
+>                                         ,[(4/7,f),(3/7,f)]]]
 
 > let d = [2/7,1/7,4/7,5/7,1,6/7,3/7]
-> in to_divisions_rq [[1,1,1,1]] d == Right [[[(2/7,_f),(1/7,_f),(4/7,_f)]
->                                           ,[(4/7,_t),(1/7,_f),(2/7,_t)]
->                                           ,[(4/7,_t),(1/7,_f),(2/7,_t)]
->                                           ,[(4/7,_f),(3/7,_f)]]]
+> in to_divisions_rq [[1,1,1,1]] d == Right [[[(2/7,f),(1/7,f),(4/7,f)]
+>                                           ,[(4/7,t),(1/7,f),(2/7,t)]
+>                                           ,[(4/7,t),(1/7,f),(2/7,t)]
+>                                           ,[(4/7,f),(3/7,f)]]]
 
 > let d = [4/7,33/28,9/20,4/5]
-> in to_divisions_rq [[1,1,1]] d == Right [[[(4/7,_f),(3/7,_t)]
->                                          ,[(3/4,_f),(1/4,_t)]
->                                          ,[(1/5,_f),(4/5,_f)]]]
+> in to_divisions_rq [[1,1,1]] d == Right [[[(4/7,f),(3/7,t)]
+>                                          ,[(3/4,f),(1/4,t)]
+>                                          ,[(1/5,f),(4/5,f)]]]
 
 > let {p = [[1/2,1,1/2],[1/2,1]]
 >     ;d = map (/6) [1,1,1,1,1,1,4,1,2,1,1,2,1,3]}
-> in to_divisions_rq p d == Right [[[(1/6,_f),(1/6,_f),(1/6,_f)]
->                                  ,[(1/6,_f),(1/6,_f),(1/6,_f),(1/2,True)]
->                                  ,[(1/6,_f),(1/6,_f),(1/6,True)]]
->                                 ,[[(1/6,_f),(1/6,_f),(1/6,_f)]
->                                  ,[(1/3,_f),(1/6,_f),(1/2,_f)]]]
+> in to_divisions_rq p d == Right [[[(1/6,f),(1/6,f),(1/6,f)]
+>                                  ,[(1/6,f),(1/6,f),(1/6,f),(1/2,True)]
+>                                  ,[(1/6,f),(1/6,f),(1/6,True)]]
+>                                 ,[[(1/6,f),(1/6,f),(1/6,f)]
+>                                  ,[(1/3,f),(1/6,f),(1/2,f)]]]
 
 -}
-to_divisions_rq :: [[RQ]] -> [RQ] -> Either String [[[RQ_T]]]
+to_divisions_rq :: [[Rq]] -> [Rq] -> Either String [[[Rq_Tied]]]
 to_divisions_rq m x =
     let m' = map sum m
     in case to_measures_rq m' x of
@@ -448,39 +424,39 @@
 -- 'Time_Signature'.
 --
 -- > let d = [3/5,2/5,1/3,1/6,7/10,17/15,1/2,1/6]
--- > in to_divisions_ts [(4,4)] d == Just [[[(3/5,_f),(2/5,_f)]
--- >                                       ,[(1/3,_f),(1/6,_f),(1/2,_t)]
--- >                                       ,[(1/5,_f),(4/5,_t)]
--- >                                       ,[(1/3,_f),(1/2,_f),(1/6,_f)]]]
+-- > in to_divisions_ts [(4,4)] d == Just [[[(3/5,f),(2/5,f)]
+-- >                                       ,[(1/3,f),(1/6,f),(1/2,t)]
+-- >                                       ,[(1/5,f),(4/5,t)]
+-- >                                       ,[(1/3,f),(1/2,f),(1/6,f)]]]
 --
 -- > let d = [3/5,2/5,1/3,1/6,7/10,29/30,1/2,1/3]
--- > in to_divisions_ts [(4,4)] d == Just [[[(3/5,_f),(2/5,_f)]
--- >                                       ,[(1/3,_f),(1/6,_f),(1/2,_t)]
--- >                                       ,[(1/5,_f),(4/5,_t)]
--- >                                       ,[(1/6,_f),(1/2,_f),(1/3,_f)]]]
+-- > in to_divisions_ts [(4,4)] d == Just [[[(3/5,f),(2/5,f)]
+-- >                                       ,[(1/3,f),(1/6,f),(1/2,t)]
+-- >                                       ,[(1/5,f),(4/5,t)]
+-- >                                       ,[(1/6,f),(1/2,f),(1/3,f)]]]
 --
 -- > let d = [3/5,2/5,1/3,1/6,7/10,4/5,1/2,1/2]
--- > in to_divisions_ts [(4,4)] d == Just [[[(3/5,_f),(2/5,_f)]
--- >                                       ,[(1/3,_f),(1/6,_f),(1/2,_t)]
--- >                                       ,[(1/5,_f),(4/5,_f)]
--- >                                       ,[(1/2,_f),(1/2,_f)]]]
+-- > in to_divisions_ts [(4,4)] d == Just [[[(3/5,f),(2/5,f)]
+-- >                                       ,[(1/3,f),(1/6,f),(1/2,t)]
+-- >                                       ,[(1/5,f),(4/5,f)]
+-- >                                       ,[(1/2,f),(1/2,f)]]]
 --
 -- > let d = [4/7,33/28,9/20,4/5]
--- > in to_divisions_ts [(3,4)] d == Just [[[(4/7,_f),(3/7,_t)]
--- >                                       ,[(3/4,_f),(1/4,_t)]
--- >                                       ,[(1/5,_f),(4/5,_f)]]]
-to_divisions_ts :: [Time_Signature] -> [RQ] -> Either String [[[RQ_T]]]
+-- > in to_divisions_ts [(3,4)] d == Just [[[(4/7,f),(3/7,t)]
+-- >                                       ,[(3/4,f),(1/4,t)]
+-- >                                       ,[(1/5,f),(4/5,f)]]]
+to_divisions_ts :: [Time_Signature] -> [Rq] -> Either String [[[Rq_Tied]]]
 to_divisions_ts ts = to_divisions_rq (map ts_divisions ts)
 
 -- * Durations
 
 -- | Pulse tuplet derivation.
 --
--- > p_tuplet_rqt [(2/3,_f),(1/3,_t)] == Just ((3,2),[(1,_f),(1/2,_t)])
--- > p_tuplet_rqt (map rq_rqt [1/3,1/6]) == Just ((3,2),[(1/2,_f),(1/4,_f)])
--- > p_tuplet_rqt (map rq_rqt [2/5,1/10]) == Just ((5,4),[(1/2,_f),(1/8,_f)])
+-- > p_tuplet_rqt [(2/3,f),(1/3,t)] == Just ((3,2),[(1,f),(1/2,t)])
+-- > p_tuplet_rqt (map rq_rqt [1/3,1/6]) == Just ((3,2),[(1/2,f),(1/4,f)])
+-- > p_tuplet_rqt (map rq_rqt [2/5,1/10]) == Just ((5,4),[(1/2,f),(1/8,f)])
 -- > p_tuplet_rqt (map rq_rqt [1/3,1/6,2/5,1/10])
-p_tuplet_rqt :: [RQ_T] -> Maybe ((Integer,Integer),[RQ_T])
+p_tuplet_rqt :: [Rq_Tied] -> Maybe ((Integer,Integer),[Rq_Tied])
 p_tuplet_rqt x =
     let f t = (t,map (rqt_un_tuplet t) x)
     in fmap f (rq_derive_tuplet (map rqt_rq x))
@@ -488,31 +464,31 @@
 -- | Notate pulse, ie. derive tuplet if neccesary. The flag indicates
 -- if the initial value is tied left.
 --
--- > p_notate False [(2/3,_f),(1/3,_t)]
--- > p_notate False [(2/5,_f),(1/10,_t)]
--- > p_notate False [(1/4,_t),(1/8,_f),(1/8,_f)]
+-- > p_notate False [(2/3,f),(1/3,t)]
+-- > p_notate False [(2/5,f),(1/10,t)]
+-- > p_notate False [(1/4,t),(1/8,f),(1/8,f)]
 -- > p_notate False (map rq_rqt [1/3,1/6])
 -- > p_notate False (map rq_rqt [2/5,1/10])
 -- > p_notate False (map rq_rqt [1/3,1/6,2/5,1/10]) == Nothing
-p_notate :: Bool -> [RQ_T] -> Either String [Duration_A]
+p_notate :: Bool -> [Rq_Tied] -> Either String [Duration_A]
 p_notate z x =
     let f = p_simplify . rqt_to_duration_a z
         d = case p_tuplet_rqt x of
               Just (t,x') -> da_tuplet t (f x')
               Nothing -> f x
-    in if rq_can_notate (map rqt_rq x)
+    in if rq_can_notate 2 (map rqt_rq x)
        then Right d
        else Left (show ("p_notate",z,x))
 
 -- | Notate measure.
 --
--- > m_notate True [[(2/3,_f),(1/3,_t)],[(1,_t)],[(1,_f)]]
+-- > m_notate True [[(2/3,f),(1/3,t)],[(1,t)],[(1,f)]]
 --
 -- > let f = m_notate False . concat
 --
 -- > fmap f (to_divisions_ts [(4,4)] [3/5,2/5,1/3,1/6,7/10,17/15,1/2,1/6])
 -- > fmap f (to_divisions_ts [(4,4)] [3/5,2/5,1/3,1/6,7/10,29/30,1/2,1/3])
-m_notate :: Bool -> [[RQ_T]] -> Either String [Duration_A]
+m_notate :: Bool -> [[Rq_Tied]] -> Either String [Duration_A]
 m_notate z m =
     let z' = z : map (is_tied_right . last) m
     in fmap concat (all_right (zipWith p_notate z' m))
@@ -533,7 +509,7 @@
 > in fmap mm_notate (to_divisions_rq p d)
 
 -}
-mm_notate :: [[[RQ_T]]] -> Either String [[Duration_A]]
+mm_notate :: [[[Rq_Tied]]] -> Either String [[Duration_A]]
 mm_notate d =
     let z = False : map (is_tied_right . last . last) d
     in all_right (zipWith m_notate z d)
@@ -542,13 +518,13 @@
 
 -- | Structure given to 'Simplify_P' to decide simplification.  The
 -- structure is /(ts,start-rq,(left-rq,right-rq))/.
-type Simplify_T = (Time_Signature,RQ,(RQ,RQ))
+type Simplify_T = (Time_Signature,Rq,(Rq,Rq))
 
 -- | Predicate function at 'Simplify_T'.
 type Simplify_P = Simplify_T -> Bool
 
 -- | Variant of 'Simplify_T' allowing multiple rules.
-type Simplify_M = ([Time_Signature],[RQ],[(RQ,RQ)])
+type Simplify_M = ([Time_Signature],[Rq],[(Rq,Rq)])
 
 -- | Transform 'Simplify_M' to 'Simplify_P'.
 meta_table_p :: Simplify_M -> Simplify_P
@@ -641,7 +617,7 @@
                 g i = if dots i <= n_dots && t && e && m && r
                       then Just (i,a)
                       else Nothing
-            in join (fmap g d)
+            in g =<< d
         z i (j,_) = i + duration_to_rq j
     in coalesce_sum z 0 f
 
@@ -667,13 +643,13 @@
 -- > p_simplify [(e,[Tie_Right]),(s,[Tie_Left]),(e',[])] == [(e',[]),(e',[])]
 --
 -- > let f = rqt_to_duration_a False
--- > in p_simplify (f [(1/8,_t),(1/4,_t),(1/8,_f)]) == f [(1/2,_f)]
+-- > in p_simplify (f [(1/8,t),(1/4,t),(1/8,f)]) == f [(1/2,f)]
 p_simplify :: [Duration_A] -> [Duration_A]
 p_simplify = m_simplify p_simplify_rule undefined
 
 -- * Notate
 
-{-| Notate RQ duration sequence.  Derive pulse divisions from
+{-| Notate Rq duration sequence.  Derive pulse divisions from
 'Time_Signature' if not given directly.  Composition of
 'to_divisions_ts', 'mm_notate' 'm_simplify'.
 
@@ -684,7 +660,7 @@
 >  in T.notate_rqp 4 sr ts (Just ts_p) rq
 
 -}
-notate_rqp :: Int -> Simplify_P -> [Time_Signature] -> Maybe [[RQ]] -> [RQ] ->
+notate_rqp :: Int -> Simplify_P -> [Time_Signature] -> Maybe [[Rq]] -> [Rq] ->
               Either String [[Duration_A]]
 notate_rqp limit r ts ts_p x = do
   let ts_p' = fromMaybe (map ts_divisions ts) ts_p
@@ -695,9 +671,8 @@
 -- | Variant of 'notate_rqp' without pulse divisions (derive).
 --
 -- > notate 4 (default_rule [((3,2),0,(2,2)),((3,2),0,(4,2))]) [(3,2)] [6]
-notate :: Int -> Simplify_P -> [Time_Signature] -> [RQ] ->
-          Either String [[Duration_A]]
-notate limit r ts x = notate_rqp limit r ts Nothing x
+notate :: Int -> Simplify_P -> [Time_Signature] -> [Rq] -> Either String [[Duration_A]]
+notate limit r ts = notate_rqp limit r ts Nothing
 
 -- * Ascribe
 
@@ -779,15 +754,15 @@
                in r : mm_ascribe mm' x'
 
 -- | 'mm_ascribe of 'notate'.
-notate_mm_ascribe :: Show a => Int -> [Simplify_T] -> [Time_Signature] -> Maybe [[RQ]] -> [RQ] -> [a] ->
+notate_mm_ascribe :: Show a => Int -> [Simplify_T] -> [Time_Signature] -> Maybe [[Rq]] -> [Rq] -> [a] ->
                      Either String [[(Duration_A,a)]]
 notate_mm_ascribe limit r ts rqp d p =
     let n = notate_rqp limit (default_rule r) ts rqp d
         f = flip mm_ascribe p
-        err str = show ("notate_ascribe",str,ts,d,p)
+        err str = show ("notate_mm_ascribe",str,ts,d,p)
     in either (Left . err) (Right . f) n
 
-notate_mm_ascribe_err :: Show a => Int -> [Simplify_T] -> [Time_Signature] -> Maybe [[RQ]] -> [RQ] -> [a] ->
+notate_mm_ascribe_err :: Show a => Int -> [Simplify_T] -> [Time_Signature] -> Maybe [[Rq]] -> [Rq] -> [a] ->
                          [[(Duration_A,a)]]
 notate_mm_ascribe_err = either error id .::::: notate_mm_ascribe
 
diff --git a/Music/Theory/Dynamic_Mark.hs b/Music/Theory/Dynamic_Mark.hs
--- a/Music/Theory/Dynamic_Mark.hs
+++ b/Music/Theory/Dynamic_Mark.hs
@@ -9,62 +9,66 @@
 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
+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)
 
--- | Case insensitive reader for 'Dynamic_Mark_T'.
---
--- > map dynamic_mark_t_parse (words "pP p Mp F")
-dynamic_mark_t_parse_ci :: String -> Maybe Dynamic_Mark_T
-dynamic_mark_t_parse_ci s =
-  case map toUpper s of
-    "NIENTE" -> Just Niente
-    uc -> readMaybe uc
+{- | Case insensitive reader for 'Dynamic_Mark'.
 
--- | 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
+> map dynamic_mark_t_parse_ci (words "pP p Mp F")
+-}
+dynamic_mark_t_parse_ci :: String -> Maybe Dynamic_Mark
+dynamic_mark_t_parse_ci =
+  let capitalise x = toUpper (head x) : map toLower (tail x)
+  in readMaybe . capitalise
+
+{- | Lookup Midi velocity for 'Dynamic_Mark'.  The range is linear in @0-127@.
+
+> let r = [0,6,17,28,39,50,61,72,83,94,105,116,127]
+> mapMaybe dynamic_mark_midi [Niente .. Fffff] == r
+
+> mapMaybe dynamic_mark_midi [Pp .. Ff] == [39,50,61,72,83,94]
+
+> map dynamic_mark_midi [Fp,Sf,Sfp,Sfpp,Sfz,Sffz] == replicate 6 Nothing
+-}
+dynamic_mark_midi :: (Num n,Enum n) => Dynamic_Mark -> Maybe n
 dynamic_mark_midi m =
     let r = zip [0..] (0 : reverse [127, 127-11 .. 0])
     in lookup (fromEnum m) r
 
 -- | Error variant.
-dynamic_mark_midi_err :: Integral n => Dynamic_Mark_T -> n
+dynamic_mark_midi_err :: Integral n => Dynamic_Mark -> n
 dynamic_mark_midi_err = fromMaybe (error "dynamic_mark_midi") . dynamic_mark_midi
 
--- | Map midi velocity (0-127) to dynamic mark.
---
--- > histogram (mapMaybe midi_dynamic_mark [0 .. 127])
-midi_dynamic_mark :: (Ord n,Num n,Enum n) => n -> Maybe Dynamic_Mark_T
+{- | Map midi velocity (0-127) to dynamic mark.
+
+> histogram (mapMaybe midi_dynamic_mark [0 .. 127])
+-}
+midi_dynamic_mark :: (Ord n,Num n,Enum n) => n -> Maybe Dynamic_Mark
 midi_dynamic_mark m =
     let r = zip (0 : [12,24 .. 132]) [0..]
     in fmap (toEnum . snd) (find ((>= m) . fst) r)
 
--- | Translate /fixed/ 'Dynamic_Mark_T's to /db/ amplitude over given
--- /range/.
---
--- > mapMaybe (dynamic_mark_db 120) [Niente,P,F,FFFFF] == [-120,-70,-40,0]
--- > mapMaybe (dynamic_mark_db 60) [Niente,P,F,FFFFF] == [-60,-35,-20,0]
-dynamic_mark_db :: Fractional n => n -> Dynamic_Mark_T -> Maybe n
+{- | Translate /fixed/ 'Dynamic_Mark's to /db/ amplitude over given /range/.
+
+> mapMaybe (dynamic_mark_db 120) [Niente,P,F,Fffff] == [-120,-70,-40,0]
+> mapMaybe (dynamic_mark_db 60) [Niente,P,F,Fffff] == [-60,-35,-20,0]
+-}
+dynamic_mark_db :: Fractional n => n -> Dynamic_Mark -> Maybe n
 dynamic_mark_db r m =
-    let u = [Niente .. FFFFF]
+    let u = [Niente .. Fffff]
         n = length u - 1
         k = r / fromIntegral n
         f i = negate r + (fromIntegral i * k)
     in fmap f (elemIndex m u)
 
--- | <http://www.csounds.com/manual/html/ampmidid.html>
---
--- > import Sound.SC3.Plot
--- > plotTable [map (ampmidid 20) [0 .. 127],map (ampmidid 60) [0 .. 127]]
+{- | <http://www.csounds.com/manual/html/ampmidid.html>
+
+> import Sound.Sc3.Plot {- hsc3-plot -}
+> plot_p1_ln [map (ampmidid 20) [0 .. 127],map (ampmidid 60) [0 .. 127]]
+-}
 ampmidid :: Floating a => a -> a -> a
 ampmidid db v =
     let r = 10 ** (db / 20)
@@ -72,26 +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
@@ -99,20 +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
@@ -127,11 +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)
@@ -139,47 +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
@@ -190,9 +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
diff --git a/Music/Theory/Either.hs b/Music/Theory/Either.hs
deleted file mode 100644
--- a/Music/Theory/Either.hs
+++ /dev/null
@@ -1,28 +0,0 @@
--- | Either
-module Music.Theory.Either where
-
-import Data.Maybe {- base -}
-
--- | Maybe 'Left' of 'Either'.
-from_left :: Either a b -> Maybe a
-from_left e =
-    case e of
-      Left x -> Just x
-      _ -> Nothing
-
-from_left_err :: Either t e -> t
-from_left_err = fromMaybe (error "from_left_err") . from_left
-
--- | Maybe 'Right' of 'Either'.
-from_right :: Either x t -> Maybe t
-from_right e =
-    case e of
-      Left _ -> Nothing
-      Right r -> Just r
-
-from_right_err :: Either e t -> t
-from_right_err = fromMaybe (error "from_right_err") . from_right
-
--- | Flip from right to left, ie. 'either' 'Right' 'Left'
-either_swap :: Either a b -> Either b a
-either_swap = either Right Left
diff --git a/Music/Theory/Enum.hs b/Music/Theory/Enum.hs
deleted file mode 100644
--- a/Music/Theory/Enum.hs
+++ /dev/null
@@ -1,38 +0,0 @@
--- | Enumeration functions.
-module Music.Theory.Enum where
-
--- | Generic variant of 'fromEnum' (p.263).
-genericFromEnum :: (Integral i,Enum e) => e -> i
-genericFromEnum = fromIntegral . fromEnum
-
--- | Generic variant of 'toEnum' (p.263).
-genericToEnum :: (Integral i,Enum e) => i -> e
-genericToEnum = toEnum . fromIntegral
-
--- | Variant of 'enumFromTo' that, if /p/ is after /q/, cycles from
--- 'maxBound' to 'minBound'.
---
--- > import Data.Word
--- > enum_from_to_cyclic (254 :: Word8) 1 == [254,255,0,1]
-enum_from_to_cyclic :: (Bounded a, Enum a) => a -> a -> [a]
-enum_from_to_cyclic p q =
-    if fromEnum p > fromEnum q
-    then [p .. maxBound] ++ [minBound .. q]
-    else [p .. q]
-
--- | Variant of 'enumFromTo' that, if /p/ is after /q/, enumerates
--- from /q/ to /p/.
---
--- > enum_from_to_reverse 5 1 == [5,4,3,2,1]
--- > enum_from_to_reverse 1 5 == enumFromTo 1 5
-enum_from_to_reverse :: Enum a => a -> a -> [a]
-enum_from_to_reverse p q =
-    if fromEnum p > fromEnum q
-    then reverse [q .. p]
-    else [p .. q]
-
--- | All elements in sequence.
---
--- > (enum_univ :: [Data.Word.Word8]) == [0 .. 255]
-enum_univ :: (Bounded t,Enum t) => [t]
-enum_univ = [minBound .. maxBound]
diff --git a/Music/Theory/Function.hs b/Music/Theory/Function.hs
deleted file mode 100644
--- a/Music/Theory/Function.hs
+++ /dev/null
@@ -1,84 +0,0 @@
--- | "Data.Function" related functions.
-module Music.Theory.Function where
-
-import Data.Function {- base -}
-
--- | Unary operator.
-type UOp t = t -> t
-
--- | Binary operator.
-type BinOp t = t -> t -> t
-
--- | Iterate the function /f/ /n/ times, the inital value is /x/.
---
--- > recur_n 5 (* 2) 1 == 32
--- > take (5 + 1) (iterate (* 2) 1) == [1,2,4,8,16,32]
-recur_n :: Integral n => n -> (t -> t) -> t -> t
-recur_n n f x = if n < 1 then x else recur_n (n - 1) f (f x)
-
--- | 'const' of 'const'.
---
--- > const2 5 undefined undefined == 5
--- > const (const 5) undefined undefined == 5
-const2 :: a -> b -> c -> a
-const2 x _ _ = x
-
--- * Predicate composition.
-
--- | '&&' of predicates, ie. do predicates /f/ and /g/ both hold at /x/.
-predicate_and :: (t -> Bool) -> (t -> Bool) -> t -> Bool
-predicate_and f g x = f x && g x
-
--- | List variant of 'predicate_and', ie. 'foldr1'
---
--- > let r = [False,False,True,False,True,False]
--- > map (predicate_all [(> 0),(< 5),even]) [0..5] == r
-predicate_all :: [t -> Bool] -> t -> Bool
-predicate_all = foldr1 predicate_and
---predicate_all p x = all id (map ($ x) p)
-
--- | '||' of predicates.
-predicate_or :: (t -> Bool) -> (t -> Bool) -> t -> Bool
-predicate_or f g x = f x || g x
-
--- | 'any' of predicates, ie. logical /or/ of list of predicates.
---
--- > let r = [True,False,True,False,True,True]
--- > map (predicate_any [(== 0),(== 5),even]) [0..5] == r
-predicate_any :: [t -> Bool] -> t -> Bool
-predicate_any p x = any id (map ($ x) p)
-
--- | '==' 'on'.
-eq_on :: Eq t => (u -> t) -> u -> u -> Bool
-eq_on f = (==) `on` f
-
--- * 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 . (.::::)
-
--- * 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)
diff --git a/Music/Theory/Gamelan.hs b/Music/Theory/Gamelan.hs
--- a/Music/Theory/Gamelan.hs
+++ b/Music/Theory/Gamelan.hs
@@ -1,3 +1,4 @@
+-- | Gamelan instruments and pitch structures.
 module Music.Theory.Gamelan where
 
 import Data.Char {- base -}
@@ -7,11 +8,12 @@
 import Data.Ratio {- base -}
 import Text.Printf {- base -}
 
+import qualified Music.Theory.Enum as T {- hmt-base -}
+
 import qualified Music.Theory.Clef as T {- hmt -}
-import qualified Music.Theory.Enum as T {- hmt -}
 import qualified Music.Theory.Pitch as T {- hmt -}
 import qualified Music.Theory.Tuning as T {- hmt -}
-import qualified Music.Theory.Tuning.ET as T {- hmt-diagrams -}
+import qualified Music.Theory.Tuning.Et as T {- hmt-diagrams -}
 
 -- | 'fromJust' with error message.
 fromJust_err :: String -> Maybe a -> a
@@ -196,14 +198,14 @@
 
 tone_24et_pitch :: Tone t -> Maybe T.Pitch
 tone_24et_pitch =
-    let f i = let (_,pt,_,_,_) = T.nearest_24et_tone i in pt
+    let f i = let (_,pt,_,_,_) = T.nearest_24et_tone_k0 (69,440) i in pt
     in fmap f . tone_frequency
 
 tone_24et_pitch' :: Tone t -> 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 . tone_frequency
+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
@@ -217,14 +219,14 @@
 
 tone_12et_pitch :: Tone t -> Maybe T.Pitch
 tone_12et_pitch =
-    let f i = let (_,pt,_,_,_) = T.nearest_12et_tone i in pt
+    let f i = let (_,pt,_,_,_) = T.nearest_12et_tone_k0 (69,440) i in pt
     in fmap f . tone_frequency
 
 tone_12et_pitch' :: Tone t -> 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 . tone_frequency
+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
@@ -305,7 +307,7 @@
 -- | 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` (maybe 0 id . tone_frequency)
+tone_compare_frequency = compare `on` (fromMaybe 0 . tone_frequency)
 
 -- | If all /f/ of /a/ are 'Just' /b/, then 'Just' /[b]/, else
 -- 'Nothing'.
@@ -354,7 +356,7 @@
 -- > degree_index Slendro 4 == Nothing
 -- > degree_index Pelog 4 == Just 3
 degree_index :: Scale -> Degree -> Maybe Int
-degree_index s d = findIndex (== d) (scale_degrees s)
+degree_index s d = elemIndex d (scale_degrees s)
 
 -- * Tone set
 
diff --git a/Music/Theory/Graph/Deacon_1934.hs b/Music/Theory/Graph/Deacon_1934.hs
--- a/Music/Theory/Graph/Deacon_1934.hs
+++ b/Music/Theory/Graph/Deacon_1934.hs
@@ -6,25 +6,27 @@
 -- Ireland, 64:129—175, 1934.
 module Music.Theory.Graph.Deacon_1934 where
 
+import Data.Bifunctor {- base -}
 import Data.List {- base -}
 
-import qualified Music.Theory.Array.Cell_Ref as T {- hmt -}
+import qualified Music.Theory.Array.Cell_Ref as T {- hmt-base -}
+import qualified Music.Theory.List as T {- hmt-base -}
+import qualified Music.Theory.Tuple as T {- hmt-base -}
+
 import qualified Music.Theory.Array.Direction as T {- hmt -}
 import qualified Music.Theory.Graph.Dot as T {- hmt -}
-import qualified Music.Theory.Graph.FGL as T {- hmt -}
-import qualified Music.Theory.List as T {- hmt -}
-import qualified Music.Theory.Tuple as T {- hmt -}
+import qualified Music.Theory.Graph.Fgl as T {- hmt -}
 
-gen_graph :: Ord v => [T.DOT_ATTR] -> T.GR_PP v e -> [T.EDGE_L v e] -> [String]
+gen_graph :: 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 :: Ord v => [T.Dot_Attr] -> (v -> String) -> [T.Edge v] -> [String]
 gen_graph_ul opt pp es = T.fgl_to_udot opt (T.gr_pp_label_v pp) (T.g_from_edges es)
 
-gen_digraph :: Ord v => [T.DOT_ATTR] -> T.GR_PP v e -> [T.EDGE_L v e] -> [String]
-gen_digraph opt pp es = T.fgl_to_dot T.G_DIGRAPH opt pp (T.g_from_edges_l es)
+gen_digraph :: Ord v => [T.Dot_Attr] -> T.Graph_Pp v e -> [T.Edge_Lbl v e] -> [String]
+gen_digraph opt pp es = T.fgl_to_dot T.Graph_Digraph opt pp (T.g_from_edges_l es)
 
-type G = ([T.EDGE String],[T.DOT_ATTR],FilePath)
+type G = ([T.Edge String],[T.Dot_Attr],FilePath)
 
 -- * E
 g1 :: G
@@ -66,7 +68,7 @@
 g9 :: G
 g9 =
     let d9' = ("E6",words "U R D LL (03/D6) U R R U L D D LL (11/C6) U R R U U R D L L D D LL (22/B6) U R R U U R R U L D D L L D D LL (38/A6) U R R U U R R U U R D L L D D L L D D LUU (56/A4) R R U U R R U L D D L L D D L UU (71/A3) R R U U R D L L D D L UU (83/A2) R R U L D D L UU (91/A1) R D L")
-        d9 = (fst d9',filter T.is_direction (snd d9'))
+        d9 = second (filter T.is_direction) d9'
         c9 = T.dir_seq_to_cell_seq d9
         o9 = [("node:shape","circle"),("edge:len","1.5"),("edge:fontsize","7")]
     in (T.adj2 1 c9,o9,"F")
@@ -74,7 +76,7 @@
 g10 :: G
 g10 =
     let d10' = ("B7",words "U R LL (03/A6) R R U L D D LUU (10/A5) R R U L D D L UU (18/A4) R R U L D D L UU (26/A3) R R U L D D L UU (34/A2) R R U L D D L UU (41/A1) R D L")
-        d10 = (fst d10',filter T.is_direction (snd d10'))
+        d10 = second (filter T.is_direction) d10'
         c10 = T.dir_seq_to_cell_seq d10
         e10 = T.adj2 1 c10
         o10 = [("node:shape","circle"),("edge:len","1.5"),("edge:fontsize","7")]
@@ -83,7 +85,7 @@
 g11 :: G
 g11 =
     let d11' = ("C3",words "DR DDL UUR U L (05/C3) DL DDR UUL U R (10/C3) D D U UL UUR DDL (16/B3) DL R U (18/B3) L DR R (21/C4) UR UUL DDR DR L (26/D4) U R DL L U (31/C3) U D (33/C3) R UUR DDDDD UUL L . (40/C4) L DDL UUUUU DDR R (44/C3)")
-        d11 = (fst d11',filter T.is_direction (snd d11'))
+        d11 = second (filter T.is_direction) d11'
         c11 = T.dir_seq_to_cell_seq d11
         e11 = T.adj2 1 c11
         o11 = [("node:shape","circle"),("edge:len","1.5"),("edge:fontsize","7")]
@@ -92,7 +94,7 @@
 g12 :: G
 g12 =
     let d12' = ("C2",words "DR UR (02/E2) L DL UL L (06/A2) DR UR UR DR (10/E2) L UL DL L (14/A2) UR DR (16/C2)")
-        d12 = (fst d12',filter T.is_direction (snd d12'))
+        d12 = second (filter T.is_direction) d12'
         c12 = T.dir_seq_to_cell_seq d12
         e12 = T.adj2 1 c12
         o12 = [("node:shape","circle"),("edge:len","1.5"),("edge:fontsize","7")]
@@ -101,7 +103,7 @@
 g13 :: G
 g13 =
     let d13' = ("B3",words "U D D U R DDL UUL R (07/C3) R UU DDL L UU DDR (11/C3)")
-        d13 = (fst d13',filter T.is_direction (snd d13'))
+        d13 = second (filter T.is_direction) d13'
         c13 = T.dir_seq_to_cell_seq d13
         e13 = T.adj2 1 c13
         o13 = [("node:shape","circle"),("edge:len","1.5"),("edge:fontsize","7")]
diff --git a/Music/Theory/Graph/Dot.hs b/Music/Theory/Graph/Dot.hs
--- a/Music/Theory/Graph/Dot.hs
+++ b/Music/Theory/Graph/Dot.hs
@@ -9,13 +9,14 @@
 
 import qualified Data.Graph.Inductive.Graph as G {- fgl -}
 
-import qualified Music.Theory.Graph.FGL as T {- hmt -}
-import qualified Music.Theory.Graph.Type as T {- hmt -}
-import qualified Music.Theory.List as List {- hmt -}
-import qualified Music.Theory.Show as Show {- hmt -}
+import qualified Music.Theory.Graph.Type as T {- hmt-base -}
+import qualified Music.Theory.List as List {- hmt-base -}
+import qualified Music.Theory.Show as Show {- hmt-base -}
 
--- * UTIL
+import qualified Music.Theory.Graph.Fgl as T {- hmt -}
 
+-- * 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 =
@@ -33,7 +34,7 @@
 --
 -- > 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 ((==) '.'))
+is_number = s_classify isDigit (\c -> isDigit c || c == '.') ((< 2) . length . filter ('.' ==))
 
 -- | Quote /s/ if 'is_symbol' or 'is_number'.
 --
@@ -41,55 +42,55 @@
 maybe_quote :: String -> String
 maybe_quote s = if is_symbol s || is_number s then s else concat ["\"",s,"\""]
 
--- * ATTR/KEY
+-- * Attr/Key
 
-type DOT_KEY = String
-type DOT_VALUE = String
-type DOT_ATTR = (DOT_KEY,DOT_VALUE)
+type Dot_Key = String
+type Dot_Value = String
+type Dot_Attr = (Dot_Key,Dot_Value)
 
--- | Format 'DOT_ATTR'.
-dot_attr_pp :: DOT_ATTR -> String
+-- | Format 'Dot_Attr'.
+dot_attr_pp :: Dot_Attr -> String
 dot_attr_pp (lhs,rhs) = concat [lhs,"=",maybe_quote rhs]
 
--- | Format sequence of DOT_ATTR.
+-- | 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 :: [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 :: [Dot_Attr] -> [Dot_Attr] -> [Dot_Attr]
 dot_attr_ext = List.assoc_merge
 
 -- | graph|node|edge
-type DOT_TYPE = String
+type Dot_Type = String
 
 -- | (type,[attr])
-type DOT_ATTR_SET = (DOT_TYPE,[DOT_ATTR])
+type Dot_Attr_Set = (Dot_Type,[Dot_Attr])
 
--- | Format DOT_ATTR_SET.
+-- | 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 :: 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_Key = String
 
-type DOT_META_ATTR = (DOT_META_KEY,DOT_VALUE)
+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 :: 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]
+-- | 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
@@ -99,19 +100,20 @@
 --
 -- > 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 :: (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
 
 -- | Graph pretty-printer, (v -> [attr],e -> [attr])
-type GR_PP v e = ((Int,v) -> [DOT_ATTR],((Int,Int),e) -> [DOT_ATTR])
+type Graph_Pp v e = ((Int,v) -> [Dot_Attr],((Int,Int),e) -> [Dot_Attr])
 
-gr_pp_label_m :: Maybe (v -> DOT_VALUE) -> Maybe (e -> DOT_VALUE) -> GR_PP v e
+-- | 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 -> []
@@ -119,11 +121,11 @@
   in (lift f_v,lift f_e)
 
 -- | Label V & E.
-gr_pp_label :: (v -> DOT_VALUE) -> (e -> DOT_VALUE) -> GR_PP 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) -> GR_PP v e
+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
@@ -134,43 +136,44 @@
       _ -> List.bracket ('{','}') (intercalate "," (map show l))
 
 -- | Graph type, directed or un-directed.
-data G_TYPE = G_DIGRAPH | G_UGRAPH
+data Graph_Type = Graph_Digraph | Graph_Ugraph
 
-g_type_to_string :: G_TYPE -> String
+g_type_to_string :: Graph_Type -> String
 g_type_to_string ty =
     case ty of
-      G_DIGRAPH -> "digraph"
-      G_UGRAPH -> "graph"
+      Graph_Digraph -> "digraph"
+      Graph_Ugraph -> "graph"
 
-g_type_to_edge_symbol :: G_TYPE -> String
+g_type_to_edge_symbol :: Graph_Type -> String
 g_type_to_edge_symbol ty =
     case ty of
-      G_DIGRAPH -> " -> "
-      G_UGRAPH -> " -- "
+      Graph_Digraph -> " -> "
+      Graph_Ugraph -> " -- "
 
-node_pos_attr :: (Show n, Real n) => (n,n) -> DOT_ATTR
+-- | 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 :: 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 :: 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 :: (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 :: G_TYPE -> [DOT_META_ATTR] -> GR_PP v e -> T.LBL v e -> [String]
+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))),";"]
@@ -182,28 +185,29 @@
               ,map e_f e
               ,["}"]]
 
-lbl_to_udot :: [DOT_META_ATTR] -> GR_PP v e -> T.LBL v e -> [String]
-lbl_to_udot o pp = lbl_to_dot G_UGRAPH o pp
+lbl_to_udot :: [Dot_Meta_Attr] -> Graph_Pp v e -> T.Lbl v e -> [String]
+lbl_to_udot = lbl_to_dot Graph_Ugraph
 
-fgl_to_dot :: G.Graph gr => G_TYPE -> [DOT_META_ATTR] -> GR_PP v e -> gr v e -> [String]
+-- | '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] -> GR_PP v e -> gr v e -> [String]
+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)
+-- * Dot-Process
 
-   /-n/ must be given to not run the layout algorithm and to use position data in the /dot/ file.
+{- | 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)
 
--- | Alias for 'dot_to_ext'
-dot_to_svg :: [String] -> FilePath -> FilePath -> IO ()
-dot_to_svg = dot_to_ext
-
+-- | '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")
diff --git a/Music/Theory/Graph/FGL.hs b/Music/Theory/Graph/FGL.hs
deleted file mode 100644
--- a/Music/Theory/Graph/FGL.hs
+++ /dev/null
@@ -1,139 +0,0 @@
--- | Graph (fgl) functions.
-module Music.Theory.Graph.FGL where
-
-import Data.List {- base -}
-import Data.Maybe {- base -}
-
-import qualified Data.Map as M {- containers -}
-
-import qualified Data.Graph.Inductive.Graph as G {- fgl -}
-import qualified Data.Graph.Inductive.Query as G {- fgl -}
-import qualified Data.Graph.Inductive.PatriciaTree as G {- fgl -}
-
-import qualified Control.Monad.Logic as L {- logict -}
-
-import qualified Music.Theory.Graph.Type as T {- hmt -}
-import qualified Music.Theory.List as T {- hmt -}
-
-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 (\n -> G.subgraph n gr) (G.components gr)
-
--- | Find first 'G.Node' with given label.
-g_node_lookup :: (Eq v,G.Graph gr) => gr v e -> v -> Maybe G.Node
-g_node_lookup gr l = fmap fst (find ((== l) . snd) (G.labNodes gr))
-
--- | Erroring variant.
-g_node_lookup_err :: (Eq v,G.Graph gr) => gr v e -> v -> G.Node
-g_node_lookup_err gr = fromMaybe (error "g_node_lookup") . g_node_lookup gr
-
--- | Set of nodes with given labels, plus all neighbours of these nodes.
--- (impl = implications)
-ug_node_set_impl :: (Eq v,G.DynGraph gr) => gr v e -> [v] -> [G.Node]
-ug_node_set_impl gr nl =
-    let n = map (g_node_lookup_err gr) nl
-    in nub (sort (n ++ concatMap (G.neighbors gr) n))
-
--- * Hamiltonian
-
-type G_NODE_SEL_F v e = G.Gr v e -> G.Node -> [G.Node]
-
--- | 'L.msum' '.' 'map' 'return'.
-ml_from_list :: L.MonadLogic m => [t] -> m t
-ml_from_list = L.msum . map return
-
--- | Use /sel_f/ of 'G.pre' for directed graphs and 'G.neighbors' for undirected.
-g_hamiltonian_path_ml :: L.MonadLogic m => G_NODE_SEL_F v e -> G.Gr v e -> G.Node -> m [G.Node]
-g_hamiltonian_path_ml sel_f gr =
-    let n_deg = g_degree gr
-        recur r c =
-            if length r == n_deg - 1
-            then return (c:r)
-            else do i <- ml_from_list (sel_f gr c)
-                    L.guard (i `notElem` r)
-                    recur (c:r) i
-    in recur []
-
--- > map (L.observeAll . ug_hamiltonian_path_ml_0) (g_partition gr)
-ug_hamiltonian_path_ml_0 :: L.MonadLogic m => G.Gr v e -> m [G.Node]
-ug_hamiltonian_path_ml_0 gr = g_hamiltonian_path_ml G.neighbors gr (G.nodes gr !! 0)
-
--- * G (from edges)
-
--- | Edge, no label.
-type EDGE v = (v,v)
-
--- | Edge, with label.
-type EDGE_L v l = (EDGE v,l)
-
--- | Generate a graph given a set of labelled edges.
-g_from_edges_l :: (Eq v,Ord v) => [EDGE_L v e] -> G.Gr v e
-g_from_edges_l e =
-    let n = nub (concatMap (\((lhs,rhs),_) -> [lhs,rhs]) e)
-        n_deg = length n
-        n_id = [0 .. n_deg - 1]
-        m = M.fromList (zip n n_id)
-        m_get k = M.findWithDefault (error "g_from_edges: m_get") k m
-        e' = map (\((lhs,rhs),label) -> (m_get lhs,m_get rhs,label)) e
-    in G.mkGraph (zip n_id n) e'
-
--- | Variant that supplies '()' as the (constant) edge label.
---
--- > let g = G.mkGraph [(0,'a'),(1,'b'),(2,'c')] [(0,1,()),(1,2,())]
--- > in g_from_edges_ul [('a','b'),('b','c')] == g
-g_from_edges :: Ord v => [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_L v Int]
-e_label_seq = map (\(k,e) -> (e,k)) . zip [1..]
-
--- | Normalised undirected labeled edge (ie. order nodes).
-e_normalise_l :: Ord v => EDGE_L v l -> EDGE_L v l
-e_normalise_l ((p,q),r) = ((min p q,max p q),r)
-
--- | Collate labels for edges that are otherwise equal.
-e_collate_l :: Ord v => [EDGE_L v l] -> [EDGE_L v [l]]
-e_collate_l = T.collate
-
--- | 'e_collate_l' of 'e_normalise_l'.
-e_collate_normalised_l :: Ord v => [EDGE_L v l] -> [EDGE_L v [l]]
-e_collate_normalised_l = e_collate_l . map e_normalise_l
-
--- | Apply predicate to universe of possible edges.
-e_univ_select_edges :: (t -> t -> Bool) -> [t] -> [EDGE t]
-e_univ_select_edges f l = [(p,q) | p <- l, q <- l, f p q]
-
--- | Consider only edges (p,q) where p < q.
-e_univ_select_u_edges :: Ord t => (t -> t -> Bool) -> [t] -> [EDGE t]
-e_univ_select_u_edges f = let g p q = p < q && f p q in e_univ_select_edges g
-
--- | Sequence of connected vertices to edges.
---
--- > e_path_to_edges "abcd" == [('a','b'),('b','c'),('c','d')]
-e_path_to_edges :: [t] -> [EDGE t]
-e_path_to_edges = T.adj2 1
-
--- | Undirected edge equality.
-e_undirected_eq :: Eq t => EDGE t -> EDGE t -> Bool
-e_undirected_eq (a,b) (c,d) = (a == c && b == d) || (a == d && b == c)
-
-elem_by :: (p -> q -> Bool) -> p -> [q] -> Bool
-elem_by f = any . f
-
--- | Is the sequence of vertices a path at the graph, ie. are all
--- adjacencies in the sequence edges.
-e_is_path :: Eq t => [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
diff --git a/Music/Theory/Graph/Fgl.hs b/Music/Theory/Graph/Fgl.hs
new file mode 100644
--- /dev/null
+++ b/Music/Theory/Graph/Fgl.hs
@@ -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
diff --git a/Music/Theory/Graph/IO.hs b/Music/Theory/Graph/IO.hs
deleted file mode 100644
--- a/Music/Theory/Graph/IO.hs
+++ /dev/null
@@ -1,72 +0,0 @@
-{- | IO for graph files, graph6, sparse6 and digraph6 encodings.
-
-<http://users.cecs.anu.edu.au/~bdm/nauty/>
-<https://users.cecs.anu.edu.au/~bdm/data/formats.html>
--}
-module Music.Theory.Graph.IO where
-
-import Data.List.Split {- split -}
-import System.Process {- process -}
-
-import qualified Music.Theory.Graph.Type as T {- hmt -}
-import qualified Music.Theory.List as T {- hmt -}
-
--- * G6 (graph6)
-
--- | Load Graph6 file, discard optional header if present.
-g6_load :: FilePath -> IO [String]
-g6_load fn = do
-  s <- readFile fn
-  let s' = if take 6 s == ">>graph6<<" then drop 6 s else s
-  return (lines s')
-
--- | Load G6 file variant where each line is "Description\tG6"
-g6_dsc_load :: FilePath -> IO [(String,String)]
-g6_dsc_load fn = do
-  s <- readFile fn
-  let r = map (T.split_on_1_err "\t") (lines s)
-  return r
-
--- | Call nauty-listg to transform a sequence of G6.
---   debian = nauty
-g6_to_edg :: [String] -> IO [T.EDG]
-g6_to_edg g6 = do
-  r <- readProcess "nauty-listg" ["-q","-l0","-e"] (unlines g6)
-  return (map T.edg_parse (chunksOf 2 (lines r)))
-
--- | 'T.edg_to_g' of 'g6_to_edg'
-g6_to_gr :: [String] -> IO [T.G]
-g6_to_gr = fmap (map T.edg_to_g) . g6_to_edg
-
--- | 'g6_to_edg' of 'g6_dsc_load'.
-g6_dsc_load_edg :: FilePath -> IO [(String,T.EDG)]
-g6_dsc_load_edg fn = do
-  dat <- g6_dsc_load fn
-  let (dsc,g6) = unzip dat
-  gr <- g6_to_edg g6
-  return (zip dsc gr)
-
--- | 'T.edg_to_g' of 'g6_dsc_load_edg'
-g6_dsc_load_gr :: FilePath -> IO [(String,T.G)]
-g6_dsc_load_gr = fmap (map (\(dsc,e) -> (dsc,T.edg_to_g e))) . g6_dsc_load_edg
-
-{- | Generate the text format read by nauty-amtog.
-
-> e = ((4,3),[(0,3),(1,3),(2,3)])
-> m = T.edg_to_adj_mtx_undir e
-> putStrLn (adj_mtx_to_am m)
-
--}
-adj_mtx_to_am :: T.ADJ_MTX -> String
-adj_mtx_to_am (nv,mtx) =
-  unlines ["n=" ++ show nv
-          ,"m"
-          ,unlines (map (unwords . map show) mtx)]
-
--- | Call nauty-amtog to transform a sequence of ADJ_MTX to G6.
---
--- > adj_mtx_to_g6 [m,m]
-adj_mtx_to_g6 :: [T.ADJ_MTX] -> IO [String]
-adj_mtx_to_g6 adj = do
-  r <- readProcess "nauty-amtog" ["-q"] (unlines (map adj_mtx_to_am adj))
-  return (lines r)
diff --git a/Music/Theory/Graph/Johnson_2014.hs b/Music/Theory/Graph/Johnson_2014.hs
--- a/Music/Theory/Graph/Johnson_2014.hs
+++ b/Music/Theory/Graph/Johnson_2014.hs
@@ -11,20 +11,21 @@
 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 -}
+import qualified Music.Theory.Combinations as T {- hmt-base -}
+import qualified Music.Theory.List as T {- hmt-base -}
+import qualified Music.Theory.Tuple as T {- hmt-base -}
+
 import qualified Music.Theory.Graph.Dot as T {- hmt -}
-import qualified Music.Theory.Graph.FGL as T {- hmt -}
+import qualified Music.Theory.Graph.Fgl as T {- hmt -}
 import qualified Music.Theory.Key as T {- hmt -}
-import qualified Music.Theory.List as T {- hmt -}
 import qualified Music.Theory.Pitch.Note as T {- hmt -}
 import qualified Music.Theory.Set.List as T {- hmt -}
 import qualified Music.Theory.Tuning as T {- hmt -}
 import qualified Music.Theory.Tuning.Graph.Euler as T {- hmt -}
-import qualified Music.Theory.Tuple 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 -}
+import qualified Music.Theory.Z.Tto as T {- hmt -}
+import qualified Music.Theory.Z.Sro as T {- hmt -}
 
 -- * Common
 
@@ -74,7 +75,7 @@
 -- > min_vl [6,11,13] [6,10,14] == 2
 min_vl :: (Num a,Ord a) => [a] -> [a] -> a
 min_vl p q =
-    let f x = sum (map absdif (zip p x))
+    let f x = sum (zipWith (curry absdif) p x)
     in minimum (map f (permutations q))
 
 min_vl_of :: (Num a, Ord a) => a -> [a] -> [a] -> Bool
@@ -89,7 +90,7 @@
 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 :: 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
@@ -118,7 +119,7 @@
 
 -- * Graph
 
-oh_def_opt :: [T.DOT_META_ATTR]
+oh_def_opt :: [T.Dot_Meta_Attr]
 oh_def_opt =
   [("graph:layout","neato")
   ,("graph:epsilon","0.000001")
@@ -126,19 +127,19 @@
   ,("node:fontsize","10")
   ,("node:fontname","century schoolbook")]
 
-gen_graph :: Ord v => [T.DOT_META_ATTR] -> T.GR_PP v e -> [T.EDGE_L v e] -> [String]
+gen_graph :: Ord v => [T.Dot_Meta_Attr] -> T.Graph_Pp v e -> [T.Edge_Lbl v e] -> [String]
 gen_graph opt pp es = T.fgl_to_udot (oh_def_opt ++ opt) pp (T.g_from_edges_l es)
 
-gen_graph_ul :: Ord v => [T.DOT_META_ATTR] -> (v -> String) -> [T.EDGE v] -> [String]
+gen_graph_ul :: 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 :: 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 :: 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 :: (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
@@ -164,7 +165,7 @@
         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_L v l]
+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]
@@ -201,7 +202,7 @@
 
 p14_mk_e :: [(Int, Int)] -> [(T.Key,T.Key)]
 p14_mk_e =
-  let pc_to_key m pc = let Just (n,a) = T.pc_to_note_alteration_ks pc in (n,a,m)
+  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
 
@@ -220,7 +221,7 @@
       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 :: [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
@@ -256,7 +257,7 @@
         f _ = error "p14_gen_tonnetz_e"
     in mapMaybe f . T.combinations 2 . p14_gen_tonnetz_n n k
 
--- NEO-RIEMANNIAN TONNETTZ
+-- Neo-Riemannian Tonnettz
 p14_nrt_gr :: [String]
 p14_nrt_gr =
   let e = p14_gen_tonnetz_e 3 [7,9,16] [48]
@@ -264,7 +265,7 @@
           ,("node:fontsize","10")
           ,("node:fontname","century schoolbook")
           ,("edge:len","1")]
-      pp = (\(_,v) -> [("label",T.pc_pp (T.z_mod T.z12 v))],\_ -> [])
+      pp = (\(_,v) -> [("label",T.pc_pp (T.z_mod T.z12 v))],const [])
   in gen_graph o pp e
 
 -- * P.31
@@ -283,7 +284,7 @@
 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 :: Show t => t -> [T.Dot_Meta_Attr]
 p114_mk_o el =
   [("node:shape","box")
   ,("edge:len",show el)
@@ -291,7 +292,7 @@
 
 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))
+  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
@@ -326,7 +327,7 @@
 p125_gr :: [String]
 p125_gr =
     let t :: [[Int]]
-        t = [[p,q,r] | p <- [0 .. 11], q <- [0 .. 11], r <- [0 ..11], q > p, r > q]
+        t = [[p,q,r] | p <- [0 .. 11], q <- [0 .. 11], q > p, r <- [0 ..11], r > q]
         c = T.collate (zip (map sum t) t)
         with_h n = lookup n c
         ch = fromJust (liftM2 (++) (with_h 15) (with_h 16))
@@ -337,7 +338,7 @@
 p131_gr :: [String]
 p131_gr =
     let c = let u = [6::Int .. 14]
-            in [[p,q,r] | p <- u, q <- u, r <- u, q > p, r > q, p + q + r == 30]
+            in [[p,q,r] | p <- u, q <- u, q > p, r <- u, r > q, p + q + r == 30]
     in gen_graph_ul [] set_pp (T.e_univ_select_u_edges (min_vl_of 2) c)
 
 -- * P.148
@@ -373,7 +374,7 @@
   in filter ((== 1) . (`mod` 4) . sum) c
 
 -- > length p162_e == 47
-p162_e :: [T.EDGE [Int]]
+p162_e :: [T.Edge [Int]]
 p162_e = T.e_univ_select_u_edges (doi_of 3) p162_ch
 
 p162_gr :: [String]
@@ -393,7 +394,7 @@
 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 :: [T.Edge Int]
 p172_nd_e_set_alt = concatMap (T.e_path_to_edges . T.close 1) p172_cyc0
 
 p172_gr :: G.Gr () ()
@@ -406,7 +407,7 @@
 -- > (length c0,length c1) == (48,48)
 p172_all_cyc :: ([[Int]], [[Int]])
 p172_all_cyc =
-    let [a,b] = T.g_partition p172_gr
+    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))
 
@@ -424,15 +425,15 @@
   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
+-- | '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
+-- | '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 :: 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 ..])
@@ -443,14 +444,14 @@
 --
 -- > 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 :: 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 :: [[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 :: (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]
@@ -570,7 +571,7 @@
 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 :: [T.Dot_Meta_Attr]
 p201_o =
   [("graph:splines","false")
   ,("node:shape","box")
diff --git a/Music/Theory/Graph/LCF.hs b/Music/Theory/Graph/LCF.hs
deleted file mode 100644
--- a/Music/Theory/Graph/LCF.hs
+++ /dev/null
@@ -1,109 +0,0 @@
-{- | LCF (Lederberg/Coxeter/Frucht) notation
-
-The notation only applies to Hamiltonian graphs, since it achieves its
-symmetry and conciseness by placing a Hamiltonian cycle in a circular
-embedding and then connecting specified pairs of nodes with edges. (EW)
-
--}
-module Music.Theory.Graph.LCF where
-
-import Data.Complex {- base -}
-import Data.List {- base -}
-
-import qualified Music.Theory.Graph.Type as T {- hmt -}
-
-type LCF = ([Int],Int)
-type R = Double
-
-lcf_seq :: LCF -> [Int]
-lcf_seq (l,k) = concat (replicate k l)
-
-lcf_degree :: LCF -> Int
-lcf_degree (l,k) = length l * k
-
--- | LCF to edge list.
-lcf_to_edg :: LCF -> T.EDG
-lcf_to_edg (l,k) =
-  let v_n = length l * k
-      add i j = (i + j) `mod` v_n
-      v = [0 .. v_n - 1]
-  in ((v_n,v_n + (v_n `div` 2))
-     ,concat [[(i,i `add` 1) | i <- v]
-             ,nub (sort (map T.e_sort (zip v (zipWith add v (lcf_seq (l,k))))))])
-
--- | LCF edge-list to graph labeled with circular co-ordinates.
-edg_circ_gr :: R -> T.EDG -> T.LBL (R,R) ()
-edg_circ_gr rad ((n,_),e) =
-  let polar_to_rectangular (mg,ph) = let c = mkPolar mg ph in (realPart c,imagPart c)
-      ph_incr = (2 * pi) / fromIntegral n
-      v = zip [0 .. n - 1] (map polar_to_rectangular (zip (repeat rad) [0, ph_incr ..]))
-  in (v,zip e (repeat ()))
-
-{- | LCF graph set given at <http://mathworld.wolfram.com/LCFNotation.html>
-
-> length lcf_mw_set == 57
-> length (nub (map snd lcf_mw_set)) == 57 -- IE. UNIQ
--}
-lcf_mw_set :: [(String, LCF)]
-lcf_mw_set =
-  [("Tetrahedral graph",([2,-2],2)) -- ([2],4)
-  ,("Utility graph",([3],6)) -- ([3,-3],3)
-  ,("3-prism graph",([-3,-2,2],2))
-  ,("Cubical graph",([3,-3],4))
-  ,("Wagner graph",([4],8))
-  ,("3-matchstick graph",([-2,-2,2,2],2))
-  ,("4-Möbius ladder",([-4],8))
-  ,("5-Möbius ladder",([-5],10))
-  ,("5-prism graph",([-5,3,-4,4,-3],2))
-  ,("Bidiakis cube",([6,4,-4],4))
-  ,("Franklin graph",([5,-5],6))
-  ,("Frucht graph",([-5,-2,-4,2,5,-2,2,5,-2,-5,4,2],1))
-  ,("Truncated tetrahedral graph",([2,6,-2],4))
-  ,("Generalized Petersen graph (6,2)",([-5,2,4,-2,-5,4,-4,5,2,-4,-2,5],1))
-  ,("6-Möbius ladder",([-6],12))
-  ,("6-prism graph",([-3,3],6))
-  ,("Heawood graph",([5,-5],7))
-  ,("Generalized Petersen graph (7,2)",([-7,-5,4,-6,-5,4,-4,-7,4,-4,5,6,-4,5],1))
-  ,("7-Möbius ladder",([-7],14))
-  ,("7-prism graph",([-7,5,3,-6,6,-3,-5],2))
-  ,("Cubic vertex-transitive graph Ct19",([-7,7],8))
-  ,("Möbius-Kantor graph",([5,-5],8))
-  ,("8-Möbius ladder",([-8],16))
-  ,("8-prism graph",([-3,3],8))
-  ,("Pappus graph",([5,7,-7,7,-7,-5],3))
-  ,("Cubic vertex-transitive graph Ct20",([-7,7],9)) -- ([5,-5],9)
-  ,("Cubic vertex-transitive graph Ct23",([-9,-2,2],6))
-  ,("Generalized Petersen graph (9,2)",([-9,-8,-4,-9,4,8],3))
-  ,("Generalized Petersen graph (9,3)",([-9,-6,2,5,-2,-9,5,-9,-5,-9,2,-5,-2,6,-9,2,-9,-2],1))
-  ,("9-Möbius ladder",([-9],18))
-  ,("9-prism graph",([-9,7,5,3,-8,8,-3,-5,-7],2))
-  ,("Desargues graph",([5,-5,9,-9],5))
-  ,("Dodecahedral graph",([10,7,4,-4,-7,10,-4,7,-7,4],2))
-  ,("Cubic vertex-transitive graph Ct25",([-7,7],10))
-  ,("Cubic vertex-transitive graph Ct28",([-6,-6,6,6],5))
-  ,("Cubic vertex-transitive graph Ct29",([-9,9],10))
-  ,("Generalized Petersen graph (10,4)",([-10,-7,5,-5,7,-6,-10,-5,5,6],2))
-  ,("Largest cubic nonplanar graph with diameter 3",([-10,-7,-5,4,7,-10,-7,-4,5,7,-10,-7,6,-5,7,-10,-7,5,-6,7],1))
-  ,("10-Möbius ladder",([-10],20))
-  ,("10-prism graph",([-3,3],10))
-  ,("McGee graph",([12,7,-7],8))
-  ,("Truncated cubical graph",([2,9,-2,2,-9,-2],4))
-  ,("Truncated octahedral graph",([3,-7,7,-3],6))
-  ,("Nauru graph",([5,-9,7,-7,9,-5],4))
-  ,("F26A graph",([-7,7],13))
-  ,("Tutte-Coxeter graph",([-13,-9,7,-7,9,13],5))
-  ,("Dyck graph",([5,-5,13,-13],8))
-  ,("Gray graph",([-25,7,-7,13,-13,25],9))
-  ,("Truncated dodecahedral graph",([30,-2,2,21,-2,2,12,-2,2,-12,-2,2,-21,-2,2,30,-2,2,-12,-2,2,21,-2,2,-21,-2,2,12,-2,2],2))
-  ,("Harries graph",([-29,-19,-13,13,21,-27,27,33,-13,13,19,-21,-33,29],5))
-  ,("Harries-Wong graph",([9,25,31,-17,17,33,9,-29,-15,-9,9,25,-25,29,17,-9,9,-27,35,-9,9,-17,21,27,-29,-9,-25,13,19,-9,-33,-17,19,-31,27,11,-25,29,-33,13,-13,21,-29,-21,25,9,-11,-19,29,9,-27,-19,-13,-35,-9,9,17,25,-9,9,27,-27,-21,15,-9,29,-29,33,-9,-25],1))
-  ,("Balaban 10-cage",([-9,-25,-19,29,13,35,-13,-29,19,25,9,-29,29,17,33,21,9,-13,-31,-9,25,17,9,-31,27,-9,17,-19,-29,27,-17,-9,-29,33,-25,25,-21,17,-17,29,35,-29,17,-17,21,-25,25,-33,29,9,17,-27,29,19,-17,9,-27,31,-9,-17,-25,9,31,13,-9,-21,-33,-17,-29,29],1))
-  ,("Foster graph",([17,-9,37,-37,9,-17],15))
-  ,("Biggs-Smith graph",([16,24,-38,17,34,48,-19,41,-35,47,-20,34,-36,21,14,48,-16,-36,-43,28,-17,21,29,-43,46,-24,28,-38,-14,-50,-45,21,8,27,-21,20,-37,39,-34,-44,-8,38,-21,25,15,-34,18,-28,-41,36,8,-29,-21,-48,-28,-20,-47,14,-8,-15,-27,38,24,-48,-18,25,38,31,-25,24,-46,-14,28,11,21,35,-39,43,36,-38,14,50,43,36,-11,-36,-24,45,8,19,-25,38,20,-24,-14,-21,-8,44,-31,-38,-28,37],1))
-  ,("Balaban 11-cage",([44,26,-47,-15,35,-39,11,-27,38,-37,43,14,28,51,-29,-16,41,-11,-26,15,22,-51,-35,36,52,-14,-33,-26,-46,52,26,16,43,33,-15,17,-53,23,-42,-35,-28,30,-22,45,-44,16,-38,-16,50,-55,20,28,-17,-43,47,34,-26,-41,11,-36,-23,-16,41,17,-51,26,-33,47,17,-11,-20,-30,21,29,36,-43,-52,10,39,-28,-17,-52,51,26,37,-17,10,-10,-45,-34,17,-26,27,-21,46,53,-10,29,-50,35,15,-47,-29,-41,26,33,55,-17,42,-26,-36,16],1))
-  ,("Ljubljana graph",([47,-23,-31,39,25,-21,-31,-41,25,15,29,-41,-19,15,-49,33,39,-35,-21,17,-33,49,41,31,-15,-29,41,31,-15,-25,21,31,-51,-25,23,9,-17,51,35,-29,21,-51,-39,33,-9,-51,51,-47,-33,19,51,-21,29,21,-31,-39],2))
-  ,("Tutte 12-cage",([17,27,-13,-59,-35,35,-11,13,-53,53,-27,21,57,11,-21,-57,59,-17],7))]
-
--- Local Variables:
--- truncate-lines:t
--- End:
diff --git a/Music/Theory/Graph/OBJ.hs b/Music/Theory/Graph/OBJ.hs
deleted file mode 100644
--- a/Music/Theory/Graph/OBJ.hs
+++ /dev/null
@@ -1,100 +0,0 @@
-{- | Graph/OBJ functions
-
-This module is primarily for reading & writing graphs where vertices are labeled (x,y,z) to OBJ files.
-
-PDF=<http://www.cs.utah.edu/~boulos/cs3505/obj_spec.pdf>
-TXT=<http://www.martinreddy.net/gfx/3d/OBJ.spec>
--}
-module Music.Theory.Graph.OBJ where
-
-import Data.Either {- base -}
-import Data.List {- base -}
-import Data.Maybe {- base -}
-
-import qualified Music.Theory.Graph.Type as T {- hmt -}
-import qualified Music.Theory.List as T {- hmt -}
-import qualified Music.Theory.Show as T {- hmt -}
-
-{- | Requires (but does not check) that graph vertices be indexed [0 .. #v - 1]
-OBJ file vertices are one-indexed.
-If /wr_p/ is True point (p) entries are written.
--}
-v3_graph_to_obj_opt :: RealFloat n => Bool -> Int -> T.LBL (n,n,n) () -> [String]
-v3_graph_to_obj_opt wr_p k (v,e) =
-  let v_pp (_,(x,y,z)) = unwords ("v" : map (T.realfloat_pp k) [x,y,z])
-      e_pp ((i,j),()) = unwords ("l" : map show [i + 1,j + 1])
-  in concat [map v_pp v
-            ,if wr_p then map (\i -> "p " ++ show i) [1 .. length v] else []
-            ,map e_pp e]
-
--- | 'v3_graph_to_obj_opt' 'False'.
-v3_graph_to_obj :: RealFloat n => Int -> T.LBL (n,n,n) () -> [String]
-v3_graph_to_obj = v3_graph_to_obj_opt False
-
--- | 'writeFile' of 'v3_graph_to_obj'.
-obj_store_v3_graph :: RealFloat n => Int -> FilePath -> (T.LBL (n,n,n) ()) -> IO ()
-obj_store_v3_graph k fn = writeFile fn . unlines . v3_graph_to_obj k
-
--- | Read OBJ file consisting only of /v/, /l/ and /f/ (and optionally /p/, which are ignored) entries.
-obj_to_v3_graph :: Read n => [String] -> T.LBL (n,n,n) ()
-obj_to_v3_graph txt =
-  let l_verify (i,j) = if i < 0 || j < 0 then error "obj_to_v3_graph?" else (i,j)
-      e_read (i,j) = l_verify (read i - 1,read j - 1)
-      f s = case words s of
-              ["v",x,y,z] -> Just (Left (read x,read y,read z))
-              "l":ix -> Just (Right (map e_read (T.adj2 1 ix)))
-              "f":ix -> Just (Right (map e_read (T.adj2_cyclic 1 ix)))
-              ["p",_] -> Nothing
-              _ -> error "obj_to_v3_graph?"
-      (v,l) = partitionEithers (mapMaybe f txt)
-  in (zip [0..] v,zip (concat l) (repeat ()))
-
--- | 'obj_to_v3_graph' of 'readFile'.
-obj_load_v3_graph :: Read n => FilePath -> IO (T.LBL (n,n,n) ())
-obj_load_v3_graph = fmap (obj_to_v3_graph . lines) . readFile
-
--- * F64
-
--- | Type-specialised.
-v3_graph_to_obj_f64 :: Int -> T.LBL (Double,Double,Double) () -> [String]
-v3_graph_to_obj_f64 = v3_graph_to_obj
-
--- | Type-specialised.
-obj_store_v3_graph_f64 :: Int -> FilePath -> (T.LBL (Double,Double,Double) ()) -> IO ()
-obj_store_v3_graph_f64 = obj_store_v3_graph
-
--- | Type-specialised.
-obj_load_v3_graph_f64 :: FilePath -> IO (T.LBL (Double,Double,Double) ())
-obj_load_v3_graph_f64 = obj_load_v3_graph
-
--- * FACES
-
--- | Rewrite a set of faces (CCW triples of (x,y,z) coordinates) as (vertices,[[v-indices]]).
---   Vertices are zero-indexed.
-obj_face_set_dat :: Ord n => [[(n,n,n)]] -> ([(n,n,n)],[[Int]])
-obj_face_set_dat t =
-  let v = nub (sort (concat t))
-      v_ix = zip [0..] v
-      f = map (map (flip T.reverse_lookup_err v_ix)) t
-  in (v,f)
-
--- | Inverse of 'obj_face_set_dat'.
-obj_face_dat_set :: ([(n,n,n)],[[Int]]) -> [[(n,n,n)]]
-obj_face_dat_set (v,f) = map (map (flip T.lookup_err (zip [0..] v))) f
-
-obj_face_dat_fmt :: (Show n, Ord n) => ([(n,n,n)],[[Int]]) -> [String]
-obj_face_dat_fmt (v,f) =
-  let v_f (x,y,z) = unwords ["v",show x,show y,show z]
-      f_f = unwords . ("f" :) . map show . map (+ 1)
-  in map v_f v ++ map f_f f
-
-obj_face_dat_store :: (Show n, Ord n) => FilePath -> ([(n,n,n)],[[Int]]) -> IO ()
-obj_face_dat_store fn = writeFile fn . unlines . obj_face_dat_fmt
-
--- | Format 'obj_face_set_dat' as an OBJ file. OBJ files are one-indexed.
-obj_face_set_fmt :: (Show n, Ord n) => [[(n,n,n)]] -> [String]
-obj_face_set_fmt = obj_face_dat_fmt . obj_face_set_dat
-
--- | 'writeFile' of 'obj_face_set_fmt'
-obj_face_set_store :: (Show n, Ord n) => FilePath -> [[(n,n,n)]] -> IO ()
-obj_face_set_store fn = writeFile fn . unlines . obj_face_set_fmt
diff --git a/Music/Theory/Graph/PLY.hs b/Music/Theory/Graph/PLY.hs
deleted file mode 100644
--- a/Music/Theory/Graph/PLY.hs
+++ /dev/null
@@ -1,87 +0,0 @@
-{- | Graph/PLY functions.
-
-This module is used instead of 'Music.Theory.Graph.OBJ' when edges are coloured.
-
-There is no reader.
-
-Greg Turk "The PLY Polygon File Format" (1994)
-
-SEE "PLY_FILES.txt" in <https://www.cc.gatech.edu/projects/large_models/files/ply.tar.gz>
-
--}
-module Music.Theory.Graph.PLY where
-
-import Data.List {- base -}
-
-import qualified Music.Theory.Graph.Type as T {- hmt -}
-import qualified Music.Theory.List as T {- hmt -}
-import qualified Music.Theory.Show as T {- hmt -}
-
--- | ASCII PLY-1.0 header for V3 graph of (#v,#e).
---   Edges and faces are (r,g,b) coloured.
---
--- > putStrLn $ unlines $ ply_header (8,6,0)
-ply_header :: (Int,Int,Int) -> [String]
-ply_header (n_v,n_f,n_e) =
-  concat
-  [["ply"
-   ,"format ascii 1.0"
-   ,"element vertex " ++ show n_v
-   ,"property float x"
-   ,"property float y"
-   ,"property float z"]
-  ,if n_f > 0
-   then ["element face " ++ show n_f
-        ,"property list uchar int vertex_index"
-        ,"property uchar red"
-        ,"property uchar green"
-        ,"property uchar blue"]
-   else []
-  ,if n_e > 0
-   then ["element edge " ++ show n_e
-        ,"property int vertex1"
-        ,"property int vertex2"
-        ,"property uchar red"
-        ,"property uchar green"
-        ,"property uchar blue"]
-   else []
-  ,["end_header"]]
-
-{- | Requires (but does not check) that graph vertices be indexed [0 .. #v - 1]
-     Edges are coloured as U8 (red,green,blue) triples.
-     It is an error (not checked) for there to be no edges.
-     PLY files are zero-indexed.
--}
-v3_graph_to_ply_clr :: Int -> T.LBL (Double,Double,Double) (Int,Int,Int) -> [String]
-v3_graph_to_ply_clr k (v,e) =
-  let v_pp (_,(x,y,z)) = unwords (map (T.double_pp k) [x,y,z])
-      e_pp ((i,j),(r,g,b)) = unwords (map show [i,j,r,g,b])
-  in concat [ply_header (length v,0,length e)
-            ,map v_pp v
-            ,map e_pp e]
-
--- * FACES
-
--- | Rewrite a set of faces as (vertices,[[v-indices]]).
---   Indices are zero-indexed.
-ply_face_set_dat :: Ord n => [([(n,n,n)],(i,i,i))] -> ([(Int,(n,n,n))],[([Int],(i,i,i))])
-ply_face_set_dat t =
-  let p = nub (sort (concat (map fst t)))
-      c = map snd t
-      v = zip [0..] p
-      f = map (map (flip T.reverse_lookup_err v)) (map fst t)
-  in (v,zip f c)
-
--- | Format a set of coloured faces as an PLY file.
---    (CCW triples of (x,y,z) coordinates, (r,g,b) colour)
---   PLY files are one-indexed.
-ply_face_set_fmt :: (Show n, Ord n,Show i) => [([(n,n,n)],(i,i,i))] -> [String]
-ply_face_set_fmt t =
-  let v_f (_,(x,y,z)) = unwords [show x,show y,show z]
-      f_f (ix,(r,g,b)) = unwords (map show (length ix : ix) ++ map show [r,g,b])
-      (v,f) = ply_face_set_dat t
-  in concat [ply_header (length v,length f,0), map v_f v, map f_f f]
-
--- | 'writeFile' of 'ply_face_set_fmt'
-ply_face_set_store :: (Show n, Ord n,Show i) => FilePath -> [([(n,n,n)],(i,i,i))] -> IO ()
-ply_face_set_store fn = writeFile fn . unlines . ply_face_set_fmt
diff --git a/Music/Theory/Graph/Type.hs b/Music/Theory/Graph/Type.hs
deleted file mode 100644
--- a/Music/Theory/Graph/Type.hs
+++ /dev/null
@@ -1,235 +0,0 @@
--- | Graph types.
-module Music.Theory.Graph.Type where
-
-import Data.Bifunctor {- base -}
-import Data.List {- base -}
-import Data.Maybe {- base -}
-
-import qualified Data.Graph as G {- containers -}
-
-import qualified Music.Theory.List as T {- hmt -}
-
--- * Type parameterised graph
-
--- | (vertices,edges)
-type GR t = ([t],[(t,t)])
-
--- | 'GR' is a functor.
-gr_map :: (t -> u) -> GR t -> GR u
-gr_map f (v,e) = (map f v,map (bimap f f) e)
-
--- | (|V|,|E|)
-gr_degree :: GR t -> (Int,Int)
-gr_degree (v,e) = (length v,length e)
-
--- | Re-label graph given table.
-gr_relabel :: Eq t => [(t,u)] -> GR t -> GR u
-gr_relabel tbl (v,e) =
-  let get z = T.lookup_err z tbl
-  in (map get v,map (\(p,q) -> (get p,get q)) e)
-
--- | Un-directed edge equality.
---
--- > e_eq_undir (0,1) (1,0) == True
-e_eq_undir :: Eq t => (t,t) -> (t,t) -> Bool
-e_eq_undir e0 e1 =
-  let swap (i,j) = (j,i)
-  in e0 == e1 || e0 == swap e1
-
--- | Sort edge.
---
--- > map e_sort [(0,1),(1,0)] == [(0,1),(0,1)]
-e_sort :: Ord t => (t, t) -> (t, t)
-e_sort (i,j) = (min i j,max i j)
-
--- | If (i,j) and (j,i) are both in E delete (j,i) where i < j.
-gr_mk_undir :: Ord t => GR t -> GR t
-gr_mk_undir (v,e) = (v,nub (sort (map e_sort e)))
-
--- | List of E to G, derives V from E.
-eset_to_gr :: Ord t => [(t,t)] -> GR t
-eset_to_gr e =
-  let v = sort (nub (concatMap (\(i,j) -> [i,j]) e))
-  in (v,e)
-
--- | Sort v and e.
-gr_sort :: Ord t => GR t -> GR t
-gr_sort (v,e) = (sort v,sort e)
-
--- * Int graph
-
--- | Vertex
-type V = Int
-
--- | Edge
-type E = (V,V)
-
--- | (vertices,edges)
-type G = GR V
-
--- | 'G.Graph' to 'G'.
-graph_to_g :: G.Graph -> G
-graph_to_g gr = (G.vertices gr,G.edges gr)
-
--- | 'G' to 'G.Graph'
---
--- > g = ([0,1,2],[(0,1),(0,2),(1,2)])
--- > g == gr_sort (graph_to_g (g_to_graph g))
-g_to_graph :: G -> G.Graph
-g_to_graph (v,e) = G.buildG (minimum v,maximum v) e
-
--- | Unlabel graph, make table.
-gr_unlabel :: Eq t => GR t -> (G,[(V,t)])
-gr_unlabel (v,e) =
-  let n = length v
-      v' = [0 .. n - 1]
-      tbl = zip v' v
-      get k = T.reverse_lookup_err k tbl
-      e' = map (\(p,q) -> (get p,get q)) e
-  in ((v',e'),tbl)
-
--- | 'g_to_graph' of 'gr_unlabel'.
---
--- > gr = ("abc",[('a','b'),('a','c'),('b','c')])
--- > (g,tbl) = gr_to_graph gr
-gr_to_graph :: Eq t => GR t -> (G.Graph,[(V,t)])
-gr_to_graph gr =
-  let ((v,e),tbl) = gr_unlabel gr
-  in (G.buildG (0,length v - 1) e,tbl)
-
--- * EDG = edge list (zero-indexed)
-
--- | ((|V|,|E|),[E])
-type EDG = ((Int,Int), [E])
-
--- | Requires V is (0 .. |v| - 1).
-edg_to_g :: EDG -> G
-edg_to_g ((nv,ne),e) =
-  let v = [0 .. nv - 1]
-  in if ne /= length e
-     then error (show ("edg_to_g",nv,ne,length e))
-     else (v,e)
-
--- | Parse EDG as printed by nauty-listg.
-edg_parse :: [String] -> EDG
-edg_parse ln =
-  let parse_int_list = map read . words
-      parse_int_pairs = T.adj2 2 . parse_int_list
-      parse_int_pair = T.unlist1_err . parse_int_pairs
-  in case ln of
-       [m,e] -> (parse_int_pair m,parse_int_pairs e)
-       _ -> error "edg_parse"
-
--- * Adjacencies
-
--- | Adjacency list
-type ADJ t = [(t,[t])]
-
--- | ADJ to G.
-adj_to_gr :: Ord t => ADJ t -> GR t
-adj_to_gr adj =
-  let e = concatMap (\(i,j) -> zip (repeat i) j) adj
-  in eset_to_gr e
-
--- | G to ADJ.
-gr_to_adj :: Ord t => (t -> (t,t) -> Maybe t) -> GR t -> ADJ t
-gr_to_adj sel_f (v,e) =
-  let f k = (k,sort (mapMaybe (sel_f k) e))
-  in filter (\(_,a) -> a /= []) (map f v)
-
--- | Directed graph to ADJ.
---
--- > g = ([0,1,2,3],[(0,1),(2,1),(0,3),(3,0)])
--- > r = [(0,[1,3]),(2,[1]),(3,[0])]
--- > gr_to_adj_dir g == r
-gr_to_adj_dir :: Ord t => GR t -> ADJ t
-gr_to_adj_dir =
-  let sel_f k (i,j) = if i == k then Just j else Nothing
-  in gr_to_adj sel_f
-
--- | Un-directed graph to ADJ.
---
--- > g = ([0,1,2,3],[(0,1),(2,1),(0,3),(3,0)])
--- > gr_to_adj_undir g == [(0,[1,3,3]),(1,[2])]
-gr_to_adj_undir :: Ord t => GR t -> ADJ t
-gr_to_adj_undir =
-  let sel_f k (i,j) =
-        if i == k && j >= k
-        then Just j
-        else if j == k && i >= k
-             then Just i
-             else Nothing
-  in gr_to_adj sel_f
-
--- | Adjacency matrix, (|v|,mtx)
-type ADJ_MTX = (Int,[[Int]])
-
-{- | EDG to ADJ_MTX for un-directed graph.
-
-> e = ((4,3),[(0,3),(1,3),(2,3)])
-> edg_to_adj_mtx_undir e == [[0,0,0,1],[0,0,0,1],[0,0,0,1],[1,1,1,0]]
-
-> e = ((4,4),[(0,1),(0,3),(1,2),(2,3)])
-> edg_to_adj_mtx_undir e == [[0,1,0,1],[1,0,1,0],[0,1,0,1],[1,0,1,0]]
-
--}
-edg_to_adj_mtx_undir :: EDG -> ADJ_MTX
-edg_to_adj_mtx_undir ((nv,_ne),e) =
-  let v = [0 .. nv - 1]
-      f i j = case find (e_eq_undir (i,j)) e of
-                Nothing -> 0
-                _ -> 1
-  in (nv,map (\i -> map (f i) v) v)
-
--- * Labels
-
--- | Labelled graph, distinct vertex and edge labels.
-type LBL_GR v v_lbl e_lbl = ([(v,v_lbl)],[((v,v),e_lbl)])
-
--- | Labelled graph, V/E typed.
-type LBL v e = LBL_GR V v e
-
-lbl_degree :: LBL v e -> (Int,Int)
-lbl_degree (v,e) = (length v,length e)
-
--- | Apply /v/ at vertex labels and /e/ at edge labels.
-lbl_bimap :: (v -> v') -> (e -> e') -> LBL v e -> LBL v' e'
-lbl_bimap v_f e_f (v,e) = (map (fmap v_f) v,map (fmap e_f) e)
-
-v_label :: v -> LBL v e -> V -> v
-v_label def (tbl,_) v = fromMaybe def (lookup v tbl)
-
-v_label_err :: LBL v e -> V -> v
-v_label_err = v_label (error "v_label")
-
-e_label :: e -> LBL v e -> E -> e
-e_label def (_,tbl) e = fromMaybe def (lookup e tbl)
-
-e_label_err :: LBL v e -> E -> e
-e_label_err = e_label (error "e_label")
-
-lbl_gr_to_lbl :: Eq v => LBL_GR v v_lbl e_lbl -> LBL v_lbl e_lbl
-lbl_gr_to_lbl (v,e) =
-  let n = length v
-      v' = [0 .. n - 1]
-      tbl = zip v' (map fst v)
-      get k = T.reverse_lookup_err k tbl
-      e' = map (\((p,q),r) -> ((get p,get q),r)) e
-  in (zip v' (map snd v),e')
-
--- > gr_to_lbl ("ab",[('a','b')]) == ([(0,'a'),(1,'b')],[((0,1),('a','b'))])
-gr_to_lbl :: Eq t => GR t -> LBL t (t,t)
-gr_to_lbl (v,e) = lbl_gr_to_lbl (zip v v,zip e e)
-
-lbl_delete_edge_labels :: LBL v e -> LBL v ()
-lbl_delete_edge_labels (v,e) = (v,map (\(x,_) -> (x,())) e)
-
-gr_to_lbl_ :: Eq t => GR t -> LBL t ()
-gr_to_lbl_ = lbl_delete_edge_labels . gr_to_lbl
-
--- | Construct LBL from set of E, derives V from E.
-eset_to_lbl :: Ord t => [(t,t)] -> LBL t ()
-eset_to_lbl e =
-  let v = nub (sort (concatMap (\(i,j) -> [i,j]) e))
-      get_ix z = fromMaybe (error "eset_to_lbl") (elemIndex z v)
-  in (zip [0..] v, map (\(i,j) -> ((get_ix i,get_ix j),())) e)
diff --git a/Music/Theory/IO.hs b/Music/Theory/IO.hs
deleted file mode 100644
--- a/Music/Theory/IO.hs
+++ /dev/null
@@ -1,34 +0,0 @@
--- | "System.IO" related functions.
-module Music.Theory.IO where
-
-import qualified Data.ByteString as B {- bytestring -}
-import qualified Data.Text as T {- text -}
-import qualified Data.Text.Encoding as T {- text -}
-import qualified Data.Text.IO as T {- text -}
-import qualified System.Directory as D {- directory -}
-
--- | 'T.decodeUtf8' of 'B.readFile'.
-read_file_utf8_text :: FilePath -> IO T.Text
-read_file_utf8_text = fmap T.decodeUtf8 . B.readFile
-
--- | Read (strictly) a UTF-8 encoded text file, implemented via "Data.Text".
-read_file_utf8 :: FilePath -> IO String
-read_file_utf8 = fmap T.unpack . read_file_utf8_text
-
--- | 'read_file_utf8', or a default value if the file doesn't exist.
-read_file_utf8_or :: String -> FilePath -> IO String
-read_file_utf8_or def f = do
-  x <- D.doesFileExist f
-  if x then read_file_utf8 f else return def
-
--- | Write UTF8 string as file, via "Data.Text".
-write_file_utf8 :: FilePath -> String -> IO ()
-write_file_utf8 fn = B.writeFile fn . T.encodeUtf8 . T.pack
-
--- | 'readFile' variant using 'Text' for @ISO 8859-1@ (Latin 1) encoding.
-read_file_iso_8859_1 :: FilePath -> IO String
-read_file_iso_8859_1 = fmap (T.unpack . T.decodeLatin1) . B.readFile
-
--- | 'readFile' variant using 'Text' for local encoding.
-read_file_locale :: FilePath -> IO String
-read_file_locale = fmap T.unpack . T.readFile
diff --git a/Music/Theory/Instrument/Names.hs b/Music/Theory/Instrument/Names.hs
--- a/Music/Theory/Instrument/Names.hs
+++ b/Music/Theory/Instrument/Names.hs
@@ -2,7 +2,7 @@
 
 import Data.List.Split {- split -}
 
--- (family,abbreviations,names,transpositions)
+-- | (family,abbreviations,names,transpositions)
 instrument_db' :: [(String,String,String,String)]
 instrument_db' =
     [("br","b.tbn","bass trombone","")
@@ -106,7 +106,7 @@
     ,("ww","oca","ocarina","")
     ]
 
--- (family,[abbreviations],[names],[transpositions])
+-- | (family,[abbreviations],[names],[transpositions])
 instrument_db :: [(String,[String],[String],[String])]
 instrument_db =
     let sep = splitOn ";"
diff --git a/Music/Theory/Interval.hs b/Music/Theory/Interval.hs
--- a/Music/Theory/Interval.hs
+++ b/Music/Theory/Interval.hs
@@ -4,17 +4,17 @@
 import Data.List {- base -}
 import Data.Maybe {- base -}
 
-import qualified Music.Theory.Ord as T
-import qualified Music.Theory.Pitch as T
-import qualified Music.Theory.Pitch.Note as T
+import qualified Music.Theory.Ord as T {- hmt -}
+import qualified Music.Theory.Pitch as T {- hmt -}
+import qualified Music.Theory.Pitch.Note as T {- hmt -}
 
 -- | Interval type or degree.
-data Interval_T = Unison | Second | Third | Fourth
+data Interval_Type = Unison | Second | Third | Fourth
                 | Fifth | Sixth | Seventh
                   deriving (Eq,Enum,Bounded,Ord,Show)
 
 -- | Interval quality.
-data Interval_Q = Diminished | Minor
+data Interval_Quality = Diminished | Minor
                 | Perfect
                 | Major | Augmented
                   deriving (Eq,Enum,Bounded,Ord,Show)
@@ -22,23 +22,23 @@
 -- | Common music notation interval.  An 'Ordering' of 'LT' indicates
 -- an ascending interval, 'GT' a descending interval, and 'EQ' a
 -- unison.
-data Interval = Interval {interval_type :: Interval_T
-                         ,interval_quality :: Interval_Q
+data Interval = Interval {interval_type :: Interval_Type
+                         ,interval_quality :: Interval_Quality
                          ,interval_direction :: Ordering
                          ,interval_octave :: T.Octave}
                 deriving (Eq,Show)
 
--- | Interval type between 'Note_T' values.
+-- | Interval type between 'Note' values.
 --
 -- > map (interval_ty C) [E,B] == [Third,Seventh]
-interval_ty :: T.Note_T -> T.Note_T -> Interval_T
+interval_ty :: T.Note -> T.Note -> Interval_Type
 interval_ty n1 n2 = toEnum ((fromEnum n2 - fromEnum n1) `mod` 7)
 
--- | Table of interval qualities.  For each 'Interval_T' gives
--- directed semitone interval counts for each allowable 'Interval_Q'.
+-- | Table of interval qualities.  For each 'Interval_Type' gives
+-- directed semitone interval counts for each allowable 'Interval_Quality'.
 -- For lookup function see 'interval_q', for reverse lookup see
 -- 'interval_q_reverse'.
-interval_q_tbl :: Integral n => [(Interval_T, [(n,Interval_Q)])]
+interval_q_tbl :: Integral n => [(Interval_Type, [(n,Interval_Quality)])]
 interval_q_tbl =
     [(Unison,[(11,Diminished)
              ,(0,Perfect)
@@ -66,20 +66,20 @@
               ,(11,Major)
               ,(12,Augmented)])]
 
--- | Lookup 'Interval_Q' for given 'Interval_T' and semitone count.
+-- | Lookup 'Interval_Quality' for given 'Interval_Type' and semitone count.
 --
 -- > interval_q Unison 11 == Just Diminished
 -- > interval_q Third 5 == Just Augmented
 -- > interval_q Fourth 5 == Just Perfect
 -- > interval_q Unison 3 == Nothing
-interval_q :: Interval_T -> Int -> Maybe Interval_Q
+interval_q :: Interval_Type -> Int -> Maybe Interval_Quality
 interval_q i n = lookup i interval_q_tbl >>= lookup n
 
--- | Lookup semitone difference of 'Interval_T' with 'Interval_Q'.
+-- | Lookup semitone difference of 'Interval_Type' with 'Interval_Quality'.
 --
 -- > interval_q_reverse Third Minor == Just 3
 -- > interval_q_reverse Unison Diminished == Just 11
-interval_q_reverse :: Interval_T -> Interval_Q -> Maybe Int
+interval_q_reverse :: Interval_Type -> Interval_Quality -> Maybe Int
 interval_q_reverse ty qu =
     case lookup ty interval_q_tbl of
       Nothing -> Nothing
@@ -98,8 +98,8 @@
 
 -- | Determine 'Interval' between two 'Pitch'es.
 --
--- > interval (Pitch C Sharp 4) (Pitch D Flat 4) == Interval Second Diminished EQ 0
--- > interval (Pitch C Sharp 4) (Pitch E Sharp 5) == Interval Third Major LT 1
+-- > interval (T.Pitch T.C T.Sharp 4) (T.Pitch T.D T.Flat 4) == Interval Second Diminished EQ 0
+-- > interval (T.Pitch T.C T.Sharp 4) (T.Pitch T.E T.Sharp 5) == Interval Third Major LT 1
 interval :: T.Pitch -> T.Pitch -> Interval
 interval p1 p2 =
     let c = compare p1 p2
@@ -109,7 +109,7 @@
         p2' = T.pitch_to_pc p2
         st = (p2' - p1') `mod` 12
         ty = interval_ty n1 n2
-        (Just qu) = interval_q ty (fromIntegral st)
+        qu = fromMaybe (error "interval?") (interval_q ty (fromIntegral st))
         o_a = if n1 > n2 then -1 else 0
     in case c of
          GT -> (interval p2 p1) { interval_direction = GT }
@@ -121,14 +121,14 @@
 invert_interval :: Interval -> Interval
 invert_interval (Interval t qu d o) = Interval t qu (T.ord_invert d) o
 
--- | The signed difference in semitones between two 'Interval_Q'
--- values when applied to the same 'Interval_T'.  Can this be written
--- correctly without knowing the Interval_T?
+-- | The signed difference in semitones between two 'Interval_Quality'
+-- values when applied to the same 'Interval_Type'.  Can this be written
+-- correctly without knowing the Interval_Type?
 --
 -- > quality_difference_m Minor Augmented == Just 2
 -- > quality_difference_m Augmented Diminished == Just (-3)
 -- > quality_difference_m Major Perfect == Nothing
-quality_difference_m :: Interval_Q -> Interval_Q -> Maybe Int
+quality_difference_m :: Interval_Quality -> Interval_Quality -> Maybe Int
 quality_difference_m a b =
     let rule (x,y) =
             if x == y
@@ -152,7 +152,7 @@
                       Nothing -> Nothing
 
 -- | Erroring variant of 'quality_difference_m'.
-quality_difference :: Interval_Q -> Interval_Q -> Int
+quality_difference :: Interval_Quality -> Interval_Quality -> Int
 quality_difference a b =
     let err = error ("quality_difference: " ++ show (a,b))
     in fromMaybe err (quality_difference_m a b)
@@ -203,7 +203,7 @@
 -- displacement.
 --
 -- > mapMaybe parse_interval_type (map show [1 .. 15])
-parse_interval_type :: String -> Maybe (Interval_T,T.Octave)
+parse_interval_type :: String -> Maybe (Interval_Type,T.Octave)
 parse_interval_type n =
     case reads n of
       [(n',[])] -> if n' == 0
@@ -215,7 +215,7 @@
 -- | Parse interval quality notation.
 --
 -- > mapMaybe parse_interval_quality "dmPMA" == [minBound .. maxBound]
-parse_interval_quality :: Char -> Maybe Interval_Q
+parse_interval_quality :: Char -> Maybe Interval_Quality
 parse_interval_quality q =
     let c = zip "dmPMA" [0..]
     in fmap toEnum (lookup q c)
@@ -224,11 +224,11 @@
 -- 'parse_interval_type'.
 --
 -- > map interval_type_degree [(Third,0),(Second,1),(Unison,2)] == [3,9,15]
-interval_type_degree :: (Interval_T,T.Octave) -> Int
+interval_type_degree :: (Interval_Type,T.Octave) -> Int
 interval_type_degree (t,o) = fromEnum t + 1 + (fromIntegral o * 7)
 
 -- | Inverse of 'parse_interval_quality.
-interval_quality_pp :: Interval_Q -> Char
+interval_quality_pp :: Interval_Quality -> Char
 interval_quality_pp q = "dmPMA" !! fromEnum q
 
 -- | Parse standard common music interval notation.
diff --git a/Music/Theory/Key.hs b/Music/Theory/Key.hs
--- a/Music/Theory/Key.hs
+++ b/Music/Theory/Key.hs
@@ -13,35 +13,35 @@
 import qualified Music.Theory.Interval as T
 
 -- | Enumeration of common music notation modes.
-data Mode_T = Minor_Mode | Major_Mode
+data Mode = Minor_Mode | Major_Mode
               deriving (Eq,Ord,Show)
 
--- | Pretty printer for 'Mode_T'.
-mode_pp :: Mode_T -> String
+-- | Pretty printer for 'Mode'.
+mode_pp :: Mode -> String
 mode_pp m =
     case m of
       Minor_Mode -> "Minor"
       Major_Mode -> "Major"
 
 -- | Lower-cased 'mode_pp'.
-mode_identifier_pp :: Mode_T -> String
+mode_identifier_pp :: Mode -> String
 mode_identifier_pp = map toLower . mode_pp
 
 -- | There are two modes, given one return the other.
-mode_parallel :: Mode_T -> Mode_T
+mode_parallel :: Mode -> Mode
 mode_parallel m = if m == Minor_Mode then Major_Mode else Minor_Mode
 
-mode_pc_seq :: Num t => Mode_T -> [t]
+mode_pc_seq :: Num t => Mode -> [t]
 mode_pc_seq md =
     case md of
       Major_Mode -> [0,2,4,5,7,9,11]
       Minor_Mode -> [0,2,3,5,7,8,10]
 
--- | A common music notation key is a 'Note_T', 'Alteration_T', 'Mode_T' triple.
-type Key = (T.Note_T,T.Alteration_T,Mode_T)
+-- | A common music notation key is a 'Note', 'Alteration', 'Mode' triple.
+type Key = (T.Note,T.Alteration,Mode)
 
--- | 'Mode_T' of 'Key'.
-key_mode :: Key -> Mode_T
+-- | 'Mode' of 'Key'.
+key_mode :: Key -> Mode
 key_mode (_,_,m) = m
 
 -- | Enumeration of 42 CMN keys.
@@ -58,7 +58,7 @@
 --
 -- > length key_sequence_30 == 30
 key_sequence_30 :: [Key]
-key_sequence_30 = filter (\k -> maybe False ((< 8) . abs) (key_fifths k)) key_sequence_42
+key_sequence_30 = filter (maybe False ((< 8) . abs) . key_fifths) key_sequence_42
 
 -- | Parallel key, ie. 'mode_parallel' of 'Key'.
 key_parallel :: Key -> Key
@@ -67,8 +67,8 @@
 -- | Transposition of 'Key'.
 key_transpose :: Key -> Int -> Key
 key_transpose (n,a,m) x =
-    let Just pc = T.note_alteration_to_pc (n,a)
-        Just (n',a') = T.pc_to_note_alteration_ks ((pc + x) `mod` 12)
+    let pc = fromMaybe (error "key_transpose?") (T.note_alteration_to_pc (n,a))
+        (n',a') = fromMaybe (error "key_transpose?") (T.pc_to_note_alteration_ks ((pc + x) `mod` 12))
     in (n',a',m)
 
 -- | Relative key (ie. 'mode_parallel' with the same number of and type of alterations.
@@ -98,7 +98,7 @@
 
 -- | Pretty-printer where 'Minor_Mode' is written in lower case (lc) and
 -- alteration symbol is shown using indicated function.
-key_lc_pp :: (T.Alteration_T -> String) -> Key -> String
+key_lc_pp :: (T.Alteration -> String) -> Key -> String
 key_lc_pp a_pp (n,a,m) =
     let c = T.note_pp n
         c' = if m == Minor_Mode then toLower c else c
@@ -121,7 +121,7 @@
 key_lc_tonh_pp = key_lc_pp T.alteration_tonh
 
 -- > map key_identifier_pp [(T.C,T.Sharp,Minor_Mode),(T.E,T.Flat,Major_Mode)]
-key_identifier_pp :: (Show a, Show a1) => (a, a1, Mode_T) -> [Char]
+key_identifier_pp :: (Show a, Show a1) => (a, a1, Mode) -> [Char]
 key_identifier_pp (n,a,m) = map toLower (intercalate "_" [show n,show a,mode_pp m])
 
 -- > import Data.Maybe
@@ -133,17 +133,15 @@
 
 -- | Parse 'Key' from /lc-uc/ string.
 --
--- > import Data.Maybe
---
 -- > let k = mapMaybe key_lc_uc_parse ["c","E","f♯","ab","G#"]
--- > in map key_lc_uc_pp k == ["c♮","E♮","f♯","a♭","G♯"]
+-- > map key_lc_uc_pp k == ["c♮","E♮","f♯","a♭","G♯"]
 key_lc_uc_parse :: String -> Maybe Key
 key_lc_uc_parse k =
     let with_k a (n,_,m) = (n,a,m)
         with_a n a = fmap (with_k a) (note_char_to_key n)
     in case k of
          [c] -> note_char_to_key c
-         [n,a] -> join (fmap (with_a n) (T.symbol_to_alteration_iso a))
+         [n,a] -> with_a n =<< T.symbol_to_alteration_unicode_plus_iso a
          _ -> Nothing
 
 -- | Distance along circle of fifths path of indicated 'Key'.  A
@@ -170,7 +168,7 @@
 -- | Table mapping 'Key' to 'key_fifths' value.
 key_fifths_tbl :: [(Key,Int)]
 key_fifths_tbl =
-    let f (k,n) = maybe Nothing (\n' -> Just (k,n')) n
+    let f (k,n) = fmap (\n' -> (k,n')) n
     in mapMaybe f (zip key_sequence_42 (map key_fifths key_sequence_42))
 
 -- | Lookup 'key_fifths' value in 'key_fifths_tbl'.
@@ -179,7 +177,7 @@
 -- > let f md = map key_lc_iso_pp . mapMaybe (fifths_to_key md)
 -- > f Minor_Mode a
 -- > f Major_Mode a
-fifths_to_key :: Mode_T -> Int -> Maybe Key
+fifths_to_key :: Mode -> Int -> Maybe Key
 fifths_to_key md n =
     let eq_f = (\((_,_,md'),n') -> md == md' && n == n')
     in fmap fst (find eq_f key_fifths_tbl)
@@ -188,18 +186,18 @@
 --
 -- > mapMaybe (implied_key Major_Mode) [[0,2,4],[1,3],[4,10],[3,9],[8,9]]
 -- > map (implied_key Major_Mode) [[0,1,2],[0,1,3,4]] == [Nothing,Nothing]
-implied_key :: Integral i => Mode_T -> [i] -> Maybe Key
+implied_key :: Integral i => Mode -> [i] -> Maybe Key
 implied_key md pc_set =
     let a_seq = [0,1,-1,2,-2,3,-3,4,-4,5,-5,6,-6]
         key_seq = mapMaybe (fifths_to_key md) a_seq
     in find (\k -> pc_set `T.is_subset` key_pc_set k) key_seq
 
 -- | 'key_fifths' of 'implied_key'.
-implied_fifths :: Integral i => Mode_T -> [i] -> Maybe Int
-implied_fifths md = join . fmap key_fifths . implied_key md
+implied_fifths :: Integral i => Mode -> [i] -> Maybe Int
+implied_fifths md = key_fifths <=< implied_key md
 
-implied_key_err :: Integral i => Mode_T -> [i] -> Key
+implied_key_err :: Integral i => Mode -> [i] -> Key
 implied_key_err md = fromMaybe (error "implied_key") . implied_key md
 
-implied_fifths_err :: Integral i => Mode_T -> [i] -> Int
+implied_fifths_err :: Integral i => Mode -> [i] -> Int
 implied_fifths_err md = fromMaybe (error "implied_fifths") . key_fifths . implied_key_err md
diff --git a/Music/Theory/List.hs b/Music/Theory/List.hs
deleted file mode 100644
--- a/Music/Theory/List.hs
+++ /dev/null
@@ -1,1475 +0,0 @@
--- | List functions.
-module Music.Theory.List where
-
-import Data.Either {- base -}
-import Data.Function {- base -}
-import Data.List {- base -}
-import Data.Maybe {- base -}
-
-import qualified Data.IntMap as Map {- containers -}
-import qualified Data.List.Ordered as O {- data-ordlist -}
-import qualified Data.List.Split as S {- split -}
-import qualified Data.Tree as Tree {- containers -}
-
-import qualified Control.Monad.Logic as L {- logict -}
-
--- | 'Data.Vector.slice', ie. starting index (zero-indexed) and number of elements.
---
--- > slice 4 5 [1..] == [5,6,7,8,9]
-slice :: Int -> Int -> [a] -> [a]
-slice i n = take n . drop i
-
--- | Variant of slice with start and end indices (zero-indexed).
---
--- > section 4 8 [1..] == [5,6,7,8,9]
-section :: Int -> Int -> [a] -> [a]
-section l r = take (r - l + 1) . drop l
-
--- | Bracket sequence with left and right values.
---
--- > bracket ('<','>') "1,2,3" == "<1,2,3>"
-bracket :: (a,a) -> [a] -> [a]
-bracket (l,r) x = l : x ++ [r]
-
--- | 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
-
--- | The first & middle & last elements of a list.
---
--- > map unbracket_el ["","{12}"] == [(Nothing,"",Nothing),(Just '{',"12",Just '}')]
-unbracket_el :: [a] -> (Maybe a,[a],Maybe a)
-unbracket_el x =
-    case x of
-      [] -> (Nothing,[],Nothing)
-      l:x' -> let (m,r) = separate_last' x' in (Just l,m,r)
-
--- | The first & middle & last elements of a list.
---
--- > map unbracket ["","{12}"] == [Nothing,Just ('{',"12",'}')]
-unbracket :: [t] -> Maybe (t,[t],t)
-unbracket x =
-    case unbracket_el x of
-      (Just l,m,Just r) -> Just (l,m,r)
-      _ -> Nothing
-
--- | Erroring variant.
-unbracket_err :: [t] -> (t,[t],t)
-unbracket_err = fromMaybe (error "unbracket") . unbracket
-
--- * Split
-
--- | Relative of 'splitOn', but only makes first separation.
---
--- > splitOn "//" "lhs//rhs//rem" == ["lhs","rhs","rem"]
--- > separate_at "//" "lhs//rhs//rem" == Just ("lhs","rhs//rem")
-separate_at :: Eq a => [a] -> [a] -> Maybe ([a],[a])
-separate_at x =
-    let n = length x
-        f lhs rhs =
-            if null rhs
-            then Nothing
-            else if x == take n rhs
-                 then Just (reverse lhs,drop n rhs)
-                 else f (head rhs : lhs) (tail rhs)
-    in f []
-
--- | Variant of 'S.splitWhen' that keeps delimiters at left.
---
--- > split_when_keeping_left (== 'r') "rab rcd re rf r" == ["","rab ","rcd ","re ","rf ","r"]
-split_when_keeping_left :: (a -> Bool) -> [a] -> [[a]]
-split_when_keeping_left = S.split . S.keepDelimsL . S.whenElt
-
-{- | Split before the indicated element, keeping it at the left of the sub-sequence it begins.
-     'split_when_keeping_left' of '=='
-
-> split_before 'x' "axbcxdefx" == ["a","xbc","xdef","x"]
-> split_before 'x' "xa" == ["","xa"]
-
-> map (flip split_before "abcde") "ae_" == [["","abcde"],["abcd","e"],["abcde"]]
-> map (flip break "abcde" . (==)) "ae_" == [("","abcde"),("abcd","e"),("abcde","")]
-
-> split_before 'r' "rab rcd re rf r" == ["","rab ","rcd ","re ","rf ","r"]
--}
-split_before :: Eq a => a -> [a] -> [[a]]
-split_before x = split_when_keeping_left (== x)
-
--- | Split before any of the indicated set of delimiters.
---
--- > split_before_any ",;" ";a,b,c;d;" == ["",";a",",b",",c",";d",";"]
-split_before_any :: Eq a => [a] -> [a] -> [[a]]
-split_before_any = S.split . S.keepDelimsL . S.oneOf
-
--- | Singleton variant of 'S.splitOn'.
---
--- > split_on_1 ":" "graph:layout" == Just ("graph","layout")
-split_on_1 :: Eq t => [t] -> [t] -> Maybe ([t],[t])
-split_on_1 e l =
-    case S.splitOn e l of
-      [p,q] -> Just (p,q)
-      _ -> Nothing
-
--- | Erroring variant.
-split_on_1_err :: Eq t => [t] -> [t] -> ([t],[t])
-split_on_1_err e = fromMaybe (error "split_on_1") . split_on_1 e
-
--- | Split function that splits only once, ie. a variant of 'break'.
---
--- > split1 ' ' "three word sentence" == Just ("three","word sentence")
-split1 :: Eq a => a -> [a] -> Maybe ([a],[a])
-split1 c l =
-    case break (== c) l of
-      (lhs,_:rhs) -> Just (lhs,rhs)
-      _ -> Nothing
-
--- | Erroring variant.
-split1_err :: (Eq a, Show a) => a -> [a] -> ([a], [a])
-split1_err e s = fromMaybe (error (show ("split1",e,s))) (split1 e s)
-
--- * Rotate
-
--- | Generic form of 'rotate_left'.
-genericRotate_left :: Integral i => i -> [a] -> [a]
-genericRotate_left n =
-    let f (p,q) = q ++ p
-    in f . genericSplitAt n
-
--- | Left rotation.
---
--- > rotate_left 1 [1..3] == [2,3,1]
--- > rotate_left 3 [1..5] == [4,5,1,2,3]
-rotate_left :: Int -> [a] -> [a]
-rotate_left = genericRotate_left
-
--- | Generic form of 'rotate_right'.
-genericRotate_right :: Integral n => n -> [a] -> [a]
-genericRotate_right n = reverse . genericRotate_left n . reverse
-
--- | Right rotation.
---
--- > rotate_right 1 [1..3] == [3,1,2]
-rotate_right :: Int -> [a] -> [a]
-rotate_right = genericRotate_right
-
--- | Rotate left by /n/ 'mod' /#p/ places.
---
--- > rotate 1 [1..3] == [2,3,1]
--- > rotate 8 [1..5] == [4,5,1,2,3]
-rotate :: (Integral n) => n -> [a] -> [a]
-rotate n p =
-    let m = n `mod` genericLength p
-    in genericRotate_left m p
-
--- | Rotate right by /n/ places.
---
--- > rotate_r 8 [1..5] == [3,4,5,1,2]
-rotate_r :: (Integral n) => n -> [a] -> [a]
-rotate_r = rotate . negate
-
--- | All rotations.
---
--- > rotations [0,1,3] == [[0,1,3],[1,3,0],[3,0,1]]
-rotations :: [a] -> [[a]]
-rotations p = map (`rotate_left` p) [0 .. length p - 1]
-
--- | Rotate list so that is starts at indicated element.
---
--- > rotate_starting_from 'c' "abcde" == Just "cdeab"
--- > rotate_starting_from '_' "abc" == Nothing
-rotate_starting_from :: Eq a => a -> [a] -> Maybe [a]
-rotate_starting_from x l =
-    case break (== x) l of
-      (_,[]) -> Nothing
-      (lhs,rhs) -> Just (rhs ++ lhs)
-
--- | Erroring variant.
-rotate_starting_from_err :: Eq a => a -> [a] -> [a]
-rotate_starting_from_err x =
-    fromMaybe (error "rotate_starting_from: non-element") .
-    rotate_starting_from x
-
--- | Sequence of /n/ adjacent elements, moving forward by /k/ places.
--- The last element may have fewer than /n/ places, but will reach the
--- end of the input sequence.
---
--- > adj 3 2 "adjacent" == ["adj","jac","cen","nt"]
-adj :: Int -> Int -> [a] -> [[a]]
-adj n k l =
-    case take n l of
-      [] -> []
-      r -> r : adj n k (drop k l)
-
--- | Variant of 'adj' where the last element has /n/ places but may
--- not reach the end of the input sequence.
---
--- > adj_trunc 4 1 "adjacent" == ["adja","djac","jace","acen","cent"]
--- > adj_trunc 3 2 "adjacent" == ["adj","jac","cen"]
-adj_trunc :: Int -> Int -> [a] -> [[a]]
-adj_trunc n k l =
-    let r = take n l
-    in if length r == n then r : adj_trunc n k (drop k l) else []
-
--- | 'adj_trunc' of 'close' by /n/-1.
---
--- > adj_cyclic_trunc 3 1 "adjacent" == ["adj","dja","jac","ace","cen","ent","nta","tad"]
-adj_cyclic_trunc :: Int -> Int -> [a] -> [[a]]
-adj_cyclic_trunc n k = adj_trunc n k . close (n - 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)]
--- > let l = [1..5] in zip l (tail l) == adj2 1 l
--- > adj2 2 [1..4] == [(1,2),(3,4)]
--- > adj2 3 [1..5] == [(1,2),(4,5)]
-adj2 :: Int -> [t] -> [(t,t)]
-adj2 = genericAdj2
-
--- | Append first /n/-elements to end of list.
---
--- > close 1 [1..3] == [1,2,3,1]
-close :: Int -> [a] -> [a]
-close k x = x ++ take k x
-
--- | 'adj2' '.' 'close' 1.
---
--- > adj2_cyclic 1 [1..3] == [(1,2),(2,3),(3,1)]
-adj2_cyclic :: Int -> [t] -> [(t,t)]
-adj2_cyclic n = adj2 n . close 1
-
--- | Adjacent triples.
---
--- > adj3 3 [1..6] == [(1,2,3),(4,5,6)]
-adj3 :: Int -> [t] -> [(t,t,t)]
-adj3 n l =
-  case l of
-      p:q:r:_ -> (p,q,r) : adj3 n (drop n l)
-      _ -> []
-
--- | 'adj3' '.' 'close' 2.
---
--- > adj3_cyclic 1 [1..4] == [(1,2,3),(2,3,4),(3,4,1),(4,1,2)]
-adj3_cyclic :: Int -> [t] -> [(t,t,t)]
-adj3_cyclic n = adj3 n . close 2
-
-{- | Adjacent quadruples.
-
-> adj4 2 [1..8] == [(1,2,3,4),(3,4,5,6),(5,6,7,8)]
-> adj4 4 [1..8] == [(1,2,3,4),(5,6,7,8)]
--}
-adj4 :: Int -> [t] -> [(t,t,t,t)]
-adj4 n l =
-  case l of
-      p:q:r:s:_ -> (p,q,r,s) : adj4 n (drop n l)
-      _ -> []
-
--- | Interleave elements of /p/ and /q/.
---
--- > interleave [1..3] [4..6] == [1,4,2,5,3,6]
--- > interleave ".+-" "abc" == ".a+b-c"
--- > interleave [1..3] [] == []
-interleave :: [a] -> [a] -> [a]
-interleave p q =
-    let u (i,j) = [i,j]
-    in concatMap u (zip p q)
-
--- | Interleave list of lists.  Allows lists to be of non-equal lenghts.
---
--- > interleave_set ["abcd","efgh","ijkl"] == "aeibfjcgkdhl"
--- > interleave_set ["abc","defg","hijkl"] == "adhbeicfjgkl"
-interleave_set :: [[a]] -> [a]
-interleave_set = concat . transpose
-
-{-
-import Safe {- safe -}
-
-interleave_set l =
-    case mapMaybe headMay l of
-      [] -> []
-      r -> r ++ interleave_set (mapMaybe tailMay l)
--}
-
--- | De-interleave /n/ lists.
---
--- > deinterleave 2 ".a+b-c" == [".+-","abc"]
--- > deinterleave 3 "aeibfjcgkdhl" == ["abcd","efgh","ijkl"]
-deinterleave :: Int -> [a] -> [[a]]
-deinterleave n = transpose . S.chunksOf n
-
--- | Special case for two-part deinterleaving.
---
--- > deinterleave2 ".a+b-c" == (".+-","abc")
-deinterleave2 :: [t] -> ([t], [t])
-deinterleave2 =
-    let f l =
-            case l of
-              p:q:l' -> (p,q) : f l'
-              _ -> []
-    in unzip . f
-
-{-
-deinterleave2 =
-    let f p q l =
-            case l of
-              [] -> (reverse p,reverse q)
-              [a] -> (reverse (a:p),reverse q)
-              a:b:l' -> rec (a:p) (b:q) l'
-    in f [] []
--}
-
--- | Variant that continues with the longer input.
---
--- > interleave_continue ".+-" "abc" == ".a+b-c"
--- > interleave_continue [1..3] [] == [1..3]
--- > interleave_continue [] [1..3] == [1..3]
-interleave_continue :: [a] -> [a] -> [a]
-interleave_continue p q =
-    case (p,q) of
-      ([],_) -> q
-      (_,[]) -> p
-      (i:p',j:q') -> i : j : interleave_continue p' q'
-
--- | 'interleave' of 'rotate_left' by /i/ and /j/.
---
--- > interleave_rotations 9 3 [1..13] == [10,4,11,5,12,6,13,7,1,8,2,9,3,10,4,11,5,12,6,13,7,1,8,2,9,3]
-interleave_rotations :: Int -> Int -> [b] -> [b]
-interleave_rotations i j s = interleave (rotate_left i s) (rotate_left j s)
-
--- | 'unzip', apply /f1/ and /f2/ and 'zip'.
-rezip :: ([t] -> [u]) -> ([v] -> [w]) -> [(t,v)] -> [(u,w)]
-rezip f1 f2 l = let (p,q) = unzip l in zip (f1 p) (f2 q)
-
--- | Generalised histogram, with equality function for grouping and comparison function for sorting.
-generic_histogram_by :: Integral i => (a->a->Bool) -> (Maybe (a->a->Ordering)) -> [a] -> [(a,i)]
-generic_histogram_by eq_f cmp_f x =
-    let g = groupBy eq_f (maybe x (\f -> sortBy f x) cmp_f)
-    in zip (map head g) (map genericLength g)
-
--- | Type specialised 'generic_histogram_by'.
-histogram_by :: (a->a->Bool) -> (Maybe (a->a->Ordering)) -> [a] -> [(a,Int)]
-histogram_by = generic_histogram_by
-
--- | Count occurences of elements in list, 'histogram_by' of '==' and 'compare'.
-generic_histogram :: (Ord a,Integral i) => [a] -> [(a,i)]
-generic_histogram = generic_histogram_by (==) (Just compare)
-
--- | Type specialised 'generic_histogram'.  Elements will be in ascending order.
---
--- > map histogram ["","hohoh","yxx"] == [[],[('h',3),('o',2)],[('x',2),('y',1)]]
-histogram :: Ord a => [a] -> [(a,Int)]
-histogram = generic_histogram
-
--- | Join two histograms, which must be sorted.
---
--- > histogram_join (zip "ab" [1,1]) (zip "bc" [1,1]) == zip "abc" [1,2,1]
-histogram_join :: Ord a => [(a,Int)] -> [(a,Int)] -> [(a,Int)]
-histogram_join p q =
-  let f (e1,n1) (e2,n2) = if e1 == e2 then Just (e1,n1 + n2) else Nothing
-  in case (p,q) of
-       (_,[]) -> p
-       ([],_) -> q
-       (p1:p',q1:q') -> case f p1 q1 of
-                          Just r -> r : histogram_join p' q'
-                          Nothing -> if p1 < q1
-                                     then p1 : histogram_join p' q
-                                     else q1 : histogram_join p q'
-
--- | 'foldr' of 'histogram_join'.
---
--- > let f x = zip x (repeat 1) in histogram_merge (map f ["ab","bcd","de"]) == zip "abcde" [1,2,1,2,1]
-histogram_merge :: Ord a => [[(a,Int)]] -> [(a,Int)]
-histogram_merge = foldr histogram_join []
-
--- | Given (k,#) histogram where k is enumerable generate filled histogram with 0 for empty k.
---
--- > histogram_fill (histogram "histogram") == zip ['a'..'t'] [1,0,0,0,0,0,1,1,1,0,0,0,1,0,1,0,0,1,1,1]
-histogram_fill :: (Ord a, Enum a) => [(a,Int)] -> [(a,Int)]
-histogram_fill h =
-  let k = map fst h
-      e = [minimum k .. maximum k]
-      f x = fromMaybe 0 (lookup x h)
-  in zip e (map f e)
-
-{- | Given two histograms p & q (sorted by key) make composite
-histogram giving for all keys the counts for (p,q).
-
-> r = zip "ABCDE" (zip [4,3,2,1,0] [2,3,4,0,5])
-> histogram_composite (zip "ABCD" [4,3,2,1]) (zip "ABCE" [2,3,4,5]) == r
--}
-histogram_composite :: Ord a => [(a,Int)] -> [(a,Int)] -> [(a,(Int,Int))]
-histogram_composite p q =
-  case (p,q) of
-    ([],_) -> map (\(k,n) -> (k,(0,n))) q
-    (_,[]) -> map (\(k,n) -> (k,(n,0))) p
-    ((k1,n1):p',(k2,n2):q') -> case compare k1 k2 of
-                                 LT -> (k1,(n1,0)) : histogram_composite p' q
-                                 EQ -> (k1,(n1,n2)) : histogram_composite p' q'
-                                 GT -> (k2,(0,n2)) : histogram_composite p q'
-
-{- | Apply '-' at count of 'histogram_composite', ie. 0 indicates
-equal number at p and q, negative indicates more elements at p than
-q and positive more elements at q than p.
-
-> histogram_diff (zip "ABCD" [4,3,2,1]) (zip "ABCE" [2,3,4,5]) == zip "ABCDE" [-2,0,2,-1,5]
--}
-histogram_diff :: Ord a => [(a,Int)] -> [(a,Int)] -> [(a,Int)]
-histogram_diff p = map (\(k,(n,m)) -> (k,m - n)) . histogram_composite p
-
--- | Elements that appear more than once in the input given equality predicate.
-duplicates_by :: Ord a => (a -> a -> Bool) -> [a] -> [a]
-duplicates_by f = map fst . filter (\(_,n) -> n > 1) . histogram_by f (Just compare)
-
--- | 'duplicates_by' of '=='.
---
--- > map duplicates ["duplicates","redundant"] == ["","dn"]
-duplicates :: Ord a => [a] -> [a]
-duplicates = duplicates_by (==)
-
--- | List segments of length /i/ at distance /j/.
---
--- > segments 2 1 [1..5] == [[1,2],[2,3],[3,4],[4,5]]
--- > segments 2 2 [1..5] == [[1,2],[3,4]]
-segments :: Int -> Int -> [a] -> [[a]]
-segments i j p =
-    let q = take i p
-        p' = drop j p
-    in if length q /= i then [] else q : segments i j p'
-
--- | 'foldl1' 'intersect'.
---
--- > intersect_l [[1,2],[1,2,3],[1,2,3,4]] == [1,2]
-intersect_l :: Eq a => [[a]] -> [a]
-intersect_l = foldl1 intersect
-
--- | 'foldl1' 'union'.
---
--- > sort (union_l [[1,3],[2,3],[3]]) == [1,2,3]
-union_l :: Eq a => [[a]] -> [a]
-union_l = foldl1 union
-
--- | Intersection of adjacent elements of list at distance /n/.
---
--- > adj_intersect 1 [[1,2],[1,2,3],[1,2,3,4]] == [[1,2],[1,2,3]]
-adj_intersect :: Eq a => Int -> [[a]] -> [[a]]
-adj_intersect n = map intersect_l . segments 2 n
-
--- | List of cycles at distance /n/.
---
--- > cycles 2 [1..6] == [[1,3,5],[2,4,6]]
--- > cycles 3 [1..9] == [[1,4,7],[2,5,8],[3,6,9]]
--- > cycles 4 [1..8] == [[1,5],[2,6],[3,7],[4,8]]
-cycles :: Int -> [a] -> [[a]]
-cycles n = transpose . S.chunksOf n
-
--- | Variant of 'filter' that has a predicate to halt processing,
--- ie. 'filter' of 'takeWhile'.
---
--- > filter_halt (even . fst) ((< 5) . snd) (zip [1..] [0..])
-filter_halt :: (a -> Bool) -> (a -> Bool) -> [a] -> [a]
-filter_halt sel end = filter sel . takeWhile end
-
--- | 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 = map (\e -> if f e then Just e else Nothing)
-
--- | Replace all /p/ with /q/ in /s/.
---
--- > replace "_x_" "-X-" "an _x_ string" == "an -X- string"
--- > replace "ab" "cd" "ab ab cd ab" == "cd cd cd cd"
-replace :: Eq a => [a] -> [a] -> [a] -> [a]
-replace p q s =
-    let n = length p
-    in case s of
-         [] -> []
-         c:s' -> if p `isPrefixOf` s
-                 then q ++ replace p q (drop n s)
-                 else c : replace p q s'
-
--- | Replace the /i/th value at /ns/ with /x/.
---
--- > replace_at "test" 2 'n' == "tent"
-replace_at :: Integral i => [a] -> i -> a -> [a]
-replace_at ns i x =
-    let f j y = if i == j then x else y
-    in zipWith f [0..] ns
-
--- * Association lists
-
--- | Equivalent to 'groupBy' /eq/ 'on' /f/.
---
--- > group_by_on (==) snd (zip [0..] "abbc") == [[(0,'a')],[(1,'b'),(2,'b')],[(3,'c')]]
-group_by_on :: (x -> x -> Bool) -> (t -> x) -> [t] -> [[t]]
-group_by_on eq f = groupBy (eq `on` f)
-
--- | 'group_by_on' of '=='.
---
--- > r = [[(1,'a'),(1,'b')],[(2,'c')],[(3,'d'),(3,'e')],[(4,'f')]]
--- > group_on fst (zip [1,1,2,3,3,4] "abcdef") == r
-group_on :: Eq x => (a -> x) -> [a] -> [[a]]
-group_on = group_by_on (==)
-
--- | Given an equality predicate and accesors for /key/ and /value/ collate adjacent values.
-collate_by_on_adjacent :: (k -> k -> Bool) -> (a -> k) -> (a -> v) -> [a] -> [(k,[v])]
-collate_by_on_adjacent eq f g =
-    let h l = case l of
-                [] -> error "collate_by_on_adjacent"
-                l0:_ -> (f l0,map g l)
-    in map h . group_by_on eq f
-
--- | 'collate_by_on_adjacent' of '=='
-collate_on_adjacent :: Eq k => (a -> k) -> (a -> v) -> [a] -> [(k,[v])]
-collate_on_adjacent = collate_by_on_adjacent (==)
-
--- | 'collate_on_adjacent' of 'fst' and 'snd'.
---
--- > collate_adjacent (zip "TDD" "xyz") == [('T',"x"),('D',"yz")]
-collate_adjacent :: Eq a => [(a,b)] -> [(a,[b])]
-collate_adjacent = collate_on_adjacent fst snd
-
--- | 'sortOn' prior to 'collate_on_adjacent'.
---
--- > r = [('A',"a"),('B',"bd"),('C',"ce"),('D',"f")]
--- > collate_on fst snd (zip "ABCBCD" "abcdef") == r
-collate_on :: Ord k => (a -> k) -> (a -> v) -> [a] -> [(k,[v])]
-collate_on f g = collate_on_adjacent f g . sortOn f
-
--- | 'collate_on' of 'fst' and 'snd'.
---
--- > collate (zip "TDD" "xyz") == [('D',"yz"),('T',"x")]
--- > collate (zip [1,2,1] "abc") == [(1,"ac"),(2,"b")]
-collate :: Ord a => [(a,b)] -> [(a,[b])]
-collate = collate_on fst snd
-
--- | Reverse of 'collate', inverse if order is not considered.
---
--- > uncollate [(1,"ac"),(2,"b")] == zip [1,1,2] "acb"
-uncollate :: [(k,[v])] -> [(k,v)]
-uncollate = concatMap (\(k,v) -> zip (repeat k) v)
-
--- | Make /assoc/ list with given /key/.
---
--- > with_key 'a' [1..3] == [('a',1),('a',2),('a',3)]
-with_key :: k -> [v] -> [(k,v)]
-with_key h = zip (repeat h)
-
--- | Left biased merge of association lists /p/ and /q/.
---
--- > assoc_merge [(5,"a"),(3,"b")] [(5,"A"),(7,"C")] == [(5,"a"),(3,"b"),(7,"C")]
-assoc_merge :: Eq k => [(k,v)] -> [(k,v)] -> [(k,v)]
-assoc_merge p q =
-    let p_k = map fst p
-        q' = filter ((`notElem` p_k) . fst) q
-    in p ++ q'
-
--- | Keys are in ascending order, the entry retrieved is the rightmose with
---   a key less than or equal to the key requested.
---   If the key requested is less than the initial key, or the list is empty, returns 'Nothing'.
---
--- > let m = [(1,'a'),(4,'x'),(4,'b'),(5,'c')]
--- > mapMaybe (ord_map_locate m) [1 .. 6] == [(1,'a'),(1,'a'),(1,'a'),(4,'b'),(5,'c'),(5,'c')]
--- > ord_map_locate m 0 == Nothing
-ord_map_locate :: Ord k => [(k,v)] -> k -> Maybe (k,v)
-ord_map_locate mp i =
-    let f (k0,v0) xs =
-          case xs of
-            [] -> if i >= k0 then Just (k0,v0) else error "ord_map_locate?"
-            ((k1,v1):xs') -> if i >= k0 && i < k1 then Just (k0,v0) else f (k1,v1) xs'
-    in case mp of
-         [] -> Nothing
-         (k0,v0):mp' -> if i < k0 then Nothing else f (k0,v0) mp'
-
--- * Δ
-
--- | 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'"
-
--- | Integration with /f/, ie. apply flip of /f/ between elements of /l/.
---
--- > d_dx_by (,) "abcd" == [('b','a'),('c','b'),('d','c')]
--- > d_dx_by (-) [0,2,4,1,0] == [2,2,-3,-1]
--- > d_dx_by (-) [2,3,0,4,1] == [1,-3,4,-3]
-d_dx_by :: (t -> t -> u) -> [t] -> [u]
-d_dx_by f l = if null l then [] else zipWith f (tail l) l
-
--- | Integrate, 'd_dx_by' '-', ie. pitch class segment to interval sequence.
---
--- > d_dx [5,6,8,11] == [1,2,3]
--- > d_dx [] == []
-d_dx :: (Num a) => [a] -> [a]
-d_dx = d_dx_by (-)
-
--- | Elements of /p/ not in /q/.
---
--- > [1,2,3] `difference` [1,2] == [3]
-difference :: Eq a => [a] -> [a] -> [a]
-difference p q = filter (`notElem` q) 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
-
--- | Erroring variant of 'findIndex'.
-findIndex_err :: (a -> Bool) -> [a] -> Int
-findIndex_err f = fromMaybe (error "findIndex?") . findIndex f
-
--- | Erroring variant of 'elemIndex'.
-elemIndex_err :: Eq a => a -> [a] -> Int
-elemIndex_err x = fromMaybe (error "ix_of") . elemIndex x
-
--- | Variant of 'elemIndices' that requires /e/ to be unique in /p/.
---
--- > elem_index_unique 'a' "abcda" == undefined
-elem_index_unique :: Eq a => a -> [a] -> Int
-elem_index_unique e p =
-    case elemIndices e p of
-      [i] -> i
-      _ -> error "elem_index_unique"
-
--- | Lookup that errors and prints message and key.
-lookup_err_msg :: (Eq k,Show k) => String -> k -> [(k,v)] -> v
-lookup_err_msg err k = fromMaybe (error (err ++ ": " ++ show k)) . lookup k
-
--- | Error variant.
-lookup_err :: Eq k => k -> [(k,v)] -> v
-lookup_err n = fromMaybe (error "lookup") . lookup n
-
--- | 'lookup' variant with default value.
-lookup_def :: Eq k => k -> v -> [(k,v)] -> v
-lookup_def k d = fromMaybe d . lookup k
-
--- | If /l/ is empty 'Nothing', else 'Just' /l/.
-non_empty :: [t] -> Maybe [t]
-non_empty l = if null l then Nothing else Just l
-
--- | Variant on 'filter' that selects all matches.
---
--- > lookup_set 1 (zip [1,2,3,4,1] "abcde") == Just "ae"
-lookup_set :: Eq k => k -> [(k,v)] -> Maybe [v]
-lookup_set k = non_empty . map snd . filter ((== k) . fst)
-
--- | Erroring variant.
-lookup_set_err :: Eq k => k -> [(k,v)] -> [v]
-lookup_set_err k = fromMaybe (error "lookup_set?") . lookup_set k
-
--- | Reverse lookup.
---
--- > reverse_lookup 'c' [] == Nothing
--- > reverse_lookup 'b' (zip [1..] ['a'..]) == Just 2
--- > lookup 2 (zip [1..] ['a'..]) == Just 'b'
-reverse_lookup :: Eq v => v -> [(k,v)] -> Maybe k
-reverse_lookup k = fmap fst . find ((== k) . snd)
-
--- | Erroring variant.
-reverse_lookup_err :: Eq v => v -> [(k,v)] -> k
-reverse_lookup_err k = fromMaybe (error "reverse_lookup") . reverse_lookup k
-
-{-
-reverse_lookup :: Eq b => b -> [(a,b)] -> Maybe a
-reverse_lookup key ls =
-    case ls of
-      [] -> Nothing
-      (x,y):ls' -> if key == y then Just x else reverse_lookup key ls'
--}
-
--- | Erroring variant of 'find'.
-find_err :: (t -> Bool) -> [t] -> t
-find_err f = fromMaybe (error "find") . find f
-
--- | Basis of 'find_bounds_scl', indicates if /x/ is to the left or
--- right of the list, and if to the right whether equal or not.
--- 'Right' values will be correct if the list is not ascending,
--- however 'Left' values only make sense for ascending ranges.
---
--- > map (find_bounds_cmp compare [(0,1),(1,2)]) [-1,0,1,2,3]
-find_bounds_cmp :: (t -> s -> Ordering) -> [(t,t)] -> s -> Either ((t,t),Ordering) (t,t)
-find_bounds_cmp f l x =
-    let g (p,q) = f p x /= GT && f q x == GT
-    in case l of
-         [] -> error "find_bounds_cmp: nil"
-         [(p,q)] -> if g (p,q) then Right (p,q) else Left ((p,q),f q x)
-         (p,q):l' -> if f p x == GT
-                     then Left ((p,q),GT)
-                     else if g (p,q) then Right (p,q) else find_bounds_cmp f l' x
-
-decide_nearest_f :: Ord o => Bool -> (p -> o) -> (p,p) -> ((x,x) -> x)
-decide_nearest_f bias_left f (p,q) =
-  case compare (f p) (f q) of
-    LT -> fst
-    EQ -> if bias_left then fst else snd
-    GT -> snd
-
--- | Decide if value is nearer the left or right value of a range, return 'fst' or 'snd'.
---
--- > (decide_nearest True 2 (1,3)) ("left","right") == "left"
-decide_nearest :: (Num o,Ord o) => Bool -> o -> (o,o) -> ((x,x) -> x)
-decide_nearest bias_left x = decide_nearest_f bias_left (abs . (x -))
-
--- | /sel_f/ gets comparison key from /t/.
-find_nearest_by :: (Ord n,Num n) => (t -> n) -> Bool -> [t] -> n -> t
-find_nearest_by sel_f bias_left l x =
-  let cmp_f i j = compare (sel_f i) j
-  in case find_bounds_cmp cmp_f (adj2 1 l) x of
-       Left ((p,_),GT) -> p
-       Left ((_,q),_) -> q
-       Right (p,q) -> (decide_nearest bias_left x (sel_f p,sel_f q)) (p,q)
-
--- | Find the number that is nearest the requested value in an
--- ascending list of numbers.
---
--- > map (find_nearest_err True [0,3.5,4,7]) [-1,1,3,5,7,9] == [0,0,3.5,4,7,7]
-find_nearest_err :: (Num n,Ord n) => Bool -> [n] -> n -> n
-find_nearest_err = find_nearest_by id
-
-find_nearest :: (Num n,Ord n) => Bool -> [n] -> n -> Maybe n
-find_nearest bias_left l x = if null l then Nothing else Just (find_nearest_err bias_left l x)
-
--- | Basis of 'find_bounds'.  There is an option to consider the last
--- element specially, and if equal to the last span is given.
---
--- scl=special-case-last
-find_bounds_scl :: Bool -> (t -> s -> Ordering) -> [(t,t)] -> s -> Maybe (t,t)
-find_bounds_scl scl f l x =
-    case find_bounds_cmp f l x of
-         Right r -> Just r
-         Left (r,EQ) -> if scl then Just r else Nothing
-         _ -> Nothing
-
--- | Find adjacent elements of list that bound element under given comparator.
---
--- > let {f = find_bounds True compare [1..5]
--- >     ;r = [Nothing,Just (1,2),Just (3,4),Just (4,5)]}
--- > in map f [0,1,3.5,5] == r
-find_bounds :: Bool -> (t -> s -> Ordering) -> [t] -> s -> Maybe (t,t)
-find_bounds scl f l = find_bounds_scl scl f (adj2 1 l)
-
--- | Special case of 'dropRight'.
---
--- > map drop_last ["","?","remove"] == ["","","remov"]
-drop_last :: [t] -> [t]
-drop_last l =
-    case l of
-      [] -> []
-      [_] -> []
-      e:l' -> e : drop_last l'
-
--- | Variant of 'drop' from right of list.
---
--- > dropRight 1 [1..9] == [1..8]
-dropRight :: Int -> [a] -> [a]
-dropRight n = reverse . drop n . reverse
-
--- | Variant of 'dropWhile' from right of list.
---
--- > dropWhileRight Data.Char.isDigit "A440" == "A"
-dropWhileRight :: (a -> Bool) -> [a] -> [a]
-dropWhileRight p = reverse . dropWhile p . reverse
-
--- | 'take' from right.
---
--- > take_right 3 "taking" == "ing"
-take_right :: Int -> [a] -> [a]
-take_right n = reverse . take n . reverse
-
--- | 'takeWhile' from right.
---
--- > take_while_right Data.Char.isDigit "A440" == "440"
-take_while_right :: (a -> Bool) -> [a] -> [a]
-take_while_right p = reverse . takeWhile p . reverse
-
--- | Variant of 'take' that allows 'Nothing' to indicate the complete list.
---
--- > maybe_take (Just 5) [1 .. ] == [1 .. 5]
--- > maybe_take Nothing [1 .. 9] == [1 .. 9]
-maybe_take :: Maybe Int -> [a] -> [a]
-maybe_take n l = maybe l (flip take l) n
-
-{- | Take until /f/ is true.  This is not the same as 'not' at
-     'takeWhile' because it keeps the last element. It is an error
-     if the predicate never succeeds.
-
-> take_until (== 'd') "tender" == "tend"
-> takeWhile (not . (== 'd')) "tend" == "ten"
-> take_until (== 'd') "seven" == undefined
--}
-take_until :: (a -> Bool) -> [a] -> [a]
-take_until f l =
-  case l of
-    [] -> error "take_until?"
-    e:l' -> if f e then [e] else e : take_until f l'
-
--- | Apply /f/ at first element, and /g/ at all other elements.
---
--- > at_head negate id [1..5] == [-1,2,3,4,5]
-at_head :: (a -> b) -> (a -> b) -> [a] -> [b]
-at_head f g x =
-    case x of
-      [] -> []
-      e:x' -> f e : map g x'
-
--- | Apply /f/ at all but last element, and /g/ at last element.
---
--- > at_last (* 2) negate [1..4] == [2,4,6,-4]
-at_last :: (a -> b) -> (a -> b) -> [a] -> [b]
-at_last f g x =
-    case x of
-      [] -> []
-      [i] -> [g i]
-      i:x' -> f i : at_last f g x'
-
--- | Separate list into an initial list and perhaps the last element tuple.
---
--- > separate_last' [] == ([],Nothing)
-separate_last' :: [a] -> ([a],Maybe a)
-separate_last' x =
-    case reverse x of
-      [] -> ([],Nothing)
-      e:x' -> (reverse x',Just e)
-
--- | Error on null input.
---
--- > separate_last [1..5] == ([1..4],5)
-separate_last :: [a] -> ([a],a)
-separate_last = fmap (fromMaybe (error "separate_last")) . separate_last'
-
--- | Replace directly repeated elements with 'Nothing'.
---
--- > indicate_repetitions "abba" == [Just 'a',Just 'b',Nothing,Just 'a']
-indicate_repetitions :: Eq a => [a] -> [Maybe a]
-indicate_repetitions =
-    let f l = case l of
-                [] -> []
-                e:l' -> Just e : map (const Nothing) l'
-    in concatMap f . group
-
--- | 'zipWith' of list and it's own tail.
---
--- > zip_with_adj (,) "abcde" == [('a','b'),('b','c'),('c','d'),('d','e')]
-zip_with_adj :: (a -> a -> b) -> [a] -> [b]
-zip_with_adj f xs = zipWith f xs (tail xs)
-
--- | Type-specialised 'zip_with_adj'.
-compare_adjacent_by :: (a -> a -> Ordering) -> [a] -> [Ordering]
-compare_adjacent_by = zip_with_adj
-
--- | 'compare_adjacent_by' of 'compare'.
---
--- > compare_adjacent [0,1,3,2] == [LT,LT,GT]
-compare_adjacent :: Ord a => [a] -> [Ordering]
-compare_adjacent = compare_adjacent_by compare
-
--- | 'Data.List.groupBy' does not make adjacent comparisons, it
--- compares each new element to the start of the group.  This function
--- is the adjacent variant.
---
--- > groupBy (<) [1,2,3,2,4,1,5,9] == [[1,2,3,2,4],[1,5,9]]
--- > adjacent_groupBy (<) [1,2,3,2,4,1,5,9] == [[1,2,3],[2,4],[1,5,9]]
-adjacent_groupBy :: (a -> a -> Bool) -> [a] -> [[a]]
-adjacent_groupBy f p =
-    case p of
-      [] -> []
-      [x] -> [[x]]
-      x:y:p' -> let r = adjacent_groupBy f (y:p')
-                    r0:r' = r
-                in if f x y
-                   then (x:r0) : r'
-                   else [x] : r
-
--- | Reduce sequences of consecutive values to ranges.
---
--- > group_ranges [-1,0,3,4,5,8,9,12] == [(-1,0),(3,5),(8,9),(12,12)]
--- > group_ranges [3,2,3,4,3] == [(3,3),(2,4),(3,3)]
-group_ranges :: (Num t, Eq t) => [t] -> [(t,t)]
-group_ranges =
-    let f l = (head l,last l)
-    in map f . adjacent_groupBy (\p q -> p + 1 == q)
-
--- | 'groupBy' on /structure/ of 'Maybe', ie. all 'Just' compare equal.
---
--- > let r = [[Just 1],[Nothing,Nothing],[Just 4,Just 5]]
--- > in group_just [Just 1,Nothing,Nothing,Just 4,Just 5] == r
-group_just :: [Maybe a] -> [[Maybe a]]
-group_just = group_on isJust
-
--- | Predicate to determine if all elements of the list are '=='.
---
--- > all_equal "aaa" == True
-all_equal :: Eq a => [a] -> Bool
-all_equal l =
-    case l of
-      [] -> True
-      [_] -> True
-      x:xs -> all id (map (== x) xs)
-
--- | Variant using 'nub'.
-all_eq :: Eq n => [n] -> Bool
-all_eq = (== 1) . length . nub
-
--- | 'nubBy' '==' 'on' /f/.
---
--- > nub_on snd (zip "ABCD" "xxyy") == [('A','x'),('C','y')]
-nub_on :: Eq b => (a -> b) -> [a] -> [a]
-nub_on f = nubBy ((==) `on` f)
-
--- | 'group_on' of 'sortOn'.
---
--- > let r = [[('1','a'),('1','c')],[('2','d')],[('3','b'),('3','e')]]
--- > in sort_group_on fst (zip "13123" "abcde") == r
-sort_group_on :: Ord b => (a -> b) -> [a] -> [[a]]
-sort_group_on f = group_on f . sortOn f
-
--- | Maybe cons element onto list.
---
--- > Nothing `mcons` "something" == "something"
--- > Just 's' `mcons` "omething" == "something"
-mcons :: Maybe a -> [a] -> [a]
-mcons e l = maybe l (:l) e
-
--- | Cons onto end of list.
---
--- > snoc 4 [1,2,3] == [1,2,3,4]
-snoc :: a -> [a] -> [a]
-snoc e 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
-
--- | 'compare' 'on' of 'two_stage_compare'
-two_stage_compare_on :: (Ord i, Ord j) => (t -> i) -> (t -> j) -> t -> t -> Ordering
-two_stage_compare_on f g = two_stage_compare (compare `on` f) (compare `on` g)
-
--- | Sequence of comparison functions, continue comparing until not EQ.
---
--- > compare (1,0) (0,1) == GT
--- > n_stage_compare [compare `on` snd,compare `on` fst] (1,0) (0,1) == LT
-n_stage_compare :: [Compare_F a] -> Compare_F a
-n_stage_compare l p q =
-    case l of
-      [] -> EQ
-      f:l' -> case f p q of
-                EQ -> n_stage_compare l' p q
-                r -> r
-
--- | 'compare' 'on' of 'two_stage_compare'
-n_stage_compare_on :: Ord i => [t -> i] -> t -> t -> Ordering
-n_stage_compare_on l = n_stage_compare (map (compare `on`) l)
-
--- | Sort sequence /a/ based on ordering of sequence /b/.
---
--- > sort_to "abc" [1,3,2] == "acb"
--- > sort_to "adbce" [1,4,2,3,5] == "abcde"
-sort_to :: Ord i => [e] -> [i] -> [e]
-sort_to e = map fst . sortOn snd . zip e
-
--- | 'flip' of 'sort_to'.
---
--- > sort_to_rev [1,4,2,3,5] "adbce" == "abcde"
-sort_to_rev :: Ord i => [i] -> [e] -> [e]
-sort_to_rev = flip sort_to
-
--- | 'sortBy' of 'two_stage_compare'.
-sort_by_two_stage :: Compare_F a -> Compare_F a -> [a] -> [a]
-sort_by_two_stage f g = sortBy (two_stage_compare f g)
-
--- | 'sortBy' of 'n_stage_compare'.
-sort_by_n_stage :: [Compare_F a] -> [a] -> [a]
-sort_by_n_stage f = sortBy (n_stage_compare f)
-
--- | 'sortBy' of 'two_stage_compare_on'.
-sort_by_two_stage_on :: (Ord b,Ord c) => (a -> b) -> (a -> c) -> [a] -> [a]
-sort_by_two_stage_on f g = sortBy (two_stage_compare_on f g)
-
--- | 'sortBy' of 'n_stage_compare_on'.
-sort_by_n_stage_on :: Ord b => [a -> b] -> [a] -> [a]
-sort_by_n_stage_on f = sortBy (n_stage_compare_on f)
-
--- | Given a comparison function, merge two ascending lists.
---
--- > mergeBy compare [1,3,5] [2,4] == [1..5]
-merge_by :: Compare_F a -> [a] -> [a] -> [a]
-merge_by = O.mergeBy
-
--- | 'merge_by' 'compare' 'on'.
-merge_on :: Ord x => (a -> x) -> [a] -> [a] -> [a]
-merge_on f = merge_by (compare `on` f)
-
--- | 'O.mergeBy' of 'two_stage_compare'.
-merge_by_two_stage :: Ord b => (a -> b) -> Compare_F c -> (a -> c) -> [a] -> [a] -> [a]
-merge_by_two_stage f cmp g = O.mergeBy (two_stage_compare (compare `on` f) (cmp `on` g))
-
--- | 'mergeBy' 'compare'.
-merge :: Ord a => [a] -> [a] -> [a]
-merge = O.merge
-
--- | Merge list of sorted lists given comparison function.  Note that
--- this is not equal to 'O.mergeAll'.
-merge_set_by :: (a -> a -> Ordering) -> [[a]] -> [a]
-merge_set_by f = foldr (merge_by f) []
-
--- | 'merge_set_by' of 'compare'.
---
--- > merge_set [[1,3,5,7,9],[2,4,6,8],[10]] == [1..10]
-merge_set :: Ord a => [[a]] -> [a]
-merge_set = merge_set_by compare
-
-{-| 'merge_by' variant that joins (resolves) equal elements.
-
-> let {left p _ = p
->     ;right _ q = q
->     ;cmp = compare `on` fst
->     ;p = zip [1,3,5] "abc"
->     ;q = zip [1,2,3] "ABC"
->     ;left_r = [(1,'a'),(2,'B'),(3,'b'),(5,'c')]
->     ;right_r = [(1,'A'),(2,'B'),(3,'C'),(5,'c')]}
-> in merge_by_resolve left cmp p q == left_r &&
->    merge_by_resolve right cmp p q == right_r
-
-> merge_by_resolve (\x _ -> x) (compare `on` fst) [(0,'A'),(1,'B'),(4,'E')] (zip [1..] "bcd")
-
--}
-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
-
--- | Merge two sorted (ascending) sequences.
---   Where elements compare equal, select element from left input.
---
--- > asc_seq_left_biased_merge_by (compare `on` fst) [(0,'A'),(1,'B'),(4,'E')] (zip [1..] "bcd")
-asc_seq_left_biased_merge_by :: (a -> a -> Ordering) -> [a] -> [a] -> [a]
-asc_seq_left_biased_merge_by = merge_by_resolve (\x _ -> x)
-
--- | Find the first two adjacent elements for which /f/ is True.
---
--- > find_adj (>) [1,2,3,3,2,1] == Just (3,2)
--- > find_adj (>=) [1,2,3,3,2,1] == Just (3,3)
-find_adj :: (a -> a -> Bool) -> [a] -> Maybe (a,a)
-find_adj f xs =
-    case xs of
-      p:q:xs' -> if f p q then Just (p,q) else find_adj f (q:xs')
-      _ -> Nothing
-
--- | 'find_adj' of '>='
---
--- > filter is_ascending (words "A AA AB ABB ABC ABA") == words "A AB ABC"
-is_ascending :: Ord a => [a] -> Bool
-is_ascending = isNothing . find_adj (>=)
-
--- | 'find_adj' of '>'
---
--- > filter is_non_descending (words "A AA AB ABB ABC ABA") == ["A","AA","AB","ABB","ABC"]
-is_non_descending :: Ord a => [a] -> Bool
-is_non_descending = isNothing . find_adj (>)
-
--- | Variant of `elem` that operates on a sorted list, halting.
---   This is 'O.member'.
---
--- > 16 `elem_ordered` [1,3 ..] == False
--- > 16 `elem` [1,3 ..] == undefined
-elem_ordered :: Ord t => t -> [t] -> Bool
-elem_ordered = O.member
-
--- | Variant of `elemIndex` that operates on a sorted list, halting.
---
--- > 16 `elemIndex_ordered` [1,3 ..] == Nothing
--- > 16 `elemIndex_ordered` [0,1,4,9,16,25,36,49,64,81,100] == Just 4
-elemIndex_ordered :: Ord t => t -> [t] -> Maybe Int
-elemIndex_ordered e =
-    let recur k l =
-            case l of
-              [] -> Nothing
-              x:l' -> if e == x
-                      then Just k
-                      else if x > e
-                           then Nothing
-                           else recur (k + 1) l'
-    in recur 0
-
--- | 'zipWith' variant that extends shorter side using given value.
-zip_with_ext :: t -> u -> (t -> u -> v) -> [t] -> [u] -> [v]
-zip_with_ext i j f p q =
-  case (p,q) of
-    ([],_) -> zipWith f (repeat i) q
-    (_,[]) -> zipWith f p (repeat j)
-    (x:p',y:q') -> f x y : zip_with_ext i j f p' q'
-
-{- | 'zip_with_ext' of ','
-
-> let f = zip_ext 'i' 'j'
-> f "" "" == []
-> f "p" "" == zip "p" "j"
-> f "" "q" == zip "i" "q"
-> f "pp" "q" == zip "pp" "qj"
-> f "p" "qq" == zip "pi" "qq"
--}
-zip_ext :: t -> u -> [t] -> [u] -> [(t,u)]
-zip_ext i j = zip_with_ext i j (,)
-
--- | Keep right variant of 'zipWith', where unused rhs values are returned.
---
--- > zip_with_kr (,) [1..3] ['a'..'e'] == ([(1,'a'),(2,'b'),(3,'c')],"de")
-zip_with_kr :: (a -> b -> c) -> [a] -> [b] -> ([c],[b])
-zip_with_kr f =
-    let go r p q =
-            case (p,q) of
-              (i:p',j:q') -> go (f i j : r) p' q'
-              _ -> (reverse r,q)
-    in go []
-
--- | A 'zipWith' variant that always consumes an element from the left
--- hand side (lhs), but only consumes an element from the right hand
--- side (rhs) if the zip function is 'Right' and not if 'Left'.
--- There's also a secondary function to continue if the rhs ends
--- before the lhs.
-zip_with_perhaps_rhs :: (a -> b -> Either c c) -> (a -> c) -> [a] -> [b] -> [c]
-zip_with_perhaps_rhs f g lhs rhs =
-    case (lhs,rhs) of
-      ([],_) -> []
-      (_,[]) -> map g lhs
-      (p:lhs',q:rhs') -> case f p q of
-                           Left r -> r : zip_with_perhaps_rhs f g lhs' rhs
-                           Right r -> r : zip_with_perhaps_rhs f g lhs' rhs'
-
--- | Fill gaps in a sorted association list, range is inclusive at both ends.
---
--- > let r = [(1,'a'),(2,'x'),(3,'x'),(4,'x'),(5,'b'),(6,'x'),(7,'c'),(8,'x'),(9,'x')]
--- > in fill_gaps_ascending' 'x' (1,9) (zip [1,5,7] "abc") == r
-fill_gaps_ascending :: (Enum n, Ord n) => t -> (n,n) -> [(n,t)] -> [(n,t)]
-fill_gaps_ascending def_e (l,r) =
-    let f i (j,e) = if j > i then Left (i,def_e) else Right (j,e)
-        g i = (i,def_e)
-    in zip_with_perhaps_rhs f g [l .. r]
-
--- | Direct definition.
-fill_gaps_ascending' :: (Num n,Enum n, Ord n) => t -> (n,n) -> [(n,t)] -> [(n,t)]
-fill_gaps_ascending' def (l,r) =
-    let recur n x =
-            if n > r
-            then []
-            else case x of
-                   [] -> zip [n .. r] (repeat def)
-                   (m,e):x' -> if n < m
-                               then (n,def) : recur (n + 1) x
-                               else (m,e) : recur (n + 1) x'
-    in recur l
-
--- | Variant with default value for empty input list case.
-minimumBy_or :: t -> (t -> t -> Ordering) -> [t] -> t
-minimumBy_or p f q = if null q then p else minimumBy f q
-
--- | 'minimum' and 'maximum' in one pass.
---
--- > minmax "minmax" == ('a','x')
-minmax :: Ord t => [t] -> (t,t)
-minmax inp =
-    case inp of
-      [] -> error "minmax: null"
-      x:xs -> let mm p (l,r) = (min p l,max p r) in foldr mm (x,x) xs
-
--- | Append /k/ to the right of /l/ until result has /n/ places.
---   Truncates long input lists.
---
--- > map (pad_right '0' 2 . return) ['0' .. '9']
--- > pad_right '0' 12 "1101" == "110100000000"
--- > map (pad_right ' '3) ["S","E-L"] == ["S  ","E-L"]
--- > pad_right '!' 3 "truncate" == "tru"
-pad_right :: a -> Int -> [a] -> [a]
-pad_right k n l = take n (l ++ repeat k)
-
--- | Variant that errors if the input list has more than /n/ places.
---
--- > map (pad_right_err '!' 3) ["x","xy","xyz","xyz!"]
-pad_right_err :: t -> Int -> [t] -> [t]
-pad_right_err k n l = if length l > n then error "pad_right_err?" else pad_right k n l
-
--- > pad_right_no_truncate '!' 3 "truncate" == "truncate"
-pad_right_no_truncate :: a -> Int -> [a] -> [a]
-pad_right_no_truncate k n l = if length l > n then l else pad_right k n l
-
--- | Append /k/ to the left of /l/ until result has /n/ places.
---
--- > map (pad_left '0' 2 . return) ['0' .. '9']
-pad_left :: a -> Int -> [a] -> [a]
-pad_left k n l = replicate (n - length l) k ++ l
-
--- * Embedding
-
--- | Locate first (leftmost) embedding of /q/ in /p/.
--- Return partial indices for failure at 'Left'.
---
--- > embedding ("embedding","ming") == Right [1,6,7,8]
--- > embedding ("embedding","mind") == Left [1,6,7]
-embedding :: Eq t => ([t],[t]) -> Either [Int] [Int]
-embedding =
-    let recur n r (p,q) =
-            case (p,q) of
-              (_,[]) -> Right (reverse r)
-              ([],_) -> Left (reverse r)
-              (x:p',y:q') ->
-                  let n' = n + 1
-                      r' = if x == y then n : r else r
-                  in recur n' r' (p',if x == y then q' else q)
-    in recur 0 []
-
-embedding_err :: Eq t => ([t],[t]) -> [Int]
-embedding_err = either (error "embedding_err") id . embedding
-
--- | Does /q/ occur in sequence, though not necessarily adjacently, in /p/.
---
--- > is_embedding [1 .. 9] [1,3,7] == True
--- > is_embedding "embedding" "ming" == True
--- > is_embedding "embedding" "mind" == False
-is_embedding :: Eq t => [t] -> [t] -> Bool
-is_embedding p q = isRight (embedding (p,q))
-
-all_embeddings_m :: (Eq t,L.MonadLogic m) => [t] -> [t] -> m [Int]
-all_embeddings_m p q =
-    let q_n = length q
-        recur p' q' n k = -- n = length k
-            if n == q_n
-            then return (reverse k)
-            else do (m,c) <- L.msum (map return p')
-                    let k0:_ = k
-                        c':_ = q'
-                    L.guard (c == c' && (null k || m > k0))
-                    let _:p'' = p'
-                        _:q'' = q'
-                    recur p'' q'' (n + 1) (m : k)
-    in recur (zip [0..] p) q 0 []
-
--- | Enumerate indices for all embeddings of /q/ in /p/.
---
--- > all_embeddings "all_embeddings" "leg" == [[1,4,12],[1,7,12],[2,4,12],[2,7,12]]
-all_embeddings :: Eq t => [t] -> [t] -> [[Int]]
-all_embeddings p = L.observeAll . all_embeddings_m p
-
--- * Un-list
-
--- | Unpack one element list.
-unlist1 :: [t] -> Maybe t
-unlist1 l =
-    case l of
-      [e] -> Just e
-      _ -> Nothing
-
--- | Erroring variant.
-unlist1_err :: [t] -> t
-unlist1_err = fromMaybe (error "unlist1") . unlist1
-
--- * Traversable
-
--- | Replace elements at 'Traversable' with result of joining with elements from list.
---
--- > let t = Node 0 [Node 1 [Node 2 [],Node 3 []],Node 4 []]
--- > putStrLn $ drawTree (fmap show t)
--- > let (_,u) = adopt_shape (\_ x -> x) "abcde" t
--- > putStrLn $ drawTree (fmap return u)
-adopt_shape :: Traversable t => (a -> b -> c) -> [b] -> t a -> ([b],t c)
-adopt_shape jn l =
-    let f (i:j) k = (j,jn k i)
-        f [] _ = error "adopt_shape: rhs ends"
-    in mapAccumL f l
-
--- | Two-level variant of 'adopt_shape'.
---
--- > adopt_shape_2 (,) [0..4] (words "a bc d") == ([4],[[('a',0)],[('b',1),('c',2)],[('d',3)]])
-adopt_shape_2 :: (Traversable t,Traversable u) => (a -> b -> c) -> [b] -> t (u a) -> ([b],t (u c))
-adopt_shape_2 jn l = mapAccumL (adopt_shape jn) l
-
--- | Two-level variant of 'zip' [1..]
---
--- > list_number_2 ["number","list","2"]
-list_number_2 :: [[x]] -> [[(Int,x)]]
-list_number_2 = snd . adopt_shape_2 (flip (,)) [1..]
-
-{- | Variant of 'adopt_shape' that considers only 'Just' elements at 'Traversable'.
-
-> let s = "a(b(cd)ef)ghi"
-> let t = group_tree (begin_end_cmp_eq '(' ')') s
-> adopt_shape_m (,) [1..13] t
--}
-adopt_shape_m :: Traversable t => (a -> b-> c) -> [b] -> t (Maybe a) -> ([b],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 mapAccumL f l
-
--- * Tree
-
-{- | Given an 'Ordering' predicate where 'LT' opens a group, 'GT'
-closes a group, and 'EQ' continues current group, construct tree
-from list.
-
-> let l = "a {b {c d} e f} g h i"
-> let t = group_tree ((==) '{',(==) '}') l
-> catMaybes (flatten t) == l
-
-> let {d = putStrLn . drawTree . fmap show}
-> in d (group_tree ((==) '(',(==) ')') "a(b(cd)ef)ghi")
-
--}
-group_tree :: (a -> Bool,a -> Bool) -> [a] -> Tree.Tree (Maybe a)
-group_tree (open_f,close_f) =
-    let unit e = Tree.Node (Just e) []
-        nil = Tree.Node Nothing []
-        insert_e (Tree.Node t l) e = Tree.Node t (e:l)
-        reverse_n (Tree.Node t l) = Tree.Node t (reverse l)
-        do_push (r,z) e =
-            case z of
-              h:z' -> (r,insert_e h (unit e) : z')
-              [] -> (unit e : r,[])
-        do_open (r,z) = (r,nil:z)
-        do_close (r,z) =
-            case z of
-              h0:h1:z' -> (r,insert_e h1 (reverse_n h0) : z')
-              h:z' -> (reverse_n h : r,z')
-              [] -> (r,z)
-        go st x =
-            case x of
-              [] -> Tree.Node Nothing (reverse (fst st))
-              e:x' -> if open_f e
-                      then go (do_push (do_open st) e) x'
-                      else if close_f e
-                           then go (do_close (do_push st e)) x'
-                           else go (do_push st e) x'
-    in go ([],[])
-
--- * Indexing
-
--- | Remove element at index.
---
--- > remove_ix 5 "remove" == "remov"
--- > remove_ix 5 "short" == undefined
-remove_ix :: Int -> [a] -> [a]
-remove_ix k l = let (p,q) = splitAt k l in p ++ tail q
-
--- | Select or remove elements at set of indices.
-operate_ixs :: Bool -> [Int] -> [a] -> [a]
-operate_ixs mode k =
-    let sel = if mode then notElem else elem
-        f (n,e) = if n `sel` k then Nothing else Just e
-    in mapMaybe f . zip [0..]
-
--- | Select elements at set of indices.
---
--- > select_ixs [1,3] "select" == "ee"
-select_ixs :: [Int] -> [a] -> [a]
-select_ixs = operate_ixs True
-
--- | Remove elements at set of indices.
---
--- > remove_ixs [1,3,5] "remove" == "rmv"
-remove_ixs :: [Int] -> [a] -> [a]
-remove_ixs = operate_ixs False
-
--- | Replace element at /i/ in /p/ by application of /f/.
---
--- > replace_ix negate 1 [1..3] == [1,-2,3]
-replace_ix :: (a -> a) -> Int -> [a] -> [a]
-replace_ix f i p =
-    let (q,r:s) = splitAt i p
-    in q ++ (f r : s)
-
--- | List equality, ignoring indicated indices.
---
--- > list_eq_ignoring_indices [3,5] "abcdefg" "abc.e.g" == True
-list_eq_ignoring_indices :: (Eq t,Integral i) => [i] -> [t] -> [t] -> Bool
-list_eq_ignoring_indices x =
-  let f n p q =
-        case (p,q) of
-          ([],[]) -> True
-          ([],_) -> False
-          (_,[]) -> False
-          (p1:p',q1:q') -> if n `elem` x || p1 == q1
-                           then f (n + 1) p' q'
-                           else False
-  in f 0
-
--- | Edit list to have /v/ at indices /k/.
---   Replacement assoc-list must be ascending.
---   All replacements must be in range.
---
--- > list_set_indices [(2,'C'),(4,'E')] "abcdefg" == "abCdEfg"
--- > list_set_indices [] "abcdefg" == "abcdefg"
--- > list_set_indices [(9,'I')] "abcdefg" == undefined
-list_set_indices :: (Eq ix, Num ix) => [(ix,t)] -> [t] -> [t]
-list_set_indices =
-  let f n r l =
-        case (r,l) of
-          ([],_) -> l
-          (_,[]) -> error "list_set_indices: out of range?"
-          ((k,v):r',l0:l') -> if n == k
-                              then v : f (n + 1) r' l'
-                              else l0 : f (n + 1) r l'
-  in f 0
-
--- | Variant of 'list_set_indices' with one replacement.
-list_set_ix :: (Eq t, Num t) => t -> a -> [a] -> [a]
-list_set_ix k v = list_set_indices [(k,v)]
-
--- | Cyclic indexing function.
---
--- > map (at_cyclic "cycle") [0..9] == "cyclecycle"
-at_cyclic :: [a] -> Int -> a
-at_cyclic l n =
-    let m = Map.fromList (zip [0..] l)
-        k = Map.size m
-        n' = n `mod` k
-    in fromMaybe (error "cyc_at") (Map.lookup n' m)
-
diff --git a/Music/Theory/List/Logic.hs b/Music/Theory/List/Logic.hs
new file mode 100644
--- /dev/null
+++ b/Music/Theory/List/Logic.hs
@@ -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
+
diff --git a/Music/Theory/Map.hs b/Music/Theory/Map.hs
deleted file mode 100644
--- a/Music/Theory/Map.hs
+++ /dev/null
@@ -1,17 +0,0 @@
--- | Map functions.
-module Music.Theory.Map where
-
-import qualified Data.Map as M {- containers -}
-import Data.Maybe {- base -}
-
--- | Erroring 'M.lookup'.
-map_lookup_err :: Ord k => k -> M.Map k c -> c
-map_lookup_err k = fromMaybe (error "M.lookup") . M.lookup k
-
--- | 'flip' of 'M.lookup'.
-map_ix :: Ord k => M.Map k c -> k -> Maybe c
-map_ix = flip M.lookup
-
--- | 'flip' of 'map_lookup_err'.
-map_ix_err :: Ord k => M.Map k c -> k -> c
-map_ix_err = flip map_lookup_err
diff --git a/Music/Theory/Math.hs b/Music/Theory/Math.hs
deleted file mode 100644
--- a/Music/Theory/Math.hs
+++ /dev/null
@@ -1,280 +0,0 @@
--- | Math functions.
-module Music.Theory.Math where
-
-import Data.List {- base -}
-import Data.Maybe {- base -}
-import Data.Ratio {- base -}
-
-import qualified Music.Theory.Math.Convert as T
-
--- | 'mod' 5.
-mod5 :: Integral i => i -> i
-mod5 n = n `mod` 5
-
--- | 'mod' 7.
-mod7 :: Integral i => i -> i
-mod7 n = n `mod` 7
-
--- | 'mod' 12.
-mod12 :: Integral i => i -> i
-mod12 n = n `mod` 12
-
--- | 'mod' 16.
-mod16 :: Integral i => i -> i
-mod16 n = n `mod` 16
-
--- | <http://reference.wolfram.com/mathematica/ref/FractionalPart.html>
---
--- > integral_and_fractional_parts 1.5 == (1,0.5)
-integral_and_fractional_parts :: (Integral i, RealFrac t) => t -> (i,t)
-integral_and_fractional_parts n =
-    if n >= 0
-    then let n' = floor n in (n',n - fromIntegral n')
-    else let n' = ceiling n in (n',n - fromIntegral n')
-
--- | Type specialised.
-integer_and_fractional_parts :: RealFrac t => t -> (Integer,t)
-integer_and_fractional_parts = integral_and_fractional_parts
-
--- | <http://reference.wolfram.com/mathematica/ref/FractionalPart.html>
---
--- > import Sound.SC3.Plot {- hsc3-plot -}
--- > plot_p1_ln [map fractional_part [-2.0,-1.99 .. 2.0]]
-fractional_part :: RealFrac a => a -> a
-fractional_part = snd . integer_and_fractional_parts
-
--- | 'floor' of 'T.real_to_double'.
-real_floor :: (Real r,Integral i)  => r -> i
-real_floor = floor . T.real_to_double
-
--- | Type specialised 'real_floor'.
-real_floor_int :: Real r => r -> Int
-real_floor_int = real_floor
-
--- | 'round' of 'T.real_to_double'.
-real_round :: (Real r,Integral i)  => r -> i
-real_round = round . T.real_to_double
-
--- | Type specialised 'real_round'.
-real_round_int :: Real r => r -> Int
-real_round_int = real_round
-
--- | Type-specialised 'fromIntegral'
-from_integral_to_int :: Integral i => i -> Int
-from_integral_to_int = fromIntegral
-
--- | Type-specialised 'id'
-int_id :: Int -> Int
-int_id = id
-
--- | Is /r/ zero to /k/ decimal places.
---
--- > map (flip zero_to_precision 0.00009) [4,5] == [True,False]
--- > map (zero_to_precision 4) [0.00009,1.00009] == [True,False]
-zero_to_precision :: Real r => Int -> r -> Bool
-zero_to_precision k r = real_floor_int (r * (fromIntegral ((10::Int) ^ k))) == 0
-
--- | Is /r/ whole to /k/ decimal places.
---
--- > map (flip whole_to_precision 1.00009) [4,5] == [True,False]
-whole_to_precision :: Real r => Int -> r -> Bool
-whole_to_precision k = zero_to_precision k . fractional_part . T.real_to_double
-
--- | <http://reference.wolfram.com/mathematica/ref/SawtoothWave.html>
---
--- > plot_p1_ln [map sawtooth_wave [-2.0,-1.99 .. 2.0]]
-sawtooth_wave :: RealFrac a => a -> a
-sawtooth_wave n = n - floor_f n
-
--- | Predicate that is true if @n/d@ can be simplified, ie. where
--- 'gcd' of @n@ and @d@ is not @1@.
---
--- > map rational_simplifies [(2,3),(4,6),(5,7)] == [False,True,False]
-rational_simplifies :: Integral a => (a,a) -> Bool
-rational_simplifies (n,d) = gcd n d /= 1
-
--- | 'numerator' and 'denominator' of rational.
-rational_nd :: Ratio t -> (t,t)
-rational_nd r = (numerator r,denominator r)
-
--- | Rational as a whole number, or 'Nothing'.
-rational_whole :: Integral a => Ratio a -> Maybe a
-rational_whole r = if denominator r == 1 then Just (numerator r) else Nothing
-
--- | Erroring variant.
-rational_whole_err :: Integral a => Ratio a -> a
-rational_whole_err = fromMaybe (error "rational_whole") . rational_whole
-
--- | Sum of numerator & denominator.
-ratio_nd_sum :: Num a => Ratio a -> a
-ratio_nd_sum r = numerator r + denominator r
-
--- | Is /n/ a whole (integral) value.
---
--- > map real_is_whole [-1.0,-0.5,0.0,0.5,1.0] == [True,False,True,False,True]
-real_is_whole :: Real n => n -> Bool
-real_is_whole = (== 1) . denominator . toRational
-
--- | 'fromInteger' . 'floor'.
-floor_f :: (RealFrac a, Num b) => a -> b
-floor_f = fromInteger . floor
-
--- | Round /b/ to nearest multiple of /a/.
---
--- > map (round_to 0.25) [0,0.1 .. 1] == [0.0,0.0,0.25,0.25,0.5,0.5,0.5,0.75,0.75,1.0,1.0]
--- > map (round_to 25) [0,10 .. 100] == [0,0,25,25,50,50,50,75,75,100,100]
-round_to :: RealFrac n => n -> n -> n
-round_to a b = if a == 0 then b else floor_f ((b / a) + 0.5) * a
-
--- | Variant of 'recip' that checks input for zero.
---
--- > map recip [1,1/2,0,-1]
--- > map recip_m [1,1/2,0,-1] == [Just 1,Just 2,Nothing,Just (-1)]
-recip_m :: (Eq a, Fractional a) => a -> Maybe a
-recip_m x = if x == 0 then Nothing else Just (recip x)
-
--- * One-indexed
-
--- | One-indexed 'mod' function.
---
--- > map (`oi_mod` 5) [1..10] == [1,2,3,4,5,1,2,3,4,5]
-oi_mod :: Integral a => a -> a -> a
-oi_mod n m = ((n - 1) `mod` m) + 1
-
--- | One-indexed 'divMod' function.
---
--- > map (`oi_divMod` 5) [1,3 .. 9] == [(0,1),(0,3),(0,5),(1,2),(1,4)]
-oi_divMod :: Integral t => t -> t -> (t, t)
-oi_divMod n m = let (i,j) = (n - 1) `divMod` m in (i,j + 1)
-
--- * I = integral
-
--- | Integral square root function.
---
--- > map i_square_root [0,1,4,9,16,25,36,49,64,81,100] == [0 .. 10]
--- > map i_square_root [4 .. 16] == [2,2,2,2,2,3,3,3,3,3,3,3,4]
-i_square_root :: Integral t => t -> t
-i_square_root n =
-    let babylon a =
-            let b  = quot (a + quot n a) 2
-            in if a > b then babylon b else a
-    in case compare n 0 of
-         GT -> babylon n
-         EQ -> 0
-         _ -> error "i_square_root: negative?"
-
--- * Interval
-
--- | (0,1) = {x | 0 < x < 1}
-in_open_interval :: Ord a => (a, a) -> a -> Bool
-in_open_interval (p,q) n = p < n && n < q
-
--- | [0,1] = {x | 0 ≤ x ≤ 1}
-in_closed_interval :: Ord a => (a, a) -> a -> Bool
-in_closed_interval (p,q) n = p <= n && n <= q
-
--- | (p,q] (0,1] = {x | 0 < x ≤ 1}
-in_left_half_open_interval :: Ord a => (a, a) -> a -> Bool
-in_left_half_open_interval (p,q) n = p < n && n <= q
-
--- | [p,q) [0,1) = {x | 0 ≤ x < 1}
-in_right_half_open_interval :: Ord a => (a, a) -> a -> Bool
-in_right_half_open_interval (p,q) n = p <= n && n < q
-
--- | Calculate /n/th root of /x/.
---
--- > 12 `nth_root` 2 == 1.0594630943592953
-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)
-        eq = uncurry (==)
-    in fst (until eq f (x, x/n))
-
--- | Arithmetic mean (average) of a list.
---
--- > map arithmetic_mean [[-3..3],[0..5],[1..5],[3,5,7],[7,7],[3,9,10,11,12]] == [0,2.5,3,5,7,9]
-arithmetic_mean :: Fractional a => [a] -> a
-arithmetic_mean x = sum x / fromIntegral (length x)
-
--- | Numerically stable mean
---
--- > map ns_mean [[-3..3],[0..5],[1..5],[3,5,7],[7,7],[3,9,10,11,12]] == [0,2.5,3,5,7,9]
-ns_mean :: Floating a => [a] -> a
-ns_mean =
-    let f (m,n) x = (m + (x - m) / (n + 1),n + 1)
-    in fst . foldl' f (0,0)
-
--- | Square of /n/.
---
--- > square 5 == 25
-square :: Num a => a -> a
-square n = n * n
-
--- | The totient function phi(n), also called Euler's totient function.
---
--- > import Sound.SC3.Plot {- hsc3-plot -}
--- > plot_p1_stp [map totient [1::Int .. 100]]
-totient :: Integral i => i -> i
-totient n = genericLength (filter (==1) (map (gcd n) [1..n]))
-
-{- | The /n/-th order Farey sequence.
-
-> farey 1 == [0,                                                                                    1]
-> farey 2 == [0,                                        1/2,                                        1]
-> farey 3 == [0,                        1/3,            1/2,            2/3,                        1]
-> farey 4 == [0,                1/4,    1/3,            1/2,            2/3,    3/4,                1]
-> farey 5 == [0,            1/5,1/4,    1/3,    2/5,    1/2,    3/5,    2/3,    3/4,4/5,            1]
-> farey 6 == [0,        1/6,1/5,1/4,    1/3,    2/5,    1/2,    3/5,    2/3,    3/4,4/5,5/6,        1]
-> farey 7 == [0,    1/7,1/6,1/5,1/4,2/7,1/3,    2/5,3/7,1/2,4/7,3/5,    2/3,5/7,3/4,4/5,5/6,6/7,    1]
-> farey 8 == [0,1/8,1/7,1/6,1/5,1/4,2/7,1/3,3/8,2/5,3/7,1/2,4/7,3/5,5/8,2/3,5/7,3/4,4/5,5/6,6/7,7/8,1]
--}
-farey :: Integral i => i -> [Ratio i]
-farey n =
-  let step (a,b,c,d) =
-        if c > n
-        then Nothing
-        else let k = (n + b) `quot` d in Just (c % d, (c,d,k * c - a,k * d - b))
-  in 0 : unfoldr step (0,1,1,n)
-
--- | The length of the /n/-th order Farey sequence.
---
--- > map farey_length [1 .. 12] == [2,3,5,7,11,13,19,23,29,33,43,47]
--- > map (length . farey) [1 .. 12] == map farey_length [1 .. 12]
-farey_length :: Integral i => i -> i
-farey_length n = if n == 0 then 1 else farey_length (n - 1) + totient n
-
--- | Function to generate the Stern-Brocot tree from an initial row.
---   '%' normalises so 1/0 cannot be written as a 'Rational', hence (n,d).
-stern_brocot_tree_f :: Num n => [(n,n)] -> [[(n,n)]]
-stern_brocot_tree_f =
-   let med_f (n1,d1) (n2,d2) = (n1 + n2,d1 + d2)
-       f x = concat (transpose [x, zipWith med_f x (tail x)])
-   in iterate f
-
-{- | The Stern-Brocot tree from (0/1,1/0).
-
-> let t = stern_brocot_tree
-> t !! 0 == [(0,1),(1,0)]
-> t !! 1 == [(0,1),(1,1),(1,0)]
-> t !! 2 == [(0,1),(1,2),(1,1),(2,1),(1,0)]
-> t !! 3 == [(0,1),(1,3),(1,2),(2,3),(1,1),(3,2),(2,1),(3,1),(1,0)]
-
-> map length (take 12 stern_brocot_tree) == [2,3,5,9,17,33,65,129,257,513,1025,2049] -- A000051
--}
-stern_brocot_tree :: Num n => [[(n,n)]]
-stern_brocot_tree = stern_brocot_tree_f [(0,1),(1,0)]
-
--- | Left-hand (rational) side of the the Stern-Brocot tree, ie, from (0/1,1/1).
-stern_brocot_tree_lhs :: Num n => [[(n,n)]]
-stern_brocot_tree_lhs = stern_brocot_tree_f [(0,1),(1,1)]
-
-{- | 'stern_brocot_tree_f' as 'Ratio's, for finite subsets.
-
-> let t = stern_brocot_tree_f_r [0,1]
-> t !! 1 == [0,1/2,1]
-> t !! 2 == [0,1/3,1/2,2/3,1]
-> t !! 3 == [0,1/4,1/3,2/5,1/2,3/5,2/3,3/4,1]
-> t !! 4 == [0,1/5,1/4,2/7,1/3,3/8,2/5,3/7,1/2,4/7,3/5,5/8,2/3,5/7,3/4,4/5,1]
--}
-stern_brocot_tree_f_r :: Integral n => [Ratio n] -> [[Ratio n]]
-stern_brocot_tree_f_r = map (map (uncurry (%))) . stern_brocot_tree_f . map rational_nd
diff --git a/Music/Theory/Math/Convert.hs b/Music/Theory/Math/Convert.hs
deleted file mode 100644
--- a/Music/Theory/Math/Convert.hs
+++ /dev/null
@@ -1,1125 +0,0 @@
-{- | Specialised type conversions, see mk/mk-convert.hs
-
-> map int_to_word8 [-1,0,255,256] == [255,0,255,0]
-> map int_to_word8_maybe [-1,0,255,256] == [Nothing,Just 0,Just 255,Nothing]
-
-> map integer_to_int64_maybe [-2 ^ 63 - 1,2 ^ 63] == [Nothing,Nothing]
-> map integer_to_word64_maybe [2 ^ 64 - 1,2 ^ 64] == [Just 18446744073709551615,Nothing]
-
-> map int16_to_float [-1,0,1] == [-1,0,1]
-
--}
-module Music.Theory.Math.Convert where
-
-import Data.Int {- base -}
-import Data.Word {- base -}
-
--- * Numerical conversions
-
--- | Type specialised 'realToFrac'
-real_to_float :: Real t => t -> Float
-real_to_float = realToFrac
-
--- | Type specialised 'realToFrac'
---
--- > let n = sqrt (-1) in (n,real_to_double n)
-real_to_double :: Real t => t -> Double
-real_to_double = realToFrac
-
--- | Type specialised 'realToFrac'
-double_to_float :: Double -> Float
-double_to_float = realToFrac
-
--- | Type specialised 'realToFrac'
-float_to_double :: Float -> Double
-float_to_double = realToFrac
-
--- AUTOGEN (see mk/mk-convert.hs)
-
--- | Type specialised 'fromIntegral'
-word8_to_word16 :: Word8 -> Word16
-word8_to_word16 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-word8_to_word32 :: Word8 -> Word32
-word8_to_word32 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-word8_to_word64 :: Word8 -> Word64
-word8_to_word64 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-word8_to_int8 :: Word8 -> Int8
-word8_to_int8 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-word8_to_int16 :: Word8 -> Int16
-word8_to_int16 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-word8_to_int32 :: Word8 -> Int32
-word8_to_int32 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-word8_to_int64 :: Word8 -> Int64
-word8_to_int64 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-word8_to_int :: Word8 -> Int
-word8_to_int = fromIntegral
-
--- | Type specialised 'fromIntegral'
-word8_to_integer :: Word8 -> Integer
-word8_to_integer = fromIntegral
-
--- | Type specialised 'fromIntegral'
-word8_to_float :: Word8 -> Float
-word8_to_float = fromIntegral
-
--- | Type specialised 'fromIntegral'
-word8_to_double :: Word8 -> Double
-word8_to_double = fromIntegral
-
--- | Type specialised 'fromIntegral'
-word16_to_word8 :: Word16 -> Word8
-word16_to_word8 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-word16_to_word32 :: Word16 -> Word32
-word16_to_word32 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-word16_to_word64 :: Word16 -> Word64
-word16_to_word64 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-word16_to_int8 :: Word16 -> Int8
-word16_to_int8 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-word16_to_int16 :: Word16 -> Int16
-word16_to_int16 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-word16_to_int32 :: Word16 -> Int32
-word16_to_int32 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-word16_to_int64 :: Word16 -> Int64
-word16_to_int64 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-word16_to_int :: Word16 -> Int
-word16_to_int = fromIntegral
-
--- | Type specialised 'fromIntegral'
-word16_to_integer :: Word16 -> Integer
-word16_to_integer = fromIntegral
-
--- | Type specialised 'fromIntegral'
-word16_to_float :: Word16 -> Float
-word16_to_float = fromIntegral
-
--- | Type specialised 'fromIntegral'
-word16_to_double :: Word16 -> Double
-word16_to_double = fromIntegral
-
--- | Type specialised 'fromIntegral'
-word32_to_word8 :: Word32 -> Word8
-word32_to_word8 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-word32_to_word16 :: Word32 -> Word16
-word32_to_word16 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-word32_to_word64 :: Word32 -> Word64
-word32_to_word64 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-word32_to_int8 :: Word32 -> Int8
-word32_to_int8 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-word32_to_int16 :: Word32 -> Int16
-word32_to_int16 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-word32_to_int32 :: Word32 -> Int32
-word32_to_int32 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-word32_to_int64 :: Word32 -> Int64
-word32_to_int64 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-word32_to_int :: Word32 -> Int
-word32_to_int = fromIntegral
-
--- | Type specialised 'fromIntegral'
-word32_to_integer :: Word32 -> Integer
-word32_to_integer = fromIntegral
-
--- | Type specialised 'fromIntegral'
-word32_to_float :: Word32 -> Float
-word32_to_float = fromIntegral
-
--- | Type specialised 'fromIntegral'
-word32_to_double :: Word32 -> Double
-word32_to_double = fromIntegral
-
--- | Type specialised 'fromIntegral'
-word64_to_word8 :: Word64 -> Word8
-word64_to_word8 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-word64_to_word16 :: Word64 -> Word16
-word64_to_word16 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-word64_to_word32 :: Word64 -> Word32
-word64_to_word32 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-word64_to_int8 :: Word64 -> Int8
-word64_to_int8 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-word64_to_int16 :: Word64 -> Int16
-word64_to_int16 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-word64_to_int32 :: Word64 -> Int32
-word64_to_int32 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-word64_to_int64 :: Word64 -> Int64
-word64_to_int64 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-word64_to_int :: Word64 -> Int
-word64_to_int = fromIntegral
-
--- | Type specialised 'fromIntegral'
-word64_to_integer :: Word64 -> Integer
-word64_to_integer = fromIntegral
-
--- | Type specialised 'fromIntegral'
-word64_to_float :: Word64 -> Float
-word64_to_float = fromIntegral
-
--- | Type specialised 'fromIntegral'
-word64_to_double :: Word64 -> Double
-word64_to_double = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int8_to_word8 :: Int8 -> Word8
-int8_to_word8 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int8_to_word16 :: Int8 -> Word16
-int8_to_word16 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int8_to_word32 :: Int8 -> Word32
-int8_to_word32 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int8_to_word64 :: Int8 -> Word64
-int8_to_word64 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int8_to_int16 :: Int8 -> Int16
-int8_to_int16 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int8_to_int32 :: Int8 -> Int32
-int8_to_int32 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int8_to_int64 :: Int8 -> Int64
-int8_to_int64 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int8_to_int :: Int8 -> Int
-int8_to_int = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int8_to_integer :: Int8 -> Integer
-int8_to_integer = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int8_to_float :: Int8 -> Float
-int8_to_float = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int8_to_double :: Int8 -> Double
-int8_to_double = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int16_to_word8 :: Int16 -> Word8
-int16_to_word8 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int16_to_word16 :: Int16 -> Word16
-int16_to_word16 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int16_to_word32 :: Int16 -> Word32
-int16_to_word32 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int16_to_word64 :: Int16 -> Word64
-int16_to_word64 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int16_to_int8 :: Int16 -> Int8
-int16_to_int8 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int16_to_int32 :: Int16 -> Int32
-int16_to_int32 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int16_to_int64 :: Int16 -> Int64
-int16_to_int64 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int16_to_int :: Int16 -> Int
-int16_to_int = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int16_to_integer :: Int16 -> Integer
-int16_to_integer = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int16_to_float :: Int16 -> Float
-int16_to_float = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int16_to_double :: Int16 -> Double
-int16_to_double = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int32_to_word8 :: Int32 -> Word8
-int32_to_word8 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int32_to_word16 :: Int32 -> Word16
-int32_to_word16 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int32_to_word32 :: Int32 -> Word32
-int32_to_word32 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int32_to_word64 :: Int32 -> Word64
-int32_to_word64 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int32_to_int8 :: Int32 -> Int8
-int32_to_int8 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int32_to_int16 :: Int32 -> Int16
-int32_to_int16 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int32_to_int64 :: Int32 -> Int64
-int32_to_int64 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int32_to_int :: Int32 -> Int
-int32_to_int = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int32_to_integer :: Int32 -> Integer
-int32_to_integer = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int32_to_float :: Int32 -> Float
-int32_to_float = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int32_to_double :: Int32 -> Double
-int32_to_double = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int64_to_word8 :: Int64 -> Word8
-int64_to_word8 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int64_to_word16 :: Int64 -> Word16
-int64_to_word16 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int64_to_word32 :: Int64 -> Word32
-int64_to_word32 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int64_to_word64 :: Int64 -> Word64
-int64_to_word64 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int64_to_int8 :: Int64 -> Int8
-int64_to_int8 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int64_to_int16 :: Int64 -> Int16
-int64_to_int16 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int64_to_int32 :: Int64 -> Int32
-int64_to_int32 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int64_to_int :: Int64 -> Int
-int64_to_int = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int64_to_integer :: Int64 -> Integer
-int64_to_integer = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int64_to_float :: Int64 -> Float
-int64_to_float = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int64_to_double :: Int64 -> Double
-int64_to_double = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int_to_word8 :: Int -> Word8
-int_to_word8 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int_to_word16 :: Int -> Word16
-int_to_word16 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int_to_word32 :: Int -> Word32
-int_to_word32 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int_to_word64 :: Int -> Word64
-int_to_word64 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int_to_int8 :: Int -> Int8
-int_to_int8 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int_to_int16 :: Int -> Int16
-int_to_int16 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int_to_int32 :: Int -> Int32
-int_to_int32 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int_to_int64 :: Int -> Int64
-int_to_int64 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int_to_integer :: Int -> Integer
-int_to_integer = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int_to_float :: Int -> Float
-int_to_float = fromIntegral
-
--- | Type specialised 'fromIntegral'
-int_to_double :: Int -> Double
-int_to_double = fromIntegral
-
--- | Type specialised 'fromIntegral'
-integer_to_word8 :: Integer -> Word8
-integer_to_word8 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-integer_to_word16 :: Integer -> Word16
-integer_to_word16 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-integer_to_word32 :: Integer -> Word32
-integer_to_word32 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-integer_to_word64 :: Integer -> Word64
-integer_to_word64 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-integer_to_int8 :: Integer -> Int8
-integer_to_int8 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-integer_to_int16 :: Integer -> Int16
-integer_to_int16 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-integer_to_int32 :: Integer -> Int32
-integer_to_int32 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-integer_to_int64 :: Integer -> Int64
-integer_to_int64 = fromIntegral
-
--- | Type specialised 'fromIntegral'
-integer_to_int :: Integer -> Int
-integer_to_int = fromIntegral
-
--- | Type specialised 'fromIntegral'
-integer_to_float :: Integer -> Float
-integer_to_float = fromIntegral
-
--- | Type specialised 'fromIntegral'
-integer_to_double :: Integer -> Double
-integer_to_double = fromIntegral
-
--- | Type specialised 'fromIntegral'
-word8_to_word16_maybe :: Word8 -> Maybe Word16
-word8_to_word16_maybe n =
-    if n < fromIntegral (minBound::Word16) ||
-       n > fromIntegral (maxBound::Word16)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-word8_to_word32_maybe :: Word8 -> Maybe Word32
-word8_to_word32_maybe n =
-    if n < fromIntegral (minBound::Word32) ||
-       n > fromIntegral (maxBound::Word32)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-word8_to_word64_maybe :: Word8 -> Maybe Word64
-word8_to_word64_maybe n =
-    if n < fromIntegral (minBound::Word64) ||
-       n > fromIntegral (maxBound::Word64)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-word8_to_int8_maybe :: Word8 -> Maybe Int8
-word8_to_int8_maybe n =
-    if n < fromIntegral (minBound::Int8) ||
-       n > fromIntegral (maxBound::Int8)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-word8_to_int16_maybe :: Word8 -> Maybe Int16
-word8_to_int16_maybe n =
-    if n < fromIntegral (minBound::Int16) ||
-       n > fromIntegral (maxBound::Int16)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-word8_to_int32_maybe :: Word8 -> Maybe Int32
-word8_to_int32_maybe n =
-    if n < fromIntegral (minBound::Int32) ||
-       n > fromIntegral (maxBound::Int32)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-word8_to_int64_maybe :: Word8 -> Maybe Int64
-word8_to_int64_maybe n =
-    if n < fromIntegral (minBound::Int64) ||
-       n > fromIntegral (maxBound::Int64)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-word8_to_int_maybe :: Word8 -> Maybe Int
-word8_to_int_maybe n =
-    if n < fromIntegral (minBound::Int) ||
-       n > fromIntegral (maxBound::Int)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-word16_to_word8_maybe :: Word16 -> Maybe Word8
-word16_to_word8_maybe n =
-    if n < fromIntegral (minBound::Word8) ||
-       n > fromIntegral (maxBound::Word8)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-word16_to_word32_maybe :: Word16 -> Maybe Word32
-word16_to_word32_maybe n =
-    if n < fromIntegral (minBound::Word32) ||
-       n > fromIntegral (maxBound::Word32)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-word16_to_word64_maybe :: Word16 -> Maybe Word64
-word16_to_word64_maybe n =
-    if n < fromIntegral (minBound::Word64) ||
-       n > fromIntegral (maxBound::Word64)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-word16_to_int8_maybe :: Word16 -> Maybe Int8
-word16_to_int8_maybe n =
-    if n < fromIntegral (minBound::Int8) ||
-       n > fromIntegral (maxBound::Int8)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-word16_to_int16_maybe :: Word16 -> Maybe Int16
-word16_to_int16_maybe n =
-    if n < fromIntegral (minBound::Int16) ||
-       n > fromIntegral (maxBound::Int16)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-word16_to_int32_maybe :: Word16 -> Maybe Int32
-word16_to_int32_maybe n =
-    if n < fromIntegral (minBound::Int32) ||
-       n > fromIntegral (maxBound::Int32)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-word16_to_int64_maybe :: Word16 -> Maybe Int64
-word16_to_int64_maybe n =
-    if n < fromIntegral (minBound::Int64) ||
-       n > fromIntegral (maxBound::Int64)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-word16_to_int_maybe :: Word16 -> Maybe Int
-word16_to_int_maybe n =
-    if n < fromIntegral (minBound::Int) ||
-       n > fromIntegral (maxBound::Int)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-word32_to_word8_maybe :: Word32 -> Maybe Word8
-word32_to_word8_maybe n =
-    if n < fromIntegral (minBound::Word8) ||
-       n > fromIntegral (maxBound::Word8)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-word32_to_word16_maybe :: Word32 -> Maybe Word16
-word32_to_word16_maybe n =
-    if n < fromIntegral (minBound::Word16) ||
-       n > fromIntegral (maxBound::Word16)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-word32_to_word64_maybe :: Word32 -> Maybe Word64
-word32_to_word64_maybe n =
-    if n < fromIntegral (minBound::Word64) ||
-       n > fromIntegral (maxBound::Word64)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-word32_to_int8_maybe :: Word32 -> Maybe Int8
-word32_to_int8_maybe n =
-    if n < fromIntegral (minBound::Int8) ||
-       n > fromIntegral (maxBound::Int8)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-word32_to_int16_maybe :: Word32 -> Maybe Int16
-word32_to_int16_maybe n =
-    if n < fromIntegral (minBound::Int16) ||
-       n > fromIntegral (maxBound::Int16)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-word32_to_int32_maybe :: Word32 -> Maybe Int32
-word32_to_int32_maybe n =
-    if n < fromIntegral (minBound::Int32) ||
-       n > fromIntegral (maxBound::Int32)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-word32_to_int64_maybe :: Word32 -> Maybe Int64
-word32_to_int64_maybe n =
-    if n < fromIntegral (minBound::Int64) ||
-       n > fromIntegral (maxBound::Int64)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-word32_to_int_maybe :: Word32 -> Maybe Int
-word32_to_int_maybe n =
-    if n < fromIntegral (minBound::Int) ||
-       n > fromIntegral (maxBound::Int)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-word64_to_word8_maybe :: Word64 -> Maybe Word8
-word64_to_word8_maybe n =
-    if n < fromIntegral (minBound::Word8) ||
-       n > fromIntegral (maxBound::Word8)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-word64_to_word16_maybe :: Word64 -> Maybe Word16
-word64_to_word16_maybe n =
-    if n < fromIntegral (minBound::Word16) ||
-       n > fromIntegral (maxBound::Word16)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-word64_to_word32_maybe :: Word64 -> Maybe Word32
-word64_to_word32_maybe n =
-    if n < fromIntegral (minBound::Word32) ||
-       n > fromIntegral (maxBound::Word32)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-word64_to_int8_maybe :: Word64 -> Maybe Int8
-word64_to_int8_maybe n =
-    if n < fromIntegral (minBound::Int8) ||
-       n > fromIntegral (maxBound::Int8)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-word64_to_int16_maybe :: Word64 -> Maybe Int16
-word64_to_int16_maybe n =
-    if n < fromIntegral (minBound::Int16) ||
-       n > fromIntegral (maxBound::Int16)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-word64_to_int32_maybe :: Word64 -> Maybe Int32
-word64_to_int32_maybe n =
-    if n < fromIntegral (minBound::Int32) ||
-       n > fromIntegral (maxBound::Int32)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-word64_to_int64_maybe :: Word64 -> Maybe Int64
-word64_to_int64_maybe n =
-    if n < fromIntegral (minBound::Int64) ||
-       n > fromIntegral (maxBound::Int64)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-word64_to_int_maybe :: Word64 -> Maybe Int
-word64_to_int_maybe n =
-    if n < fromIntegral (minBound::Int) ||
-       n > fromIntegral (maxBound::Int)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-int8_to_word8_maybe :: Int8 -> Maybe Word8
-int8_to_word8_maybe n =
-    if n < fromIntegral (minBound::Word8) ||
-       n > fromIntegral (maxBound::Word8)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-int8_to_word16_maybe :: Int8 -> Maybe Word16
-int8_to_word16_maybe n =
-    if n < fromIntegral (minBound::Word16) ||
-       n > fromIntegral (maxBound::Word16)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-int8_to_word32_maybe :: Int8 -> Maybe Word32
-int8_to_word32_maybe n =
-    if n < fromIntegral (minBound::Word32) ||
-       n > fromIntegral (maxBound::Word32)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-int8_to_word64_maybe :: Int8 -> Maybe Word64
-int8_to_word64_maybe n =
-    if n < fromIntegral (minBound::Word64) ||
-       n > fromIntegral (maxBound::Word64)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-int8_to_int16_maybe :: Int8 -> Maybe Int16
-int8_to_int16_maybe n =
-    if n < fromIntegral (minBound::Int16) ||
-       n > fromIntegral (maxBound::Int16)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-int8_to_int32_maybe :: Int8 -> Maybe Int32
-int8_to_int32_maybe n =
-    if n < fromIntegral (minBound::Int32) ||
-       n > fromIntegral (maxBound::Int32)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-int8_to_int64_maybe :: Int8 -> Maybe Int64
-int8_to_int64_maybe n =
-    if n < fromIntegral (minBound::Int64) ||
-       n > fromIntegral (maxBound::Int64)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-int8_to_int_maybe :: Int8 -> Maybe Int
-int8_to_int_maybe n =
-    if n < fromIntegral (minBound::Int) ||
-       n > fromIntegral (maxBound::Int)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-int16_to_word8_maybe :: Int16 -> Maybe Word8
-int16_to_word8_maybe n =
-    if n < fromIntegral (minBound::Word8) ||
-       n > fromIntegral (maxBound::Word8)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-int16_to_word16_maybe :: Int16 -> Maybe Word16
-int16_to_word16_maybe n =
-    if n < fromIntegral (minBound::Word16) ||
-       n > fromIntegral (maxBound::Word16)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-int16_to_word32_maybe :: Int16 -> Maybe Word32
-int16_to_word32_maybe n =
-    if n < fromIntegral (minBound::Word32) ||
-       n > fromIntegral (maxBound::Word32)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-int16_to_word64_maybe :: Int16 -> Maybe Word64
-int16_to_word64_maybe n =
-    if n < fromIntegral (minBound::Word64) ||
-       n > fromIntegral (maxBound::Word64)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-int16_to_int8_maybe :: Int16 -> Maybe Int8
-int16_to_int8_maybe n =
-    if n < fromIntegral (minBound::Int8) ||
-       n > fromIntegral (maxBound::Int8)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-int16_to_int32_maybe :: Int16 -> Maybe Int32
-int16_to_int32_maybe n =
-    if n < fromIntegral (minBound::Int32) ||
-       n > fromIntegral (maxBound::Int32)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-int16_to_int64_maybe :: Int16 -> Maybe Int64
-int16_to_int64_maybe n =
-    if n < fromIntegral (minBound::Int64) ||
-       n > fromIntegral (maxBound::Int64)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-int16_to_int_maybe :: Int16 -> Maybe Int
-int16_to_int_maybe n =
-    if n < fromIntegral (minBound::Int) ||
-       n > fromIntegral (maxBound::Int)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-int32_to_word8_maybe :: Int32 -> Maybe Word8
-int32_to_word8_maybe n =
-    if n < fromIntegral (minBound::Word8) ||
-       n > fromIntegral (maxBound::Word8)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-int32_to_word16_maybe :: Int32 -> Maybe Word16
-int32_to_word16_maybe n =
-    if n < fromIntegral (minBound::Word16) ||
-       n > fromIntegral (maxBound::Word16)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-int32_to_word32_maybe :: Int32 -> Maybe Word32
-int32_to_word32_maybe n =
-    if n < fromIntegral (minBound::Word32) ||
-       n > fromIntegral (maxBound::Word32)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-int32_to_word64_maybe :: Int32 -> Maybe Word64
-int32_to_word64_maybe n =
-    if n < fromIntegral (minBound::Word64) ||
-       n > fromIntegral (maxBound::Word64)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-int32_to_int8_maybe :: Int32 -> Maybe Int8
-int32_to_int8_maybe n =
-    if n < fromIntegral (minBound::Int8) ||
-       n > fromIntegral (maxBound::Int8)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-int32_to_int16_maybe :: Int32 -> Maybe Int16
-int32_to_int16_maybe n =
-    if n < fromIntegral (minBound::Int16) ||
-       n > fromIntegral (maxBound::Int16)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-int32_to_int64_maybe :: Int32 -> Maybe Int64
-int32_to_int64_maybe n =
-    if n < fromIntegral (minBound::Int64) ||
-       n > fromIntegral (maxBound::Int64)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-int32_to_int_maybe :: Int32 -> Maybe Int
-int32_to_int_maybe n =
-    if n < fromIntegral (minBound::Int) ||
-       n > fromIntegral (maxBound::Int)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-int64_to_word8_maybe :: Int64 -> Maybe Word8
-int64_to_word8_maybe n =
-    if n < fromIntegral (minBound::Word8) ||
-       n > fromIntegral (maxBound::Word8)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-int64_to_word16_maybe :: Int64 -> Maybe Word16
-int64_to_word16_maybe n =
-    if n < fromIntegral (minBound::Word16) ||
-       n > fromIntegral (maxBound::Word16)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-int64_to_word32_maybe :: Int64 -> Maybe Word32
-int64_to_word32_maybe n =
-    if n < fromIntegral (minBound::Word32) ||
-       n > fromIntegral (maxBound::Word32)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-int64_to_word64_maybe :: Int64 -> Maybe Word64
-int64_to_word64_maybe n =
-    if n < fromIntegral (minBound::Word64) ||
-       n > fromIntegral (maxBound::Word64)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-int64_to_int8_maybe :: Int64 -> Maybe Int8
-int64_to_int8_maybe n =
-    if n < fromIntegral (minBound::Int8) ||
-       n > fromIntegral (maxBound::Int8)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-int64_to_int16_maybe :: Int64 -> Maybe Int16
-int64_to_int16_maybe n =
-    if n < fromIntegral (minBound::Int16) ||
-       n > fromIntegral (maxBound::Int16)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-int64_to_int32_maybe :: Int64 -> Maybe Int32
-int64_to_int32_maybe n =
-    if n < fromIntegral (minBound::Int32) ||
-       n > fromIntegral (maxBound::Int32)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-int64_to_int_maybe :: Int64 -> Maybe Int
-int64_to_int_maybe n =
-    if n < fromIntegral (minBound::Int) ||
-       n > fromIntegral (maxBound::Int)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-int_to_word8_maybe :: Int -> Maybe Word8
-int_to_word8_maybe n =
-    if n < fromIntegral (minBound::Word8) ||
-       n > fromIntegral (maxBound::Word8)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-int_to_word16_maybe :: Int -> Maybe Word16
-int_to_word16_maybe n =
-    if n < fromIntegral (minBound::Word16) ||
-       n > fromIntegral (maxBound::Word16)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-int_to_word32_maybe :: Int -> Maybe Word32
-int_to_word32_maybe n =
-    if n < fromIntegral (minBound::Word32) ||
-       n > fromIntegral (maxBound::Word32)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-int_to_word64_maybe :: Int -> Maybe Word64
-int_to_word64_maybe n =
-    if n < fromIntegral (minBound::Word64) ||
-       n > fromIntegral (maxBound::Word64)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-int_to_int8_maybe :: Int -> Maybe Int8
-int_to_int8_maybe n =
-    if n < fromIntegral (minBound::Int8) ||
-       n > fromIntegral (maxBound::Int8)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-int_to_int16_maybe :: Int -> Maybe Int16
-int_to_int16_maybe n =
-    if n < fromIntegral (minBound::Int16) ||
-       n > fromIntegral (maxBound::Int16)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-int_to_int32_maybe :: Int -> Maybe Int32
-int_to_int32_maybe n =
-    if n < fromIntegral (minBound::Int32) ||
-       n > fromIntegral (maxBound::Int32)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-int_to_int64_maybe :: Int -> Maybe Int64
-int_to_int64_maybe n =
-    if n < fromIntegral (minBound::Int64) ||
-       n > fromIntegral (maxBound::Int64)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-integer_to_word8_maybe :: Integer -> Maybe Word8
-integer_to_word8_maybe n =
-    if n < fromIntegral (minBound::Word8) ||
-       n > fromIntegral (maxBound::Word8)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-integer_to_word16_maybe :: Integer -> Maybe Word16
-integer_to_word16_maybe n =
-    if n < fromIntegral (minBound::Word16) ||
-       n > fromIntegral (maxBound::Word16)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-integer_to_word32_maybe :: Integer -> Maybe Word32
-integer_to_word32_maybe n =
-    if n < fromIntegral (minBound::Word32) ||
-       n > fromIntegral (maxBound::Word32)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-integer_to_word64_maybe :: Integer -> Maybe Word64
-integer_to_word64_maybe n =
-    if n < fromIntegral (minBound::Word64) ||
-       n > fromIntegral (maxBound::Word64)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-integer_to_int8_maybe :: Integer -> Maybe Int8
-integer_to_int8_maybe n =
-    if n < fromIntegral (minBound::Int8) ||
-       n > fromIntegral (maxBound::Int8)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-integer_to_int16_maybe :: Integer -> Maybe Int16
-integer_to_int16_maybe n =
-    if n < fromIntegral (minBound::Int16) ||
-       n > fromIntegral (maxBound::Int16)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-integer_to_int32_maybe :: Integer -> Maybe Int32
-integer_to_int32_maybe n =
-    if n < fromIntegral (minBound::Int32) ||
-       n > fromIntegral (maxBound::Int32)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-integer_to_int64_maybe :: Integer -> Maybe Int64
-integer_to_int64_maybe n =
-    if n < fromIntegral (minBound::Int64) ||
-       n > fromIntegral (maxBound::Int64)
-    then Nothing
-    else Just (fromIntegral n)
-
--- | Type specialised 'fromIntegral'
-integer_to_int_maybe :: Integer -> Maybe Int
-integer_to_int_maybe n =
-    if n < fromIntegral (minBound::Int) ||
-       n > fromIntegral (maxBound::Int)
-    then Nothing
-    else Just (fromIntegral n)
diff --git a/Music/Theory/Math/Convert/FX.hs b/Music/Theory/Math/Convert/FX.hs
deleted file mode 100644
--- a/Music/Theory/Math/Convert/FX.hs
+++ /dev/null
@@ -1,1288 +0,0 @@
--- | 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 -}
-
--- AUTOGEN
-
--- | 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
diff --git a/Music/Theory/Math/Convert/Fx.hs b/Music/Theory/Math/Convert/Fx.hs
new file mode 100644
--- /dev/null
+++ b/Music/Theory/Math/Convert/Fx.hs
@@ -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
diff --git a/Music/Theory/Math/Nichomachus.hs b/Music/Theory/Math/Nichomachus.hs
--- a/Music/Theory/Math/Nichomachus.hs
+++ b/Music/Theory/Math/Nichomachus.hs
@@ -42,7 +42,7 @@
 > 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
+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
 
@@ -50,4 +50,4 @@
 > 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
+subcont_geometric_mean a c = (a - c + sqrt (a * a - 2 * a * c + 5 * c * c)) / 2
diff --git a/Music/Theory/Math/OEIS.hs b/Music/Theory/Math/OEIS.hs
deleted file mode 100644
--- a/Music/Theory/Math/OEIS.hs
+++ /dev/null
@@ -1,470 +0,0 @@
--- | The On-Line Encyclopedia of Integer Sequences, <http://oeis.org/>
-module Music.Theory.Math.OEIS where
-
-import Data.List {- base -}
-import Data.Ratio {- base -}
-
-import qualified Music.Theory.Math as Math {- hmt -}
-
-{- | <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 =
-  let phi n = genericLength (filter (==1) (map (gcd n) [1..n]))
-  in map phi [1::Integer ..]
-
-{- | <http://oeis.org/A000045>
-
-Fibonacci numbers
-
-> [0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610] `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/A000079>
-
-Powers of 2: a(n) = 2^n
-
-> [1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384,32768,65536] `isPrefixOf` a000079
--}
-a000079 :: Num n => [n]
-a000079 = iterate (* 2) 1
-
-{- | <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)
-
-{- | <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/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
-
-{- | <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)
-
-> [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..]))
-
-{- | <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/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
-
--- | <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)
-
-{- | <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/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/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/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
--}
-a007318 :: Integral i => [[i]]
-a007318 =
-  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/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/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/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/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..]
-
--- | <http://oeis.org/A080992>
---
--- Entries in Durer's magic square.
-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/A126709>
---
--- Loh-Shu magic square, attributed to the legendary Fu Xi (Fuh-Hi).
-a126709 :: Num n => [n]
-a126709 =
-  [4,9,2
-  ,3,5,7
-  ,8,1,6]
-
--- | <http://oeis.org/A126710>
---
--- Jaina inscription of the twelfth or thirteenth century, Khajuraho, India.
-a126710 :: Num n => [n]
-a126710 =
-  [07,12,01,14
-  ,02,13,08,11
-  ,16,03,10,05
-  ,09,06,15,04]
-
--- | <http://oeis.org/A126976>
---
--- 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]
-
-{- | <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)])
diff --git a/Music/Theory/Math/Oeis.hs b/Music/Theory/Math/Oeis.hs
new file mode 100644
--- /dev/null
+++ b/Music/Theory/Math/Oeis.hs
@@ -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]
diff --git a/Music/Theory/Math/Prime.hs b/Music/Theory/Math/Prime.hs
--- a/Music/Theory/Math/Prime.hs
+++ b/Music/Theory/Math/Prime.hs
@@ -5,25 +5,28 @@
 import Data.Maybe {- base -}
 import Data.Ratio {- base -}
 
-import qualified Data.Numbers.Primes as P {- primes -}
+import qualified Data.Numbers.Primes as Primes {- primes -}
 
-import qualified Music.Theory.Function as T {- hmt -}
-import qualified Music.Theory.List as T {- hmt -}
-import qualified Music.Theory.Math as T {- hmt -}
+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 'P.primes'.
+-- | 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 = P.primes
+primes_list = Primes.primes
 
--- | Give zero-index of prime.
+-- | 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 P.isPrime i then Just (T.findIndex_err (== i) P.primes) else Nothing
+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
@@ -31,17 +34,17 @@
 {- | Generate list of factors of /n/ from /x/.
 
 > factor primes_list 315 == [3,3,5,7]
-> P.primeFactors 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 == []
-> P.primeFactors 1 == []
+> Primes.primeFactors 1 == []
 -}
 factor :: Integral i => [i] -> i -> [i]
 factor x n =
     case x of
-      [] -> undefined
+      [] -> error "factor: null primes_list input"
       i:x' -> if n < i
               then [] -- ie. prime factors of 1...
               else if i * i > n
@@ -54,9 +57,9 @@
 --
 -- > map prime_factors [-1,0,1] == [[],[],[]]
 -- > map prime_factors [1,4,231,315] == [[],[2,2],[3,7,11],[3,3,5,7]]
--- > map P.primeFactors [1,4,231,315] == [[],[2,2],[3,7,11],[3,3,5,7]]
+-- > map Primes.primeFactors [1,4,231,315] == [[],[2,2],[3,7,11],[3,3,5,7]]
 prime_factors :: Integral i => i -> [i]
-prime_factors n = factor primes_list n
+prime_factors = factor primes_list
 
 -- | 'maximum' of 'prime_factors'
 --
@@ -69,7 +72,7 @@
 --
 -- > multiplicities [1,1,1,2,2,3] == [(1,3),(2,2),(3,1)]
 multiplicities :: Eq t => [t] -> [(t,Int)]
-multiplicities = T.generic_histogram_by (==) Nothing
+multiplicities = List.generic_histogram_by (==) Nothing
 
 -- | Pretty printer for histogram (multiplicites).
 --
@@ -79,12 +82,12 @@
   let f (x,y) = show x ++ "×" ++ show y
   in unwords . map f
 
--- | 'multiplicities' of 'P.primeFactors'.
+-- | '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 . P.primeFactors
+prime_factors_m = multiplicities . Primes.primeFactors
 
 -- | 'multiplicities_pp' of 'prime_factors_m'.
 prime_factors_m_pp :: (Show i,Integral i) => i -> String
@@ -92,11 +95,11 @@
 
 -- | Prime factors of /n/ and /d/.
 rat_prime_factors :: Integral i => (i,i) -> ([i],[i])
-rat_prime_factors = T.bimap1 P.primeFactors
+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 . T.rational_nd
+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.
@@ -109,18 +112,20 @@
 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 . T.rational_nd
+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 . T.bimap1 prime_limit
+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 . T.rational_nd
+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)]
@@ -149,15 +154,16 @@
 > 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 . T.rational_nd
+rational_prime_factors_m = rat_prime_factors_m . Math.rational_nd
 
--- | Variant of 'rational_prime_factors_m' giving results in a list.
+-- | 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]
@@ -168,22 +174,61 @@
   case rat_prime_factors_m x of
     [] -> []
     r -> let lm = maximum (map fst r)
-         in map (\i -> fromMaybe 0 (lookup i r)) (T.take_until (== lm) P.primes)
+         in map (\i -> fromMaybe 0 (lookup i r)) (List.take_until (== lm) primes_list)
 
 -- | 'Ratio' variant of 'rat_prime_factors_l'
 --
--- > rational_prime_factors_l (256/243) == [8,-5]
+-- > 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 . T.rational_nd
+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/.
 --
--- > rat_prime_factors_t 6 (12,7) == [2,1,0,-1,0,0]
+-- > 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 = T.pad_right_err 0 k . rat_prime_factors_l
+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 . T.rational_nd
+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
+
diff --git a/Music/Theory/Maybe.hs b/Music/Theory/Maybe.hs
deleted file mode 100644
--- a/Music/Theory/Maybe.hs
+++ /dev/null
@@ -1,78 +0,0 @@
--- | Extensions to "Data.Maybe".
-module Music.Theory.Maybe where
-
-import Data.Maybe {- base -}
-
--- | Variant with error text.
-from_just :: String -> Maybe a -> a
-from_just err = fromMaybe (error err)
-
--- | Variant of unzip.
---
--- > let r = ([Just 1,Nothing,Just 3],[Just 'a',Nothing,Just 'c'])
--- > in maybe_unzip [Just (1,'a'),Nothing,Just (3,'c')] == r
-maybe_unzip :: [Maybe (a,b)] -> ([Maybe a],[Maybe b])
-maybe_unzip =
-    let f x = case x of
-                Nothing -> (Nothing,Nothing)
-                Just (i,j) -> (Just i,Just j)
-    in unzip . map f
-
--- | Replace 'Nothing' elements with last 'Just' value.  This does not
--- alter the length of the list.
---
--- > maybe_latch 1 [Nothing,Just 2,Nothing,Just 4] == [1,2,2,4]
-maybe_latch :: a -> [Maybe a] -> [a]
-maybe_latch i x =
-    case x of
-      [] -> []
-      Just e:x' -> e : maybe_latch e x'
-      Nothing:x' -> i : maybe_latch i x'
-
--- | Variant requiring initial value is not 'Nothing'.
---
--- > maybe_latch1 [Just 1,Nothing,Nothing,Just 4] == [1,1,1,4]
-maybe_latch1 :: [Maybe a] -> [a]
-maybe_latch1 = maybe_latch (error "maybe_latch1")
-
--- | 'map' of 'fmap'.
---
--- > maybe_map negate [Nothing,Just 2] == [Nothing,Just (-2)]
-maybe_map :: (a -> b) -> [Maybe a] -> [Maybe b]
-maybe_map = map . fmap
-
--- | If either is 'Nothing' then 'False', else /eq/ of values.
-maybe_eq_by :: (t -> u -> Bool) -> Maybe t -> Maybe u -> Bool
-maybe_eq_by eq_fn p q =
-    case (p,q) of
-      (Just p',Just q') -> eq_fn p' q'
-      _ -> False
-
--- | Join two values, either of which may be missing.
-maybe_join' :: (s -> t) -> (s -> s -> t) -> Maybe s -> Maybe s -> Maybe t
-maybe_join' f g p q =
-    case (p,q) of
-      (Nothing,_) -> fmap f q
-      (_,Nothing) -> fmap f p
-      (Just p',Just q') -> Just (p' `g` q')
-
--- | 'maybe_join'' of 'id'
-maybe_join :: (t -> t -> t) -> Maybe t -> Maybe t -> Maybe t
-maybe_join = maybe_join' id
-
--- | Apply predicate inside 'Maybe'.
---
--- > maybe_predicate even (Just 3) == Nothing
-maybe_predicate :: (a -> Bool) -> Maybe a -> Maybe a
-maybe_predicate f i =
-    case i of
-      Nothing -> Nothing
-      Just j -> if f j then Just j else Nothing
-
--- | 'map' of 'maybe_predicate'.
---
--- > let r = [Nothing,Nothing,Nothing,Just 4]
--- > in maybe_filter even [Just 1,Nothing,Nothing,Just 4] == r
-maybe_filter :: (a -> Bool) -> [Maybe a] -> [Maybe a]
-maybe_filter = map . maybe_predicate
-
diff --git a/Music/Theory/Meter/Barlow_1987.hs b/Music/Theory/Meter/Barlow_1987.hs
--- a/Music/Theory/Meter/Barlow_1987.hs
+++ b/Music/Theory/Meter/Barlow_1987.hs
@@ -8,7 +8,7 @@
 
 import qualified Data.Numbers.Primes as P {- primes -}
 
-import qualified Music.Theory.Math as T {- hmt -}
+import qualified Music.Theory.Math as T {- hmt-base -}
 
 traceShow :: a -> b -> b
 traceShow _ x = x
diff --git a/Music/Theory/Metric/Polansky_1996.hs b/Music/Theory/Metric/Polansky_1996.hs
--- a/Music/Theory/Metric/Polansky_1996.hs
+++ b/Music/Theory/Metric/Polansky_1996.hs
@@ -6,8 +6,9 @@
 import Data.Maybe {- base -}
 import Data.Ratio {- base -}
 
+import qualified Music.Theory.List as L {- hmt-base -}
+
 import qualified Music.Theory.Contour.Polansky_1992 as C {- hmt -}
-import qualified Music.Theory.List as L {- hmt -}
 
 -- | Distance function, ordinarily /n/ below is in 'Num', 'Fractional' or 'Real'.
 type Interval a n = (a -> a -> n)
diff --git a/Music/Theory/Monad.hs b/Music/Theory/Monad.hs
deleted file mode 100644
--- a/Music/Theory/Monad.hs
+++ /dev/null
@@ -1,22 +0,0 @@
--- | Monad functions.
-module Music.Theory.Monad where
-
--- | 'sequence_' of 'repeat'.
-repeatM_ :: Monad m => m a -> m ()
-repeatM_ = sequence_ . repeat
-
--- | Monadic variant of 'iterate'.
-iterateM_ :: Monad m => (st -> m st) -> st -> m ()
-iterateM_ f st = do
-  st' <- f st
-  iterateM_ f st'
-
--- | 'fmap' of 'concat' of 'mapM'
-concatMapM :: Monad m => (t -> m [u]) -> [t] -> m [u]
-concatMapM f = fmap concat . mapM f
-
--- | If i then j else k.
-m_if :: Monad m => (m Bool,m t,m t) -> m t
-m_if (i,j,k) = do
-  r <- i
-  if r then j else k
diff --git a/Music/Theory/Opt.hs b/Music/Theory/Opt.hs
deleted file mode 100644
--- a/Music/Theory/Opt.hs
+++ /dev/null
@@ -1,146 +0,0 @@
-{- | Very simple CLI option parser.
-
-Only allows options of the form --key=value, with the form --key equal to --key=True.
-
-A list of OPT_USR describes the options and provides default values.
-
-'get_opt_arg' merges user and default values into a table with values for all options.
-
-To fetch options use 'opt_get' and 'opt_read'.
-
--}
-module Music.Theory.Opt where
-
-import Control.Monad {- base -}
-import Data.Either {- base -}
-import Data.List {- base -}
-import Data.Maybe {- base -}
-import System.Environment {- base -}
-import System.Exit {- base -}
-
-import qualified Data.List.Split as Split {- split -}
-
-import qualified Music.Theory.Read as T {- hmt -}
-
--- | (KEY,VALUE)
---   Key does not include leading '--'.
-type OPT = (String,String)
-
--- | (KEY,DEFAULT-VALUE,TYPE,NOTE)
-type OPT_USR = (String,String,String,String)
-
--- | Re-write default values at USR_OPT.
-opt_usr_rw_def :: [OPT] -> [OPT_USR] -> [OPT_USR]
-opt_usr_rw_def rw =
-  let f (k,v,ty,dsc) = case lookup k rw of
-                         Just v' -> (k,v',ty,dsc)
-                         Nothing -> (k,v,ty,dsc)
-  in map f
-
--- | OPT_USR to OPT.
-opt_plain :: OPT_USR -> OPT
-opt_plain (k,v,_,_) = (k,v)
-
--- | OPT_USR to help string, indent is two spaces.
-opt_usr_help :: OPT_USR -> String
-opt_usr_help (k,v,t,n) = concat ["  ",k,":",t," -- ",n,"; default=",v]
-
--- | 'unlines' of 'opt_usr_help'
-opt_help :: [OPT_USR] -> String
-opt_help = unlines . map opt_usr_help
-
--- | Lookup KEY in OPT, error if non-existing.
-opt_get :: [OPT] -> String -> String
-opt_get o k = fromMaybe (error ("opt_get: " ++ k)) (lookup k o)
-
--- | Variant that returns Nothing if the result is the empty string, else Just the result.
-opt_get_nil :: [OPT] -> String -> Maybe String
-opt_get_nil o k = let r = opt_get o k in if null r then Nothing else Just r
-
--- | 'read' of 'get_opt'
-opt_read :: Read t => [OPT] -> String -> t
-opt_read o = T.read_err . opt_get o
-
--- | Parse k or k=v string, else error.
-opt_param_parse :: String -> OPT
-opt_param_parse p =
-  case Split.splitOn "=" p of
-    [lhs] -> (lhs,"True")
-    [lhs,rhs] -> (lhs,rhs)
-    _ -> error ("opt_param_parse: " ++ p)
-
--- | Parse option string of form "--opt" or "--key=value".
---
--- > opt_parse "--opt" == Just ("opt","True")
--- > opt_parse "--key=value" == Just ("key","value")
-opt_parse :: String -> Maybe OPT
-opt_parse s =
-  case s of
-    '-':'-':p -> Just (opt_param_parse p)
-    _ -> Nothing
-
--- | Parse option sequence, collating options and non-options.
---
--- > opt_set_parse (words "--a --b=c d") == ([("a","True"),("b","c")],["d"])
-opt_set_parse :: [String] -> ([OPT],[String])
-opt_set_parse =
-  let f s = maybe (Right s) Left (opt_parse s)
-  in partitionEithers . map f
-
--- | Left-biased OPT merge.
-opt_merge :: [OPT] -> [OPT] -> [OPT]
-opt_merge p q =
-  let x = map fst p
-  in p ++ filter (\(k,_) -> k `notElem` x) q
-
--- | Process argument list.
-opt_proc :: [OPT_USR] -> [String] -> ([OPT], [String])
-opt_proc def arg =
-  let (o,a) = opt_set_parse arg
-  in (opt_merge o (map opt_plain def),a)
-
--- | Usage text
-type OPT_USG = [String]
-
--- | Print usage pre-amble and 'opt_help'.
-opt_usage :: OPT_USG -> [OPT_USR] -> IO ()
-opt_usage usg def = putStrLn (unlines (usg ++ ["",opt_help def])) >> exitWith ExitSuccess
-
--- | Verify that all OPT have keys that are in OPT_USR
-opt_verify :: OPT_USG -> [OPT_USR] -> [OPT] -> IO ()
-opt_verify usg def =
-  let k_set = map (fst . opt_plain) def
-      f (k,_) = if k `elem` k_set
-                then return ()
-                else putStrLn ("UNKNOWN KEY: " ++ k ++ "\n") >> opt_usage usg def
-  in mapM_ f
-
--- | 'opt_set_parse' and maybe 'opt_verify' and 'opt_merge' of 'getArgs'.
---   If arguments include -h or --help run 'opt_usage'
-opt_get_arg :: Bool -> OPT_USG -> [OPT_USR] -> IO ([OPT],[String])
-opt_get_arg chk usg def = do
-  a <- getArgs
-  when ("-h" `elem` a || "--help" `elem` a) (opt_usage usg def)
-  let (o,p) = opt_set_parse a
-  when chk (opt_verify usg def o)
-  return (opt_merge o (map opt_plain def),p)
-
--- | Parse param set, one parameter per line.
---
--- > opt_param_set_parse "a\nb=c" == [("a","True"),("b","c")]
-opt_param_set_parse :: String -> [OPT]
-opt_param_set_parse = map opt_param_parse . lines
-
--- | Simple scanner over argument list.
-opt_scan :: [String] -> String -> Maybe String
-opt_scan a k =
-  let (o,_) = opt_set_parse a
-  in fmap snd (find ((== k) . fst) o)
-
--- | Scanner with default value.
-opt_scan_def :: [String] -> (String,String) -> String
-opt_scan_def a (k,v) = fromMaybe v (opt_scan a k)
-
--- | Reading scanner with default value.
-opt_scan_read :: Read t => [String] -> (String,t) -> t
-opt_scan_read a (k,v) = maybe v read (opt_scan a k)
diff --git a/Music/Theory/Ord.hs b/Music/Theory/Ord.hs
deleted file mode 100644
--- a/Music/Theory/Ord.hs
+++ /dev/null
@@ -1,42 +0,0 @@
--- | 'Ordering' functions
-module Music.Theory.Ord where
-
--- | Minimum by /f/.
-min_by :: Ord a => (t -> a) -> t -> t -> t
-min_by f p q = if f p <= f q then p else q
-
--- | Specialised 'fromEnum'.
-ord_to_int :: Ordering -> Int
-ord_to_int = fromEnum
-
--- | Specialised 'toEnum'.
-int_to_ord :: Int -> Ordering
-int_to_ord = toEnum
-
--- | Invert 'Ordering'.
---
--- > map ord_invert [LT,EQ,GT] == [GT,EQ,LT]
-ord_invert :: Ordering -> Ordering
-ord_invert x =
-    case x of
-      LT -> GT
-      EQ -> EQ
-      GT -> LT
-
--- | Given 'Ordering', re-order pair,
-order_pair :: Ordering -> (t,t) -> (t,t)
-order_pair o (x,y) =
-    case o of
-      LT -> (x,y)
-      EQ -> (x,y)
-      GT -> (y,x)
-
--- | Sort a pair of equal type values using given comparison function.
---
--- > sort_pair compare ('b','a') == ('a','b')
-sort_pair :: (t -> t -> Ordering) -> (t,t) -> (t,t)
-sort_pair fn (x,y) = order_pair (fn x y) (x,y)
-
--- | Variant where the comparison function may not compute a value.
-sort_pair_m :: (t -> t -> Maybe Ordering) -> (t,t) -> Maybe (t,t)
-sort_pair_m fn (x,y) = fmap (`order_pair` (x,y)) (fn x y)
diff --git a/Music/Theory/Parse.hs b/Music/Theory/Parse.hs
--- a/Music/Theory/Parse.hs
+++ b/Music/Theory/Parse.hs
@@ -1,3 +1,4 @@
+-- | Parsing utilities
 module Music.Theory.Parse where
 
 import Data.Maybe {- base -}
@@ -15,3 +16,12 @@
 -- | Parse 'Integral'.
 parse_int :: Integral i => P i
 parse_int = fmap (fromInteger . read) (P.many1 P.digit)
+
+run_parser :: P t -> String -> Either P.ParseError t
+run_parser p = P.runParser p () ""
+
+run_parser_maybe :: P t -> String -> Maybe t
+run_parser_maybe p = either (const Nothing) Just . run_parser p
+
+run_parser_error :: P c -> String -> c
+run_parser_error p = either (error . show) id . run_parser p
diff --git a/Music/Theory/Permutations.hs b/Music/Theory/Permutations.hs
deleted file mode 100644
--- a/Music/Theory/Permutations.hs
+++ /dev/null
@@ -1,162 +0,0 @@
--- | Permutation functions.
-module Music.Theory.Permutations where
-
-import qualified Data.Permute as P {- permutation -}
-import qualified Numeric {- base -}
-
-import qualified Music.Theory.List as L {- hmt -}
-
--- | 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.
---
--- > let f = nk_permutations in (f 4 3,f 13 3,f 12 12) == (24,1716,479001600)
-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 12 == 479001600
--- > 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 "abc" "bac") "abc" == "bac"
-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]
--- > apply_permutation p [1..4] == [4,3,2,1]
-apply_permutation :: P.Permute -> [a] -> [a]
-apply_permutation f p = map (p !!) (P.elems f)
-
--- | Composition of 'apply_permutation' and 'from_cycles'.
---
--- > apply_permutation_c [[0,3],[1,2]] [1..4] == [4,3,2,1]
--- > apply_permutation_c [[0,2],[1],[3,4]] [1..5] == [3,2,1,5,4]
--- > apply_permutation_c [[0,1,4],[2,3]] [1..5] == [2,5,4,3,1]
--- > apply_permutation_c [[0,1,3],[2,4]] [1..5] == [2,4,5,1,3]
-apply_permutation_c :: [[Int]] -> [a] -> [a]
-apply_permutation_c = apply_permutation . from_cycles
-
--- | True if the inverse of /p/ is /p/.
---
--- > non_invertible (permutation [0,1,3] [1,0,3]) == True
---
--- > let p = permutation [1..4] [4,3,2,1]
--- > 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/.
---
--- > let r = [[1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1]]
--- > map one_line (permutations_n 3) == r
-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]]
--- > let q = from_cycles [[0,1,4],[2,3]]
--- > let r = p `compose` q
--- > 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]
---
--- > let r = [[1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1]]
--- > map one_line (permutations_n 3) == r
-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
--- > 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 Numeric.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)
-
-import Data.List {- base -}
-partition not (map non_invertible (permutations_n 4))
-putStrLn $ unlines $ map unwords $ permutations ["A0","A1","B0"]
-
--}
diff --git a/Music/Theory/Permutations/List.hs b/Music/Theory/Permutations/List.hs
--- a/Music/Theory/Permutations/List.hs
+++ b/Music/Theory/Permutations/List.hs
@@ -2,9 +2,10 @@
 module Music.Theory.Permutations.List where
 
 import Data.List {- base -}
+
 import qualified Math.Combinatorics.Multiset as C {- multiset-comb -}
 
-import qualified Music.Theory.Permutations as P {- hmt -}
+import qualified Music.Theory.Permutations as P {- hmt-base -}
 
 -- | Generate all permutations.
 --
@@ -15,25 +16,31 @@
     let f p = P.apply_permutation p i
     in map f (P.permutations_n (length i))
 
+-- | /k/-element permutations of a set of /n/-elements.
+--
+-- > permutations_nk_l 3 2 "abc" == ["ab","ac","ba","bc","ca","cb"]
+permutations_nk_l :: Eq e => Int -> Int -> [e] -> [[e]]
+permutations_nk_l n k e =
+  if length e /= n
+  then error "permutations_nk_l"
+  else nub (map (take k) (permutations_l e))
+
 -- | Generate all distinct permutations of a multi-set.
 --
 -- > multiset_permutations [0,1,1] == [[0,1,1],[1,1,0],[1,0,1]]
-multiset_permutations :: (Ord a) => [a] -> [[a]]
+multiset_permutations :: Ord a => [a] -> [[a]]
 multiset_permutations = C.permutations . C.fromList
 
-factorial :: (Enum a, Num a) => a -> a
-factorial n = product [1..n]
-
 -- | Calculate number of permutations of a multiset.
 --
--- > let r = factorial 11 `div` product (map factorial [1,4,4,2])
--- > in multiset_permutations_n "MISSISSIPPI" == r
+-- > let r = P.factorial 11 `div` product (map P.factorial [1,4,4,2])
+-- > multiset_permutations_n "MISSISSIPPI" == r
 --
 -- > multiset_permutations_n "MISSISSIPPI" == 34650
 -- > length (multiset_permutations "MISSISSIPPI") == 34650
 multiset_permutations_n :: Ord a => [a] -> Int
 multiset_permutations_n x =
     let occ = map length . group . sort
-        n = factorial (length x)
-        d = product $ map factorial $ occ x
+        n = P.factorial (length x)
+        d = product $ map P.factorial $ occ x
     in n `div` d
diff --git a/Music/Theory/Permutations/Morris_1984.hs b/Music/Theory/Permutations/Morris_1984.hs
--- a/Music/Theory/Permutations/Morris_1984.hs
+++ b/Music/Theory/Permutations/Morris_1984.hs
@@ -9,28 +9,37 @@
 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.
 --
@@ -39,58 +48,64 @@
 split_changes :: String -> [String]
 split_changes = filter (/= ".") . split (dropInitBlank (oneOf "-x."))
 
--- | Parse 'Method' from the sequence of changes with possible lead end.
---
--- > parse_method ("-38-14-1258-36-14-58-16-78",Just "12")
-parse_method :: (String,Maybe String) -> Method
+-- | Place notation, sequence of changes with possible lead end.
+type Place = (String,Maybe String)
+
+-- | Parse 'Method' given 'PLACE' notation.
+parse_method :: Place -> Method
 parse_method (p,q) =
-    let c = map parse_change (split_changes p)
-        le = fmap parse_change q
-    in Method c le
+    let f = map parse_change . split_changes
+    in Method (f p) (fmap f q)
 
--- > map is_swap_all ["-","x","38"] == [True,True,False]
-is_swap_all :: String -> Bool
-is_swap_all s =
-    case s of
-      [c] -> c `elem` "-x"
-      _ -> False
+-- | Parse string into 'Place'.
+--
+-- > parse_method (parse_place "-38-14-1258-36-14-58-16-78,12")
+parse_place :: String -> Place
+parse_place txt =
+  case splitOn "," txt of
+    [p] -> (p,Nothing)
+    [p,q] -> (p,Just q)
+    _ -> error "parse_place?"
 
--- | Swap elemets of two-tuple (pair).
+-- | - or x?
 --
--- > swap_pair (1,2) == (2,1)
-swap_pair :: (s,t) -> (t,s)
-swap_pair (p,q) = (q,p)
+-- > map is_swap_all ["-","x","38"] == [True,True,False]
+is_swap_all :: String -> Bool
+is_swap_all = flip elem ["-","x"]
 
 -- | Flatten list of pairs.
 --
 -- > flatten_pairs [(1,2),(3,4)] == [1..4]
 flatten_pairs :: [(a,a)] -> [a]
-flatten_pairs l =
-    case l of
-      [] -> []
-      (p,q):l' -> p : q : flatten_pairs l'
+flatten_pairs = concatMap T.t2_to_list
 
 -- | Swap all adjacent pairs at list.
 --
 -- > swap_all [1 .. 8] == [2,1,4,3,6,5,8,7]
 swap_all :: [a] -> [a]
-swap_all = flatten_pairs . map swap_pair . T.adj2 2
+swap_all = flatten_pairs . map T.p2_swap . T.adj2 2
 
 numeric_spelling_tbl :: [(Char,Int)]
-numeric_spelling_tbl = zip "1234567890ETABCD" [1 .. 16]
+numeric_spelling_tbl = zip "1234567890ETABCDFGHJKL" [1 .. 22]
 
--- | Parse abbreviated 'Hold' notation, characters are hexedecimal.
+-- | Parse abbreviated 'Hold' notation, characters are NOT hexadecimal.
 --
--- > to_abbrev "380ETA" == [3,8,10,11,12,13]
-to_abbrev :: String -> [Int]
-to_abbrev = map (fromMaybe (error "to_abbrev") . flip lookup numeric_spelling_tbl)
+-- > map nchar_to_int "380ETA" == [3,8,10,11,12,13]
+nchar_to_int :: Char -> Int
+nchar_to_int = fromMaybe (error "nchar_to_int") . flip lookup numeric_spelling_tbl
 
+-- | Inverse of 'nchar_to_int'.
+--
+-- > map int_to_nchar [3,8,10,11,12,13] == "380ETA"
+int_to_nchar :: Int -> Char
+int_to_nchar = flip T.reverse_lookup_err numeric_spelling_tbl
+
 -- | Given a 'Hold' notation, generate permutation cycles.
 --
 -- > let r = [Right (1,2),Left 3,Right (4,5),Right (6,7),Left 8]
--- > in gen_swaps 8 [3,8] == r
+-- > gen_swaps 8 [3,8] == r
 --
--- > let r = [Left 1,Left 2,Right (3,4),Right (5,6),Right (7,8)]
+-- > r = [Left 1,Left 2,Right (3,4),Right (5,6),Right (7,8)]
 -- > gen_swaps 8 [1,2] == r
 gen_swaps :: (Num t, Ord t) => t -> [t] -> [Either t (t,t)]
 gen_swaps k =
@@ -124,7 +139,7 @@
 -- | One-indexed permutation cycles to zero-indexed.
 --
 -- > let r = [[0],[1],[2,3],[4,5],[6,7]]
--- > in to_zero_indexed [[1],[2],[3,4],[5,6],[7,8]] == r
+-- > to_zero_indexed [[1],[2],[3,4],[5,6],[7,8]] == r
 to_zero_indexed :: Enum t => [[t]] -> [[t]]
 to_zero_indexed = map (map pred)
 
@@ -134,7 +149,7 @@
 swap_abbrev :: Int -> [Int] -> [a] -> [a]
 swap_abbrev k a =
     let c = to_zero_indexed (swaps_to_cycles (gen_swaps k a))
-        p = T.from_cycles c
+        p = T.from_cycles_zero_indexed c
     in T.apply_permutation p
 
 -- | Apply a 'Change'.
@@ -150,7 +165,7 @@
 -- > let r = ([1,2,4,5,3]
 -- >         ,[[1,2,3,4,5],[2,1,3,4,5],[2,3,1,4,5],[3,2,4,1,5],[3,4,2,5,1]
 -- >          ,[4,3,2,5,1],[4,2,3,1,5],[2,4,1,3,5],[2,1,4,3,5],[1,2,4,3,5]])
--- > in apply_method cambridgeshire_slow_course_doubles [1..5] == r
+-- > apply_method cambridgeshire_slow_course_doubles [1..5] == r
 apply_method :: Method -> [a] -> ([a],[[a]])
 apply_method m l =
     let k = length l
@@ -171,60 +186,69 @@
     in rec l []
 
 -- | 'concat' of 'closed_method' with initial sequence appended.
-closed_method' :: Eq a => Method -> [a] -> [[a]]
-closed_method' m l = concat (closed_method m l) ++ [l]
+closed_method_lp :: Eq a => Method -> [a] -> [[a]]
+closed_method_lp m l = concat (closed_method m l) ++ [l]
 
+-- | 'closed_method' of 'parse_method'
+closed_place :: Eq t => Place -> [t] -> [[[t]]]
+closed_place pl = closed_method (parse_method pl)
+
 -- * Methods
 
--- | <https://rsw.me.uk/blueline/methods/view/Cambridgeshire_Slow_Course_Doubles>
+-- | <https://rsw.me.uk/blueline/methods/view/Cambridgeshire_Place_Doubles>
 --
--- > length (closed_method cambridgeshire_slow_course_doubles [1..5]) == 3
+-- > length (closed_place cambridgeshire_place_doubles_pl [1..5]) == 3
+cambridgeshire_place_doubles_pl :: Place
+cambridgeshire_place_doubles_pl = ("345.145.5.1.345",Just "123")
+
+-- | 'parse_method' of 'cambridgeshire_place_doubles_pl'
 cambridgeshire_slow_course_doubles :: Method
-cambridgeshire_slow_course_doubles =
-    let a = ("345.145.5.1.345",Just "123")
-    in parse_method a
+cambridgeshire_slow_course_doubles = parse_method cambridgeshire_place_doubles_pl
 
--- | Double Cambridge Cyclic Bob Minor.
---
--- <https://rsw.me.uk/blueline/methods/view/Double_Cambridge_Cyclic_Bob_Minor>
+-- | <https://rsw.me.uk/blueline/methods/view/Double_Cambridge_Cyclic_Bob_Minor>
 --
--- > length (closed_method double_cambridge_cyclic_bob_minor [1..6]) == 5
+-- > length (closed_place double_cambridge_cyclic_bob_minor_pl [1..6]) == 5
+double_cambridge_cyclic_bob_minor_pl :: Place
+double_cambridge_cyclic_bob_minor_pl = ("-14-16-56-36-16-12",Nothing)
+
+-- | 'parse_method' of 'double_cambridge_cyclic_bob_minor_pl'
 double_cambridge_cyclic_bob_minor :: Method
-double_cambridge_cyclic_bob_minor =
-    let a = ("-14-16-56-36-16-12",Nothing)
-    in parse_method a
+double_cambridge_cyclic_bob_minor = parse_method double_cambridge_cyclic_bob_minor_pl
 
--- | Hammersmith Bob Triples
---
--- <https://rsw.me.uk/blueline/methods/view/Hammersmith_Bob_Triples>
+-- | <https://rsw.me.uk/blueline/methods/view/Hammersmith_Bob_Triples>
 --
--- > length (closed_method hammersmith_bob_triples [1..7]) == 6
+-- > length (closed_place hammersmith_bob_triples_pl [1..7]) == 6
+hammersmith_bob_triples_pl :: Place
+hammersmith_bob_triples_pl = ("7.1.5.123.7.345.7",Just "127")
+
 hammersmith_bob_triples :: Method
-hammersmith_bob_triples =
-    let a = ("7.1.5.123.7.345.7",Just "127")
-    in parse_method a
+hammersmith_bob_triples = parse_method hammersmith_bob_triples_pl
 
 -- | <https://rsw.me.uk/blueline/methods/view/Cambridge_Surprise_Major>
 --
--- > length (closed_method cambridge_surprise_major [1..8]) == 7
+-- > length (closed_place cambridge_surprise_major_pl [1..8]) == 7
+cambridge_surprise_major_pl :: Place
+cambridge_surprise_major_pl = ("-38-14-1258-36-14-58-16-78",Just "12")
+
 cambridge_surprise_major :: Method
-cambridge_surprise_major =
-    let a = ("-38-14-1258-36-14-58-16-78",Just "12")
-    in parse_method a
+cambridge_surprise_major = parse_method cambridge_surprise_major_pl
 
 -- | <https://rsw.me.uk/blueline/methods/view/Smithsonian_Surprise_Royal>
 --
--- > let m = closed_method smithsonian_surprise_royal [1..10]
--- > (length m,nub (map length m),sum (map length m)) == (9,[40],360)
+-- > let c = closed_place smithsonian_surprise_royal_pl [1..10]
+-- > (length c,nub (map length c),sum (map length c)) == (9,[40],360)
+smithsonian_surprise_royal_pl :: Place
+smithsonian_surprise_royal_pl = ("-30-14-50-16-3470-18-1456-50-16-70",Just "12")
+
 smithsonian_surprise_royal :: Method
-smithsonian_surprise_royal =
-    let a = ("-30-14-50-16-3470-18-1456-50-16-70",Just "12")
-    in parse_method a
+smithsonian_surprise_royal = parse_method smithsonian_surprise_royal_pl
 
 -- | <https://rsw.me.uk/blueline/methods/view/Ecumenical_Surprise_Maximus>
 --
--- > let m = closed_method ecumenical_surprise_maximus [1..12]
--- > (length m,nub (map length m),sum (map length m)) == (11,[48],528)
+-- > c = closed_place ecumenical_surprise_maximus_pl [1..12]
+-- > (length c,nub (map length c),sum (map length c)) == (11,[48],528)
+ecumenical_surprise_maximus_pl :: Place
+ecumenical_surprise_maximus_pl = ("x3Tx14x5Tx16x7Tx1238x149Tx50x16x7Tx18.90.ET",Just "12")
+
 ecumenical_surprise_maximus :: Method
-ecumenical_surprise_maximus =
-  parse_method ("x3Tx14x5Tx16x7Tx1238x149Tx50x16x7Tx18.90.ET",Just "12")
+ecumenical_surprise_maximus = parse_method ecumenical_surprise_maximus_pl
diff --git a/Music/Theory/Pitch.hs b/Music/Theory/Pitch.hs
--- a/Music/Theory/Pitch.hs
+++ b/Music/Theory/Pitch.hs
@@ -5,14 +5,14 @@
 import Data.Function {- base -}
 import Data.List {- base -}
 import Data.Maybe {- base -}
-import Data.Word {- base -}
 import Text.Printf {- base -}
 
 import qualified Text.Parsec as P {- parsec -}
-import qualified Text.Parsec.String as P {- parsec -}
 
 import qualified Music.Theory.List as T {- hmt -}
 import qualified Music.Theory.Math as T {- hmt -}
+import qualified Music.Theory.Math.Convert as T {- hmt -}
+import qualified Music.Theory.Parse as T {- hmt -}
 import qualified Music.Theory.Pitch.Note as T {- hmt -}
 import qualified Music.Theory.Show as T {- hmt -}
 import qualified Music.Theory.Tuning as T {- hmt -}
@@ -50,61 +50,78 @@
 midi_to_octave_pitchclass :: (Integral m,Integral i) => m -> Octave_PitchClass i
 midi_to_octave_pitchclass n = (fromIntegral n - 12) `divMod` 12
 
+{- | One-indexed piano key number (for standard 88 key piano) to pitch class.
+     This has the mnemonic that 49 maps to (4,9).
+
+> map pianokey_to_octave_pitchclass [1,49,88] == [(0,9),(4,9),(8,0)]
+-}
+pianokey_to_octave_pitchclass :: (Integral m,Integral i) => m -> Octave_PitchClass i
+pianokey_to_octave_pitchclass = midi_to_octave_pitchclass . (+) 20
+
 -- * Octave & PitchClass
 
--- | Pitch classes are modulo twelve integers.
+-- | Pitch classes are modulo twelve integers (0-11)
 type PitchClass = Int
 
 -- | Octaves are integers, the octave of middle C is @4@.
 type Octave = Int
 
 -- | 'Octave' and 'PitchClass' duple.
-type OctPC = (Octave,PitchClass)
+type OctPc = (Octave,PitchClass)
 
 -- | Translate from generic octave & pitch-class duple.
-octave_pitchclass_to_octpc :: (Integral pc, Integral oct) => (oct,pc) -> OctPC
+octave_pitchclass_to_octpc :: (Integral pc, Integral oct) => (oct,pc) -> OctPc
 octave_pitchclass_to_octpc (oct,pc) = (fromIntegral oct,fromIntegral pc)
 
--- | Normalise 'OctPC'.
+-- | Normalise 'OctPc'.
 --
 -- > octpc_nrm (4,16) == (5,4)
-octpc_nrm :: OctPC -> OctPC
+octpc_nrm :: OctPc -> OctPc
 octpc_nrm = octave_pitchclass_nrm
 
--- | Transpose 'OctPC'.
+-- | Transpose 'OctPc'.
 --
 -- > octpc_trs 7 (4,9) == (5,4)
 -- > octpc_trs (-11) (4,9) == (3,10)
-octpc_trs :: Int -> OctPC -> OctPC
+octpc_trs :: Int -> OctPc -> OctPc
 octpc_trs = octave_pitchclass_trs
 
 -- | Enumerate range, inclusive.
 --
 -- > octpc_range ((3,8),(4,1)) == [(3,8),(3,9),(3,10),(3,11),(4,0),(4,1)]
-octpc_range :: (OctPC,OctPC) -> [OctPC]
+octpc_range :: (OctPc,OctPc) -> [OctPc]
 octpc_range (l,r) =
     let (l',r') = (octpc_to_midi l,octpc_to_midi r)
     in map midi_to_octpc [l' .. r']
 
 -- * Midi note number (0 - 127)
 
--- | Midi note number
-type Midi = Word8
+{- | 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 = fromIntegral
+midi_to_int = id
 
--- | 'OctPC' value to integral /midi/ note number.
+-- | 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 = fromIntegral . octave_pitchclass_to_midi
+octpc_to_midi :: OctPc -> Midi
+octpc_to_midi = octave_pitchclass_to_midi
 
 -- | Inverse of 'octpc_to_midi'.
 --
 -- > map midi_to_octpc [40,69] == [(2,4),(4,9)]
-midi_to_octpc :: Midi -> OctPC
+midi_to_octpc :: Midi -> OctPc
 midi_to_octpc = midi_to_octave_pitchclass
 
 -- * Octave & fractional pitch-class
@@ -135,7 +152,7 @@
 type FMidi = Double
 
 -- | Fractional octave pitch-class (octave is integral, pitch-class is fractional).
-type FOctPC = (Int,Double)
+type FOctPc = (Int,Double)
 
 -- | 'fromIntegral' of 'octpc_to_midi'.
 octpc_to_fmidi :: (Integral i,Num n) => Octave_PitchClass i -> n
@@ -174,8 +191,8 @@
 -- * Pitch
 
 -- | Common music notation pitch value.
-data Pitch = Pitch {note :: T.Note_T
-                   ,alteration :: T.Alteration_T
+data Pitch = Pitch {note :: T.Note
+                   ,alteration :: T.Alteration
                    ,octave :: Octave}
            deriving (Eq,Show)
 
@@ -239,12 +256,12 @@
 -- * Spelling
 
 -- | Function to spell a 'PitchClass'.
-type Spelling n = n -> (T.Note_T,T.Alteration_T)
+type Spelling n = n -> (T.Note,T.Alteration)
 
 -- | Variant of 'Spelling' for incomplete functions.
-type Spelling_M i = i -> Maybe (T.Note_T,T.Alteration_T)
+type Spelling_M i = i -> Maybe (T.Note,T.Alteration)
 
--- | Given 'Spelling' function translate from 'OctPC' notation to 'Pitch'.
+-- | Given 'Spelling' function translate from 'OctPc' notation to 'Pitch'.
 --
 -- > octpc_to_pitch T.pc_spell_sharp (4,6) == Pitch T.F T.Sharp 4
 octpc_to_pitch :: Integral i => Spelling i -> Octave_PitchClass i -> Pitch
@@ -260,9 +277,11 @@
 midi_to_pitch :: (Integral i,Integral k) => Spelling k -> i -> Pitch
 midi_to_pitch sp = octpc_to_pitch sp . midi_to_octave_pitchclass
 
--- | Fractional midi note number to 'Pitch'.
---
--- > fmidi_to_pitch T.pc_spell_ks 69.25 == Nothing
+{- | 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
@@ -286,9 +305,9 @@
 --
 -- > import Music.Theory.Pitch.Name as T
 -- > import Music.Theory.Pitch.Spelling as T
--- > pitch_tranpose T.pc_spell_ks 2 T.ees5 == T.f5
-pitch_tranpose :: (RealFrac n,Show n) => Spelling Int -> n -> Pitch -> Pitch
-pitch_tranpose sp n p =
+-- > pitch_transpose_fmidi T.pc_spell_ks 2 T.ees5 == T.f5
+pitch_transpose_fmidi :: (RealFrac n,Show n) => Spelling Int -> n -> Pitch -> Pitch
+pitch_transpose_fmidi sp n p =
     let m = pitch_to_fmidi p
     in fmidi_to_pitch_err sp (m + n)
 
@@ -369,7 +388,7 @@
         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
@@ -378,7 +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
@@ -408,25 +427,29 @@
 
 -- * Frequency (CPS)
 
+-- | 'fmidi_to_cps' of 'pitch_to_fmidi', given (k0,f0).
+pitch_to_cps_k0 :: Floating n => (n,n) -> Pitch -> n
+pitch_to_cps_k0 o = T.fmidi_to_cps_k0 o . pitch_to_fmidi
+
 -- | 'fmidi_to_cps' of 'pitch_to_fmidi', given frequency of ISO A4.
 pitch_to_cps_f0 :: Floating n => n -> Pitch -> n
-pitch_to_cps_f0 f0 = T.fmidi_to_cps_f0 f0 . pitch_to_fmidi
+pitch_to_cps_f0 f0 = pitch_to_cps_k0 (69,f0)
 
--- | 'pitch_to_cps_f0' 440.
+-- | 'pitch_to_cps_k0' (60,440).
 pitch_to_cps :: Floating n => Pitch -> n
-pitch_to_cps = pitch_to_cps_f0 440
+pitch_to_cps = pitch_to_cps_k0 (69,440)
 
 -- | Frequency (cps = cycles per second) to fractional /midi/ note
 -- number, given frequency of ISO A4 (mnn = 69).
-cps_to_fmidi_f0 :: Floating a => a -> a -> a
-cps_to_fmidi_f0 f0 a = (logBase 2 (a * (1 / f0)) * 12) + 69
+cps_to_fmidi_k0 :: Floating a => (a,a) -> a -> a
+cps_to_fmidi_k0 (k0,f0) a = (logBase 2 (a * (1 / f0)) * 12) + k0
 
--- | 'cps_to_fmidi_f0' @440@.
+-- | 'cps_to_fmidi_k0' @(69,440)@.
 --
 -- > cps_to_fmidi 440 == 69
 -- > cps_to_fmidi (fmidi_to_cps 60.25) == 60.25
 cps_to_fmidi :: Floating a => a -> a
-cps_to_fmidi = cps_to_fmidi_f0 440
+cps_to_fmidi = cps_to_fmidi_k0 (69,440)
 
 -- | Frequency (cycles per second) to /midi/ note number,
 -- ie. 'round' of 'cps_to_fmidi'.
@@ -435,15 +458,16 @@
 cps_to_midi :: (Integral i,Floating f,RealFrac f) => f -> i
 cps_to_midi = round . cps_to_fmidi
 
--- | 'midi_to_cps_f0' of 'octpc_to_midi', given frequency of ISO A4.
-octpc_to_cps_f0 :: (Integral i,Floating n) => n -> Octave_PitchClass i -> n
-octpc_to_cps_f0 f0 = T.midi_to_cps_f0 f0 . octave_pitchclass_to_midi
+-- | 'midi_to_cps_f0' of 'octpc_to_midi', given (k0,f0)
+octpc_to_cps_k0 :: (Integral i,Floating n) => (n,n) -> Octave_PitchClass i -> n
+octpc_to_cps_k0 o = T.midi_to_cps_k0 o . octave_pitchclass_to_midi
 
--- | 'octpc_to_cps_f0' 440.
---
--- > octpc_to_cps (4,9) == 440
+{- | 'octpc_to_cps_k0' (69,440).
+
+> map (round . octpc_to_cps) [(-1,0),(0,0),(4,9),(9,0)] == [8,16,440,8372]
+-}
 octpc_to_cps :: (Integral i,Floating n) => Octave_PitchClass i -> n
-octpc_to_cps = octpc_to_cps_f0 440
+octpc_to_cps = octpc_to_cps_k0 (69,440)
 
 -- | 'midi_to_octpc' of 'cps_to_midi'.
 cps_to_octpc :: (Floating f,RealFrac f,Integral i) => f -> Octave_PitchClass i
@@ -575,7 +599,7 @@
 -- * Pitch, rational alteration.
 
 -- | Generalised pitch, given by a generalised alteration.
-data Pitch_R = Pitch_R T.Note_T T.Alteration_R Octave
+data Pitch_R = Pitch_R T.Note T.Alteration_R Octave
                deriving (Eq,Show)
 
 -- | Pretty printer for 'Pitch_R'.
@@ -588,19 +612,39 @@
 
 -- * Parsers
 
+-- | Parser for single digit ISO octave (C4 = middle-C)
+p_octave_iso :: T.P Octave
+p_octave_iso = fmap digitToInt P.digit
+
+-- | Parser for single digit ISO octave with default value in case of no parse.
+p_octave_iso_opt :: Octave -> T.P Octave
+p_octave_iso_opt def_o = do
+  o <- P.optionMaybe p_octave_iso
+  return (fromMaybe def_o o)
+
+-- | Parser for ISO pitch notation.
+p_iso_pitch_strict :: T.P Pitch
+p_iso_pitch_strict = do
+  n <- T.p_note_t
+  a <- T.p_alteration_t_iso True
+  o <- p_octave_iso
+  return (Pitch  n a o)
+
+-- | Parser for extended form of ISO pitch notation.
+p_iso_pitch_oct :: Octave -> T.P Pitch
+p_iso_pitch_oct def_o = do
+  n <- T.p_note_t_ci -- ISO is requires upper case note names
+  a <- T.p_alteration_t_iso False -- ISO does not allow ##
+  o <- p_octave_iso_opt def_o -- ISO requires octave
+  return (Pitch  n a o)
+
 -- | Parse possible octave from single integer.
 --
--- > map (parse_octave 2) ["","4","x","11"] == [Just 2,Just 4,Nothing,Nothing]
-parse_octave :: Num a => a -> String -> Maybe a
-parse_octave def_o o =
-    case o of
-      [] -> Just def_o
-      [n] -> if isDigit n
-             then Just (fromIntegral (digitToInt n))
-             else Nothing
-      _ -> Nothing
+-- > map (parse_octave 2) ["","4","x","11"] == [2,4,2,1]x
+parse_octave :: Octave -> String -> Octave
+parse_octave def_o = T.run_parser_error (p_octave_iso_opt def_o)
 
--- | Slight generalisation of ISO pitch representation.  Allows octave
+-- | Generalisation of ISO pitch representation.  Allows octave
 -- to be elided, pitch names to be lower case, and double sharps
 -- written as @##@.
 --
@@ -609,18 +653,7 @@
 -- > let r = [Pitch T.C T.Natural 4,Pitch T.A T.Flat 5,Pitch T.F T.DoubleSharp 6]
 -- > mapMaybe (parse_iso_pitch_oct 4) ["C","Ab5","f##6",""] == r
 parse_iso_pitch_oct :: Octave -> String -> Maybe Pitch
-parse_iso_pitch_oct def_o s =
-    let mk n a o = case T.parse_note_t True n of
-                   Nothing -> Nothing
-                   Just n' -> fmap (Pitch n' a) (parse_octave def_o o)
-    in case s of
-         [] -> Nothing
-         n:'b':'b':o -> mk n T.DoubleFlat o
-         n:'#':'#':o -> mk n T.DoubleSharp o
-         n:'x':o -> mk n T.DoubleSharp o
-         n:'b':o -> mk n T.Flat o
-         n:'#':o -> mk n T.Sharp o
-         n:o -> mk n T.Natural o
+parse_iso_pitch_oct def_o = T.run_parser_maybe (p_iso_pitch_oct def_o)
 
 -- | Variant of 'parse_iso_pitch_oct' requiring octave.
 parse_iso_pitch :: String -> Maybe Pitch
@@ -725,16 +758,13 @@
 
 -- * Parsers
 
-p_octave_iso :: P.GenParser Char () Octave
-p_octave_iso = fmap digitToInt P.digit
-
-p_octave_ly :: P.GenParser Char () Octave
+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 :: P.GenParser Char () Pitch
+p_pitch_ly :: T.P Pitch
 p_pitch_ly = do
   (n,a) <- T.p_note_alteration_ly
   o <- P.optionMaybe p_octave_ly
@@ -744,23 +774,16 @@
 --
 -- > 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 s =
-  case P.runP p_pitch_ly () "pitch_parse_ly" s of
-    Left err -> error (show err)
-    Right r -> r
+pitch_parse_ly_err = T.run_parser_error p_pitch_ly
 
 -- | Parser for hly notation.
-p_pitch_hly :: P.GenParser Char () Pitch
+p_pitch_hly :: T.P Pitch
 p_pitch_hly = do
   (n,a) <- T.p_note_alteration_ly
-  o <- p_octave_iso
-  return (Pitch n (fromMaybe T.Natural a) o)
+  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 s =
-  case P.runP p_pitch_hly () "pitch_parse_hly" s of
-    Left err -> error (show err)
-    Right r -> r
+pitch_parse_hly = T.run_parser_error p_pitch_hly
diff --git a/Music/Theory/Pitch/Chord.hs b/Music/Theory/Pitch/Chord.hs
--- a/Music/Theory/Pitch/Chord.hs
+++ b/Music/Theory/Pitch/Chord.hs
@@ -4,15 +4,15 @@
 import Data.Maybe {- base -}
 
 import qualified Text.Parsec as P {- parsec -}
-import qualified Text.Parsec.String as P {- parsec -}
 
 import qualified Music.Theory.Key as T {- hmt -}
 import qualified Music.Theory.List as T {- hmt -}
+import qualified Music.Theory.Parse as T {- hmt -}
 import qualified Music.Theory.Pitch.Note as T {- hmt -}
 
-type PC = (T.Note_T,T.Alteration_T)
+type Pc = (T.Note,T.Alteration)
 
-pc_pp :: (T.Note_T, T.Alteration_T) -> [Char]
+pc_pp :: Pc -> [Char]
 pc_pp (n,a) = T.note_pp n : T.alteration_iso a
 
 -- | D = dominant, M = major
@@ -62,25 +62,25 @@
 chord_type_pcset = snd . chord_type_dat
 
 -- (root,mode,extensions,bass)
-data Chord = CH PC Chord_Type (Maybe Extension) (Maybe PC)
+data Chord = Chord Pc Chord_Type (Maybe Extension) (Maybe Pc)
              deriving (Show)
 
 chord_pcset :: Chord -> (Maybe Int,[Int])
-chord_pcset (CH pc ty ex bs) =
+chord_pcset (Chord pc ty ex bs) =
     let get = m_error "chord_pcset" . T.note_alteration_to_pc
         pc' = get pc
         ty' = chord_type_pcset ty
         ex' = fmap extension_to_pc ex
         bs' = fmap get bs
         ch = map ((`mod` 12) . (+ pc')) (ty' ++ maybe [] return ex')
-        ch' = maybe ch (flip delete ch) bs'
+        ch' = maybe ch (`delete` ch) bs'
     in (bs',ch')
 
-bass_pp :: PC -> String
+bass_pp :: Pc -> String
 bass_pp = ('/' :) . pc_pp
 
 chord_pp :: Chord -> String
-chord_pp (CH pc ty ex bs) =
+chord_pp (Chord pc ty ex bs) =
     let (pre_ty,post_ty) = if is_suspended ty
                            then (Nothing,Just ty)
                            else (Just ty,Nothing)
@@ -90,21 +90,19 @@
               ,maybe "" chord_type_pp post_ty
               ,maybe "" bass_pp bs]
 
-type P a = P.GenParser Char () a
-
 m_error :: String -> Maybe a -> a
 m_error txt = fromMaybe (error txt)
 
-p_pc :: P PC
+p_pc :: T.P Pc
 p_pc = do
   n <- T.p_note_t
-  a <- P.optionMaybe T.p_alteration_t_iso
+  a <- P.optionMaybe (T.p_alteration_t_iso True)
   return (n,fromMaybe T.Natural a)
 
-p_mode_m :: P T.Mode_T
+p_mode_m :: T.P T.Mode
 p_mode_m = P.option T.Major_Mode (P.char 'm' >> return T.Minor_Mode)
 
-p_chord_type :: P Chord_Type
+p_chord_type :: T.P Chord_Type
 p_chord_type =
     let m = P.char 'm' >> return Minor
         au = P.char '+' >> return Augmented
@@ -115,16 +113,16 @@
         sus4 = P.try (P.string "sus4" >> return Suspended_4)
     in P.option Major (P.choice [dm7,dm,hdm,au,sus2,sus4,m])
 
-p_extension :: P Extension
+p_extension :: T.P Extension
 p_extension =
     let d7 = P.char '7' >> return D7
         m7 = P.try (P.string "M7" >> return M7)
     in P.choice [d7,m7]
 
-p_bass :: P (Maybe PC)
+p_bass :: T.P (Maybe Pc)
 p_bass = P.optionMaybe (P.char '/' >> p_pc)
 
-p_chord :: P Chord
+p_chord :: T.P Chord
 p_chord = do
   pc <- p_pc
   ty <- p_chord_type
@@ -136,7 +134,7 @@
                (Major,Suspended_4) -> Suspended_4
                (_,Major) -> ty -- ie. nothing
                _ -> error ("trailing type not sus2 or sus4: " ++ show ty')
-  return (CH pc ty'' ex b)
+  return (Chord pc ty'' ex b)
 
 -- | Parse chord.
 --
diff --git a/Music/Theory/Pitch/Note.hs b/Music/Theory/Pitch/Note.hs
--- a/Music/Theory/Pitch/Note.hs
+++ b/Music/Theory/Pitch/Note.hs
@@ -5,68 +5,71 @@
 import Data.Maybe {- base -}
 
 import qualified Text.Parsec as P {- parsec -}
-import qualified Text.Parsec.String as P {- parsec -}
 
 import qualified Music.Theory.List as T {- hmt -}
+import qualified Music.Theory.Parse as T {- hmt -}
 
--- * Note_T
+-- * Note
 
 -- | Enumeration of common music notation note names (@C@ to @B@).
-data Note_T = C | D | E | F | G | A | B
+data Note = C | D | E | F | G | A | B
               deriving (Eq,Enum,Bounded,Ord,Read,Show)
 
 -- | Note sequence as usually understood, ie. 'C' - 'B'.
-note_seq :: [Note_T]
+note_seq :: [Note]
 note_seq = [C .. B]
 
 -- | Char variant of 'show'.
-note_pp :: Note_T -> Char
+note_pp :: Note -> Char
 note_pp = head . show
 
 -- | Note name in lilypond syntax (ie. lower case).
-note_pp_ly :: Note_T -> String
+note_pp_ly :: Note -> String
 note_pp_ly = map toLower . show
 
--- | Table of 'Note_T' and corresponding pitch-classes.
-note_pc_tbl :: Num i => [(Note_T,i)]
+-- | Table of 'Note' and corresponding pitch-classes.
+note_pc_tbl :: Num i => [(Note,i)]
 note_pc_tbl = zip [C .. B] [0,2,4,5,7,9,11]
 
--- | Transform 'Note_T' to pitch-class number.
+-- | Transform 'Note' to pitch-class number.
 --
 -- > map note_to_pc [C,E,G] == [0,4,7]
-note_to_pc :: Num i => Note_T -> i
+note_to_pc :: Num i => Note -> i
 note_to_pc n = T.lookup_err_msg "note_to_pc" n note_pc_tbl
 
 -- | Inverse of 'note_to_pc'.
 --
 -- > mapMaybe pc_to_note [0,4,7] == [C,E,G]
-pc_to_note :: (Eq i,Num i) => i -> Maybe Note_T
+pc_to_note :: (Eq i,Num i) => i -> Maybe Note
 pc_to_note i = T.reverse_lookup i note_pc_tbl
 
--- | Modal transposition of 'Note_T' value.
+-- | Modal transposition of 'Note' value.
 --
 -- > note_t_transpose C 2 == E
-note_t_transpose :: Note_T -> Int -> Note_T
+note_t_transpose :: Note -> Int -> Note
 note_t_transpose x n =
     let x' = fromEnum x
-        n' = fromEnum (maxBound::Note_T) + 1
+        n' = fromEnum (maxBound::Note) + 1
     in toEnum ((x' + n) `mod` n')
 
 -- | Parser from 'Char', case insensitive flag.
 --
 -- > mapMaybe (parse_note True) "CDEFGab" == [C,D,E,F,G,A,B]
-parse_note_t :: Bool -> Char -> Maybe Note_T
+parse_note_t :: Bool -> Char -> Maybe Note
 parse_note_t ci c =
     let tbl = zip "CDEFGAB" [C,D,E,F,G,A,B]
     in lookup (if ci then toUpper c else c) tbl
 
--- | Inclusive set of 'Note_T' within indicated interval.  This is not
+char_to_note_t :: Bool -> Char -> Note
+char_to_note_t ci = fromMaybe (error "char_to_note_t") . parse_note_t ci
+
+-- | Inclusive set of 'Note' within indicated interval.  This is not
 -- equal to 'enumFromTo' which is not circular.
 --
 -- > note_span E B == [E,F,G,A,B]
 -- > note_span B D == [B,C,D]
 -- > enumFromTo B D == []
-note_span :: Note_T -> Note_T -> [Note_T]
+note_span :: Note -> Note -> [Note]
 note_span n1 n2 =
     let fn x = toEnum (x `mod` 7)
         n1' = fromEnum n1
@@ -77,7 +80,7 @@
 -- * Alteration
 
 -- | Enumeration of common music notation note alterations.
-data Alteration_T =
+data Alteration =
     DoubleFlat
   | ThreeQuarterToneFlat | Flat | QuarterToneFlat
   | Natural
@@ -86,7 +89,7 @@
     deriving (Eq,Enum,Bounded,Ord,Show)
 
 -- | Generic form.
-generic_alteration_to_diff :: Integral i => Alteration_T -> Maybe i
+generic_alteration_to_diff :: Integral i => Alteration -> Maybe i
 generic_alteration_to_diff a =
     case a of
       DoubleFlat -> Just (-2)
@@ -96,30 +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
@@ -128,12 +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
@@ -147,29 +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
@@ -177,10 +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
@@ -190,7 +193,7 @@
       _ -> x
 
 -- | Table of Unicode characters for alterations.
-alteration_symbol_tbl :: [(Alteration_T,Char)]
+alteration_symbol_tbl :: [(Alteration,Char)]
 alteration_symbol_tbl =
     [(DoubleFlat,'𝄫')
     ,(ThreeQuarterToneFlat,'𝄭')
@@ -208,19 +211,35 @@
 -- UP@.
 --
 -- > map alteration_symbol [minBound .. maxBound] == "𝄫𝄭♭𝄳♮𝄲♯𝄰𝄪"
-alteration_symbol :: Alteration_T -> Char
+alteration_symbol :: Alteration -> Char
 alteration_symbol a = fromMaybe (error "alteration_symbol") (lookup a alteration_symbol_tbl)
 
 -- | Inverse of 'alteration_symbol'.
 --
 -- > mapMaybe symbol_to_alteration "♭♮♯" == [Flat,Natural,Sharp]
-symbol_to_alteration :: Char -> Maybe Alteration_T
+symbol_to_alteration :: Char -> Maybe Alteration
 symbol_to_alteration c = T.reverse_lookup c alteration_symbol_tbl
 
--- | Variant of 'symbol_to_alteration' that /also/ recognises @b@ for 'Flat'
--- and @#@ for 'Sharp' and 'x' for double sharp.
-symbol_to_alteration_iso :: Char -> Maybe Alteration_T
-symbol_to_alteration_iso c =
+-- | ISO alteration notation.  When not strict extended to allow ## for x.
+symbol_to_alteration_iso :: Bool -> String -> Maybe Alteration
+symbol_to_alteration_iso strict txt =
+    case txt of
+      "bb" -> Just DoubleFlat
+      "b" -> Just Flat
+      "#" -> Just Sharp
+      "##" -> if strict then Nothing else Just DoubleSharp
+      "x" -> Just DoubleSharp
+      "" -> Just Natural
+      _ -> Nothing
+
+symbol_to_alteration_iso_err :: Bool -> String -> Alteration
+symbol_to_alteration_iso_err strict =
+  fromMaybe (error "symbol_to_alteration_iso") .
+  symbol_to_alteration_iso strict
+
+-- | 'symbol_to_alteration' extended to allow single character ISO notations.
+symbol_to_alteration_unicode_plus_iso :: Char -> Maybe Alteration
+symbol_to_alteration_unicode_plus_iso c =
     case c of
       'b' -> Just Flat
       '#' -> Just Sharp
@@ -228,7 +247,7 @@
       _ -> symbol_to_alteration c
 
 -- | ISO alteration table, strings not characters because of double flat.
-alteration_iso_tbl :: [(Alteration_T,String)]
+alteration_iso_tbl :: [(Alteration,String)]
 alteration_iso_tbl =
     [(DoubleFlat,"bb")
     ,(Flat,"b")
@@ -241,17 +260,17 @@
 --
 -- > mapMaybe alteration_iso_m [Flat .. Sharp] == ["b","","#"]
 -- > mapMaybe alteration_iso_m [DoubleFlat,DoubleSharp] == ["bb","x"]
-alteration_iso_m :: Alteration_T -> Maybe String
+alteration_iso_m :: Alteration -> Maybe String
 alteration_iso_m a = lookup a alteration_iso_tbl
 
 -- | The @ISO@ ASCII spellings for alterations.
-alteration_iso :: Alteration_T -> String
+alteration_iso :: Alteration -> String
 alteration_iso =
     let qt = error "alteration_iso: quarter tone"
     in fromMaybe qt . alteration_iso_m
 
 -- | The /Tonhöhe/ ASCII spellings for alterations.
-alteration_tonh_tbl :: [(Alteration_T, String)]
+alteration_tonh_tbl :: [(Alteration, String)]
 alteration_tonh_tbl =
   [(DoubleFlat,"eses")
   ,(ThreeQuarterToneFlat,"eseh")
@@ -269,19 +288,22 @@
 -- <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 :: Alteration -> String
 alteration_tonh a = T.lookup_err a alteration_tonh_tbl
 
 -- | Inverse of 'alteration_tonh'.
 --
 -- > mapMaybe tonh_to_alteration ["es","eh","","ih","is"] == [Flat .. Sharp]
-tonh_to_alteration :: String -> Maybe Alteration_T
+tonh_to_alteration :: String -> Maybe Alteration
 tonh_to_alteration s = T.reverse_lookup s alteration_tonh_tbl
 
+tonh_to_alteration_err :: String -> Alteration
+tonh_to_alteration_err = fromMaybe (error "tonh_to_alteration") . tonh_to_alteration
+
 -- * 12-ET
 
 -- | Note and alteration to pitch-class, or not.
-note_alteration_to_pc :: (Note_T,Alteration_T) -> Maybe Int
+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)
@@ -289,21 +311,21 @@
 -- | Error variant.
 --
 -- > map note_alteration_to_pc_err [(A,DoubleSharp),(B,Sharp),(C,Flat),(C,DoubleFlat)]
-note_alteration_to_pc_err :: (Note_T, Alteration_T) -> Int
+note_alteration_to_pc_err :: (Note, Alteration) -> Int
 note_alteration_to_pc_err = fromMaybe (error "note_alteration_to_pc") . note_alteration_to_pc
 
 -- | Note & alteration sequence in key-signature spelling.
-note_alteration_ks :: [(Note_T, Alteration_T)]
+note_alteration_ks :: [(Note, Alteration)]
 note_alteration_ks =
     [(C,Natural),(C,Sharp),(D,Natural),(E,Flat),(E,Natural),(F,Natural)
     ,(F,Sharp),(G,Natural),(A,Flat),(A,Natural),(B,Flat),(B,Natural)]
 
 -- | Table connecting pitch class number with 'note_alteration_ks'.
-pc_note_alteration_ks_tbl :: Integral i => [((Note_T,Alteration_T),i)]
+pc_note_alteration_ks_tbl :: Integral i => [((Note,Alteration),i)]
 pc_note_alteration_ks_tbl = zip note_alteration_ks [0..11]
 
 -- | 'T.reverse_lookup' of 'pc_note_alteration_ks_tbl'.
-pc_to_note_alteration_ks :: Integral i => i -> Maybe (Note_T,Alteration_T)
+pc_to_note_alteration_ks :: Integral i => i -> Maybe (Note,Alteration)
 pc_to_note_alteration_ks i = T.reverse_lookup i pc_note_alteration_ks_tbl
 
 -- * Rational Alteration
@@ -312,44 +334,41 @@
 -- and a string representation of the alteration.
 type Alteration_R = (Rational,String)
 
--- | Transform 'Alteration_T' to 'Alteration_R'.
+-- | Transform 'Alteration' to 'Alteration_R'.
 --
 -- > let r = [(-1,"♭"),(0,"♮"),(1,"♯")]
 -- > map alteration_r [Flat,Natural,Sharp] == r
-alteration_r :: Alteration_T -> Alteration_R
+alteration_r :: Alteration -> Alteration_R
 alteration_r a = (alteration_to_fdiff a,[alteration_symbol a])
 
 -- * Parsers
 
--- > map (P.runP p_note_t () "" . return) "ABCDEFG"
-p_note_t :: P.GenParser Char () Note_T
-p_note_t =
-    fmap
-    (fromMaybe (error "p_note_t") . parse_note_t False)
-    (P.oneOf "ABCDEFG")
+-- | 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")
 
-p_note_t_lc :: P.GenParser Char () Note_T
-p_note_t_lc =
-    fmap
-    (fromMaybe (error "p_note_t_lc") . parse_note_t False . toUpper)
-    (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")
 
--- > map (P.runP p_alteration_t_iso () "" . return) "b#x"
-p_alteration_t_iso :: P.GenParser Char () Alteration_T
-p_alteration_t_iso =
-    fmap
-    (fromMaybe (error "p_alteration_t_iso") . symbol_to_alteration_iso)
-    (P.oneOf "b#x")
+-- | 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")
 
--- > map (P.runP p_alteration_t_tonh () "") ["eses","es","is","isis"]
-p_alteration_t_tonh :: P.GenParser Char () Alteration_T
-p_alteration_t_tonh =
-    fmap
-    (fromMaybe (error "p_alteration_t_tonh") . tonh_to_alteration)
-    (P.many1 (P.oneOf "ehis"))
+-- | 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 (P.runP p_note_alteration_ly () "") ["c","ees","fis","aeses"]
-p_note_alteration_ly :: P.GenParser Char () (Note_T,Maybe Alteration_T)
+-- > 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
diff --git a/Music/Theory/Pitch/Note/Name.hs b/Music/Theory/Pitch/Note/Name.hs
--- a/Music/Theory/Pitch/Note/Name.hs
+++ b/Music/Theory/Pitch/Note/Name.hs
@@ -6,7 +6,7 @@
 
 import Music.Theory.Pitch.Note
 
-ceses,deses,eeses,feses,geses,aeses,beses :: (Note_T,Alteration_T)
+ceses,deses,eeses,feses,geses,aeses,beses :: (Note,Alteration)
 ceses = (C,DoubleFlat)
 deses = (D,DoubleFlat)
 eeses = (E,DoubleFlat)
@@ -15,7 +15,7 @@
 aeses = (A,DoubleFlat)
 beses = (B,DoubleFlat)
 
-ceseh,deseh,eeseh,feseh,geseh,aeseh,beseh :: (Note_T,Alteration_T)
+ceseh,deseh,eeseh,feseh,geseh,aeseh,beseh :: (Note,Alteration)
 ceseh = (C,ThreeQuarterToneFlat)
 deseh = (D,ThreeQuarterToneFlat)
 eeseh = (E,ThreeQuarterToneFlat)
@@ -24,7 +24,7 @@
 aeseh = (A,ThreeQuarterToneFlat)
 beseh = (B,ThreeQuarterToneFlat)
 
-ces,des,ees,fes,ges,aes,bes :: (Note_T,Alteration_T)
+ces,des,ees,fes,ges,aes,bes :: (Note,Alteration)
 ces = (C,Flat)
 des = (D,Flat)
 ees = (E,Flat)
@@ -33,7 +33,7 @@
 aes = (A,Flat)
 bes = (B,Flat)
 
-ceh,deh,eeh,feh,geh,aeh,beh :: (Note_T,Alteration_T)
+ceh,deh,eeh,feh,geh,aeh,beh :: (Note,Alteration)
 ceh = (C,QuarterToneFlat)
 deh = (D,QuarterToneFlat)
 eeh = (E,QuarterToneFlat)
@@ -42,7 +42,7 @@
 aeh = (A,QuarterToneFlat)
 beh = (B,QuarterToneFlat)
 
-c,d,e,f,g,a,b :: (Note_T,Alteration_T)
+c,d,e,f,g,a,b :: (Note,Alteration)
 c = (C,Natural)
 d = (D,Natural)
 e = (E,Natural)
@@ -51,7 +51,7 @@
 a = (A,Natural)
 b = (B,Natural)
 
-cih,dih,eih,fih,gih,aih,bih :: (Note_T,Alteration_T)
+cih,dih,eih,fih,gih,aih,bih :: (Note,Alteration)
 cih = (C,QuarterToneSharp)
 dih = (D,QuarterToneSharp)
 eih = (E,QuarterToneSharp)
@@ -60,7 +60,7 @@
 aih = (A,QuarterToneSharp)
 bih = (B,QuarterToneSharp)
 
-cis,dis,eis,fis,gis,ais,bis :: (Note_T,Alteration_T)
+cis,dis,eis,fis,gis,ais,bis :: (Note,Alteration)
 cis = (C,Sharp)
 dis = (D,Sharp)
 eis = (E,Sharp)
@@ -69,7 +69,7 @@
 ais = (A,Sharp)
 bis = (B,Sharp)
 
-cisih,disih,eisih,fisih,gisih,aisih,bisih :: (Note_T,Alteration_T)
+cisih,disih,eisih,fisih,gisih,aisih,bisih :: (Note,Alteration)
 cisih = (C,ThreeQuarterToneSharp)
 disih = (D,ThreeQuarterToneSharp)
 eisih = (E,ThreeQuarterToneSharp)
@@ -78,7 +78,7 @@
 aisih = (A,ThreeQuarterToneSharp)
 bisih = (B,ThreeQuarterToneSharp)
 
-cisis,disis,eisis,fisis,gisis,aisis,bisis :: (Note_T,Alteration_T)
+cisis,disis,eisis,fisis,gisis,aisis,bisis :: (Note,Alteration)
 cisis = (C,DoubleSharp)
 disis = (D,DoubleSharp)
 eisis = (E,DoubleSharp)
diff --git a/Music/Theory/Pitch/Spelling.hs b/Music/Theory/Pitch/Spelling.hs
--- a/Music/Theory/Pitch/Spelling.hs
+++ b/Music/Theory/Pitch/Spelling.hs
@@ -6,7 +6,7 @@
 import qualified Music.Theory.Pitch.Spelling.Key as T {- hmt -}
 import qualified Music.Theory.Pitch.Spelling.Table as T {- hmt -}
 
-spell_octpc_set :: [T.OctPC] -> [T.Pitch]
+spell_octpc_set :: [T.OctPc] -> [T.Pitch]
 spell_octpc_set o =
   case T.octpc_spell_implied_key o of
     Just r -> r
diff --git a/Music/Theory/Pitch/Spelling/Cluster.hs b/Music/Theory/Pitch/Spelling/Cluster.hs
--- a/Music/Theory/Pitch/Spelling/Cluster.hs
+++ b/Music/Theory/Pitch/Spelling/Cluster.hs
@@ -14,12 +14,12 @@
 cluster_normal_order :: [T.PitchClass] -> [T.PitchClass]
 cluster_normal_order =
     let with_bounds x = ((last x - head x) `mod` 12,x)
-    in snd . head . sort . map with_bounds . T.rotations
+    in snd . minimum . map with_bounds . T.rotations
 
 -- | Normal order starting in indicated octave.
 --
 -- > cluster_normal_order_octpc 3 [0,1,11] == [(3,11),(4,0),(4,1)]
-cluster_normal_order_octpc :: T.Octave -> [T.PitchClass] -> [T.OctPC]
+cluster_normal_order_octpc :: T.Octave -> [T.PitchClass] -> [T.OctPc]
 cluster_normal_order_octpc o pc =
     let pc_n = cluster_normal_order pc
         pc_0 = head pc_n
@@ -36,7 +36,7 @@
 --
 -- > let f (p,q) = (p == map T.note_alteration_to_pc_err q)
 -- > in all f spell_cluster_table
-spell_cluster_table :: [([T.PitchClass],[(T.Note_T,T.Alteration_T)])]
+spell_cluster_table :: [([T.PitchClass],[(T.Note,T.Alteration)])]
 spell_cluster_table =
     [([0,1,2,3],[bis,cis,d,ees])
     ,([0,1,2],[bis,cis,d])
@@ -130,13 +130,13 @@
     ,([9,10],[a,bes])
     ,([9],[a])]
 
-spell_cluster :: [T.PitchClass] -> Maybe [(T.Note_T,T.Alteration_T)]
+spell_cluster :: [T.PitchClass] -> Maybe [(T.Note,T.Alteration)]
 spell_cluster = flip lookup spell_cluster_table
 
--- | Spell an arbitrary sequence of 'T.OctPC' values.
+-- | Spell an arbitrary sequence of 'T.OctPc' values.
 --
 -- > fmap (map T.pitch_pp_iso) (spell_cluster_octpc [(3,11),(4,3),(4,11),(5,1)])
-spell_cluster_octpc :: [T.OctPC] -> Maybe [T.Pitch]
+spell_cluster_octpc :: [T.OctPc] -> Maybe [T.Pitch]
 spell_cluster_octpc o =
     let p = cluster_normal_order (sort (nub (map snd o)))
         na_f na =
@@ -159,7 +159,7 @@
         oct = map fst (cluster_normal_order_octpc o_0 p)
     in case spell_cluster p of
          Nothing -> Nothing
-         Just na -> Just (map (\((n,alt),o) -> T.Pitch n alt o) (zip na oct))
+         Just na -> Just (zipWith (\(n,alt) o -> T.Pitch n alt o) na oct)
 
 -- | Variant of 'spell_cluster_c4' that runs 'pitch_edit_octave'.  An
 -- octave of @4@ is the identitiy, @3@ an octave below, @5@ an octave
@@ -177,10 +177,10 @@
 --
 -- > import Data.Maybe
 --
--- > let {f n = if n >= 11 then 3 else 4
--- >     ;g = map T.pitch_pp .fromJust . spell_cluster_f f
--- >     ;r = [["B3","C4"],["B3"],["C4"],["A♯4","B4"]]}
--- > in map g [[11,0],[11],[0],[10,11]] == r
+-- > let f n = if n >= 11 then 3 else 4
+-- > let g = map T.pitch_pp .fromJust . spell_cluster_f f
+-- > let r = [["B3","C4"],["B3"],["C4"],["A♯4","B4"]]
+-- > map g [[11,0],[11],[0],[10,11]] == r
 --
 -- > map (spell_cluster_f (const 4)) [[0,11],[11,0],[6,7],[7,6]]
 spell_cluster_f :: (T.PitchClass -> T.Octave) -> [T.PitchClass] -> Maybe [T.Pitch]
@@ -189,7 +189,7 @@
                 [] -> []
                 l:_ -> let (o,n) = T.pitch_to_octpc l
                            oct_f = (+ (o_f n - o))
-                       in (map (T.pitch_edit_octave oct_f) r)
+                       in map (T.pitch_edit_octave oct_f) r
     in fmap fn (spell_cluster_c4 p)
 
 -- | Variant of 'spell_cluster_c4' that runs 'pitch_edit_octave' so
diff --git a/Music/Theory/Pitch/Spelling/Key.hs b/Music/Theory/Pitch/Spelling/Key.hs
--- a/Music/Theory/Pitch/Spelling/Key.hs
+++ b/Music/Theory/Pitch/Spelling/Key.hs
@@ -16,14 +16,14 @@
                      else Just T.pc_spell_sharp
 
 -- > map pcset_spell_implied_key [[0,1],[4,10],[3,9],[3,11]]
-pcset_spell_implied_key :: Integral i => [i] -> Maybe [(T.Note_T, T.Alteration_T)]
+pcset_spell_implied_key :: Integral i => [i] -> Maybe [(T.Note, T.Alteration)]
 pcset_spell_implied_key x =
     case pcset_spell_implied_key_f x of
       Just f -> Just (map f x)
       Nothing -> Nothing
 
 -- > map octpc_spell_implied_key [[(3,11),(4,1)],[(3,11),(4,10)]]
-octpc_spell_implied_key :: [T.OctPC] -> Maybe [T.Pitch]
+octpc_spell_implied_key :: [T.OctPc] -> Maybe [T.Pitch]
 octpc_spell_implied_key x =
     let f o (n,a) = T.Pitch n a o
     in fmap (zipWith f (map fst x)) (pcset_spell_implied_key (map snd x))
diff --git a/Music/Theory/Pitch/Spelling/Table.hs b/Music/Theory/Pitch/Spelling/Table.hs
--- a/Music/Theory/Pitch/Spelling/Table.hs
+++ b/Music/Theory/Pitch/Spelling/Table.hs
@@ -6,7 +6,7 @@
 import qualified Music.Theory.Pitch as T {- hmt -}
 import Music.Theory.Pitch.Note {- hmt -}
 
-type Spelling_Table i = [(i,(Note_T,Alteration_T))]
+type Spelling_Table i = [(i,(Note,Alteration))]
 
 -- | Spelling table for natural (♮) notes only.
 pc_spell_natural_tbl :: Integral i => Spelling_Table i
@@ -90,7 +90,7 @@
 octpc_to_pitch_ks :: Integral i => T.Octave_PitchClass i -> T.Pitch
 octpc_to_pitch_ks = T.octpc_to_pitch pc_spell_ks
 
--- | 'midi_to_pitch' 'T.pc_spell_ks'.
+-- | '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)
 
@@ -99,3 +99,7 @@
 
 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)
diff --git a/Music/Theory/Random/I_Ching.hs b/Music/Theory/Random/I_Ching.hs
--- a/Music/Theory/Random/I_Ching.hs
+++ b/Music/Theory/Random/I_Ching.hs
@@ -6,10 +6,10 @@
 import Data.Int {- base -}
 import System.Random {- random -}
 
-import qualified Music.Theory.Bits as T {- hmt -}
-import qualified Music.Theory.Read as T {- hmt -}
-import qualified Music.Theory.Tuple as T {- hmt -}
-import qualified Music.Theory.Unicode as T {- hmt -}
+import qualified Music.Theory.Bits as T {- hmt-base -}
+import qualified Music.Theory.Read as T {- hmt-base -}
+import qualified Music.Theory.Tuple as T {- hmt-base -}
+import qualified Music.Theory.Unicode as T {- hmt-base -}
 
 -- * LINE
 
@@ -41,7 +41,7 @@
 
 -- | Seven character ASCII string for line.
 line_ascii_pp :: Line -> String
-line_ascii_pp n = fromMaybe (error "line_ascii_pp") (fmap T.p5_fifth (lookup n i_ching_chart))
+line_ascii_pp n = maybe (error "line_ascii_pp") T.p5_fifth (lookup n i_ching_chart)
 
 -- | Is line (ie. sum) moving (ie. 6 or 9).
 line_is_moving :: Line -> Bool
diff --git a/Music/Theory/Read.hs b/Music/Theory/Read.hs
deleted file mode 100644
--- a/Music/Theory/Read.hs
+++ /dev/null
@@ -1,194 +0,0 @@
--- | Read functions.
-module Music.Theory.Read where
-
-import Data.Char {- base -}
-import Data.List {- base -}
-import Data.Maybe {- base -}
-import Data.Ratio {- base -}
-import Data.Word {- base -}
-import Numeric {- base -}
-
--- | Transform 'ReadS' function into precise 'Read' function.
--- Requires using all the input to produce a single token.  The only
--- exception is a singular trailing white space character.
-reads_to_read_precise :: ReadS t -> (String -> Maybe t)
-reads_to_read_precise f s =
-    case f s of
-      [(r,[])] -> Just r
-      [(r,[c])] -> if isSpace c then Just r else Nothing
-      _ -> Nothing
-
--- | Error variant of 'reads_to_read_precise'.
-reads_to_read_precise_err :: String -> ReadS t -> String -> t
-reads_to_read_precise_err err f =
-    fromMaybe (error ("reads_to_read_precise_err:" ++ err)) .
-    reads_to_read_precise f
-
--- | 'reads_to_read_precise' of 'reads'.
---
--- > read_maybe "1.0" :: Maybe Int
-read_maybe :: Read a => String -> Maybe a
-read_maybe = reads_to_read_precise reads
-
--- | Variant of 'read_maybe' with default value.
---
--- > map (read_def 0) ["2","2:","2\n"] == [2,0,2]
-read_def :: Read a => a -> String -> a
-read_def x s = maybe x id (read_maybe s)
-
--- | Variant of 'read_maybe' that errors on 'Nothing', printing message.
-read_err_msg :: Read a => String -> String -> a
-read_err_msg msg s = maybe (error ("read_err: " ++ msg ++ ": " ++ s)) id (read_maybe s)
-
--- | Default message.
-read_err :: Read a => String -> a
-read_err = read_err_msg "read_maybe failed"
-
--- | Variant of 'reads' requiring exact match, no trailing white space.
---
--- > map reads_exact ["1.5","2,5"] == [Just 1.5,Nothing]
-reads_exact :: Read a => String -> Maybe a
-reads_exact s =
-    case reads s of
-      [(r,"")] -> Just r
-      _ -> Nothing
-
--- | Variant of 'reads_exact' that errors on failure.
-reads_exact_err :: Read a => String -> String -> a
-reads_exact_err err_txt str =
-    let err = error ("reads: " ++ err_txt ++ ": " ++ str)
-    in fromMaybe err (reads_exact str)
-
--- * Type specific variants
-
--- | Allow commas as thousand separators.
---
--- > let r = [Just 123456,Just 123456,Nothing,Just 123456789]
--- > in map read_integral_allow_commas_maybe ["123456","123,456","1234,56","123,456,789"]
-read_integral_allow_commas_maybe :: Read i => String -> Maybe i
-read_integral_allow_commas_maybe s =
-    let c = filter ((== ',') . fst) (zip (reverse s) [0..])
-    in if null c
-       then read_maybe s
-       else if map snd c `isPrefixOf` [3::Int,7..]
-            then read_maybe (filter (not . (== ',')) s)
-            else Nothing
-
-read_integral_allow_commas_err :: (Integral i,Read i) => String -> i
-read_integral_allow_commas_err s =
-    let err = error ("read_integral_allow_commas: misplaced commas: " ++ s)
-    in fromMaybe err (read_integral_allow_commas_maybe s)
-
-read_int_allow_commas :: String -> Int
-read_int_allow_commas = read_integral_allow_commas_err
-
--- | Read a ratio where the division is given by @/@ instead of @%@
--- and the integers allow commas.
---
--- > map read_ratio_with_div_err ["123,456/7","123,456,789"] == [123456/7,123456789]
-read_ratio_with_div_err :: (Integral i, Read i) => String -> Ratio i
-read_ratio_with_div_err s =
-    let f = read_integral_allow_commas_err
-    in case break (== '/') s of
-         (n,'/':d) -> f n % f d
-         _ -> read_integral_allow_commas_err s % 1
-
--- | Read 'Ratio', allow commas for thousand separators.
---
--- > read_ratio_allow_commas_err "327,680" "177,147" == 327680 / 177147
-read_ratio_allow_commas_err :: (Integral i,Read i) => String -> String -> Ratio i
-read_ratio_allow_commas_err n d = let f = read_integral_allow_commas_err in f n % f d
-
--- | Delete trailing @.@, 'read' fails for @700.@.
-delete_trailing_point :: String -> String
-delete_trailing_point s =
-    case reverse s of
-      '.':s' -> reverse s'
-      _ -> s
-
--- | 'read_err' disallows trailing decimal points.
---
--- > map read_fractional_allow_trailing_point_err ["123.","123.4"] == [123.0,123.4]
-read_fractional_allow_trailing_point_err :: Read n => String -> n
-read_fractional_allow_trailing_point_err = read_err . delete_trailing_point
-
--- * Plain type specialisations
-
--- | Type specialised 'read_maybe'.
---
--- > map read_maybe_int ["2","2:","2\n","x"] == [Just 2,Nothing,Just 2,Nothing]
-read_maybe_int :: String -> Maybe Int
-read_maybe_int = read_maybe
-
--- | Type specialised 'read_err'.
-read_int :: String -> Int
-read_int = read_err
-
--- | Type specialised 'read_maybe'.
-read_maybe_double :: String -> Maybe Double
-read_maybe_double = read_maybe
-
--- | Type specialised 'read_err'.
-read_double :: String -> Double
-read_double = read_err
-
--- | Type specialised 'read_maybe'.
---
--- > map read_maybe_rational ["1","1%2","1/2"] == [Nothing,Just (1/2),Nothing]
-read_maybe_rational :: String -> Maybe Rational
-read_maybe_rational = read_maybe
-
--- | Type specialised 'read_err'.
---
--- > read_rational "1%4"
-read_rational :: String -> Rational
-read_rational = read_err
-
--- * Numeric variants
-
--- | Read binary integer.
---
--- > mapMaybe read_bin (words "000 001 010 011 100 101 110 111") == [0 .. 7]
-read_bin :: Integral a => String -> Maybe a
-read_bin = fmap fst . listToMaybe . readInt 2 (`elem` "01") digitToInt
-
--- | Erroring variant.
-read_bin_err :: Integral a => String -> a
-read_bin_err = fromMaybe (error "read_bin") . read_bin
-
--- * HEX
-
--- | Error variant of 'readHex'.
---
--- > read_hex_err "F0B0" == 61616
-read_hex_err :: (Eq n,Num n) => String -> n
-read_hex_err = reads_to_read_precise_err "readHex" readHex
-
--- | Read hex value from string of at most /k/ places.
-read_hex_sz :: (Eq n, Num n) => Int -> String -> n
-read_hex_sz k str =
-  if length str > k
-  then error "read_hex_sz? = > K"
-  else case readHex str of
-         [(r,[])] -> r
-         _ -> error "read_hex_sz? = PARSE"
-
--- | Read hexadecimal representation of 32-bit unsigned word.
---
--- > map read_hex_word32 ["00000000","12345678","FFFFFFFF"] == [minBound,305419896,maxBound]
-read_hex_word32 :: String -> Word32
-read_hex_word32 = read_hex_sz 8
-
--- * RATIONAL
-
--- | Parser for 'rational_pp'.
---
--- > map rational_parse ["1","3/2","5/4","2"] == [1,3/2,5/4,2]
--- > rational_parse "" == undefined
-rational_parse :: (Read t,Integral t) => String -> Ratio t
-rational_parse s =
-  case break (== '/') s of
-    ([],_) -> error "rational_parse"
-    (n,[]) -> read n % 1
-    (n,_:d) -> read n % read d
-
diff --git a/Music/Theory/Set/List.hs b/Music/Theory/Set/List.hs
--- a/Music/Theory/Set/List.hs
+++ b/Music/Theory/Set/List.hs
@@ -3,9 +3,10 @@
 
 import Control.Monad {- base -}
 import Data.List {- base -}
+
 import qualified Math.Combinatorics.Multiset as M {- multiset-comb -}
 
-import qualified Music.Theory.List as T {- hmt -}
+import qualified Music.Theory.List as T {- hmt-base -}
 
 -- | 'sort' then 'nub'.
 --
@@ -28,9 +29,9 @@
 
 -- | Variant where result is sorted and the empty set is not given.
 --
--- > powerset' [1,2,3] == [[1],[2],[3],[1,2],[1,3],[2,3],[1,2,3]]
-powerset' :: Ord a => [a] -> [[a]]
-powerset' = tail . T.sort_by_two_stage_on length id . powerset
+-- > powerset_sorted [1,2,3] == [[1],[2],[3],[1,2],[1,3],[2,3],[1,2,3]]
+powerset_sorted :: Ord a => [a] -> [[a]]
+powerset_sorted = tail . T.sort_by_two_stage_on length id . powerset
 
 -- | Two element subsets.
 --
@@ -41,12 +42,14 @@
       [] -> []
       x:s' -> [(x,y) | y <- s'] ++ pairs s'
 
--- | Three element subsets.
---
--- > triples [1..4] == [(1,2,3),(1,2,4),(1,3,4),(2,3,4)]
---
--- > let f n = genericLength (triples [1..n]) == nk_combinations n 3
--- > in all f [1..15]
+{- | Three element subsets.
+
+> triples [1..4] == [(1,2,3),(1,2,4),(1,3,4),(2,3,4)]
+
+> import Music.Theory.Combinations
+> let f n = genericLength (triples [1..n]) == nk_combinations n 3
+> all f [1..15]
+-}
 triples :: [a] -> [(a,a,a)]
 triples s =
     case s of
@@ -62,23 +65,18 @@
     then [xs]
     else nub (concatMap (expand_set n) [sort (y : xs) | y <- xs])
 
--- | All distinct multiset partitions, see 'M.partitions'.
---
--- > partitions "aab" == [["aab"],["a","ab"],["b","aa"],["b","a","a"]]
---
--- > partitions "abc" == [["abc"]
--- >                     ,["bc","a"],["b","ac"],["c","ab"]
--- >                     ,["c","b","a"]]
+{- | All distinct multiset partitions, see 'M.partitions'.
+
+> partitions "aab" == [["aab"],["a","ab"],["b","aa"],["b","a","a"]]
+> partitions "abc" == [["abc"],["bc","a"],["b","ac"],["c","ab"],["c","b","a"]]
+-}
 partitions :: Eq a => [a] -> [[[a]]]
 partitions = map (map M.toList . M.toList) . M.partitions . M.fromListEq
 
 {- | Cartesian product of two sets.
 
-> let r = [('a',1),('a',2),('b',1),('b',2),('c',1),('c',2)]
-> in cartesian_product "abc" [1,2] == r
-
+> cartesian_product "abc" [1,2] == [('a',1),('a',2),('b',1),('b',2),('c',1),('c',2)]
 > cartesian_product "abc" "" == []
-
 -}
 cartesian_product :: [a] -> [b] -> [(a,b)]
 cartesian_product p q = [(i,j) | i <- p, j <- q]
@@ -94,3 +92,10 @@
       [_] -> []
       [x,y] -> [[i,j] | i <- x, j <- y]
       x:l' -> concatMap (\e -> map (e :) (nfold_cartesian_product l')) x
+
+{- | Generate all distinct cycles, aka necklaces, with elements taken from a multiset.
+
+> concatMap multiset_cycles [replicate i 0 ++ replicate (6 - i) 1 | i <- [0 .. 6]]
+-}
+multiset_cycles :: Ord t => [t] -> [[t]]
+multiset_cycles = M.cycles . M.fromList
diff --git a/Music/Theory/Set/Set.hs b/Music/Theory/Set/Set.hs
--- a/Music/Theory/Set/Set.hs
+++ b/Music/Theory/Set/Set.hs
@@ -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
diff --git a/Music/Theory/Show.hs b/Music/Theory/Show.hs
deleted file mode 100644
--- a/Music/Theory/Show.hs
+++ /dev/null
@@ -1,130 +0,0 @@
--- | Show functions.
-module Music.Theory.Show where
-
-import Data.Char {- base -}
-import Data.List {- base -}
-import Data.Ratio {- base -}
-import Numeric {- base -}
-
-import qualified Music.Theory.List as T {- hmt -}
-import qualified Music.Theory.Math as T {- hmt -}
-import qualified Music.Theory.Math.Convert as T {- hmt -}
-
--- * DIFF
-
--- | Show positive and negative values always with sign, maybe show zero, maybe right justify.
---
--- > map (num_diff_str_opt (True,2)) [-2,-1,0,1,2] == ["-2","-1"," 0","+1","+2"]
-num_diff_str_opt :: (Ord a, Num a, Show a) => (Bool,Int) -> a -> String
-num_diff_str_opt (wr_0,k) n =
-  let r = case compare n 0 of
-            LT -> '-' : show (abs n)
-            EQ -> if wr_0 then "0" else ""
-            GT -> '+' : show n
-  in if k > 0 then T.pad_left ' ' k r else r
-
--- | 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 = num_diff_str_opt (False,0)
-
--- * RATIONAL
-
--- | Pretty printer for 'Rational' using @/@ and eliding denominators of @1@.
---
--- > map rational_pp [1,3/2,5/4,2] == ["1","3/2","5/4","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, if /nil/ is True elide unit denominator.
---
--- > map (ratio_pp_opt True) [1,3/2,2] == ["1","3:2","2"]
-ratio_pp_opt :: Bool -> Rational -> String
-ratio_pp_opt nil r =
-  let f :: (Integer,Integer) -> String
-      f (n,d) = concat [show n,":",show d]
-  in case T.rational_nd r of
-       (n,1) -> if nil then show n else f (n,1)
-       x -> f x
-
--- | 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 = ratio_pp_opt False
-
--- | Show rational to /n/ decimal places.
---
--- > let r = approxRational pi 1e-100
--- > r == 884279719003555 / 281474976710656
--- > show_rational_decimal 12 r == "3.141592653590"
--- > show_rational_decimal 3 (-100) == "-100.000"
-show_rational_decimal :: Int -> Rational -> String
-show_rational_decimal n = double_pp n . fromRational
-
--- * REAL
-
--- | Show /r/ as float to /k/ places.
---
--- > real_pp 4 (1/3 :: Rational) == "0.3333"
--- > map (real_pp 4) [1,1.1,1.12,1.123,1.1234,1/0,sqrt (-1)]
-real_pp :: Real t => Int -> t -> String
-real_pp k = realfloat_pp k . T.real_to_double
-
--- | Variant that writes `∞` for Infinity.
---
--- > putStrLn $ unwords $ map (real_pp_unicode 4) [1/0,-1/0]
-real_pp_unicode :: Real t => Int -> t -> [Char]
-real_pp_unicode k r =
-  case real_pp k r of
-    "Infinity" -> "∞"
-    "-Infinity" -> "-∞"
-    s -> s
-
--- | Prints /n/ as integral or to at most /k/ decimal places. Does not print -0.
---
--- > real_pp_trunc 4 (1/3 :: Rational) == "0.3333"
--- > map (real_pp_trunc 4) [1,1.1,1.12,1.123,1.1234] == ["1","1.1","1.12","1.123","1.1234"]
--- > map (real_pp_trunc 4) [1.00009,1.00001] == ["1.0001","1"]
--- > map (real_pp_trunc 2) [59.999,60.001,-0.00,-0.001]
-real_pp_trunc :: Real t => Int -> t -> String
-real_pp_trunc k n =
-  case break (== '.') (real_pp k n) of
-    (i,[]) -> i
-    (i,j) -> case dropWhileEnd (== '0') j of
-               "." -> if i == "-0" then "0" else i
-               z -> i ++ z
-
--- | 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"]
--- > map (realfloat_pp 4) [1,1.1,1.12,1.123,1.1234,1/0,sqrt (-1)]
-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 4 0
-double_pp :: Int -> Double -> String
-double_pp = realfloat_pp
-
--- * BIN
-
--- | Read binary integer.
---
--- > unwords (map (show_bin Nothing) [0 .. 7]) == "0 1 10 11 100 101 110 111"
--- > unwords (map (show_bin (Just 3)) [0 .. 7]) == "000 001 010 011 100 101 110 111"
-show_bin :: (Integral i,Show i) => Maybe Int -> i -> String
-show_bin k n = (maybe id (\x -> T.pad_left '0' x) k) (showIntAtBase 2 intToDigit n "")
diff --git a/Music/Theory/String.hs b/Music/Theory/String.hs
deleted file mode 100644
--- a/Music/Theory/String.hs
+++ /dev/null
@@ -1,40 +0,0 @@
--- | String functions.
-module Music.Theory.String where
-
-import Data.Char {- base -}
-
--- | Case-insensitive '=='.
---
--- > map (str_eq_ci "ci") (words "CI ci Ci cI")
-str_eq_ci :: String -> String -> Bool
-str_eq_ci x y = map toUpper x == map toUpper y
-
--- | Remove @\r@.
-filter_cr :: String -> String
-filter_cr = filter (not . (==) '\r')
-
--- | Delete trailing 'Char' where 'isSpace' holds.
---
--- > delete_trailing_whitespace "   str   " == "   str"
-delete_trailing_whitespace :: String -> String
-delete_trailing_whitespace = reverse . dropWhile isSpace . reverse
-
-{- | Variant of 'unwords' that does not write spaces for NIL elements.
-
-> unwords_nil [] == ""
-> unwords_nil ["a"] == "a"
-> unwords_nil ["a",""] == "a"
-> unwords_nil ["a","b"] == "a b"
-> unwords_nil ["a","","b"] == "a b"
-> unwords_nil ["a","","","b"] == "a b"
-> unwords_nil ["a","b",""] == "a b"
-> unwords_nil ["a","b","",""] == "a b"
-> unwords_nil ["","a","b"] == "a b"
-> unwords_nil ["","","a","b"] == "a b"
--}
-unwords_nil :: [String] -> String
-unwords_nil = unwords . filter (not . null)
-
--- | Variant of 'unlines' that does not write empty lines for NIL elements.
-unlines_nil :: [String] -> String
-unlines_nil = unlines . filter (not . null)
diff --git a/Music/Theory/Tempo_Marking.hs b/Music/Theory/Tempo_Marking.hs
--- a/Music/Theory/Tempo_Marking.hs
+++ b/Music/Theory/Tempo_Marking.hs
@@ -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
diff --git a/Music/Theory/Tiling/Canon.hs b/Music/Theory/Tiling/Canon.hs
--- a/Music/Theory/Tiling/Canon.hs
+++ b/Music/Theory/Tiling/Canon.hs
@@ -1,5 +1,6 @@
 module Music.Theory.Tiling.Canon where
 
+import Control.Monad {- base -}
 import Data.List {- base -}
 import Data.List.Split {- split -}
 import Text.Printf {- base -}
@@ -37,16 +38,17 @@
 e_to_seq :: E -> [Int]
 e_to_seq (s,m,o) = map ((+ o) . (* m)) s
 
--- | Infer 'E' from sequence.
---
--- > e_from_seq [1,5,11] == ([0,2,5],2,1)
--- > e_from_seq [4,7] == ([0,1],3,4)
--- > e_from_seq [2] == ([0],1,2)
+{- | Infer 'E' from sequence.
+
+> e_from_seq [1,5,11] == ([0,2,5],2,1)
+> e_from_seq [4,7] == ([0,1],3,4)
+> e_from_seq [2] == ([0],1,2)
+-}
 e_from_seq :: [Int] -> E
 e_from_seq p =
-    let i:_ = p
+    let i = head p
         q = map (+ negate i) p
-        _:r = q
+        r = tail q
         n = if null r then 1 else foldl1 gcd r
     in (map (`div` n) q,n,i)
 
@@ -63,7 +65,7 @@
 -- | Retrograde of 'T', the result 'T' is sorted.
 --
 -- > let r = [[0,7,14],[1,5,9],[2,4,6],[3,8,13],[10,11,12]]
--- > in t_retrograde [[0,7,14],[1,6,11],[2,3,4],[5,9,13],[8,10,12]] == r
+-- > t_retrograde [[0,7,14],[1,6,11],[2,3,4],[5,9,13],[8,10,12]] == r
 t_retrograde :: T -> T
 t_retrograde t =
     let n = maximum (concat t)
@@ -72,46 +74,47 @@
 -- | The normal form of 'T' is the 'min' of /t/ and it's 't_retrograde'.
 --
 -- > let r = [[0,7,14],[1,5,9],[2,4,6],[3,8,13],[10,11,12]]
--- > in t_normal [[0,7,14],[1,6,11],[2,3,4],[5,9,13],[8,10,12]] == r
+-- > t_normal [[0,7,14],[1,6,11],[2,3,4],[5,9,13],[8,10,12]] == r
 t_normal :: T -> T
 t_normal t = min t (t_retrograde t)
 
--- | Derive set of 'R' from 'T'.
---
--- > let {r = [(21,[0,1,2],[10,8,2,4,7,5,1],[0,1,2,3,5,8,14])]
--- >     ;t = [[0,10,20],[1,9,17],[2,4,6],[3,7,11],[5,12,19],[8,13,18],[14,15,16]]}
--- > in r_from_t t == r
+{- | Derive set of 'R' from 'T'.
+
+> let r = [(21,[0,1,2],[10,8,2,4,7,5,1],[0,1,2,3,5,8,14])]
+> let t = [[0,10,20],[1,9,17],[2,4,6],[3,7,11],[5,12,19],[8,13,18],[14,15,16]]
+> r_from_t t == r
+-}
 r_from_t :: T -> [R]
 r_from_t t =
     let e = map e_from_seq t
         n = maximum (concat t) + 1
         t3_1 (i,_,_) = i
-        f z = let (s:_,m,o) = unzip3 z in (n,s,m,o)
+        f z = let (s,m,o) = unzip3 z in (n,head s,m,o)
     in map f (T.group_on t3_1 e)
 
 -- * Construction
 
 -- | 'msum' '.' 'map' 'return'.
 --
--- > observeAll (fromList [1..7]) == [1..7]
-fromList :: L.MonadPlus m => [a] -> m a
-fromList = L.msum . map return
+-- > L.observeAll (fromList [1..7]) == [1..7]
+fromList :: MonadPlus m => [a] -> m a
+fromList = msum . map return
 
 -- | Search for /perfect/ tilings of the sequence 'S' using
 -- multipliers from /m/ to degree /n/ with /k/ parts.
-perfect_tilings_m :: L.MonadPlus m => [S] -> [Int] -> Int -> Int -> m T
+perfect_tilings_m :: MonadPlus m => [S] -> [Int] -> Int -> Int -> m T
 perfect_tilings_m s m n k =
     let rec p q =
             if length q == k
             then return (sort q)
             else do m' <- fromList m
-                    L.guard (m' `notElem` p)
+                    guard (m' `notElem` p)
                     s' <- fromList s
                     let i = n - (maximum s' * m') - 1
                     o <- fromList [0..i]
                     let s'' = e_to_seq (s',m',o)
                         q' = concat q
-                    L.guard (all (`notElem` q') s'')
+                    guard (all (`notElem` q') s'')
                     rec (m':p) (s'':q)
     in rec [] []
 
@@ -120,14 +123,12 @@
 > perfect_tilings [[0,1]] [1..3] 6 3 == []
 
 > let r = [[[0,7,14],[1,5,9],[2,4,6],[3,8,13],[10,11,12]]]
-> in perfect_tilings [[0,1,2]] [1,2,4,5,7] 15 5 == r
+> perfect_tilings [[0,1,2]] [1,2,4,5,7] 15 5 == r
 
 > length (perfect_tilings [[0,1,2]] [1..12] 15 5) == 1
 
-> let r = [[[0,1],[2,5],[3,7],[4,6]]
->         ,[[0,1],[2,6],[3,5],[4,7]]
->         ,[[0,2],[1,4],[3,7],[5,6]]]
-> in perfect_tilings [[0,1]] [1..4] 8 4 == r
+> let r = [[[0,1],[2,5],[3,7],[4,6]], [[0,1],[2,6],[3,5],[4,7]] ,[[0,2],[1,4],[3,7],[5,6]]]
+> perfect_tilings [[0,1]] [1..4] 8 4 == r
 
 > let r = [[[0,1],[2,5],[3,7],[4,9],[6,8]]
 >         ,[[0,1],[2,7],[3,5],[4,8],[6,9]]
@@ -139,10 +140,10 @@
 Johnson 2004, p.2
 
 > let r = [[0,6,12],[1,8,15],[2,11,20],[3,5,7],[4,9,14],[10,13,16],[17,18,19]]
-> in perfect_tilings [[0,1,2]] [1,2,3,5,6,7,9] 21 7 == [r]
+> perfect_tilings [[0,1,2]] [1,2,3,5,6,7,9] 21 7 == [r]
 
 > let r = [[0,10,20],[1,9,17],[2,4,6],[3,7,11],[5,12,19],[8,13,18],[14,15,16]]
-> in perfect_tilings [[0,1,2]] [1,2,4,5,7,8,10] 21 7 == [t_retrograde r]
+> perfect_tilings [[0,1,2]] [1,2,4,5,7,8,10] 21 7 == [t_retrograde r]
 
 -}
 perfect_tilings :: [S] -> [Int] -> Int -> Int -> [T]
diff --git a/Music/Theory/Time/Bel1990/R.hs b/Music/Theory/Time/Bel1990/R.hs
--- a/Music/Theory/Time/Bel1990/R.hs
+++ b/Music/Theory/Time/Bel1990/R.hs
@@ -11,7 +11,7 @@
   Centre National de la Recherche Scientifique, 1992. /GRTC 458/
   (<http://www.lpl.univ-aix.fr/~belbernard/music/2algorithms.pdf>)
 
-For details see <http://rd.slavepianos.org/t/hmt-texts>.
+For details see <http://rohandrape.net/?t=hmt-texts>.
 -}
 
 module Music.Theory.Time.Bel1990.R where
@@ -22,18 +22,16 @@
 import Data.Ratio {- base -}
 
 import qualified Text.Parsec as P {- parsec -}
-import qualified Text.Parsec.String as P {- parsec -}
 
 import qualified Music.Theory.List 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)
@@ -45,6 +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
@@ -53,25 +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
@@ -89,13 +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
@@ -135,14 +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)
@@ -159,6 +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]
 
@@ -194,18 +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')
 
@@ -273,10 +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
 
@@ -313,9 +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
@@ -324,55 +376,52 @@
 
 -- * Parsing
 
--- | A 'Char' parser.
-type P a = P.GenParser Char () a
-
 -- | Parse 'Rest' 'Term'.
 --
 -- > P.parse p_rest "" "-"
-p_rest :: P (Term a)
-p_rest = liftM (const Rest) (P.char '-')
+p_rest :: T.P (Term a)
+p_rest = fmap (const Rest) (P.char '-')
 
 -- | Parse 'Rest' 'Term'.
 --
 -- > P.parse p_nrests "" "3"
-p_nrests :: P (Bel a)
-p_nrests = liftM nrests p_non_negative_integer
+p_nrests :: T.P (Bel a)
+p_nrests = fmap nrests p_non_negative_integer
 
 -- | Parse 'Continue' 'Term'.
 --
 -- > P.parse p_continue "" "_"
-p_continue :: P (Term a)
-p_continue = liftM (const Continue) (P.char '_')
+p_continue :: T.P (Term a)
+p_continue = fmap (const Continue) (P.char '_')
 
 -- | Parse 'Char' 'Value' 'Term'.
 --
 -- > P.parse p_char_value "" "a"
-p_char_value :: P (Term Char)
-p_char_value = liftM Value P.lower
+p_char_value :: T.P (Term Char)
+p_char_value = fmap Value P.lower
 
 -- | Parse 'Char' 'Term'.
 --
 -- > P.parse (P.many1 p_char_term) "" "-_a"
-p_char_term :: P (Term Char)
+p_char_term :: T.P (Term Char)
 p_char_term = P.choice [p_rest,p_continue,p_char_value]
 
 -- | Parse 'Char' 'Node'.
 --
 -- > P.parse (P.many1 p_char_node) "" "-_a"
-p_char_node :: P (Bel Char)
-p_char_node = liftM Node p_char_term
+p_char_node :: T.P (Bel Char)
+p_char_node = fmap Node p_char_term
 
 -- | Parse non-negative 'Integer'.
 --
 -- > P.parse p_non_negative_integer "" "3"
-p_non_negative_integer :: P Integer
-p_non_negative_integer = liftM read (P.many1 P.digit)
+p_non_negative_integer :: T.P Integer
+p_non_negative_integer = fmap read (P.many1 P.digit)
 
 -- | Parse non-negative 'Rational'.
 --
 -- > P.parse (p_non_negative_rational `P.sepBy` (P.char ',')) "" "3%5,2/3"
-p_non_negative_rational :: P Rational
+p_non_negative_rational :: T.P Rational
 p_non_negative_rational = do
   n <- p_non_negative_integer
   _ <- P.oneOf "%/"
@@ -383,7 +432,7 @@
 --
 -- > P.parse p_non_negative_double "" "3.5"
 -- > P.parse (p_non_negative_double `P.sepBy` (P.char ',')) "" "3.5,7.2,1.0"
-p_non_negative_double :: P Double
+p_non_negative_double :: T.P Double
 p_non_negative_double = do
   a <- P.many1 P.digit
   _ <- P.char '.'
@@ -393,16 +442,16 @@
 -- | Parse non-negative number as 'Rational'.
 --
 -- > P.parse (p_non_negative_number `P.sepBy` (P.char ',')) "" "7%2,3.5,3"
-p_non_negative_number :: P Rational
+p_non_negative_number :: T.P Rational
 p_non_negative_number =
     P.choice [P.try p_non_negative_rational
-             ,P.try (liftM toRational p_non_negative_double)
-             ,P.try (liftM toRational p_non_negative_integer)]
+             ,P.try (fmap toRational p_non_negative_double)
+             ,P.try (fmap toRational p_non_negative_integer)]
 
 -- | Parse 'Mul'.
 --
 -- > P.parse (P.many1 p_mul) "" "/3*3/2"
-p_mul :: P (Bel a)
+p_mul :: T.P (Bel a)
 p_mul = do
   op <- P.oneOf "*/"
   n <- p_non_negative_number
@@ -413,50 +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'.
diff --git a/Music/Theory/Time/Duration.hs b/Music/Theory/Time/Duration.hs
deleted file mode 100644
--- a/Music/Theory/Time/Duration.hs
+++ /dev/null
@@ -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')
diff --git a/Music/Theory/Time/KeyKit.hs b/Music/Theory/Time/KeyKit.hs
new file mode 100644
--- /dev/null
+++ b/Music/Theory/Time/KeyKit.hs
@@ -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)
diff --git a/Music/Theory/Time/KeyKit/Basic.hs b/Music/Theory/Time/KeyKit/Basic.hs
new file mode 100644
--- /dev/null
+++ b/Music/Theory/Time/KeyKit/Basic.hs
@@ -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
diff --git a/Music/Theory/Time/KeyKit/Parser.hs b/Music/Theory/Time/KeyKit/Parser.hs
new file mode 100644
--- /dev/null
+++ b/Music/Theory/Time/KeyKit/Parser.hs
@@ -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
diff --git a/Music/Theory/Time/Notation.hs b/Music/Theory/Time/Notation.hs
deleted file mode 100644
--- a/Music/Theory/Time/Notation.hs
+++ /dev/null
@@ -1,465 +0,0 @@
--- | Time and duration notations.
-module Music.Theory.Time.Notation where
-
-import Data.List.Split {- split -}
-import qualified Data.Time as T {- time -}
-import Text.Printf {- base -}
-
-import Music.Theory.Function {- hmt -}
-
--- * Integral types
-
--- | Week, one-indexed, ie. 1-52
-type WEEK = Int
-
--- | Week, one-indexed, ie. 1-31
-type DAY = Int
-
--- | Hour, zero-indexed, ie. 0-23
-type HOUR = Int
-
--- | Minute, zero-indexed, ie. 0-59
-type MIN = Int
-
--- | Second, zero-indexed, ie. 0-59
-type SEC = Int
-
--- | Centi-seconds, one-indexed, ie. 0-99
-type CSEC = Int -- (0-99)
-
--- * Composite types
-
--- | Minutes, seconds as @(min,sec)@
-type MinSec n = (n,n)
-
--- | Type specialised.
-type MINSEC = (MIN,SEC)
-
--- | Minutes, seconds, centi-seconds as @(min,sec,csec)@
-type MinCsec n = (n,n,n)
-
--- | Type specialised.
-type MINCSEC = (MIN,SEC,CSEC)
-
--- | (Hours,Minutes,Seconds)
-type HMS = (HOUR,MIN,SEC)
-
--- | (Days,Hours,Minutes,Seconds)
-type DHMS = (DAY,HOUR,MIN,SEC)
-
--- * Fractional types
-
--- | Fractional days.
-type FDAY = Double
-
--- | Fractional hour, ie. 1.50 is one and a half hours, ie. 1 hour and 30 minutes.
-type FHOUR = Double
-
--- | Fractional seconds.
-type FSEC = Double
-
--- | Fractional minutes and seconds (mm.ss, ie. 01.45 is 1 minute and 45 seconds).
-type FMINSEC = Double
-
--- * T.UTCTime format strings.
-
--- | 'T.parseTimeOrError' with 'T.defaultTimeLocale'.
-parse_time_str :: T.ParseTime t => String -> String -> t
-parse_time_str = T.parseTimeOrError True T.defaultTimeLocale
-
-format_time_str :: T.FormatTime t => String -> t -> String
-format_time_str = T.formatTime T.defaultTimeLocale
-
--- * ISO-8601
-
--- | Parse date in ISO-8601 extended (@YYYY-MM-DD@) or basic (@YYYYMMDD@) form.
---
--- > T.toGregorian (T.utctDay (parse_iso8601_date "2011-10-09")) == (2011,10,09)
--- > T.toGregorian (T.utctDay (parse_iso8601_date "20190803")) == (2019,08,03)
-parse_iso8601_date :: String -> T.UTCTime
-parse_iso8601_date s =
-  case length s of
-    8 -> parse_time_str "%Y%m%d" s -- basic
-    10 -> parse_time_str "%F" s -- extended
-    _ -> error "parse_iso8601_date?"
-
--- | Format date in ISO-8601 form.
---
--- > format_iso8601_date True (parse_iso8601_date "2011-10-09") == "2011-10-09"
--- > format_iso8601_date False (parse_iso8601_date "20190803") == "20190803"
-format_iso8601_date :: T.FormatTime t => Bool -> t -> String
-format_iso8601_date ext = if ext then format_time_str "%F" else format_time_str "%Y%m%d"
-
-{- | Format date in ISO-8601 (@YYYY-WWW@) form.
-
-> r = ["2016-W52","2011-W40"]
-> map (format_iso8601_week . parse_iso8601_date) ["2017-01-01","2011-10-09"] == r
-
--}
-format_iso8601_week :: T.FormatTime t => t -> String
-format_iso8601_week = format_time_str "%G-W%V"
-
--- | Parse ISO-8601 time is extended (@HH:MM:SS@) or basic (@HHMMSS@) form.
---
--- > format_iso8601_time True (parse_iso8601_time "21:44:00") == "21:44:00"
--- > format_iso8601_time False (parse_iso8601_time "172511") == "172511"
-parse_iso8601_time :: String -> T.UTCTime
-parse_iso8601_time s =
-  case length s of
-    6 -> parse_time_str "%H%M%S" s -- basic
-    8 -> parse_time_str "%H:%M:%S" s -- extended
-    _ -> error "parse_iso8601_time?"
-
--- | Format time in ISO-8601 form.
---
--- > format_iso8601_time True (parse_iso8601_date_time "2011-10-09T21:44:00") == "21:44:00"
--- > format_iso8601_time False (parse_iso8601_date_time "20190803T172511") == "172511"
-format_iso8601_time :: T.FormatTime t => Bool -> t -> String
-format_iso8601_time ext = format_time_str (if ext then "%H:%M:%S" else "%H%M%S")
-
--- | Parse date and time in extended or basic forms.
---
--- > T.utctDayTime (parse_iso8601_date_time "2011-10-09T21:44:00") == T.secondsToDiffTime 78240
--- > T.utctDayTime (parse_iso8601_date_time "20190803T172511") == T.secondsToDiffTime 62711
-parse_iso8601_date_time :: String -> T.UTCTime
-parse_iso8601_date_time s =
-  case length s of
-    15 -> parse_time_str "%Y%m%dT%H%M%S" s -- basic
-    19 -> parse_time_str "%FT%H:%M:%S" s -- extended
-    _ -> error "parse_iso8601_date_time?"
-
-{- | Format date in @YYYY-MM-DD@ and time in @HH:MM:SS@ forms.
-
-> t = parse_iso8601_date_time "2011-10-09T21:44:00"
-> format_iso8601_date_time True t == "2011-10-09T21:44:00"
-> format_iso8601_date_time False t == "20111009T214400"
-
--}
-format_iso8601_date_time :: T.FormatTime t => Bool -> t -> String
-format_iso8601_date_time ext = format_time_str (if ext then "%FT%H:%M:%S" else "%Y%m%dT%H%M%S")
-
--- * FSEC
-
--- | Translate fractional seconds to picoseconds.
---
--- > fsec_to_picoseconds 78240.05
-fsec_to_picoseconds :: FSEC -> Integer
-fsec_to_picoseconds s = floor (s * (10 ** 12))
-
-fsec_to_difftime :: FSEC -> T.DiffTime
-fsec_to_difftime = T.picosecondsToDiffTime . fsec_to_picoseconds
-
--- * FMINSEC
-
--- | Translate fractional minutes.seconds to picoseconds.
---
--- > map fminsec_to_fsec [0.45,15.355] == [45,935.5]
-fminsec_to_fsec :: FMINSEC -> FSEC
-fminsec_to_fsec n =
-    let m = ffloor n
-        s = (n - m) * 100
-    in (m * 60) + s
-
-fminsec_to_sec_generic :: (RealFrac f,Integral i) => f -> i
-fminsec_to_sec_generic n =
-    let m = floor n
-        s = round ((n - fromIntegral m) * 100)
-    in (m * 60) + s
-
--- | Fractional minutes are mm.ss, so that 15.35 is 15 minutes and 35 seconds.
---
--- > map fminsec_to_sec [0.45,15.35] == [45,935]
-fminsec_to_sec :: FMINSEC -> SEC
-fminsec_to_sec = fminsec_to_sec_generic
-
--- > fsec_to_fminsec 935.5 == 15.355
-fsec_to_fminsec :: FSEC -> FMINSEC
-fsec_to_fminsec n =
-    let m = ffloor (n / 60)
-        s = n - (m * 60)
-    in m + (s / 100)
-
--- > sec_to_fminsec 935 == 15.35
-sec_to_fminsec :: SEC -> FMINSEC
-sec_to_fminsec n =
-    let m = ffloor (fromIntegral n / 60)
-        s = fromIntegral n - (m * 60)
-    in m + (s / 100)
-
--- > fminsec_add 1.30 0.45 == 2.15
--- > fminsec_add 1.30 0.45 == 2.15
-fminsec_add :: BinOp FMINSEC
-fminsec_add p q = fsec_to_fminsec (fminsec_to_fsec p + fminsec_to_fsec q)
-
-fminsec_sub :: BinOp FMINSEC
-fminsec_sub p q = fsec_to_fminsec (fminsec_to_fsec p - fminsec_to_fsec q)
-
--- > fminsec_mul 0.45 2 == 1.30
-fminsec_mul :: BinOp FMINSEC
-fminsec_mul t n = fsec_to_fminsec (fminsec_to_fsec t * n)
-
--- * FHOUR
-
--- | Type specialised 'fromInteger' of 'floor'.
-ffloor :: Double -> Double
-ffloor = fromInteger . floor
-
--- | Fractional hour to (hours,minutes,seconds).
---
--- > fhour_to_hms 21.75 == (21,45,0)
-fhour_to_hms :: FHOUR -> HMS
-fhour_to_hms h =
-    let m = (h - ffloor h) * 60
-        s = (m - ffloor m) * 60
-    in (floor h,floor m,round s)
-
--- | HMS to fractional hours.
---
--- > hms_to_fhour (21,45,0) == 21.75
-hms_to_fhour :: HMS -> FHOUR
-hms_to_fhour (h,m,s) = fromIntegral h + (fromIntegral m / 60) + (fromIntegral s / (60 * 60))
-
--- | Fractional hour to seconds.
---
--- > fhour_to_fsec 21.75 == 78300.0
-fhour_to_fsec :: FHOUR -> FSEC
-fhour_to_fsec = (*) (60 * 60)
-
-fhour_to_difftime :: FHOUR -> T.DiffTime
-fhour_to_difftime = fsec_to_difftime . fhour_to_fsec
-
--- * FDAY
-
--- | Time in fractional days.
---
--- > round (utctime_to_fday (parse_iso8601_date_time "2011-10-09T09:00:00")) == 55843
--- > round (utctime_to_fday (parse_iso8601_date_time "2011-10-09T21:00:00")) == 55844
-utctime_to_fday :: T.UTCTime -> FDAY
-utctime_to_fday t =
-    let d = T.utctDay t
-        d' = fromIntegral (T.toModifiedJulianDay d)
-        s = T.utctDayTime t
-        s_max = 86401
-    in d' + (fromRational (toRational s) / s_max)
-
--- * DiffTime
-
--- | 'T.DiffTime' in fractional seconds.
---
--- > difftime_to_fsec (hms_to_difftime (21,44,30)) == 78270
-difftime_to_fsec :: T.DiffTime -> FSEC
-difftime_to_fsec = fromRational . toRational
-
--- | 'T.DiffTime' in fractional minutes.
---
--- > difftime_to_fmin (hms_to_difftime (21,44,30)) == 1304.5
-difftime_to_fmin :: T.DiffTime -> Double
-difftime_to_fmin = (/ 60) . difftime_to_fsec
-
--- | 'T.DiffTime' in fractional hours.
---
--- > difftime_to_fhour (hms_to_difftime (21,45,00)) == 21.75
-difftime_to_fhour :: T.DiffTime -> FHOUR
-difftime_to_fhour = (/ 60) . difftime_to_fmin
-
-hms_to_difftime :: HMS -> T.DiffTime
-hms_to_difftime = fhour_to_difftime . hms_to_fhour
-
--- * HMS
-
-hms_to_sec :: HMS -> SEC
-hms_to_sec (h,m,s) = h * 60 * 60 + m * 60 + s
-
--- | Seconds to (hours,minutes,seconds).
---
--- > map sec_to_hms [60-1,60+1,60*60-1,60*60+1] == [(0,0,59),(0,1,1),(0,59,59),(1,0,1)]
-sec_to_hms :: SEC -> HMS
-sec_to_hms s =
-  let (h,s') = s `divMod` (60 * 60)
-      (m,s'') = sec_to_minsec s'
-  in (h,m,s'')
-
--- | 'HMS' pretty printer.
---
--- > map (hms_pp True) [(0,1,2),(1,2,3)] == ["01:02","01:02:03"]
-hms_pp :: Bool -> HMS -> String
-hms_pp trunc (h,m,s) =
-  if trunc && h == 0
-  then printf "%02d:%02d" m s
-  else printf "%02d:%02d:%02d" h m s
-
--- * 'HMS' parser.
---
--- > hms_parse "0:01:00" == (0,1,0)
-hms_parse :: String -> HMS
-hms_parse x =
-    case splitOn ":" x of
-      [h,m,s] -> (read h,read m,read s)
-      _ -> error "parse_hms"
-
--- * MINSEC
-
--- | 'divMod' by @60@.
---
--- > sec_to_minsec 123 == (2,3)
-sec_to_minsec :: Integral n => n -> MinSec n
-sec_to_minsec = flip divMod 60
-
--- | Inverse of 'sec_minsec'.
---
--- > minsec_to_sec (2,3) == 123
-minsec_to_sec :: Num n => MinSec n -> n
-minsec_to_sec (m,s) = m * 60 + s
-
--- | Convert /p/ and /q/ to seconds, apply /f/, and convert back to 'MinSec'.
-minsec_binop :: Integral t => (t -> t -> t) -> MinSec t -> MinSec t -> MinSec t
-minsec_binop f p q = sec_to_minsec (f (minsec_to_sec p) (minsec_to_sec q))
-
--- | 'minsec_binop' '-', assumes /q/ precedes /p/.
---
--- > minsec_sub (2,35) (1,59) == (0,36)
-minsec_sub :: Integral n => MinSec n -> MinSec n -> MinSec n
-minsec_sub = minsec_binop (-)
-
--- | 'minsec_binop' 'subtract', assumes /p/ precedes /q/.
---
--- > minsec_diff (1,59) (2,35) == (0,36)
-minsec_diff :: Integral n => MinSec n -> MinSec n -> MinSec n
-minsec_diff = minsec_binop subtract
-
--- | 'minsec_binop' '+'.
---
--- > minsec_add (1,59) (2,35) == (4,34)
-minsec_add :: Integral n => MinSec n -> MinSec n -> MinSec n
-minsec_add = minsec_binop (+)
-
--- | 'foldl' of 'minsec_add'
---
--- > minsec_sum [(1,59),(2,35),(4,34)] == (9,08)
-minsec_sum :: Integral n => [MinSec n] -> MinSec n
-minsec_sum = foldl minsec_add (0,0)
-
--- | 'round' fractional seconds to @(min,sec)@.
---
--- > map fsec_to_minsec [59.49,60,60.51] == [(0,59),(1,0),(1,1)]
-fsec_to_minsec :: FSEC -> MINSEC
-fsec_to_minsec = sec_to_minsec . round
-
--- | 'MINSEC' pretty printer.
---
--- > map (minsec_pp . fsec_to_minsec) [59,61] == ["00:59","01:01"]
-minsec_pp :: MINSEC -> String
-minsec_pp (m,s) = printf "%02d:%02d" m s
-
--- * 'MinSec' parser.
-minsec_parse :: (Num n,Read n) => String -> MinSec n
-minsec_parse x =
-    case splitOn ":" x of
-      [m,s] -> (read m,read s)
-      _ -> error "parse_minsec"
-
--- * MINCSEC
-
--- | Fractional seconds to @(min,sec,csec)@, csec value is 'round'ed.
---
--- > map fsec_to_mincsec [1,1.5,4/3] == [(0,1,0),(0,1,50),(0,1,33)]
-fsec_to_mincsec :: FSEC -> MINCSEC
-fsec_to_mincsec tm =
-    let tm' = floor tm
-        (m,s) = sec_to_minsec tm'
-        cs = round ((tm - fromIntegral tm') * 100)
-    in (m,s,cs)
-
--- | Inverse of 'fsec_mincsec'.
-mincsec_to_fsec :: Real n => MinCsec n -> FSEC
-mincsec_to_fsec (m,s,cs) = realToFrac m * 60 + realToFrac s + (realToFrac cs / 100)
-
--- > map (mincsec_to_csec . fsec_to_mincsec) [1,6+2/3,123.45] == [100,667,12345]
-mincsec_to_csec :: Num n => MinCsec n -> n
-mincsec_to_csec (m,s,cs) = m * 60 * 100 + s * 100 + cs
-
--- | Centi-seconds to 'MinCsec'.
---
--- > map csec_to_mincsec [123,12345] == [(0,1,23),(2,3,45)]
-csec_to_mincsec :: Integral n => n -> MinCsec n
-csec_to_mincsec csec =
-    let (m,cs) = csec `divMod` 6000
-        (s,cs') = cs `divMod` 100
-    in (m,s,cs')
-
--- | 'MINCSEC' pretty printer, concise mode omits centiseconds when zero.
---
--- > map (mincsec_pp_opt True . fsec_to_mincsec) [1,60.5] == ["00:01","01:00.50"]
-mincsec_pp_opt :: Bool -> MINCSEC -> String
-mincsec_pp_opt concise (m,s,cs) =
-  if concise && cs == 0
-  then printf "%02d:%02d" m s
-  else printf "%02d:%02d.%02d" m s cs
-
--- | 'MINCSEC' pretty printer.
---
--- > let r = ["00:01.00","00:06.67","02:03.45"]
--- > map (mincsec_pp . fsec_to_mincsec) [1,6+2/3,123.45] == r
-mincsec_pp :: MINCSEC -> String
-mincsec_pp = mincsec_pp_opt False
-
-mincsec_binop :: Integral t => (t -> t -> t) -> MinCsec t -> MinCsec t -> MinCsec t
-mincsec_binop f p q = csec_to_mincsec (f (mincsec_to_csec p) (mincsec_to_csec q))
-
--- * DHMS
-
--- | Convert seconds into (days,hours,minutes,seconds).
-sec_to_dhms_generic :: Integral n => n -> (n,n,n,n)
-sec_to_dhms_generic n =
-    let (d,h') = n `divMod` (24 * 60 * 60)
-        (h,m') = h' `divMod` (60 * 60)
-        (m,s) = m' `divMod` 60
-    in (d,h,m,s)
-
--- | Type specialised 'sec_to_dhms_generic'.
---
--- > sec_to_dhms 1475469 == (17,1,51,9)
-sec_to_dhms :: SEC -> DHMS
-sec_to_dhms = sec_to_dhms_generic
-
--- | Inverse of 'seconds_to_dhms'.
---
--- > dhms_to_sec (17,1,51,9) == 1475469
-dhms_to_sec :: Num n => (n,n,n,n) -> n
-dhms_to_sec (d,h,m,s) = sum [d * 24 * 60 * 60,h * 60 * 60,m * 60,s]
-
--- | Generic form of 'parse_dhms'.
-parse_dhms_generic :: (Integral n,Read n) => String -> (n,n,n,n)
-parse_dhms_generic =
-    let sep_elem = split . keepDelimsR . oneOf
-        sep_last x = let e:x' = reverse x in (reverse x',e)
-        p x = case sep_last x of
-                (n,'d') -> read n * 24 * 60 * 60
-                (n,'h') -> read n * 60 * 60
-                (n,'m') -> read n * 60
-                (n,'s') -> read n
-                _ -> error "parse_dhms"
-    in sec_to_dhms_generic . sum . map p . filter (not . null) . sep_elem "dhms"
-
--- | Parse DHMS text.  All parts are optional, order is not
--- significant, multiple entries are allowed.
---
--- > parse_dhms "17d1h51m9s" == (17,1,51,9)
--- > parse_dhms "1s3d" == (3,0,0,1)
--- > parse_dhms "1h1h" == (0,2,0,0)
-parse_dhms :: String -> DHMS
-parse_dhms = parse_dhms_generic
-
--- * WEEK
-
--- | Week that /t/ lies in.
---
--- > map (time_to_week . parse_iso8601_date) ["2017-01-01","2011-10-09"] == [52,40]
-time_to_week :: T.UTCTime -> WEEK
-time_to_week = read . format_time_str "%V"
-
--- * UTIL
-
--- | Given printer, pretty print time span.
-span_pp :: (t -> String) -> (t,t) -> String
-span_pp f (t1,t2) = concat [f t1," - ",f t2]
diff --git a/Music/Theory/Time/Seq.hs b/Music/Theory/Time/Seq.hs
--- a/Music/Theory/Time/Seq.hs
+++ b/Music/Theory/Time/Seq.hs
@@ -9,12 +9,12 @@
 import Safe {- safe -}
 
 import qualified Data.List.Ordered as O {- data-ordlist -}
-import qualified Data.Map as M {- containers -}
+import qualified Data.Map as Map {- containers -}
 
-import qualified Music.Theory.List as T {- hmt -}
-import qualified Music.Theory.Math as T {- hmt -}
-import qualified Music.Theory.Ord as T {- hmt -}
-import qualified Music.Theory.Tuple as T {- hmt -}
+import qualified 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
 
@@ -34,30 +34,36 @@
 
 -- | Pattern sequence.
 -- The duration is a triple of /logical/, /sounding/ and /forward/ durations.
--- Ie. the time it conceptually takes, the time it actually takes, and the time to the next event.
+-- 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.
--- /t/ is the start-time of the value.
+-- /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.
 -- /t/ is a duple of /start-time/ and /duration/.
--- Holes exist where @st(n) + du(n)@ '<' @st(n+1)@.
+-- 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
 
@@ -221,6 +227,10 @@
 wseq_merge_set :: Ord t => [Wseq t a] -> Wseq t a
 wseq_merge_set = T.merge_set_by w_compare
 
+-- | Merge considering only start times.
+eseq_merge :: Ord t => Eseq t a -> Eseq t a -> Eseq t a
+eseq_merge = O.mergeBy (compare `on` (T.t3_fst . fst))
+
 -- * Lookup
 
 -- | Locate nodes to the left and right of indicated time.
@@ -253,13 +263,16 @@
 -- * Lseq
 
 -- | Iterpolation type enumeration.
-data Interpolation_T = None | Linear
-                     deriving (Eq,Enum,Show)
+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
@@ -290,11 +303,11 @@
 
 -- | 'map' over time (/t/) data.
 seq_tmap :: (t1 -> t2) -> [(t1,a)] -> [(t2,a)]
-seq_tmap f = map (\(p,q) -> (f p,q))
+seq_tmap f = map (first f)
 
 -- | 'map' over element (/e/) data.
 seq_map :: (e1 -> e2) -> [(t,e1)] -> [(t,e2)]
-seq_map f = map (\(p,q) -> (p,f q))
+seq_map f = map (second f)
 
 -- | 'map' /t/ and /e/ simultaneously.
 --
@@ -319,7 +332,7 @@
 -- | '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'.
@@ -350,11 +363,11 @@
 
 -- | Apply /f/ at time points of 'Wseq'.
 wseq_tmap_st :: (t -> t) -> Wseq t a -> Wseq t a
-wseq_tmap_st f = seq_tmap (bimap f id)
+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 = seq_tmap (bimap id f)
+wseq_tmap_dur f = seq_tmap (second f)
 
 -- * Partition
 
@@ -362,11 +375,11 @@
 -- a sequence into voices.
 seq_partition :: Ord v => (a -> v) -> [(t,a)] -> [(v,[(t,a)])]
 seq_partition voice sq =
-    let assign m (t,a) = M.insertWith (++) (voice a) [(t,a)] m
+    let assign m (t,a) = Map.insertWith (++) (voice a) [(t,a)] m
         from_map = sortOn fst .
-                   map (\(v,l) -> (v,reverse l)) .
-                   M.toList
-    in from_map (foldl assign M.empty sq)
+                   map (second reverse) .
+                   Map.toList
+    in from_map (foldl assign Map.empty sq)
 
 -- | Type specialised 'seq_partition'.
 --
@@ -405,16 +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')]
--- > 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
@@ -429,7 +443,7 @@
 -- > 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
@@ -570,7 +584,7 @@
   let recur sq =
         case sq of
           [] -> False
-          e0:sq' -> if wseq_find_overlap_1 eq_fn e0 sq' then True else recur sq'
+          e0:sq' -> wseq_find_overlap_1 eq_fn e0 sq' || recur sq'
   in recur
 
 {- | Remove overlaps by deleting any overlapping nodes.
@@ -616,10 +630,11 @@
 > 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 -}
+> 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 =
@@ -834,6 +849,13 @@
 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"
@@ -870,6 +892,27 @@
          [] -> []
          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 a /dur/
@@ -888,6 +931,17 @@
               Nothing -> T.d_dx t
     in wseq_zip t d 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|"
@@ -938,6 +992,9 @@
          ((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
@@ -960,7 +1017,7 @@
 wseq_cycle_ls sq =
     let (_,et) = wseq_tspan sq
         t_sq = iterate (+ et) 0
-    in map (\x -> wseq_tmap (\(t,d) -> (x + t,d)) sq) t_sq
+    in map (\x -> wseq_tmap (first (+ x)) sq) t_sq
 
 -- | Only finite 'Wseq' can be cycled, the resulting Wseq is infinite.
 --
@@ -1046,3 +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
diff --git a/Music/Theory/Time_Signature.hs b/Music/Theory/Time_Signature.hs
--- a/Music/Theory/Time_Signature.hs
+++ b/Music/Theory/Time_Signature.hs
@@ -6,7 +6,7 @@
 
 import Music.Theory.Duration
 import Music.Theory.Duration.Name
-import Music.Theory.Duration.RQ
+import Music.Theory.Duration.Rq
 import Music.Theory.Math
 
 -- | A Time Signature is a /(numerator,denominator)/ pair.
@@ -49,26 +49,26 @@
       (6,2) -> [dotted_breve]
       _ -> error ("ts_whole_note: " ++ show t)
 
--- | Duration of measure in 'RQ'.
+-- | Duration of measure in 'Rq'.
 --
 -- > map ts_whole_note_rq [(3,8),(2,2)] == [3/2,4]
-ts_whole_note_rq :: Time_Signature -> RQ
+ts_whole_note_rq :: Time_Signature -> Rq
 ts_whole_note_rq = sum . map duration_to_rq . ts_whole_note
 
--- | Duration, in 'RQ', of a measure of indicated 'Time_Signature'.
+-- | Duration, in 'Rq', of a measure of indicated 'Time_Signature'.
 --
 -- > map ts_rq [(3,4),(5,8)] == [3,5/2]
-ts_rq :: Time_Signature -> RQ
+ts_rq :: Time_Signature -> Rq
 ts_rq (n,d) = (4 * n) % d
 
 -- | 'compare' 'on' 'ts_rq'.
 ts_compare :: Time_Signature -> Time_Signature -> Ordering
 ts_compare = compare `on` ts_rq
 
--- | 'Time_Signature' derived from whole note duration in 'RQ' form.
+-- | 'Time_Signature' derived from whole note duration in 'Rq' form.
 --
 -- > map rq_to_ts [4,3/2,7/4,6] == [(4,4),(3,8),(7,16),(6,4)]
-rq_to_ts :: RQ -> Time_Signature
+rq_to_ts :: Rq -> Time_Signature
 rq_to_ts rq =
     let n = numerator rq
         d = denominator rq * 4
@@ -81,7 +81,7 @@
 -- > ts_divisions (2,2) == [2,2]
 -- > ts_divisions (1,1) == [4]
 -- > ts_divisions (7,4) == [1,1,1,1,1,1,1]
-ts_divisions :: Time_Signature -> [RQ]
+ts_divisions :: Time_Signature -> [Rq]
 ts_divisions (i,j) =
     let k = fromIntegral i
     in replicate k (recip (j % 4))
@@ -123,23 +123,23 @@
 -- | A composite time signature is a sequence of 'Time_Signature's.
 type Composite_Time_Signature = [Time_Signature]
 
--- | The 'RQ' is the 'sum' of 'ts_rq' of the elements.
+-- | The 'Rq' is the 'sum' of 'ts_rq' of the elements.
 --
 -- > cts_rq [(3,4),(1,8)] == 3 + 1/2
-cts_rq :: Composite_Time_Signature -> RQ
+cts_rq :: Composite_Time_Signature -> Rq
 cts_rq = sum . map ts_rq
 
 -- | The divisions are the 'concat' of the 'ts_divisions' of the
 -- elements.
 --
 -- > cts_divisions [(3,4),(1,8)] == [1,1,1,1/2]
-cts_divisions :: Composite_Time_Signature -> [RQ]
+cts_divisions :: Composite_Time_Signature -> [Rq]
 cts_divisions = concatMap ts_divisions
 
--- | Pulses are 1-indexed, RQ locations are 0-indexed.
+-- | Pulses are 1-indexed, Rq locations are 0-indexed.
 --
 -- > map (cts_pulse_to_rq [(2,4),(1,8),(1,4)]) [1 .. 4] == [0,1,2,2 + 1/2]
-cts_pulse_to_rq :: Composite_Time_Signature -> Int -> RQ
+cts_pulse_to_rq :: Composite_Time_Signature -> Int -> Rq
 cts_pulse_to_rq cts p =
     let dv = cts_divisions cts
     in sum (take (p - 1) dv)
@@ -149,7 +149,7 @@
 --
 -- > let r = [(0,1),(1,1),(2,1/2),(2 + 1/2,1)]
 -- > in map (cts_pulse_to_rqw [(2,4),(1,8),(1,4)]) [1 .. 4] == r
-cts_pulse_to_rqw :: Composite_Time_Signature -> Int -> (RQ,RQ)
+cts_pulse_to_rqw :: Composite_Time_Signature -> Int -> (Rq,Rq)
 cts_pulse_to_rqw cts p = (cts_pulse_to_rq cts p,cts_divisions cts !! (p - 1))
 
 -- * Rational Time Signatures
@@ -158,11 +158,11 @@
 -- the parts are 'Rational'.
 type Rational_Time_Signature = [(Rational,Rational)]
 
--- | The 'sum' of the RQ of the elements.
+-- | The 'sum' of the Rq of the elements.
 --
 -- > rts_rq [(3,4),(1,8)] == 3 + 1/2
 -- > rts_rq [(3/2,4),(1/2,8)] == 3/2 + 1/4
-rts_rq :: Rational_Time_Signature -> RQ
+rts_rq :: Rational_Time_Signature -> Rq
 rts_rq =
     let f (n,d) = (4 * n) / d
     in sum . map f
@@ -171,7 +171,7 @@
 --
 -- > rts_divisions [(3,4),(1,8)] == [1,1,1,1/2]
 -- > rts_divisions [(3/2,4),(1/2,8)] == [1,1/2,1/4]
-rts_divisions :: Rational_Time_Signature -> [[RQ]]
+rts_divisions :: Rational_Time_Signature -> [[Rq]]
 rts_divisions =
     let f (n,d) = let (ni,nf) = integral_and_fractional_parts n
                       rq = recip (d / 4)
@@ -181,14 +181,14 @@
 
 -- > rts_derive [1,1,1,1/2]
 -- > rts_derive [1,1/2,1/4]
-rts_derive :: [RQ] -> Rational_Time_Signature
+rts_derive :: [Rq] -> Rational_Time_Signature
 rts_derive = let f rq = (rq,4) in map f
 
--- | Pulses are 1-indexed, RQ locations are 0-indexed.
+-- | Pulses are 1-indexed, Rq locations are 0-indexed.
 --
 -- > map (rts_pulse_to_rq [(2,4),(1,8),(1,4)]) [1 .. 4] == [0,1,2,2 + 1/2]
 -- > map (rts_pulse_to_rq [(3/2,4),(1/2,8),(1/4,4)]) [1 .. 4] == [0,1,3/2,7/4]
-rts_pulse_to_rq :: Rational_Time_Signature -> Int -> RQ
+rts_pulse_to_rq :: Rational_Time_Signature -> Int -> Rq
 rts_pulse_to_rq rts p =
     let dv = concat (rts_divisions rts)
     in sum (take (p - 1) dv)
@@ -198,5 +198,5 @@
 --
 -- > let r = [(0,1),(1,1),(2,1/2),(2 + 1/2,1)]
 -- > in map (rts_pulse_to_rqw [(2,4),(1,8),(1,4)]) [1 .. 4] == r
-rts_pulse_to_rqw :: Rational_Time_Signature -> Int -> (RQ,RQ)
+rts_pulse_to_rqw :: Rational_Time_Signature -> Int -> (Rq,Rq)
 rts_pulse_to_rqw ts p = (rts_pulse_to_rq ts p,concat (rts_divisions ts) !! (p - 1))
diff --git a/Music/Theory/Tuning.hs b/Music/Theory/Tuning.hs
--- a/Music/Theory/Tuning.hs
+++ b/Music/Theory/Tuning.hs
@@ -11,25 +11,33 @@
 
 -- * Math/Floating
 
--- | Fractional /midi/ note number to cycles per second, given frequency of ISO A4.
+-- | Fractional /midi/ note number to cycles per second, given (k0,f0) pair.
+--
+-- > 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)))
+
+-- | '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 i = f0 * (2 ** ((i - 69) * (1 / 12)))
+fmidi_to_cps_f0 f0 = fmidi_to_cps_k0 (69,f0)
 
--- | 'fmidi_to_cps_f0' 440.
+-- | 'fmidi_to_cps_k0' (69,440)
 --
 -- > map fmidi_to_cps [69,69.1] == [440.0,442.5488940698553]
 fmidi_to_cps :: Floating a => a -> a
-fmidi_to_cps = fmidi_to_cps_f0 440
+fmidi_to_cps = fmidi_to_cps_k0 (69,440)
 
 -- | /Midi/ note number to cycles per second, given frequency of ISO A4.
-midi_to_cps_f0 :: (Integral i,Floating f) => f -> i -> f
-midi_to_cps_f0 f0 = fmidi_to_cps_f0 f0 . fromIntegral
+midi_to_cps_k0 :: (Integral i,Floating f) => (f,f) -> i -> f
+midi_to_cps_k0 o = fmidi_to_cps_k0 o . fromIntegral
 
--- | 'midi_to_cps_f0' 440.
+-- | '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_f0 440
+midi_to_cps = midi_to_cps_k0 (69,440)
 
 -- | Convert from interval in cents to frequency ratio.
 --
diff --git a/Music/Theory/Tuning/Anamark.hs b/Music/Theory/Tuning/Anamark.hs
new file mode 100644
--- /dev/null
+++ b/Music/Theory/Tuning/Anamark.hs
@@ -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
diff --git a/Music/Theory/Tuning/DB.hs b/Music/Theory/Tuning/DB.hs
deleted file mode 100644
--- a/Music/Theory/Tuning/DB.hs
+++ /dev/null
@@ -1,74 +0,0 @@
--- | DB of locally defined tunings, but for ordinary use see "Music.Theory.Tuning.Scala".
-module Music.Theory.Tuning.DB where
-
-import Data.List {- base -}
-
-import Music.Theory.Tuning.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)
-
--}
-
diff --git a/Music/Theory/Tuning/DB/Alves.hs b/Music/Theory/Tuning/DB/Alves.hs
deleted file mode 100644
--- a/Music/Theory/Tuning/DB/Alves.hs
+++ /dev/null
@@ -1,30 +0,0 @@
--- | 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
diff --git a/Music/Theory/Tuning/DB/Gann.hs b/Music/Theory/Tuning/DB/Gann.hs
deleted file mode 100644
--- a/Music/Theory/Tuning/DB/Gann.hs
+++ /dev/null
@@ -1,130 +0,0 @@
--- | 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 = [1/1,25/24,10/9,9/8,32/27,6/5,5/4,4/3,25/18,45/32,3/2,25/16,5/3,16/9,9/5,15/8]
-
--- | 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
-    ,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>
---
--- > 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 =
-    [1/1,21/20,16/15,9/8,7/6,6/5,11/9,5/4,21/16,4/3,27/20,7/5
-    ,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]
--- > 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 =
-    [1/1,11/10,10/9,9/8,8/7,7/6,6/5,5/4,9/7,4/3
-    ,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>.
---
--- > 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
diff --git a/Music/Theory/Tuning/DB/Microtonal_Synthesis.hs b/Music/Theory/Tuning/DB/Microtonal_Synthesis.hs
deleted file mode 100644
--- a/Music/Theory/Tuning/DB/Microtonal_Synthesis.hs
+++ /dev/null
@@ -1,231 +0,0 @@
--- | <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 =
-    [1,81/80,33/32,21/20,16/15,12/11,11/10,10/9,9/8,8/7
-    ,7/6,32/27,6/5,11/9,5/4,14/11,9/7
-    ,21/16,4/3,27/20
-    ,11/8,7/5,10/7,16/11
-    ,40/27,3/2,32/21,14/9,11/7,8/5,18/11,5/3,27/16,12/7
-    ,7/4,16/9,9/5,20/11,11/6,15/8,40/21,64/33,160/81]
-
--- | Harry Partch 43 tone scale, see
--- <http://www.microtonal-synthesis.com/scale_partch.html>
---
--- > cents_i partch_43 == [0,22,53,84,112,151,165
--- >                      ,182,204,231,267,294,316
--- >                      ,347,386,418,435
--- >                      ,471,498,520,551,583,617,649
--- >                      ,680,702,729,765,782,814,853,884,906,933
--- >                      ,969,996,1018,1035,1049,1088,1116,1147,1178]
---
--- > scl <- scl_load "partch_43"
--- > cents_i (scale_tuning 0.1 scl) == cents_i partch_43
-partch_43 :: Tuning
-partch_43 = Tuning (Left partch_43_r) Nothing
-
--- | Ratios for 'ben_johnston_25'.
-ben_johnston_25_r :: [Rational]
-ben_johnston_25_r =
-    [1/1,25/24,135/128,16/15,10/9
-    ,9/8,75/64,6/5,5/4,81/64
-    ,32/25,4/3,27/20,45/32,36/25
-    ,3/2,25/16,8/5,5/3,27/16
-    ,225/128,16/9,9/5,15/8,48/25]
-
--- | Ben Johnston 25 note just enharmonic scale, see
--- <http://www.microtonal-synthesis.com/scale_johnston_25.html>
---
--- > scl <- scl_load "johnston_25"
--- > cents_i (scale_tuning 0.1 scl) == cents_i ben_johnston_25
-ben_johnston_25 :: Tuning
-ben_johnston_25 = Tuning (Left ben_johnston_25_r) Nothing
diff --git a/Music/Theory/Tuning/DB/Riley.hs b/Music/Theory/Tuning/DB/Riley.hs
deleted file mode 100644
--- a/Music/Theory/Tuning/DB/Riley.hs
+++ /dev/null
@@ -1,22 +0,0 @@
--- | 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 = [1/1,16/15,9/8,6/5,5/4,4/3,64/45,3/2,8/5,5/3,16/9,15/8]
-
--- | 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
diff --git a/Music/Theory/Tuning/DB/Werckmeister.hs b/Music/Theory/Tuning/DB/Werckmeister.hs
deleted file mode 100644
--- a/Music/Theory/Tuning/DB/Werckmeister.hs
+++ /dev/null
@@ -1,118 +0,0 @@
--- | 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
diff --git a/Music/Theory/Tuning/Db.hs b/Music/Theory/Tuning/Db.hs
new file mode 100644
--- /dev/null
+++ b/Music/Theory/Tuning/Db.hs
@@ -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)
+
+-}
+
diff --git a/Music/Theory/Tuning/Db/Alves.hs b/Music/Theory/Tuning/Db/Alves.hs
new file mode 100644
--- /dev/null
+++ b/Music/Theory/Tuning/Db/Alves.hs
@@ -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
diff --git a/Music/Theory/Tuning/Db/Gann.hs b/Music/Theory/Tuning/Db/Gann.hs
new file mode 100644
--- /dev/null
+++ b/Music/Theory/Tuning/Db/Gann.hs
@@ -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
diff --git a/Music/Theory/Tuning/Db/Microtonal_Synthesis.hs b/Music/Theory/Tuning/Db/Microtonal_Synthesis.hs
new file mode 100644
--- /dev/null
+++ b/Music/Theory/Tuning/Db/Microtonal_Synthesis.hs
@@ -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
diff --git a/Music/Theory/Tuning/Db/Riley.hs b/Music/Theory/Tuning/Db/Riley.hs
new file mode 100644
--- /dev/null
+++ b/Music/Theory/Tuning/Db/Riley.hs
@@ -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
diff --git a/Music/Theory/Tuning/Db/Werckmeister.hs b/Music/Theory/Tuning/Db/Werckmeister.hs
new file mode 100644
--- /dev/null
+++ b/Music/Theory/Tuning/Db/Werckmeister.hs
@@ -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
diff --git a/Music/Theory/Tuning/EFG.hs b/Music/Theory/Tuning/EFG.hs
deleted file mode 100644
--- a/Music/Theory/Tuning/EFG.hs
+++ /dev/null
@@ -1,111 +0,0 @@
--- | 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 ..])
diff --git a/Music/Theory/Tuning/ET.hs b/Music/Theory/Tuning/ET.hs
deleted file mode 100644
--- a/Music/Theory/Tuning/ET.hs
+++ /dev/null
@@ -1,259 +0,0 @@
--- | Equal temperament tuning tables.
-module Music.Theory.Tuning.ET where
-
-import Data.List {- base -}
-import Data.List.Split {- split -}
-import Data.Ratio {- base -}
-import Text.Printf {- base -}
-
-import qualified Music.Theory.List as T {- hmt -}
-import Music.Theory.Pitch {- hmt -}
-import Music.Theory.Pitch.Note {- hmt -}
-import Music.Theory.Pitch.Spelling.Table {- hmt -}
-import Music.Theory.Tuning {- hmt -}
-
--- | 'octpc_to_pitch' and 'octpc_to_cps'.
-octpc_to_pitch_cps_f0 :: (Floating n) => n -> OctPC -> (Pitch,n)
-octpc_to_pitch_cps_f0 f0 x = (octpc_to_pitch pc_spell_ks x,octpc_to_cps_f0 f0 x)
-
--- | 'octpc_to_pitch' and 'octpc_to_cps'.
-octpc_to_pitch_cps :: (Floating n) => OctPC -> (Pitch,n)
-octpc_to_pitch_cps = octpc_to_pitch_cps_f0 440
-
--- | 12-tone equal temperament table equating 'Pitch' and frequency
--- over range of human hearing, where @A4@ has given frequency.
---
--- > tbl_12et_f0 415
-tbl_12et_f0 :: Double -> [(Pitch,Double)]
-tbl_12et_f0 f0 =
-    let z = [(o,pc) | o <- [0..10], pc <- [0..11]]
-    in map (octpc_to_pitch_cps_f0 f0) z
-
--- | 'tbl_12et_f0' @440@hz.
---
--- > length tbl_12et == 132
--- > minmax (map (round . snd) tbl_12et) == (16,31609)
-tbl_12et :: [(Pitch,Double)]
-tbl_12et = tbl_12et_f0 440
-
--- | 24-tone equal temperament variant of 'tbl_12et_f0'.
-tbl_24et_f0 :: Double -> [(Pitch,Double)]
-tbl_24et_f0 f0 =
-    let f x = let p = fmidi_to_pitch_err pc_spell_ks x
-                  p' = pitch_rewrite_threequarter_alteration p
-              in (p',fmidi_to_cps_f0 f0 x)
-    in map f [12,12.5 .. 143.5]
-
--- | 'tbl_24et_f0' @440@.
---
--- > length tbl_24et == 264
--- > T.minmax (map (round . snd) tbl_24et) == (16,32535)
-tbl_24et :: [(Pitch,Double)]
-tbl_24et = tbl_24et_f0 440
-
--- | Given an @ET@ table (or like) find bounds of frequency.
---
--- import qualified Music.Theory.Tuple as T
---
--- > let r = Just (T.t2_map octpc_to_pitch_cps ((3,11),(4,0)))
--- > in bounds_et_table tbl_12et 256 == r
-bounds_et_table :: Ord s => [(t,s)] -> s -> Maybe ((t,s),(t,s))
-bounds_et_table = T.find_bounds True (compare . snd)
-
--- | 'bounds_et_table' of 'tbl_12et'.
---
--- > map bounds_12et_tone (hsn 17 55)
-bounds_12et_tone :: Double -> Maybe ((Pitch,Double),(Pitch,Double))
-bounds_12et_tone = bounds_et_table tbl_12et
-
--- | Tuple indicating nearest 'Pitch' to /frequency/ with @ET@
--- frequency, and deviation in hertz and 'Cents'.
---
--- (cps,nearest-pitch,cps-of-nearest-pitch,cps-deviation,cents-deviation)
-type HS_R p = (Double,p,Double,Double,Cents)
-
--- | /n/-decimal places.
---
--- > ndp 3 (1/3) == "0.333"
-ndp :: Int -> Double -> String
-ndp = printf "%.*f"
-
--- | Pretty print 'HS_R'.
-hs_r_pp :: (p -> String) -> Int -> HS_R p -> [String]
-hs_r_pp pp n (f,p,pf,fd,c) =
-    let dp = ndp n
-    in [dp f
-       ,pp p
-       ,dp pf
-       ,dp fd
-       ,dp c]
-
-hs_r_pitch_pp :: Int -> HS_R Pitch -> [String]
-hs_r_pitch_pp = hs_r_pp pitch_pp
-
-{- | Form 'HS_R' for /frequency/ by consulting table.
-
-> let {f = 256
->     ;f' = octpc_to_cps (4,0)
->     ;r = (f,Pitch C Natural 4,f',f-f',fratio_to_cents (f/f'))}
-> in nearest_et_table_tone tbl_12et 256 == r
-
--}
-nearest_et_table_tone :: [(p,Double)] -> Double -> HS_R p
-nearest_et_table_tone tbl f =
-    case bounds_et_table tbl f of
-      Nothing -> error "nearest_et_table_tone: no bounds?"
-      Just ((lp,lf),(rp,rf)) ->
-          let ld = f - lf
-              rd = f - rf
-          in if abs ld < abs rd
-             then (f,lp,lf,ld,fratio_to_cents (f/lf))
-             else (f,rp,rf,rd,fratio_to_cents (f/rf))
-
--- | 'nearest_et_table_tone' for 'tbl_12et'.
-nearest_12et_tone :: Double -> HS_R Pitch
-nearest_12et_tone = nearest_et_table_tone tbl_12et
-
--- | 'nearest_et_table_tone' for 'tbl_24et'.
---
--- > let r = "55.0 A1 55.0 0.0 0.0"
--- > in unwords (hs_r_pitch_pp 1 (nearest_24et_tone 55)) == r
-nearest_24et_tone :: Double -> HS_R Pitch
-nearest_24et_tone = nearest_et_table_tone tbl_24et
-
--- * 72ET
-
--- | Monzo 72-edo HEWM notation.  The domain is (-9,9).
--- <http://www.tonalsoft.com/enc/number/72edo.aspx>
---
--- > let r = ["+",">","^","#<","#-","#","#+","#>","#^"]
--- > in map alteration_72et_monzo [1 .. 9] == r
---
--- > let r = ["-","<","v","b>","b+","b","b-","b<","bv"]
--- > in map alteration_72et_monzo [-1,-2 .. -9] == r
-alteration_72et_monzo :: Integral n => n -> String
-alteration_72et_monzo n =
-    let spl = splitOn ","
-        asc = spl ",+,>,^,#<,#-,#,#+,#>,#^"
-        dsc = spl ",-,<,v,b>,b+,b,b-,b<,bv"
-    in case compare n 0 of
-         LT -> genericIndex dsc (- n)
-         EQ -> ""
-         GT -> genericIndex asc n
-
--- | Given a midi note number and @1/6@ deviation determine 'Pitch''
--- and frequency.
---
--- > let {f = pitch'_pp . fst . pitch_72et
--- >     ;r = "C4 C+4 C>4 C^4 C#<4 C#-4 C#4 C#+4 C#>4 C#^4"}
--- > in unwords (map f (zip (repeat 60) [0..9])) == r
---
--- > let {f = pitch'_pp . fst . pitch_72et
--- >     ;r = "A4 A+4 A>4 A^4 Bb<4 Bb-4 Bb4 Bb+4 Bb>4 Bv4"}
--- > in unwords (map f (zip (repeat 69) [0..9]))
---
--- > let {f = pitch'_pp . fst . pitch_72et
--- >     ;r = "Bb4 Bb+4 Bb>4 Bv4 B<4 B-4 B4 B+4 B>4 B^4"}
--- > in unwords (map f (zip (repeat 70) [0..9])) == r
-pitch_72et :: (Midi,Int) -> (Pitch_R,Double)
-pitch_72et (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 x')
-        r' = if n > 3
-             then pitch_72et (x + 1,n - 6)
-             else if n < (-3)
-                  then pitch_72et (x - 1,n + 6)
-                  else r
-    in case a of
-         Natural -> r'
-         _ -> r
-
--- | 72-tone equal temperament table equating 'Pitch'' and frequency
--- over range of human hearing, where @A4@ = @440@hz.
---
--- > length tbl_72et == 792
--- > min_max (map (round . snd) tbl_72et) == (16,33167)
-tbl_72et :: [(Pitch_R,Double)]
-tbl_72et =
-    let f n = map pitch_72et (zip (replicate 6 n) [0..5])
-    in concatMap f [12 .. 143]
-
--- | 'nearest_et_table_tone' for 'tbl_72et'.
---
--- > let r = "324.0 E<4 323.3 0.7 3.5"
--- > in unwords (hs_r_pp pitch'_pp 1 (nearest_72et_tone 324))
---
--- > let {f = take 2 . hs_r_pp pitch'_pp 1 . nearest_72et_tone . snd}
--- > in mapM_ (print . unwords . f) tbl_72et
-nearest_72et_tone :: Double -> HS_R Pitch_R
-nearest_72et_tone = nearest_et_table_tone tbl_72et
-
--- * Detune
-
--- | 'Pitch' with 12-ET/24-ET tuning deviation given in 'Cents'.
-type Pitch_Detune = (Pitch,Cents)
-
--- | Extract 'Pitch_Detune' from 'HS_R'.
-hsr_to_pitch_detune :: HS_R Pitch -> Pitch_Detune
-hsr_to_pitch_detune (_,p,_,_,c) = (p,c)
-
--- | Nearest 12-ET 'Pitch_Detune' to indicated frequency (hz).
---
--- > nearest_pitch_detune_12et 452.8929841231365
-nearest_pitch_detune_12et :: Double -> Pitch_Detune
-nearest_pitch_detune_12et = hsr_to_pitch_detune . nearest_12et_tone
-
--- | Nearest 24-ET 'Pitch_Detune' to indicated frequency (hz).
---
--- > nearest_pitch_detune_24et 452.8929841231365
-nearest_pitch_detune_24et :: Double -> Pitch_Detune
-nearest_pitch_detune_24et = hsr_to_pitch_detune . nearest_24et_tone
-
--- | Given /near/ function, /f0/ and ratio derive 'Pitch_Detune'.
-ratio_to_pitch_detune :: (Double -> HS_R Pitch) -> OctPC -> Rational -> Pitch_Detune
-ratio_to_pitch_detune near_f f0 r =
-    let f = octpc_to_cps f0 * realToFrac r
-        (_,p,_,_,c) = near_f f
-    in (p,c)
-
--- | Frequency (hz) of 'Pitch_Detune'.
---
--- > pitch_detune_to_cps (octpc_to_pitch pc_spell_ks (4,9),50)
-pitch_detune_to_cps :: Floating n => Pitch_Detune -> n
-pitch_detune_to_cps (p,d) = cps_shift_cents (pitch_to_cps p) (realToFrac d)
-
--- | 'ratio_to_pitch_detune' of 'nearest_12et_tone'
-ratio_to_pitch_detune_12et :: OctPC -> Rational -> Pitch_Detune
-ratio_to_pitch_detune_12et = ratio_to_pitch_detune nearest_12et_tone
-
--- | 'ratio_to_pitch_detune' of 'nearest_24et_tone'
-ratio_to_pitch_detune_24et :: OctPC -> Rational -> Pitch_Detune
-ratio_to_pitch_detune_24et = ratio_to_pitch_detune nearest_24et_tone
-
-pitch_detune_in_octave_nearest  :: Pitch -> Pitch_Detune -> Pitch_Detune
-pitch_detune_in_octave_nearest p1 (p2,d2) = (pitch_in_octave_nearest p1 p2,d2)
-
--- | Markdown pretty-printer for 'Pitch_Detune'.
-pitch_detune_md :: Pitch_Detune -> String
-pitch_detune_md (p,c) = pitch_pp p ++ cents_diff_md (round c :: Integer)
-
--- | HTML pretty-printer for 'Pitch_Detune'.
-pitch_detune_html :: Pitch_Detune -> String
-pitch_detune_html (p,c) = pitch_pp p ++ cents_diff_html (round c :: Integer)
-
--- | No-octave variant of 'pitch_detune_md'.
-pitch_class_detune_md :: Pitch_Detune -> String
-pitch_class_detune_md (p,c) = pitch_class_pp p ++ cents_diff_md (round c :: Integer)
-
--- | No-octave variant of 'pitch_detune_html'.
-pitch_class_detune_html :: Pitch_Detune -> String
-pitch_class_detune_html (p,c) = pitch_class_pp p ++ cents_diff_html (round c :: Integer)
diff --git a/Music/Theory/Tuning/Efg.hs b/Music/Theory/Tuning/Efg.hs
new file mode 100644
--- /dev/null
+++ b/Music/Theory/Tuning/Efg.hs
@@ -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 ..])
diff --git a/Music/Theory/Tuning/Et.hs b/Music/Theory/Tuning/Et.hs
new file mode 100644
--- /dev/null
+++ b/Music/Theory/Tuning/Et.hs
@@ -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)
diff --git a/Music/Theory/Tuning/Gann_1993.hs b/Music/Theory/Tuning/Gann_1993.hs
--- a/Music/Theory/Tuning/Gann_1993.hs
+++ b/Music/Theory/Tuning/Gann_1993.hs
@@ -84,7 +84,7 @@
 
 -}
 lmy_wtp_uniq :: [(Rational,[(T.PitchClass,T.PitchClass)])]
-lmy_wtp_uniq = sortOn (T.ratio_nd_sum . fst) $ T.collate_on fst snd $ lmy_wtp_univ
+lmy_wtp_uniq = sortOn (T.ratio_nd_sum . fst) (T.collate_on fst snd lmy_wtp_univ)
 
 {- | Gann, 1993, p.137.
 
@@ -136,6 +136,6 @@
 lmy_wtp_euler =
     let {l1 = T.tun_seq 4 (3/2) (49/32)
         ;l2 = T.tun_seq 5 (3/2) (7/4)
-        ;l3 = T.tun_seq 3 (3/2) (1/1)
+        ;l3 = T.tun_seq 3 (3/2) 1
         ;(c1,c2) = T.euler_align_rat (7/4,7/4) (l1,l2,l3)}
     in ([l1,l2,l3],c1 ++ c2)
diff --git a/Music/Theory/Tuning/Graph/ISET.hs b/Music/Theory/Tuning/Graph/ISET.hs
deleted file mode 100644
--- a/Music/Theory/Tuning/Graph/ISET.hs
+++ /dev/null
@@ -1,126 +0,0 @@
--- | 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.Dot as T {- hmt -}
-import qualified Music.Theory.Graph.FGL as T {- hmt -}
-import qualified Music.Theory.Graph.Type as T {- hmt -}
-import qualified Music.Theory.List as T {- hmt -}
-import qualified Music.Theory.Show 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.GR_PP v e -> [T.EDGE_L 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
--}
diff --git a/Music/Theory/Tuning/Graph/Iset.hs b/Music/Theory/Tuning/Graph/Iset.hs
new file mode 100644
--- /dev/null
+++ b/Music/Theory/Tuning/Graph/Iset.hs
@@ -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
+-}
diff --git a/Music/Theory/Tuning/HS.hs b/Music/Theory/Tuning/HS.hs
deleted file mode 100644
--- a/Music/Theory/Tuning/HS.hs
+++ /dev/null
@@ -1,81 +0,0 @@
--- | 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) (map recip [1..])
-
--- | /n/ elements of 'harmonic_series_cps'.
---
--- > let r = [1760,880,587,440,352,293,251,220,196,176,160,147,135,126,117,110,104]
--- > 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 :: (Ord a, 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
-
diff --git a/Music/Theory/Tuning/Hs.hs b/Music/Theory/Tuning/Hs.hs
new file mode 100644
--- /dev/null
+++ b/Music/Theory/Tuning/Hs.hs
@@ -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
+
diff --git a/Music/Theory/Tuning/Load.hs b/Music/Theory/Tuning/Load.hs
--- a/Music/Theory/Tuning/Load.hs
+++ b/Music/Theory/Tuning/Load.hs
@@ -3,15 +3,16 @@
 
 import System.Random {- random -}
 
-import qualified Music.Theory.Array.CSV as T
-import qualified Music.Theory.Pitch as T
+import qualified Music.Theory.Array.Csv as T {- hmt-base -}
+
+import qualified Music.Theory.Pitch as T {- hmt -}
 import qualified Music.Theory.Tuning as T
 import qualified Music.Theory.Tuning.Midi as T
 import qualified Music.Theory.Tuning.Scala as T
 import qualified Music.Theory.Tuning.Type as T
 
 -- | Load possibly sparse and possibly one-to-many
--- (midi-note-number,cps-frequency) table from CSV file.
+-- (midi-note-number,cps-frequency) table from Csv file.
 --
 -- > load_cps_tbl "/home/rohan/dr.csv"
 load_cps_tbl :: FilePath -> IO [(T.Midi,Double)]
@@ -28,22 +29,22 @@
 
 -- | 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)
+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 :: 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 :: 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 :: 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)
@@ -58,7 +59,7 @@
     in (l !! i,g')
 
 -- | Load tuning table with stateful selection function for one-to-many entries.
-load_tuning_tbl_st :: Choose_f st (T.Midi,Double) -> LOAD_TUNING_OPT -> IO (T.Sparse_Midi_Tuning_ST_F st)
+load_tuning_tbl_st :: Choose_f st (T.Midi,Double) -> Load_Tuning_Opt -> IO (T.Sparse_Midi_Tuning_St_f st)
 load_tuning_tbl_st choose_f (nm,dt,k) =
     let from_cps = T.cps_to_midi_detune . flip T.cps_shift_cents dt
         f tbl g mnn = case filter ((== (mnn + k)) . fst) tbl of
@@ -67,7 +68,7 @@
                              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 :: String -> Load_Tuning_Opt -> IO T.Sparse_Midi_Tuning_f
 load_tuning_ty ty opt =
     case ty of
       "cps" -> load_tuning_cps opt
@@ -75,7 +76,7 @@
       "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 :: 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)
diff --git a/Music/Theory/Tuning/Midi.hs b/Music/Theory/Tuning/Midi.hs
--- a/Music/Theory/Tuning/Midi.hs
+++ b/Music/Theory/Tuning/Midi.hs
@@ -4,7 +4,6 @@
 import Data.List {- base -}
 import qualified Data.Map as M {- containers -}
 import Data.Maybe {- base -}
-import Data.Word {- base -}
 import qualified Safe {- safe -}
 
 import qualified Music.Theory.List as T {- hmt -}
@@ -18,20 +17,20 @@
 -- | (/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
+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
+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)
+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 '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_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
@@ -40,11 +39,11 @@
 --   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'.
+-- | '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 :: 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]
@@ -56,15 +55,15 @@
 
 -- | (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)
+type Cps_Midi_Tuning = (Tuning,Double,T.Midi,Int)
 
--- | 'Midi_Tuning_F' for 'CPS_Midi_Tuning'.  The function is sparse, it is only
+-- | '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 :: 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)
@@ -73,10 +72,10 @@
 -- * Midi tuning tables.
 
 -- | midi-note-number -> fractional-midi-note-number table, possibly sparse.
-type MNN_FMNN_Table = [(Word8,Double)]
+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
+-- | 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
@@ -84,15 +83,15 @@
               _ -> 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)]
+-- | 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@.
+-- | 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 :: 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)
@@ -101,8 +100,8 @@
 
 -- * 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/.
+-- | 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 =
@@ -117,13 +116,13 @@
       _ -> 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 :: 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 :: 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
diff --git a/Music/Theory/Tuning/Partch.hs b/Music/Theory/Tuning/Partch.hs
--- a/Music/Theory/Tuning/Partch.hs
+++ b/Music/Theory/Tuning/Partch.hs
@@ -1,3 +1,4 @@
+-- | Tuning, Harry Partch
 module Music.Theory.Tuning.Partch where
 
 import qualified Data.Map.Strict as M {- containers -}
@@ -14,7 +15,6 @@
 -- | Incipient Tonality Diamond
 --
 -- > itd_map [4 .. 6]
--- > itd_tbl [4 .. 13]
 itd_map :: [Integer] -> M.Map (Int,Int) Rational
 itd_map relation =
   let limit = length relation
@@ -29,6 +29,9 @@
 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"
@@ -38,76 +41,28 @@
 {-
 
 import Data.List {- base -}
-import qualified Music.Theory.Array.MD as T {- hmt -}
-import qualified Music.Theory.Math as T {- hmt -}
+import qualified Music.Theory.Array.Text as T {- hmt -}
+import qualified Music.Theory.Show as T {- hmt -}
 
-pp tbl = putStrLn $ unlines $ intersperse "" $ T.md_table Nothing (map (map T.rational_pp) tbl)
+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
-$
-
-pp (itd_tbl [4 .. 6])
-
-    --- --- ---
-      1 8/5 4/3
-
-    5/4   1 5/3
-
-    3/2 6/5   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
-
 $
-
-pp (itd_tbl [4 .. 13])
-
-    ---- ----- ----- ---- ---- ---- ----- ----- ----- -----
-
-       1   8/5   4/3  8/7    1 16/9   8/5 16/11   4/3 16/13
-
-     5/4     1   5/3 10/7  5/4 10/9     1 20/11   5/3 20/13
-
-     3/2   6/5     1 12/7  3/2  4/3   6/5 12/11     1 24/13
-
-     7/4   7/5   7/6    1  7/4 14/9   7/5 14/11   7/6 14/13
-
-       1   8/5   4/3  8/7    1 16/9   8/5 16/11   4/3 16/13
-
-     9/8   9/5   3/2  9/7  9/8    1   9/5 18/11   3/2 18/13
-
-     5/4     1   5/3 10/7  5/4 10/9     1 20/11   5/3 20/13
-
-    11/8 11/10  11/6 11/7 11/8 11/9 11/10     1  11/6 22/13
-
-     3/2   6/5     1 12/7  3/2  4/3   6/5 12/11     1 24/13
-
-    13/8 13/10 13/12 13/7 13/8 13/9 13/10 13/11 13/12     1
-
-    ---- ----- ----- ---- ---- ---- ----- ----- ----- -----
 
 -}
diff --git a/Music/Theory/Tuning/Polansky_1985c.hs b/Music/Theory/Tuning/Polansky_1985c.hs
--- a/Music/Theory/Tuning/Polansky_1985c.hs
+++ b/Music/Theory/Tuning/Polansky_1985c.hs
@@ -1,5 +1,5 @@
 -- | 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.Type {- hmt -}
@@ -7,10 +7,10 @@
 -- | 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))
+    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))
diff --git a/Music/Theory/Tuning/Rosenboom_1979.hs b/Music/Theory/Tuning/Rosenboom_1979.hs
--- a/Music/Theory/Tuning/Rosenboom_1979.hs
+++ b/Music/Theory/Tuning/Rosenboom_1979.hs
@@ -11,7 +11,7 @@
 import qualified Music.Theory.List as T
 import qualified Music.Theory.Pitch as T
 import qualified Music.Theory.Pitch.Name as T
-import qualified Music.Theory.Tuning.ET as T
+import qualified Music.Theory.Tuning.Et as T
 import qualified Music.Theory.Tuning.Scala as Scala
 import qualified Music.Theory.Tuple as T
 
@@ -36,7 +36,7 @@
 -- | Actual scale, in CPS.
 --
 -- > let r = [52,69,76,83,92,104,119,138,156,166,185,208,234,260,277,286,311,332,363]
--- > in map round dr_scale == r
+-- > map round dr_scale == r
 dr_scale :: [Double]
 dr_scale =
     let f0 = T.octpc_to_cps (1::Int,8)
@@ -46,38 +46,14 @@
 -- > putStrLn (unlines (map (unwords . T.hs_r_pitch_pp 1)  dr_scale_tbl_12et))
 -- > map (\(f,p,_,_,_) -> (T.pitch_to_midi p,f)) dr_scale_tbl_12et
 dr_scale_tbl_12et :: [T.HS_R T.Pitch]
-dr_scale_tbl_12et = map T.nearest_12et_tone dr_scale
-
-{-
-
-51.9 A♭1 51.9 0.0 0.0
-69.2 C♯2 69.3 -0.1 -2.0
-75.5 D2 73.4 2.1 48.7
-83.1 E2 82.4 0.7 13.7
-92.3 F♯2 92.5 -0.2 -3.9
-103.8 A♭2 103.8 0.0 0.0
-118.7 B♭2 116.5 2.1 31.2
-138.4 C♯3 138.6 -0.2 -2.0
-155.7 E♭3 155.6 0.2 2.0
-166.1 E3 164.8 1.3 13.7
-184.6 F♯3 185.0 -0.4 -3.9
-207.7 A♭3 207.7 0.0 0.0
-233.6 B♭3 233.1 0.5 3.9
-259.6 C4 261.6 -2.1 -13.7
-276.9 C♯4 277.2 -0.3 -2.0
-285.5 D4 293.7 -8.1 -48.7
-311.5 E♭4 311.1 0.4 2.0
-332.2 E4 329.6 2.6 13.7
-363.4 F♯4 370.0 -6.6 -31.2
-
--}
+dr_scale_tbl_12et = map (T.nearest_12et_tone_k0 (69,440)) dr_scale
 
 -- > Scala.scale_verify dr_scale_scala
 -- > putStrLn $ unlines $ Scala.scale_pp dr_scale_scala
 dr_scale_scala :: Scala.Scale
 dr_scale_scala =
-    let f (r,(_,p,_,_,_)) = (T.pitch_to_midi p :: Int,r)
-        sq = map f (zip dr_tuning dr_scale_tbl_12et)
+    let f r (_,p,_,_,_) = (T.pitch_to_midi p :: Int,r)
+        sq = zipWith f dr_tuning dr_scale_tbl_12et
         g z k = case lookup k sq of
                   Nothing -> (z,(k,z))
                   Just r -> (r,(k,r))
@@ -86,31 +62,7 @@
 
 -- > putStrLn (unlines (map (unwords . T.hs_r_pitch_pp 1)  dr_scale_tbl_24et))
 dr_scale_tbl_24et :: [T.HS_R T.Pitch]
-dr_scale_tbl_24et = map T.nearest_24et_tone dr_scale
-
-{-
-
-51.9 A♭1 51.9 0.0 0.0
-69.2 C♯2 69.3 -0.1 -2.0
-75.5 D𝄲2 75.6 -0.1 -1.3
-83.1 E2 82.4 0.7 13.7
-92.3 F♯2 92.5 -0.2 -3.9
-103.8 A♭2 103.8 0.0 0.0
-118.7 B𝄳2 120.0 -1.3 -18.8
-138.4 C♯3 138.6 -0.2 -2.0
-155.7 E♭3 155.6 0.2 2.0
-166.1 E3 164.8 1.3 13.7
-184.6 F♯3 185.0 -0.4 -3.9
-207.7 A♭3 207.7 0.0 0.0
-233.6 B♭3 233.1 0.5 3.9
-259.6 C4 261.6 -2.1 -13.7
-276.9 C♯4 277.2 -0.3 -2.0
-285.5 D𝄳4 285.3 0.2 1.3
-311.5 E♭4 311.1 0.4 2.0
-332.2 E4 329.6 2.6 13.7
-363.4 F𝄲4 359.5 3.9 18.8
-
--}
+dr_scale_tbl_24et = map (T.nearest_24et_tone_k0 (69,440)) dr_scale
 
 dr_chords :: [[T.Pitch]]
 dr_chords =
@@ -161,8 +113,8 @@
     ,[(8,1),(1,10)]
     ]
 
--- > import Data.Function
--- > import Data.List
+-- > import Data.Function {- base -}
+-- > import Data.List {- base -}
 -- > reverse (sortBy (compare `on` snd) dr_ratio_seq_hist)
 dr_ratio_seq_hist :: (Ord n,Num n) => [((n,n),Int)]
 dr_ratio_seq_hist = T.histogram (concat dr_ratio_seq)
diff --git a/Music/Theory/Tuning/Scala.hs b/Music/Theory/Tuning/Scala.hs
--- a/Music/Theory/Tuning/Scala.hs
+++ b/Music/Theory/Tuning/Scala.hs
@@ -2,7 +2,7 @@
 
 See <http://www.huygens-fokker.org/scala/scl_format.html> for details.
 
-This module succesfully parses all scales in v.89 of the scale library.
+This module succesfully parses all scales in v.91 of the scale library.
 
 -}
 module Music.Theory.Tuning.Scala where
@@ -16,13 +16,13 @@
 import System.Environment {- base -}
 import System.FilePath {- filepath -}
 
-import qualified Music.Theory.Array.CSV as T {- hmt -}
-import qualified Music.Theory.Directory as T {- hmt -}
-import qualified Music.Theory.Either as T {- hmt -}
-import qualified Music.Theory.Function as T {- hmt -}
-import qualified Music.Theory.IO as T {- hmt -}
-import qualified Music.Theory.List as T {- hmt -}
-import qualified Music.Theory.Math.Prime as T {- hmt -}
+import qualified Music.Theory.Array.Csv as Csv {- hmt -}
+import qualified Music.Theory.Directory as Directory {- hmt -}
+import qualified Music.Theory.Either as Either {- hmt -}
+import qualified Music.Theory.Function as Function {- hmt -}
+import qualified Music.Theory.Io as Io {- hmt -}
+import qualified Music.Theory.List as List {- hmt -}
+import qualified Music.Theory.Math.Prime as Prime {- hmt -}
 import qualified Music.Theory.Read as T {- hmt -}
 import qualified Music.Theory.Show as T {- hmt -}
 import qualified Music.Theory.String as T {- hmt -}
@@ -145,7 +145,7 @@
 
 -- | Are the pitches in ascending sequence.
 is_scale_ascending :: Scale -> Bool
-is_scale_ascending = T.is_ascending . map pitch_cents . scale_pitches
+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
@@ -172,7 +172,7 @@
   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 . T.from_right) p)
+       Just Pitch_Ratio -> Just (1 : map (fromMaybe err . Either.from_right) p)
        _ -> Nothing
 
 -- | Erroring variant of 'scale_ratios_u.
@@ -198,7 +198,7 @@
 
 -- | 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 (intersect p0 p1) >= k
+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
@@ -208,7 +208,7 @@
 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 && all id (zipWith (~=) p0 p1)
+    in d0 == d1 && and (zipWith (~=) p0 p1)
 
 -- * Parser
 
@@ -231,7 +231,7 @@
 filter_comments :: [String] -> [String]
 filter_comments =
     map remove_eol_comments .
-    filter (not . T.predicate_any [is_comment])
+    filter (not . Function.predicate_any [is_comment])
 
 -- | Pitches are either cents (with decimal point, possibly trailing) or ratios (with @/@).
 --
@@ -260,13 +260,13 @@
                in scale_verify_err scl
       _ -> error "parse"
 
--- * IO
+-- * Io
 
 -- | Read the environment variable @SCALA_SCL_DIR@, which is a
 -- sequence of directories used to locate scala files on.
 --
--- > setEnv "SCALA_DIST_DIR" "/home/rohan/data/scala/89/scl"
-scl_get_dir :: IO [String]
+-- > setEnv "SCALA_SCL_DIR" "/home/rohan/data/scala/90/scl"
+scl_get_dir :: IO [FilePath]
 scl_get_dir = fmap splitSearchPath (getEnv "SCALA_SCL_DIR")
 
 -- | Lookup the @SCALA_SCL_DIR@ environment variable, which must exist, and derive the filepath.
@@ -278,14 +278,14 @@
   dir <- scl_get_dir
   when (null dir) (error "scl_derive_filename: SCALA_SCL_DIR: nil")
   when (hasExtension nm) (error "scl_derive_filename: name has extension")
-  T.path_scan_err dir (nm <.> "scl")
+  Directory.path_scan_err dir (nm <.> "scl")
 
 -- | If the name is an absolute file path and has a @.scl@ extension,
 -- then return it, else run 'scl_derive_filename'.
 --
 -- > scl_resolve_name "young-lm_piano"
--- > scl_resolve_name "/home/rohan/data/scala/89/scl/young-lm_piano.scl"
--- > scl_resolve_name "/home/rohan/data/scala/89/scl/unknown-tuning.scl"
+-- > scl_resolve_name "/home/rohan/data/scala/90/scl/young-lm_piano.scl"
+-- > scl_resolve_name "/home/rohan/data/scala/90/scl/unknown-tuning.scl"
 scl_resolve_name :: String -> IO FilePath
 scl_resolve_name nm =
     let ex_f x = if x then return nm else error "scl_resolve_name: file does not exist"
@@ -301,19 +301,18 @@
 scl_load :: String -> IO Scale
 scl_load nm = do
   fn <- scl_resolve_name nm
-  s <- T.read_file_iso_8859_1 fn
+  s <- Io.read_file_iso_8859_1 fn
   return (parse_scl (takeBaseName nm) s)
 
 {- | Load all @.scl@ files at /dir/, associate with file-name.
 
-> db <- scl_load_dir_fn "/home/rohan/data/scala/89/scl"
-> length db == 5050 -- v.89
+> 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 <- T.dir_subset [".scl"] d
+  fn <- Directory.dir_subset [".scl"] d
   scl <- mapM scl_load fn
   return (zip fn scl)
 
@@ -331,7 +330,7 @@
   r <- mapM scl_load_dir dir
   return (concat r)
 
--- * PP
+-- * Pp
 
 -- | <http://www.huygens-fokker.org/docs/scalesdir.txt>
 scales_dir_txt_tbl :: [Scale] -> [[String]]
@@ -344,7 +343,7 @@
 -- > db <- scl_load_db
 -- > writeFile "/tmp/scl.csv" (scales_dir_txt_csv db)
 scales_dir_txt_csv :: [Scale] -> String
-scales_dir_txt_csv db = T.csv_table_pp id T.def_csv_opt (Nothing,scales_dir_txt_tbl db)
+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.
 --
@@ -394,11 +393,11 @@
 scale_wr_dir :: FilePath -> Scale -> IO ()
 scale_wr_dir dir scl = scale_wr (dir </> scale_name scl <.> "scl") scl
 
--- * DIST
+-- * Dist
 
 -- | @scala@ distribution directory, given at @SCALA_DIST_DIR@.
 --
--- > fmap (== "/home/rohan/opt/build/scala-22-pc64-linux") dist_get_dir
+-- > setEnv "SCALA_DIST_DIR" "/home/rohan/opt/build/scala-22"
 dist_get_dir :: IO String
 dist_get_dir = getEnv "SCALA_DIST_DIR"
 
@@ -408,14 +407,15 @@
   d <- dist_get_dir
   readFile (d </> nm)
 
--- | 'fmap' 'lines' 'load_dist_file'
---
--- > s <- load_dist_file_ln "intnam.par"
--- > length s == 533 -- Scala 2.42p
+{- | '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
+-- * Query
 
 -- | Is scale just-intonation (ie. are all pitches ratios)
 scl_is_ji :: Scale -> Bool
@@ -423,12 +423,12 @@
 
 -- | Calculate limit for JI scale (ie. largest prime factor)
 scl_ji_limit :: Scale -> Integer
-scl_ji_limit = maximum . map fst . concatMap T.rational_prime_factors_m . scale_ratios_req
+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 (T.dx_d 0) (T.rotations (T.d_dx (sort (scale_cents 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..])
 
@@ -471,10 +471,8 @@
 
 -- | Find scale(s) that are 'scale_cmp_ji' to /x/.
 --   Usual /cmp/ are (==) and 'is_subset'.
-scl_find_ji :: ([Rational] -> [Rational] -> Bool) -> [Rational] -> IO [Scale]
-scl_find_ji cmp x = do
-  db <- scl_load_db
-  return (filter (scale_cmp_ji cmp x) db)
+scl_find_ji :: ([Rational] -> [Rational] -> Bool) -> [Rational] -> [Scale] -> [Scale]
+scl_find_ji cmp x = filter (scale_cmp_ji cmp x)
 
 -- * Tuning
 
@@ -483,11 +481,11 @@
 scale_to_tuning :: Scale -> T.Tuning
 scale_to_tuning (_,_,_,p) =
     case partitionEithers p of
-      ([],r) -> let (r',o) = T.separate_last r
+      ([],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) = T.separate_last p
+      _ -> 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 (T.either_swap o)
+               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'.
@@ -496,7 +494,7 @@
 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 ++ [T.either_swap (T.tn_octave_def tn)]
+        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'.
diff --git a/Music/Theory/Tuning/Scala/Cli.hs b/Music/Theory/Tuning/Scala/Cli.hs
new file mode 100644
--- /dev/null
+++ b/Music/Theory/Tuning/Scala/Cli.hs
@@ -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
diff --git a/Music/Theory/Tuning/Scala/Functions.hs b/Music/Theory/Tuning/Scala/Functions.hs
new file mode 100644
--- /dev/null
+++ b/Music/Theory/Tuning/Scala/Functions.hs
@@ -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
diff --git a/Music/Theory/Tuning/Scala/Interval.hs b/Music/Theory/Tuning/Scala/Interval.hs
--- a/Music/Theory/Tuning/Scala/Interval.hs
+++ b/Music/Theory/Tuning/Scala/Interval.hs
@@ -3,6 +3,7 @@
 
 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 -}
@@ -20,10 +21,27 @@
 > 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")
-> map (intnam_search_ratio db) [3/2,4/3,7/4,7/6,9/7,12/7,14/9]
+> 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.
 --
diff --git a/Music/Theory/Tuning/Scala/KBM.hs b/Music/Theory/Tuning/Scala/KBM.hs
deleted file mode 100644
--- a/Music/Theory/Tuning/Scala/KBM.hs
+++ /dev/null
@@ -1,132 +0,0 @@
-{- | 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 qualified Music.Theory.Directory as T {- hmt -}
-import qualified Music.Theory.List as T {- hmt -}
-import qualified Music.Theory.Tuning.Scala as T {- 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])
-
--- | 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 maybe Nothing (\dgr -> Just (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 = T.pad_right_no_truncate Nothing sz . map f -- _err -- some scala .kbm have |m| > sz?
-  in case T.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 :: FilePath -> IO KBM
-kbm_load = fmap kbm_parse . readFile
-
-{- | 'kbm_parse' of 'T.load_dist_file'
-
-> kbm_load_dist "example.kbm"
-> kbm_load_dist "bp.kbm"
-> kbm_load_dist "7.kbm" -- error
-> kbm_load_dist "8.kbm" -- error
-> kbm_load_dist "white.kbm" -- error
-> kbm_load_dist "black.kbm" -- error
-> kbm_load_dist "128.kbm"
-> kbm_load_dist "a440.kbm"
-> kbm_load_dist "61.kbm"
--}
-kbm_load_dist :: FilePath -> IO KBM
-kbm_load_dist = fmap kbm_parse . T.load_dist_file
-
-kbm_load_dir_fn :: FilePath -> IO [(FilePath, KBM)]
-kbm_load_dir_fn d = do
-  fn <- T.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
-> x = map (\(fn,(sz,_,_,_,o,m)) -> (System.FilePath.takeFileName fn,sz,length m,o)) db
-> filter (\(_,i,j,_) -> i < j) x
-> filter (\(_,i,_,k) -> i == 0 && k == 0) x
-
-> 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 = T.dist_get_dir >>= kbm_load_dir_fn
-
-{- | Pretty-printer for scala .kbm file.
-
-> m <- kbm_load_dist "7.kbm"
-> kbm_parse (kbm_pp m) == m
--}
-kbm_pp :: KBM -> String
-kbm_pp (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_pp'
-kbm_wr :: FilePath -> KBM -> IO ()
-kbm_wr fn = writeFile fn . kbm_pp
-
-{- | Standard 12-tone mapping with A=440hz (ie. example.kbm)
-
-> fmap (== kbm_d12_a440) (kbm_load_dist "example.kbm")
--}
-kbm_d12_a440 :: KBM
-kbm_d12_a440 = (12,(0,127),60,(69,440.0),12,map Just [0 .. 11])
diff --git a/Music/Theory/Tuning/Scala/Kbm.hs b/Music/Theory/Tuning/Scala/Kbm.hs
new file mode 100644
--- /dev/null
+++ b/Music/Theory/Tuning/Scala/Kbm.hs
@@ -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
+
+-}
diff --git a/Music/Theory/Tuning/Scala/Meta.hs b/Music/Theory/Tuning/Scala/Meta.hs
--- a/Music/Theory/Tuning/Scala/Meta.hs
+++ b/Music/Theory/Tuning/Scala/Meta.hs
@@ -55,6 +55,7 @@
     ,"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"
@@ -77,15 +78,16 @@
     ,"harrison_slye"
     ,"harrison_songs"
     ,"hexany10"
+    ,"hirajoshi2"
     ,"korea_5"
+    ,"olympos"
     ,"pelog_jc" -- STRICT SONGS
     ,"pelog_laras" -- NON-STEP
     ,"prime_5"
-    ,"slendro5_1"
-    ,"slendro_7_1"
-    ,"slendro_7_2"
-    ,"slendro_7_3"
-    ,"slendro_7_4"]) -- "slendro_laras" -- NON-OCT
+    ,"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"
@@ -135,17 +137,35 @@
     -- "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_diat2","ptolemy_idiat"
-    ,"slendro5_2"
+    ,"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"
diff --git a/Music/Theory/Tuning/Scala/Mode.hs b/Music/Theory/Tuning/Scala/Mode.hs
--- a/Music/Theory/Tuning/Scala/Mode.hs
+++ b/Music/Theory/Tuning/Scala/Mode.hs
@@ -1,4 +1,15 @@
--- | Parser for the @modename.par@ file.
+{- | Parser for the @modename.par@ file.
+
+The terminology here is:
+
+- a mode is a subset of the notes of a tuning system (which in scala is called a scale)
+
+- the length (or degree) of the mode is the number of tones in the mode
+
+- the universe (or scale) of the mode is the number of tones in the
+  tuning system (or scale) the mode is a subset of
+
+-}
 module Music.Theory.Tuning.Scala.Mode where
 
 import Data.Char {- base -}
@@ -9,29 +20,50 @@
 import qualified Music.Theory.List as List {- hmt -}
 import qualified Music.Theory.Tuning.Scala as Scala {- hmt -}
 
--- | (start-degree,intervals,description)
-type MODE = (Int,[Int],String)
+-- | (mode-start-degree,mode-intervals,mode-description)
+type Mode = (Int,[Int],String)
 
-mode_starting_degree :: MODE -> Int
+-- | Starting degree of mode in underlying scale.  If non-zero the
+-- mode will not lie within an ordinary octave of the tuning.
+mode_starting_degree :: Mode -> Int
 mode_starting_degree (d,_,_) = d
 
-mode_intervals :: MODE -> [Int]
+-- | Intervals (in steps) between adjacent elements of the mode.
+mode_intervals :: Mode -> [Int]
 mode_intervals (_,i,_) = i
 
-mode_description :: MODE -> String
+-- | Interval set of mode (ie. 'nub' of 'sort' of 'mode_intervals')
+mode_iset :: Mode -> [Int]
+mode_iset = nub . sort . mode_intervals
+
+-- | Histogram ('List.histogram') of 'mode_intervals'
+mode_histogram :: Mode -> [(Int, Int)]
+mode_histogram = List.histogram . mode_intervals
+
+-- | The text description of the mode, ordinarily a comma separated list of names.
+mode_description :: Mode -> String
 mode_description (_,_,d) = d
 
-mode_degree :: MODE -> Int
-mode_degree = sum . mode_intervals
+-- | 'length' (or degree) of 'mode_intervals' (ie. number of notes in mode)
+mode_length :: Mode -> Int
+mode_length = length . mode_intervals
 
--- | (mode-count,_,mode-list)
-type MODENAM = (Int,Int,[MODE])
+-- | 'sum' of 'mode_intervals' (ie. number of notes in tuning system)
+mode_univ :: Mode -> Int
+mode_univ = sum . mode_intervals
 
-modenam_modes :: MODENAM -> [MODE]
+-- | 'List.dx_d' of 'mode_intervals'.  This seqence includes the octave.
+mode_degree_seq :: Mode -> [Int]
+mode_degree_seq = List.dx_d 0 . mode_intervals
+
+-- | (mode-count,mode-length-maxima,mode-list)
+type ModeNam = (Int,Int,[Mode])
+
+modenam_modes :: ModeNam -> [Mode]
 modenam_modes (_,_,m) = m
 
 -- | Search for mode by interval list.
-modenam_search_seq :: MODENAM -> [Int] -> [MODE]
+modenam_search_seq :: ModeNam -> [Int] -> [Mode]
 modenam_search_seq (_,_,m) x = filter ((== x) . mode_intervals) m
 
 -- | Expect /one/ result.
@@ -45,23 +77,49 @@
 -- > sq [1,2,1,2,1,2,1,2]
 -- > sq [2,1,2,1,2,1,2,1]
 -- > sq (replicate 12 1)
-modenam_search_seq1 :: MODENAM -> [Int] -> Maybe MODE
+modenam_search_seq1 :: ModeNam -> [Int] -> Maybe Mode
 modenam_search_seq1 mn = List.unlist1 . modenam_search_seq mn
 
 -- | Search for mode by description text.
 --
 -- > map (modenam_search_description mn) ["Messiaen","Xenakis","Raga"]
-modenam_search_description :: MODENAM -> String -> [MODE]
+modenam_search_description :: ModeNam -> String -> [Mode]
 modenam_search_description (_,_,m) x = filter (isInfixOf x . mode_description) m
 
--- | Pretty printer.
-mode_stat :: MODE -> [String]
-mode_stat (d,i,s) =
-    ["mode-start-degree : " ++ show d
-    ,"mode-intervals    : " ++ intercalate "," (map show i)
-    ,"mode-degree       : " ++ show (sum i)
-    ,"mode-description  : " ++ s]
+-- | Is /p/ an element of the set of rotations of /q/.
+mode_rot_eqv :: Mode -> Mode -> Bool
+mode_rot_eqv p q =
+  (mode_length p == mode_length q) &&
+  (mode_univ p == mode_univ q) &&
+  (mode_intervals p `elem` List.rotations (mode_intervals q))
 
+{- | Pretty printer.
+
+> mn <- load_modenam
+
+> let r = filter ((/=) 0 . mode_starting_degree) (modenam_modes mn) -- non-zero starting degrees
+> let r = filter ((== [(1,2),(2,5)]) . mode_histogram) (modenam_modes mn) -- 2×1 and 5×2
+> let r = filter ((== 22) . mode_univ) (modenam_search_description mn "Raga") -- raga of 22 shruti univ
+
+> [(p,q) | p <- r, q <- r, p < q, mode_rot_eqv p q] -- rotationally equivalent elements of r
+
+> length r
+> putStrLn $ unlines $ intercalate ["\n"] $ map mode_stat r
+-}
+mode_stat :: Mode -> [String]
+mode_stat m =
+  let hst = mode_histogram m
+      comma_map f = intercalate "," . map f
+  in ["mode-start-degree : " ++ show (mode_starting_degree m)
+     ,"mode-intervals    : " ++ comma_map show (mode_intervals m)
+     ,"mode-description  : " ++ mode_description m
+     ,"mode-length       : " ++ show (mode_length m)
+     ,"mode-univ         : " ++ show (mode_univ m)
+     ,"mode-interval-set : " ++ intercalate "," (map show (mode_iset m))
+     ,"mode-histogram    : " ++ intercalate "," (map (\(e,n) -> concat [show n,"×",show e]) hst)
+     ,"mode-degree-seq   : " ++ comma_map show (mode_degree_seq m)
+     ]
+
 -- * Parser
 
 -- | Bracketed integers are a non-implicit starting degree.
@@ -80,12 +138,12 @@
 is_integer :: String -> Bool
 is_integer = all isDigit
 
-parse_modenam_entry :: [String] -> MODE
+parse_modenam_entry :: [String] -> Mode
 parse_modenam_entry w =
-    let (n0:n,c) = span (Function.predicate_or is_non_implicit_degree is_integer) w
-    in case non_implicit_degree n0 of
-         Nothing -> (0,map read (n0:n),unwords c)
-         Just d -> (d,map read n,unwords c)
+    let (n,c) = span (Function.predicate_or is_non_implicit_degree is_integer) w
+    in case non_implicit_degree (n !! 0) of
+         Nothing -> (0,map read n,unwords c)
+         Just d -> (d,map read (tail n),unwords c)
 
 -- | Lines ending with @\@ continue to next line.
 join_long_lines :: [String] -> [String]
@@ -97,7 +155,7 @@
       _ -> l
 
 -- | Parse joined non-comment lines of modenam file.
-parse_modenam :: [String] -> MODENAM
+parse_modenam :: [String] -> ModeNam
 parse_modenam l =
     case l of
       n_str:x_str:m_str ->
@@ -107,14 +165,15 @@
         in if n == length m then (n,x,m) else error "parse_modenam"
       _ -> error "parse_modenam"
 
--- * IO
+-- * Io
 
--- | 'parse_modenam' of 'Scala.load_dist_file' of @modenam.par@.
---
--- > mn <- load_modenam
--- > let (n,x,m) = mn
--- > n == 2933 && x == 15 && length m == n -- Scala 2.42p
-load_modenam :: IO MODENAM
+{- | 'parse_modenam' of 'Scala.load_dist_file' of @modenam.par@.
+
+> mn <- load_modenam
+> let (n,x,m) = mn
+> (n, x, length m) == (3087,15,3087) -- Scala 2.64p
+-}
+load_modenam :: IO ModeNam
 load_modenam = do
   l <- Scala.load_dist_file_ln "modenam.par"
   return (parse_modenam (Scala.filter_comments (join_long_lines l)))
diff --git a/Music/Theory/Tuning/Sethares_1994.hs b/Music/Theory/Tuning/Sethares_1994.hs
--- a/Music/Theory/Tuning/Sethares_1994.hs
+++ b/Music/Theory/Tuning/Sethares_1994.hs
@@ -1,16 +1,26 @@
 -- | William A. Sethares.
 -- "Adaptive Tunings for Musical Scales".
 -- /Journal of the Acoustical Society of America/, 96(1), July 1994.
---
--- <http://sethares.engr.wisc.edu/consemi.html>
 module Music.Theory.Tuning.Sethares_1994 where
 
-import qualified Music.Theory.Tuning as T
+import Data.Maybe {- base -}
 
--- > import Sound.SC3.Plot
--- > plotTable1 (map (\f -> d (220,1) (f,1)) [220 .. 440])
-d :: (Floating n, Ord n) => (n,n) -> (n,n) -> n
-d (f1,v1) (f2,v2) =
+import qualified Music.Theory.Tuning as T {- hmt -}
+
+{- | Plomp-Levelt consonance curve.
+
+R. Plomp and W. J. M. Levelt,
+"Tonal Consonance and Critical Bandwidth,"
+Journal of the Acoustical Society of America.38, 548-560 (1965).
+
+"Relating Tuning and Timbre" <http://sethares.engr.wisc.edu/consemi.html>
+MATLAB: <https://sethares.engr.wisc.edu/comprog.html>
+
+> import Sound.SC3.Plot {- hsc3-plot -}
+> plot_p1_ln [map (\f -> pl_dissonance (220,1) (f,1)) [220 .. 440]]
+-}
+pl_dissonance :: (Floating n, Ord n) => (n,n) -> (n,n) -> n
+pl_dissonance (f1,v1) (f2,v2) =
     let d_star = 0.24
         s1 = 0.0207
         s2 = 18.96
@@ -24,16 +34,52 @@
         e2 = c2 * exp (a2 * s * f_dif)
     in v1 * v2 * (e1 + e2)
 
--- > plotTable fig_1
-fig_1 :: (Floating n,Enum n,Ord n) => [[n]]
-fig_1 =
+-- | Sum of 'pl_dissonance' for all p in s1 and all q in s2.
+pl_dissonance_h :: (Floating n, Ord n) => [(n,n)] -> [(n,n)] -> n
+pl_dissonance_h s1 s2 = sum [pl_dissonance p q | p <- s1, q <- s2]
+
+-- | Return local minima of sequence with index.
+local_minima :: Ord t => [t] -> [(Int,t)]
+local_minima =
+  let f (ix,i,j,k) = if j <= i && j <= k then Just (ix,j) else Nothing
+      triples ix l = case l of
+                       i:j:k:_ -> (ix,i,j,k) : triples (ix + 1) (tail l)
+                       _ -> []
+  in mapMaybe f . triples 1
+
+-- | William A. Sethares "Adaptive Tunings for Musical Scales".
+--
+-- > plot_p1_ln atms_fig_1
+atms_fig_1 :: (Floating n,Enum n,Ord n) => [[n]]
+atms_fig_1 =
     let f0 = [125,250,500,1000,2000]
         r_seq = map T.cents_to_fratio [0 .. 1200]
-    in map (\f -> map (\r -> d (f,1) (f * r,1)) r_seq) f0
+    in map (\f -> map (\r -> pl_dissonance (f,1) (f * r,1)) r_seq) f0
 
--- > let a_seq = take 7 (iterate (* 0.88) 1.0)
--- > let gen f0 = zipWith (\r a -> (f0 * r,a)) [1 .. 7] a_seq
--- > let r_seq = map T.cents_to_ratio [0,1 .. 1200]
--- > plotTable1 (let f0 = 880 in map (\r -> d_h (gen f0) (gen (f0 * r))) r_seq)
-d_h :: (Floating n, Ord n) => [(n,n)] -> [(n,n)] -> n
-d_h s1 s2 = sum [d p q | p <- s1, q <- s2]
+-- > plot_p1_ln [atms_fig_2 880]
+-- > map fst (local_minima (atms_fig_2 880)) == [204,231,267,316,386,435,498,583,702,814,884,969,1018]
+atms_fig_2 :: (Ord t, Floating t, Enum t) => t -> [t]
+atms_fig_2 f0 =
+  let gen fq = map (\r -> (fq * r,1)) [1 .. 9]
+      r_seq = map T.cents_to_fratio [0,1 .. 1200]
+  in map (\r -> pl_dissonance_h (gen f0) (gen (f0 * r))) r_seq
+
+-- > Sound.SC3.Plot.plot_p1_ln [atms_fig_3 880]
+-- > map fst (local_minima (atms_fig_3 880)) == [267,400,533,667,800,933,1043]
+atms_fig_3 :: (Ord t, Floating t, Enum t) => t -> [t]
+atms_fig_3 f0 =
+  let b = 2 ** (1/9)
+      gen fq = map (\r -> (fq * r,1)) (1 : map (b **) [9,14,18,21,25,27,30])
+      r_seq = map T.cents_to_fratio [0,1 .. 1200]
+  in map (\r -> pl_dissonance_h (gen f0) (gen (f0 * r))) r_seq
+
+-- | "Relating Tuning and Timbre" <http://sethares.engr.wisc.edu/consemi.html>
+--
+-- > plot_p1_ln [rtt_fig_2 880]
+-- > map fst (local_minima (rtt_fig_2 880)) == [267,316,386,498,582,702,884,969]
+rtt_fig_2 :: (Ord t, Floating t, Enum t) => t -> [t]
+rtt_fig_2 f0 =
+  let a_seq = take 7 (iterate (* 0.88) 1.0)
+      gen fq = zipWith (\r a -> (fq * r,a)) [1 .. 7] a_seq
+      r_seq = map T.cents_to_fratio [0,1 .. 1200]
+  in map (\r -> pl_dissonance_h (gen f0) (gen (f0 * r))) r_seq
diff --git a/Music/Theory/Tuning/Syntonic.hs b/Music/Theory/Tuning/Syntonic.hs
--- a/Music/Theory/Tuning/Syntonic.hs
+++ b/Music/Theory/Tuning/Syntonic.hs
@@ -3,11 +3,18 @@
 
 import Data.List {- base -}
 
-import Music.Theory.Tuning {- hmt -}
-import Music.Theory.Tuning.Type {- 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)
@@ -22,9 +29,9 @@
 -- > [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/.
@@ -35,7 +42,7 @@
 -- 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
@@ -48,8 +55,8 @@
 > 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 :: Tuning
-syntonic_697 = Tuning (Right (mk_syntonic_tuning 697)) Nothing
+syntonic_697 :: T.Tuning
+syntonic_697 = T.Tuning (Right (mk_syntonic_tuning 697)) Nothing
 
 -- | 'mk_syntonic_tuning' of @702@.
 --
@@ -57,5 +64,5 @@
 --
 -- > let c = [0,24,114,204,294,318,408,498,522,612,702,792,816,906,996,1020,1110]
 -- > tn_cents_i syntonic_702 == c
-syntonic_702 :: Tuning
-syntonic_702 = Tuning (Right (mk_syntonic_tuning 702)) Nothing
+syntonic_702 :: T.Tuning
+syntonic_702 = T.Tuning (Right (mk_syntonic_tuning 702)) Nothing
diff --git a/Music/Theory/Tuning/Type.hs b/Music/Theory/Tuning/Type.hs
--- a/Music/Theory/Tuning/Type.hs
+++ b/Music/Theory/Tuning/Type.hs
@@ -33,7 +33,7 @@
 
 -- | Tuning octave, defaulting to 2:1.
 tn_octave_def :: Tuning -> Either Rational T.Cents
-tn_octave_def = maybe (Left 2) id . tn_octave
+tn_octave_def = fromMaybe (Left 2) . tn_octave
 
 -- | Tuning octave in cents.
 tn_octave_cents :: Tuning -> T.Cents
@@ -110,7 +110,7 @@
 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)
+    in o_ratio * (tn_approximate_ratios t !! pc)
 
 -- | 'Maybe' exact ratios reconstructed from possibly inexact 'Cents'
 -- of 'Tuning'.
diff --git a/Music/Theory/Tuning/Wilson.hs b/Music/Theory/Tuning/Wilson.hs
--- a/Music/Theory/Tuning/Wilson.hs
+++ b/Music/Theory/Tuning/Wilson.hs
@@ -4,29 +4,31 @@
 import Control.Monad {- base -}
 import Data.List {- base -}
 import Data.Maybe {- base -}
+import Data.Ord {- base -}
 import Data.Ratio {- base -}
-import Safe {- safe -}
-import System.FilePath {- filepath -}
 import Text.Printf {- base -}
 
-import qualified Music.Theory.Array.Text as T {- hmt -}
-import qualified Music.Theory.Function as T {- hmt -}
-import qualified Music.Theory.Graph.Dot as T {- hmt -}
-import qualified Music.Theory.Graph.Type as T {- hmt -}
-import qualified Music.Theory.Interval.Barlow_1987 as T {- hmt -}
-import qualified Music.Theory.List as T {- hmt -}
-import qualified Music.Theory.Math as T {- hmt -}
-import qualified Music.Theory.Math.Convert as T {- hmt -}
-import qualified Music.Theory.Math.OEIS as T {- hmt -}
-import qualified Music.Theory.Math.Prime as T {- hmt -}
-import qualified Music.Theory.Set.List as T {- hmt -}
-import qualified Music.Theory.Show as T {- hmt -}
-import qualified Music.Theory.Tuning as T {- hmt -}
-import qualified Music.Theory.Tuning.Scala as T {- hmt -}
-import qualified Music.Theory.Tuple as T {- hmt -}
+import qualified Safe {- safe -}
 
--- * GEOM (SEE "Data.CG.Minus.Plain")
+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)
@@ -39,7 +41,7 @@
 v2_scale :: Num n => n -> V2 n -> V2 n
 v2_scale n = v2_map (* n)
 
--- * PT SET
+-- * Pt Set
 
 {- | Normalise set of points to lie in (-1,-1) - (1,1), scaling symetrically about (0,0)
 
@@ -47,84 +49,92 @@
 > 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 . T.bimap1 abs) x) in map (v2_scale (recip z)) x
+pt_set_normalise_sym x =
+  let z = maximum (map (uncurry max . Function.bimap1 abs) x)
+  in map (v2_scale (recip z)) x
 
--- * LATTICE CO-ORD
+-- * Lattice Design
 
 -- | /k/-unit co-ordinates for /k/-lattice.
-type LC n = [V2 n]
+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 => LC n
-ew_lc_std = [(20,0),(0,20),(4,3),(-3,4),(-1,2)]
+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 => LC n
-kg_lc_std = [(40,0),(0,40),(13,11),(-14,18),(-8,4)]
+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, used especially when working with hexanies or 7 limit tunings
+-- | 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 => LC n
-ew_lc_tetradic = [(-4,-2),(6,1),(5,-2)]
-
--- | Resolve POS against LC to V2
-lc_pos_to_pt :: (Fractional n, Ord n) => LC n -> POS -> V2 n
-lc_pos_to_pt lc x = v2_sum (zipWith (v2_scale . fromIntegral) x (pt_set_normalise_sym lc))
+ew_lc_tetradic :: Num n => Lattice_Design n
+ew_lc_tetradic = (3,[(-4,-2),(6,1),(5,-2)])
 
--- * LAT
+-- * Lattice_Factors
 
 -- | A discrete /k/-lattice is described by a sequence of /k/-factors.
---   LAT values are ordinarily though not necessarily primes.
-type LAT = [Integer]
+--   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 POS = [Int]
+type Lattice_Position = (Int,[Int])
 
--- | White-space pretty printer for POS.
+-- | 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 [0,-2,1] == "  0 -2  1"
-pos_pp_ws :: POS -> String
-pos_pp_ws = let f x = printf "%3d" x in concatMap f
+-- > 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 LAT [X,Y,Z..] and POS [x,y,z..], calculate the indicated ratio.
+-- | Given Lattice_Factors [X,Y,Z..] and Lattice_Position [x,y,z..], calculate the indicated ratio.
 --
--- > lat_res [3,5] [-5,2] == (5 * 5) / (3 * 3 * 3 * 3 * 3)
-lat_res :: LAT -> POS -> Rational
-lat_res p q =
+-- > 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 ^ T.int_to_integer j) % 1
+                GT -> (i ^ Convert.int_to_integer j) % 1
                 EQ -> 1
-                LT -> 1 % (i ^ abs (T.int_to_integer j))
+                LT -> 1 % (i ^ abs (Convert.int_to_integer j))
   in product (zipWith f p q)
 
--- * RAT (n,d)
+-- * Rat (n,d)
 
 -- | Ratio given as (/n/,/d/)
-type RAT = (Integer,Integer)
+type Rat = (Integer,Integer)
 
 -- | Remove all octaves from /n/ and /d/.
-rat_rem_oct :: RAT -> RAT
-rat_rem_oct = T.bimap1 (product . filter (/= 2)) . T.rat_prime_factors
+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 . T.rational_nd
+-- | Lift 'Rat' function to 'Rational'.
+rat_lift_1 :: (Rat -> Rat) -> Rational -> Rational
+rat_lift_1 f = uncurry (%) . f . Math.rational_nd
 
-rat_to_ratio :: RAT -> Rational
+-- | 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 :: Rat -> Rat -> Rat
 rat_mediant (n1,d1) (n2,d2) = (n1 + n2,d1 + d2)
 
-rat_pp :: RAT -> String
+-- | Rat written as n/d
+rat_pp :: Rat -> String
 rat_pp (n,d) = concat [show n,"/",show d]
 
 -- * Rational
@@ -143,63 +153,84 @@
 --
 -- > r_seq_limit [1] == 1
 r_seq_limit :: [Rational] -> Integer
-r_seq_limit = maximum . map T.rational_prime_limit
+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
 
--- > map (rat_fact_lm 11) [3,5,7,11] == [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
-rat_fact_lm :: Integer -> Rational -> POS
-rat_fact_lm lm = tail . T.rat_prime_factors_t (fromMaybe 1 (T.prime_k lm) + 1) . T.rational_nd
+-- | 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 :: Integer -> [Rational] -> [[String]]
-tbl_txt lm_z rs =
+tbl_txt :: Bool -> Integer -> [Rational] -> [[String]]
+tbl_txt del lm_z rs =
   let lm = r_seq_limit rs
-      scl = map (rat_fact_lm lm) rs
-      cs = map (T.ratio_to_cents . T.fold_ratio_to_octave_err) rs
-      hs = map (T.harmonicity_r T.barlow) rs :: [Double]
+      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 "..."
-                      ,T.ratio_pp r
-                      ,T.real_pp 2 c
-                      ,T.real_pp_unicode 2 h]
+                      ,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 [1,7/6,5/4,4/3,3/2]
-tbl_wr :: [Rational] -> IO ()
-tbl_wr = putStr . unlines . T.table_pp (False,True,False," ",False) . tbl_txt 31
+-- > 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-lc,gr-attr,vertex-pp)
-type EW_GR_OPT = (Maybe (LC Rational),[T.DOT_META_ATTR],Rational -> String)
+-- | (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 :: Ew_Gr_Opt -> Bool
 ew_gr_opt_pos (lc_m,_,_) = isJust lc_m
 
-ew_gr_r_pos :: LC Rational -> Rational -> T.DOT_ATTR
-ew_gr_r_pos lc =
+-- > 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 T.node_pos_attr . f 160 . lc_pos_to_pt lc . Safe.tailDef [] . T.rational_prime_factors_l
+  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
 
-ew_gr_udot :: EW_GR_OPT -> T.LBL Rational () -> [String]
+-- | '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 -> ("neato",Just . ew_gr_r_pos lc)
-  in T.lbl_to_udot
+                  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) -> T.mcons (p_f v) [("label",v_pp v)]
-     ,\_ -> [])
+     (\(_,v) -> List.mcons (p_f v) [("label",v_pp v)]
+     ,const [])
 
-ew_gr_udot_wr :: EW_GR_OPT -> FilePath -> T.LBL Rational () -> IO ()
+-- | '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 -> T.LBL Rational () -> IO ()
+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 (T.dot_to_svg (if ew_gr_opt_pos opt then ["-n"] else []) fn (replaceExtension fn "svg"))
+  void (Dot.dot_to_svg (if ew_gr_opt_pos opt then ["-n"] else []) fn)
 
--- * ZIG-ZAG
+-- * 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)
@@ -223,7 +254,7 @@
 zz_seq :: (Eq n, Num n) => [Int] -> [[(n, n)]]
 zz_seq k_seq = zz_recur k_seq [(0,1),(1,1)]
 
--- * MOS
+-- * Mos
 
 -- > gen_coprime 12 == [1,5]
 -- > gen_coprime 49 == [1..24] \\ [7,14,21]
@@ -247,7 +278,7 @@
 mos_unfold :: (Ord b, Num b) => (b, b) -> [(b, b)]
 mos_unfold x =
   let y = mos_step x
-  in if T.t2_sum y == 3 then [x,y] else x : mos_unfold y
+  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 =
@@ -265,7 +296,7 @@
 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 = mos p g
+      ((i0,j0), r) = List.headTail (mos p g)
   in recur_f r [i0,j0]
 
 mos_cell_pp :: (Integral i,Show i) => i -> String
@@ -281,7 +312,7 @@
 mos_tbl_wr :: (Integral i,Show i) => [[i]] -> IO ()
 mos_tbl_wr = putStrLn . unlines . mos_tbl_pp
 
--- * MOS/LOG
+-- * 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))
@@ -294,29 +325,29 @@
 mos_log_kseq :: Double -> [Int]
 mos_log_kseq = map fst . mos_log
 
--- * STERN-BROCOT TREE
+-- * Stern-Brocot Tree
 
 data SBT_DIV = NIL | LHS | RHS deriving (Show)
-type SBT_NODE = (SBT_DIV,RAT,RAT,RAT)
+type Sbt_Node = (SBT_DIV,Rat,Rat,Rat)
 
-sbt_step :: SBT_NODE -> [SBT_NODE]
+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 :: Sbt_Node
 sbt_root = (NIL,(0,1),(1,1),(1,0))
 
-sbt_half :: SBT_NODE
+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 :: Sbt_Node -> [[Sbt_Node]]
 sbt_from = iterate (concatMap sbt_step) . return
 
-sbt_k_from :: Int -> SBT_NODE -> [[SBT_NODE]]
+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 :: 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
@@ -324,153 +355,155 @@
        LHS -> edge_pp r m
        RHS -> edge_pp l m
 
-sbt_node_elem :: SBT_NODE -> [RAT]
+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 :: [Sbt_Node] -> [String]
 sbt_dot n =
   let e = map sbt_node_to_edge n
   in concat [["graph {","node [shape=plain]"],e,["}"]]
 
--- * M-GEN
+-- * M-Gen
 
 (^.) :: Rational -> Int -> Rational
 (^.) = (^)
 
 r_normalise :: [Rational] -> [Rational]
-r_normalise = nub . sortOn T.fold_ratio_to_octave_err
+r_normalise = nub . sortOn Tuning.fold_ratio_to_octave_err
 
 -- | (ratio,multiplier,steps)
-type M_GEN = (Rational,Rational,Int)
+type M_Gen = (Rational,Rational,Int)
 
-m_gen_unfold :: M_GEN -> [Rational]
+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 :: [M_Gen] -> [Rational]
 m_gen_to_r = r_normalise . concatMap m_gen_unfold
 
--- * M3-GEN
+-- * M3-Gen
 
 -- | (ratio,M3-steps)
-type M3_GEN = (Rational,Int)
+type M3_Gen = (Rational,Int)
 
-m3_to_m :: M3_GEN -> M_GEN
+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 :: M3_Gen -> [Rational]
 m3_gen_unfold = m_gen_unfold . m3_to_m
 
-m3_gen_to_r :: [M3_GEN] -> [Rational]
+m3_gen_to_r :: [M3_Gen] -> [Rational]
 m3_gen_to_r = r_normalise . concatMap m3_gen_unfold
 
--- * SCALA
+-- * Scala
 
-r_to_scale :: String -> String -> [Rational] -> T.Scale
+r_to_scale :: String -> String -> [Rational] -> Scala.Scale
 r_to_scale nm dsc r =
-  let r' = map T.fold_ratio_to_octave_err (tail r) ++ [2]
-  in if r !! 0 /= 1 || not (T.is_ascending 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] -> IO [String]
+ew_scl_find_r :: [Rational] -> [Scala.Scale] -> [String]
 ew_scl_find_r r =
   let set_eq x y = sort x == sort y
-  in if head r /= 1
-     then error "ew_scl_find_r?"
-     else fmap (map T.scale_name) (T.scl_find_ji set_eq (map T.fold_ratio_to_octave_err r ++ [2]))
+      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 :: [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}
+{- | P.3 7-limit {Scala=nil}
 
-> ew_scl_find_r (1 : ew_1357_3_r)
+> 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 :: T.Scale
+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}
+{- | P.7 11-limit {Scala=nil}
 
-> ew_scl_find_r ew_el12_7_r
+> 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 :: T.Scale
+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}
+{- | P.9 7-limit {Scala=wilson_class}
 
-> ew_scl_find_r ew_el12_9_r
+> 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 :: T.Scale
+--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}
+{- | P.12 11-limit {Scala=nil}
 
-> ew_scl_find_r ew_el12_12_r
+> 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 :: T.Scale
+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}
+{- | P.2 11-limit {Scala=wilson_l4}
 
-> ew_scl_find_r ew_el22_2_r
+> 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}
+{- | P.3 11-limit {Scala=wilson_l5}
 
-> ew_scl_find_r ew_el22_3_r
+> 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}
+{- | P.4 11-limit {Scala=wilson_l3}
 
-> ew_scl_find_r ew_el22_4_r
+> 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}
+{- | P.5 11-limit {Scala=wilson_l1}
 
-> ew_scl_find_r ew_el22_5_r
+> 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}
+{- | P.6 11-limit {Scala=wilson_l2}
 
-> ew_scl_find_r ew_el22_6_r
+> ew_scl_find_r ew_el22_6_r db
 -}
 ew_el22_6_r :: [Rational]
 ew_el22_6_r =
@@ -483,26 +516,26 @@
 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 :: [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}
+{- | P.7 & P.12 11-limit {Scala=partch_29}
 
 1,3,5,7,9,11 diamond
 
-> ew_scl_find_r ew_diamond_12_r -- partch_29
+> 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}
+{- | 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 -- novaro15
+> 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]
@@ -518,38 +551,38 @@
 hel_1_i :: HEL
 hel_1_i =
   let i = take 6 (hel_r_asc (7,6))
-  in (take 5 i,take 5 (T.rotate_left 2 i))
+  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 (T.rotate_left 3 (tail i))
+  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 (T.rotate_left 6 (take 14 i)),take 14 (tail i))
+  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}
+{- | P.12 {Scala=nil}
 
 22-tone 23-limit Evangalina tuning (2001)
 
-> ew_scl_find_r ew_hel_12_r
+> 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 :: T.Scale
+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>
@@ -558,7 +591,7 @@
 she_div :: Eq a => [a] -> [[[a]]]
 she_div x =
   let f = (== [1,length x - 1]) . sort . map length
-  in map (reverse . sortOn length) (filter f (T.partitions x))
+  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]
@@ -571,16 +604,16 @@
 
 -- > 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_mul_r r = [x * y | x <- r,y <- r,x <= y]
 
-{- | she = Stellate Hexany Expansions, P.10 {SCALA=stelhex1,stelhex2,stelhex5,stelhex6}
+{- | 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 (ew_scl_find_r . 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]) -- NIL
+> 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 T.fold_ratio_to_octave_err (she_mul_r r ++ she_div_r r)))
+she r = nub (sort (map Tuning.fold_ratio_to_octave_err (she_mul_r r ++ she_div_r r)))
 
 -- * <http://anaphoria.com/meru.pdf>
 
@@ -593,7 +626,7 @@
 
 meru :: Num n => [[n]]
 meru =
-  let f xs = zipWith (+) ([0] ++ xs) (xs ++ [0])
+  let f xs = zipWith (+) (0 : xs) (xs ++ [0])
   in iterate f [1]
 
 -- > meru_k 13
@@ -602,26 +635,26 @@
 
 -- > 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 (\x l -> atDef 0 l x) [0..] (reverse (meru_k k))
+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 T.a000045
+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 (\x l -> atDef 0 l x) [0..] (every_nth (reverse (meru_k k)) 2)
+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 = T.a000930
+meru_2_direct = OEIS.a000930
 
 -- | meru_3 = META-SLENDRO
 meru_3 :: Num n => Int -> [[n]]
 meru_3 k =
-  let f t = zipWith (\x l -> atDef 0 l x) [0,2..] t
+  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]
@@ -632,20 +665,20 @@
 
 -- > 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 T.a000931
+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 (\x l -> atDef 0 l x) [0..] (every_nth (reverse (meru_k k)) 3)
+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 T.a003269
+meru_4_direct = tail OEIS.a003269
 
 -- > map meru_5 [1..4]
 meru_5 :: Num n => Int -> [[n]]
 meru_5 k =
-  let f t = zipWith (\x l -> atDef 0 l x) [0,3..] t
+  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]
 
@@ -655,25 +688,25 @@
 
 -- > take 39 meru_5_direct == map sum (meru_5_seq 13)
 meru_5_direct :: Num n => [n]
-meru_5_direct = T.a017817
+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 (\x l -> atDef 0 l x) [0..] (every_nth (reverse (meru_k k)) 4)
+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 = T.a003520
+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 = T.a001687
+meru_7_direct = OEIS.a001687
 
 -- * <http://anaphoria.com/mos.pdf>
 
-{- | P.13, tanabe {SCALA=chin_7}
+{- | P.13, tanabe {Scala=chin_7}
 
-> ew_scl_find_r ew_mos_13_tanabe_r
+> 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]
@@ -682,62 +715,62 @@
 
 ew_novarotreediamond_1 :: ([[Rational]],[[Rational]])
 ew_novarotreediamond_1 =
-  let rem_oct x = if last x /= 2 then error "rem_oct?" else T.drop_last x
+  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 = T.d_dx_by (/) . add_oct
+      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 = T.rotations i_0
+      i = List.rotations i_0
   in (i,map i_to_r i)
 
-{- | P.1 {SCALA=NIL}
+{- | P.1 {Scala=nil}
 
 23-tone 7-limit (2004)
 
-> ew_scl_find_r ew_novarotreediamond_1_r
+> 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 :: T.Scale
+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}
+{- | P.2 {Scala=nil}
 
 9-tone Pelog cycle (1988)
 
-> ew_scl_find_r ew_pelogFlute_2
+> 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 :: T.Scale
+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 :: (Sbt_Node,Int)
 xen1_fig3 = ((NIL,(1,3),(2,5),(1,2)),5)
 
 -- | P.9, Fig. 4
-xen1_fig4 :: (SBT_NODE,Int)
+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}
+-- | 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 :: T.Scale
+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]
@@ -751,10 +784,10 @@
 
 {- | P.9 {SCALA 5=nil 7=ptolemy_idiat 12=nil 19=wilson2 31=wilson_31}
 
-> mapM ew_scl_find_r xen3b_9_r
+> mapM ew_scl_find_r xen3b_9_r db
 -}
 xen3b_9_r :: [[Rational]]
-xen3b_9_r = map (T.drop_last . scanl (*) 1) xen3b_9_i
+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]]
@@ -767,7 +800,7 @@
 
 -- | P.13 {SCALA 5=slendro5_2 7=ptolemy_diat2 12=nil 17=nil 22=wilson7_4}
 xen3b_13_r :: [[Rational]]
-xen3b_13_r = map (T.drop_last . scanl (*) 1) xen3b_13_i
+xen3b_13_r = map (List.drop_last . scanl (*) 1) xen3b_13_i
 
 -- * <http://anaphoria.com/xen3bappendix.pdf>
 
@@ -775,7 +808,7 @@
 
 17,31,41 lattices from XEN3B (1975)
 -}
-ew_xen3b_apx_gen :: [(Int,[M3_GEN])]
+ew_xen3b_apx_gen :: [(Int,[M3_Gen])]
 ew_xen3b_apx_gen =
   [(17,[(1/729,12)
        ,(5/3,3)
@@ -802,19 +835,19 @@
 
 -- * <http://anaphoria.com/xen456.pdf>
 
-ew_xen456_7_gen :: [M3_GEN]
+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}
+{- P.7 {Scala=wilson1}
 
 19-tone "A Scale for Scott" (1976)
 
-> L.ew_find_scl_name ew_xen456_7_r -- wilson1
+> 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 :: [M3_Gen]
 ew_xen456_9_gen =
   [(1/(3^.3),4)
   ,(1/(5*(3^.2)),3)
@@ -823,68 +856,68 @@
   ,(5/(11*3),4)
   ,(7/11,2)]
 
-{- | P.9 {SCALA=NIL}
+{- | P.9 {Scala=nil ; Scala:Rot=wilson11}
 
 19-tone scale for the Clavichord-19 (1976)
 
-> ew_scl_find_r ew_xen456_9_r
+> ew_scl_find_r ew_xen456_9_r db
 
-> import qualified Music.Theory.List as T {- hmt -}
-> T.scl_find_ji T.is_subset ew_xen456_9_r -- NIL
+> 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 :: T.Scale
+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
+-- * Gems
 
 {- | <http://wilsonarchives.blogspot.com/2010/10/scale-for-rod-poole.html>
 
-13-limit 22-tone scale {SCALA=nil}
+13-limit 22-tone scale {Scala=nil}
 
-> ew_scl_find_r ew_poole_r
+> 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 :: T.Scale
+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}
+11-limit 17-tone scale {Scala=wilcent17}
 
-> ew_scl_find_r ew_centaur17_r
+> 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}
+7-limit 22-tone scale {Scala=nil}
 
-> ew_scl_find_r ew_two_22_7_r
+> ew_scl_find_r ew_two_22_7_r db
 -}
 ew_two_22_7_r :: [Rational]
 ew_two_22_7_r =
-  [1/1,9/35,1/15,35/1,9/1,7/3,3/5,315/1,245/3,21/1,27/5
-  ,7/5,735/1,189/1,49/1,63/5,5/3,3/7,1/9,1/35,15/1,35/9]
+  [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 :: T.Scale
+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
+-- * Db
 
 {- | Scales /not/ present in the standard scala file set.
 
-> mapM_ (T.scale_wr_dir "/home/rohan/sw/hmt/data/scl/") ew_scl_db
-> map T.scale_name ew_scl_db
+> mapM_ (Scala.scale_wr_dir "/home/rohan/sw/hmt/data/scl/") ew_scl_db
+> map Scala.scale_name ew_scl_db
 -}
-ew_scl_db :: [T.Scale]
+ew_scl_db :: [Scala.Scale]
 ew_scl_db =
   [ew_1357_3_scl
   ,ew_el12_7_scl
diff --git a/Music/Theory/Tuple.hs b/Music/Theory/Tuple.hs
deleted file mode 100644
--- a/Music/Theory/Tuple.hs
+++ /dev/null
@@ -1,369 +0,0 @@
--- | Tuple functions.
---
--- Uniform tuples have types 'T2', 'T3' etc. and functions names are
--- prefixed @t2_@ etc.
---
--- Heterogenous tuples (products) are prefixed @p2_@ etc.
-module Music.Theory.Tuple where
-
--- * P2 (2-product)
-
-p2_swap :: (s,t) -> (t,s)
-p2_swap (i,j) = (j,i)
-
--- * T2 (2-tuple, regular)
-
--- | Uniform two-tuple.
-type T2 a = (a,a)
-
-t2_from_list :: [t] -> T2 t
-t2_from_list l = case l of {[p,q] -> (p,q);_ -> error "t2_from_list"}
-
-t2_to_list :: T2 a -> [a]
-t2_to_list (i,j) = [i,j]
-
-t2_swap :: T2 t -> T2 t
-t2_swap = p2_swap
-
-t2_map :: (p -> q) -> T2 p -> T2 q
-t2_map f (p,q) = (f p,f q)
-
-t2_zipWith :: (p -> q -> r) -> T2 p -> T2 q -> T2 r
-t2_zipWith f (p,q) (p',q') = (f p p',f q q')
-
-t2_infix :: (a -> a -> b) -> T2 a -> b
-t2_infix f (i,j) = i `f` j
-
--- | Infix 'mappend'.
---
--- > t2_join ([1,2],[3,4]) == [1,2,3,4]
-t2_join :: Monoid m => T2 m -> m
-t2_join = t2_infix mappend
-
-t2_concat :: [T2 [a]] -> T2 [a]
-t2_concat = t2_map mconcat . unzip
-
-t2_sort :: Ord t => (t,t) -> (t,t)
-t2_sort (p,q) = (min p q,max p q)
-
--- | T2 variant of 'sum'
-t2_sum :: Num n => (n,n) -> n
-t2_sum (i,j) = i + j
-
--- * P3 (3-product)
-
--- | Left rotation.
---
--- > p3_rotate_left (1,2,3) == (2,3,1)
-p3_rotate_left :: (s,t,u) -> (t,u,s)
-p3_rotate_left (i,j,k) = (j,k,i)
-
-p3_fst :: (a,b,c) -> a
-p3_fst (a,_,_) = a
-
-p3_snd :: (a,b,c) -> b
-p3_snd (_,b,_) = b
-
-p3_third :: (a,b,c) -> c
-p3_third (_,_,c) = c
-
--- * T3 (3 triple, regular)
-
-type T3 a = (a,a,a)
-
-t3_from_list :: [t] -> T3 t
-t3_from_list l = case l of {[p,q,r] -> (p,q,r);_ -> error "t3_from_list"}
-
-t3_to_list :: T3 a -> [a]
-t3_to_list (i,j,k) = [i,j,k]
-
-t3_rotate_left :: T3 t -> T3 t
-t3_rotate_left = p3_rotate_left
-
-t3_fst :: T3 t -> t
-t3_fst = p3_fst
-
-t3_snd :: T3 t -> t
-t3_snd = p3_snd
-
-t3_third :: T3 t -> t
-t3_third = p3_third
-
-t3_map :: (p -> q) -> T3 p -> T3 q
-t3_map f (p,q,r) = (f p,f q,f r)
-
-t3_zipWith :: (p -> q -> r) -> T3 p -> T3 q -> T3 r
-t3_zipWith f (p,q,r) (p',q',r') = (f p p',f q q',f r r')
-
-t3_infix :: (a -> a -> a) -> T3 a -> a
-t3_infix f (i,j,k) = (i `f` j) `f` k
-
-t3_join :: T3 [a] -> [a]
-t3_join = t3_infix (++)
-
--- * P4 (4-product)
-
-p4_fst :: (a,b,c,d) -> a
-p4_fst (a,_,_,_) = a
-
-p4_snd :: (a,b,c,d) -> b
-p4_snd (_,b,_,_) = b
-
-p4_third :: (a,b,c,d) -> c
-p4_third (_,_,c,_) = c
-
-p4_fourth :: (a,b,c,d) -> d
-p4_fourth (_,_,_,d) = d
-
-p4_zip :: (a,b,c,d) -> (e,f,g,h) -> ((a,e),(b,f),(c,g),(d,h))
-p4_zip (a,b,c,d) (e,f,g,h) = ((a,e),(b,f),(c,g),(d,h))
-
--- * T4 (4-tuple, regular)
-
-type T4 a = (a,a,a,a)
-
-t4_from_list :: [t] -> T4 t
-t4_from_list l = case l of {[p,q,r,s] -> (p,q,r,s); _ -> error "t4_from_list"}
-
-t4_to_list :: T4 t -> [t]
-t4_to_list (p,q,r,s) = [p,q,r,s]
-
-t4_fst :: T4 t -> t
-t4_fst = p4_fst
-
-t4_snd :: T4 t -> t
-t4_snd = p4_snd
-
-t4_third :: T4 t -> t
-t4_third = p4_third
-
-t4_fourth :: T4 t -> t
-t4_fourth = p4_fourth
-
-t4_map :: (p -> q) -> T4 p -> T4 q
-t4_map f (p,q,r,s) = (f p,f q,f r,f s)
-
-t4_zipWith :: (p -> q -> r) -> T4 p -> T4 q -> T4 r
-t4_zipWith f (p,q,r,s) (p',q',r',s') = (f p p',f q q',f r r',f s s')
-
-t4_infix :: (a -> a -> a) -> T4 a -> a
-t4_infix f (i,j,k,l) = ((i `f` j) `f` k) `f` l
-
-t4_join :: T4 [a] -> [a]
-t4_join = t4_infix (++)
-
--- * P5 (5-product)
-
-p5_fst :: (a,b,c,d,e) -> a
-p5_fst (a,_,_,_,_) = a
-
-p5_snd :: (a,b,c,d,e) -> b
-p5_snd (_,b,_,_,_) = b
-
-p5_third :: (a,b,c,d,e) -> c
-p5_third (_,_,c,_,_) = c
-
-p5_fourth :: (a,b,c,d,e) -> d
-p5_fourth (_,_,_,d,_) = d
-
-p5_fifth :: (a,b,c,d,e) -> e
-p5_fifth (_,_,_,_,e) = e
-
-p5_from_list :: (t -> t1, t -> t2, t -> t3, t -> t4, t -> t5) -> [t] -> (t1,t2,t3,t4,t5)
-p5_from_list (f1,f2,f3,f4,f5) l =
-  case l of
-    [c1,c2,c3,c4,c5] -> (f1 c1,f2 c2,f3 c3,f4 c4,f5 c5)
-    _ -> error "p5_from_list"
-
-
-p5_to_list :: (t1 -> t, t2 -> t, t3 -> t, t4 -> t, t5 -> t) -> (t1, t2, t3, t4, t5) -> [t]
-p5_to_list (f1,f2,f3,f4,f5) (c1,c2,c3,c4,c5) = [f1 c1,f2 c2,f3 c3,f4 c4,f5 c5]
-
--- * T5 (5-tuple, regular)
-
-type T5 a = (a,a,a,a,a)
-
-t5_from_list :: [t] -> T5 t
-t5_from_list l = case l of {[p,q,r,s,t] -> (p,q,r,s,t); _ -> error "t5_from_list"}
-
-t5_to_list :: T5 t -> [t]
-t5_to_list (p,q,r,s,t) = [p,q,r,s,t]
-
-t5_map :: (p -> q) -> T5 p -> T5 q
-t5_map f (p,q,r,s,t) = (f p,f q,f r,f s,f t)
-
-t5_fst :: T5 t -> t
-t5_fst (p,_,_,_,_) = p
-
-t5_snd :: T5 t -> t
-t5_snd (_,q,_,_,_) = q
-
-t5_fourth :: T5 t -> t
-t5_fourth (_,_,_,t,_) = t
-
-t5_fifth :: T5 t -> t
-t5_fifth (_,_,_,_,u) = u
-
-t5_infix :: (a -> a -> a) -> T5 a -> a
-t5_infix f (i,j,k,l,m) = (((i `f` j) `f` k) `f` l) `f` m
-
-t5_join :: T5 [a] -> [a]
-t5_join = t5_infix (++)
-
--- * P6 (6-product)
-
-p6_fst :: (a,b,c,d,e,f) -> a
-p6_fst (a,_,_,_,_,_) = a
-
-p6_snd :: (a,b,c,d,e,f) -> b
-p6_snd (_,b,_,_,_,_) = b
-
-p6_third :: (a,b,c,d,e,f) -> c
-p6_third (_,_,c,_,_,_) = c
-
-p6_fourth :: (a,b,c,d,e,f) -> d
-p6_fourth (_,_,_,d,_,_) = d
-
-p6_fifth :: (a,b,c,d,e,f) -> e
-p6_fifth (_,_,_,_,e,_) = e
-
-p6_sixth :: (a,b,c,d,e,f) -> f
-p6_sixth (_,_,_,_,_,f) = f
-
--- * T6 (6-tuple, regular)
-
-type T6 a = (a,a,a,a,a,a)
-
-t6_from_list :: [t] -> T6 t
-t6_from_list l = case l of {[p,q,r,s,t,u] -> (p,q,r,s,t,u);_ -> error "t6_from_list"}
-
-t6_to_list :: T6 t -> [t]
-t6_to_list (p,q,r,s,t,u) = [p,q,r,s,t,u]
-
-t6_map :: (p -> q) -> T6 p -> T6 q
-t6_map f (p,q,r,s,t,u) = (f p,f q,f r,f s,f t,f u)
-
--- * T7 (7-tuple, regular)
-
-type T7 a = (a,a,a,a,a,a,a)
-
-t7_to_list :: T7 t -> [t]
-t7_to_list (p,q,r,s,t,u,v) = [p,q,r,s,t,u,v]
-
-t7_map :: (p -> q) -> T7 p -> T7 q
-t7_map f (p,q,r,s,t,u,v) = (f p,f q,f r,f s,f t,f u,f v)
-
--- * T8 (8-tuple, regular)
-
-type T8 a = (a,a,a,a,a,a,a,a)
-
-t8_to_list :: T8 t -> [t]
-t8_to_list (p,q,r,s,t,u,v,w) = [p,q,r,s,t,u,v,w]
-
-t8_map :: (p -> q) -> T8 p -> T8 q
-t8_map f (p,q,r,s,t,u,v,w) = (f p,f q,f r,f s,f t,f u,f v,f w)
-
--- * P8 (8-product)
-
-p8_third :: (a,b,c,d,e,f,g,h) -> c
-p8_third (_,_,c,_,_,_,_,_) = c
-
--- * T9 (9-tuple, regular)
-
-type T9 a = (a,a,a,a,a,a,a,a,a)
-
-t9_to_list :: T9 t -> [t]
-t9_to_list (p,q,r,s,t,u,v,w,x) = [p,q,r,s,t,u,v,w,x]
-
-t9_map :: (p -> q) -> T9 p -> T9 q
-t9_map f (p,q,r,s,t,u,v,w,x) = (f p,f q,f r,f s,f t,f u,f v,f w,f x)
-
--- * T10 (10-tuple, regular)
-
-type T10 a = (a,a,a,a,a,a,a,a,a,a)
-
-t10_to_list :: T10 t -> [t]
-t10_to_list (p,q,r,s,t,u,v,w,x,y) = [p,q,r,s,t,u,v,w,x,y]
-
-t10_map :: (p -> q) -> T10 p -> T10 q
-t10_map f (p,q,r,s,t,u,v,w,x,y) = (f p,f q,f r,f s,f t,f u,f v,f w,f x,f y)
-
--- * T11 (11-tuple, regular)
-
-type T11 a = (a,a,a,a,a,a,a,a,a,a,a)
-
-t11_to_list :: T11 t -> [t]
-t11_to_list (p,q,r,s,t,u,v,w,x,y,z) = [p,q,r,s,t,u,v,w,x,y,z]
-
-t11_map :: (p -> q) -> T11 p -> T11 q
-t11_map f (p,q,r,s,t,u,v,w,x,y,z) = (f p,f q,f r,f s,f t,f u,f v,f w,f x,f y,f z)
-
--- * T12 (12-tuple, regular)
-
-type T12 t = (t,t,t,t,t,t,t,t,t,t,t,t)
-
-t12_to_list :: T12 t -> [t]
-t12_to_list (p,q,r,s,t,u,v,w,x,y,z,a) = [p,q,r,s,t,u,v,w,x,y,z,a]
-
-t12_from_list :: [t] -> T12 t
-t12_from_list l =
-    case l of
-      [p,q,r,s,t,u,v,w,x,y,z,a] -> (p,q,r,s,t,u,v,w,x,y,z,a)
-      _ -> error "t12_from_list"
-
--- | 'foldr1' of 't12_to_list'.
---
--- > t12_foldr1 (+) (1,2,3,4,5,6,7,8,9,10,11,12) == 78
-t12_foldr1 :: (t -> t -> t) -> T12 t -> t
-t12_foldr1 f = foldr1 f . t12_to_list
-
--- | 'sum' of 't12_to_list'.
---
--- > t12_sum (1,2,3,4,5,6,7,8,9,10,11,12) == 78
-t12_sum :: Num n => T12 n -> n
-t12_sum t =
-    let (n1,n2,n3,n4,n5,n6,n7,n8,n9,n10,n11,n12) = t
-    in n1 + n2 + n3 + n4 + n5 + n6 + n7 + n8 + n9 + n10 + n11 + n12
-
--- * Family of 'uncurry' functions.
-
-uncurry3 :: (a->b->c -> z) -> (a,b,c) -> z
-uncurry3 fn (a,b,c) = fn a b c
-uncurry4 :: (a->b->c->d -> z) -> (a,b,c,d) -> z
-uncurry4 fn (a,b,c,d) = fn a b c d
-uncurry5 :: (a->b->c->d->e -> z) -> (a,b,c,d,e) -> z
-uncurry5 fn (a,b,c,d,e) = fn a b c d e
-uncurry6 :: (a->b->c->d->e->f -> z) -> (a,b,c,d,e,f) -> z
-uncurry6 fn (a,b,c,d,e,f) = fn a b c d e f
-uncurry7 :: (a->b->c->d->e->f->g -> z) -> (a,b,c,d,e,f,g) -> z
-uncurry7 fn (a,b,c,d,e,f,g) = fn a b c d e f g
-uncurry8 :: (a->b->c->d->e->f->g->h -> z) -> (a,b,c,d,e,f,g,h) -> z
-uncurry8 fn (a,b,c,d,e,f,g,h) = fn a b c d e f g h
-uncurry9 :: (a->b->c->d->e->f->g->h->i -> z) -> (a,b,c,d,e,f,g,h,i) -> z
-uncurry9 fn (a,b,c,d,e,f,g,h,i) = fn a b c d e f g h i
-uncurry10 :: (a->b->c->d->e->f->g->h->i->j -> z) -> (a,b,c,d,e,f,g,h,i,j) -> z
-uncurry10 fn (a,b,c,d,e,f,g,h,i,j) = fn a b c d e f g h i j
-uncurry11 :: (a->b->c->d->e->f->g->h->i->j->k -> z) -> (a,b,c,d,e,f,g,h,i,j,k) -> z
-uncurry11 fn (a,b,c,d,e,f,g,h,i,j,k) = fn a b c d e f g h i j k
-uncurry12 :: (a->b->c->d->e->f->g->h->i->j->k->l -> z) -> (a,b,c,d,e,f,g,h,i,j,k,l) -> z
-uncurry12 fn (a,b,c,d,e,f,g,h,i,j,k,l) = fn a b c d e f g h i j k l
-uncurry13 :: (a->b->c->d->e->f->g->h->i->j->k->l->m -> z) -> (a,b,c,d,e,f,g,h,i,j,k,l,m) -> z
-uncurry13 fn (a,b,c,d,e,f,g,h,i,j,k,l,m) = fn a b c d e f g h i j k l m
-uncurry14 :: (a->b->c->d->e->f->g->h->i->j->k->l->m->n -> z) -> (a,b,c,d,e,f,g,h,i,j,k,l,m,n) -> z
-uncurry14 fn (a,b,c,d,e,f,g,h,i,j,k,l,m,n) = fn a b c d e f g h i j k l m n
-uncurry15 :: (a->b->c->d->e->f->g->h->i->j->k->l->m->n->o -> z) -> (a,b,c,d,e,f,g,h,i,j,k,l,m,n,o) -> z
-uncurry15 fn (a,b,c,d,e,f,g,h,i,j,k,l,m,n,o) = fn a b c d e f g h i j k l m n o
-uncurry16 :: (a->b->c->d->e->f->g->h->i->j->k->l->m->n->o->p -> z) -> (a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p) -> z
-uncurry16 fn (a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p) = fn a b c d e f g h i j k l m n o p
-uncurry17 :: (a->b->c->d->e->f->g->h->i->j->k->l->m->n->o->p->q -> z) -> (a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q) -> z
-uncurry17 fn (a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q) = fn a b c d e f g h i j k l m n o p q
-uncurry18 :: (a->b->c->d->e->f->g->h->i->j->k->l->m->n->o->p->q->r -> z) -> (a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r) -> z
-uncurry18 fn (a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r) = fn a b c d e f g h i j k l m n o p q r
-uncurry19 :: (a->b->c->d->e->f->g->h->i->j->k->l->m->n->o->p->q->r->s -> z) -> (a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s) -> z
-uncurry19 fn (a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s) = fn a b c d e f g h i j k l m n o p q r s
-uncurry20 :: (a->b->c->d->e->f->g->h->i->j->k->l->m->n->o->p->q->r->s->t -> z) -> (a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t) -> z
-uncurry20 fn (a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t) = fn a b c d e f g h i j k l m n o p q r s t
-
--- Local Variables:
--- truncate-lines:t
--- End:
diff --git a/Music/Theory/Unicode.hs b/Music/Theory/Unicode.hs
deleted file mode 100644
--- a/Music/Theory/Unicode.hs
+++ /dev/null
@@ -1,508 +0,0 @@
--- | <http://www.unicode.org/charts/PDF/U1D100.pdf>
---
--- These symbols are in <http://www.gnu.org/software/freefont/>,
--- debian=ttf-freefont.
-module Music.Theory.Unicode where
-
-import Data.Char {- base -}
-import Data.List {- base -}
-import Numeric {- base -}
-
-import qualified Text.CSV.Lazy.String as C {- lazy-csv -}
-
-import qualified Music.Theory.IO as T {- hmt -}
-import qualified Music.Theory.List as T {- hmt -}
-import qualified Music.Theory.Read as T {- hmt -}
-
--- * Non-music
-
--- | Unicode non breaking hypen character.
---
--- > non_breaking_hypen == '‑'
-non_breaking_hypen :: Char
-non_breaking_hypen = toEnum 0x2011
-
--- | Unicode non breaking space character.
---
--- > non_breaking_space == ' '
-non_breaking_space :: Char
-non_breaking_space = toEnum 0x00A0
-
--- | Unicode interpunct.
---
--- > middle_dot == '·'
-middle_dot :: Char
-middle_dot = toEnum 0x00B7
-
--- | The superscript variants of the digits 0-9
-superscript_digits :: [Char]
-superscript_digits = "⁰¹²³⁴⁵⁶⁷⁸⁹"
-
--- | Map 'show' of 'Int' to 'superscript_digits'.
---
--- > unwords (map int_show_superscript [0,12,345,6789]) == "⁰ ¹² ³⁴⁵ ⁶⁷⁸⁹"
-int_show_superscript :: Int -> String
-int_show_superscript = map ((superscript_digits !!) . digitToInt) . show
-
--- | The subscript variants of the digits 0-9
-subscript_digits :: [Char]
-subscript_digits = "₀₁₂₃₄₅₆₇₈₉"
-
--- | The combining over line character.
---
--- > ['1',combining_overline] == "1̅"
-combining_overline :: Char
-combining_overline = toEnum 0x0305
-
--- | Add 'combining_overline' to each 'Char'.
---
--- > overline "1234" == "1̅2̅3̅4̅"
-overline :: String -> String
-overline = let f x = [x,combining_overline] in concatMap f
-
--- | The combining under line character.
---
--- > ['1',combining_underline] == "1̲"
-combining_underline :: Char
-combining_underline = toEnum 0x0332
-
--- | Add 'combining_underline' to each 'Char'.
---
--- > underline "1234" == "1̲2̲3̲4̲"
-underline :: String -> String
-underline = let f x = [x,combining_underline] in concatMap f
-
--- * Table
-
-type Unicode_Index = Int
-type Unicode_Name = String
-type Unicode_Range = (Unicode_Index,Unicode_Index)
-type Unicode_Point = (Unicode_Index,Unicode_Name)
-type Unicode_Table = [Unicode_Point]
-
-{- | <http://unicode.org/Public/11.0.0/ucd/UnicodeData.txt>
-
-> let fn = "/home/rohan/data/unicode.org/Public/11.0.0/ucd/UnicodeData.txt"
-> tbl <- unicode_data_table_read fn
-> length tbl == 32292
-> T.reverse_lookup_err "MIDDLE DOT" tbl == 0x00B7
-> putStrLn $ unwords $ map (\(n,x) -> toEnum n : x) $ filter (\(_,x) -> "EMPTY SET" `isInfixOf` x) tbl
-> T.lookup_err 0x22C5 tbl == "DOT OPERATOR"
--}
-unicode_data_table_read :: FilePath -> IO Unicode_Table
-unicode_data_table_read fn = do
-  s <- T.read_file_utf8 fn
-  let t = C.fromCSVTable (C.csvTable (C.parseDSV False ';' s))
-      f x = (T.read_hex_err (x !! 0),x !! 1)
-  return (map f t)
-
-unicode_table_block :: (Unicode_Index,Unicode_Index) -> Unicode_Table -> Unicode_Table
-unicode_table_block (l,r) = takeWhile ((<= r) . fst) . dropWhile ((< l) . fst)
-
-unicode_point_hs :: Unicode_Point -> String
-unicode_point_hs (n,s) = concat ["(0x",showHex n "",",\"",s,"\")"]
-
-unicode_table_hs :: Unicode_Table -> String
-unicode_table_hs = T.bracket ('[',']') . intercalate "," . map unicode_point_hs
-
--- * Music
-
--- > putStrLn$ map (toEnum . fst) (concat music_tbl)
-music_tbl :: [Unicode_Table]
-music_tbl = [barlines_tbl,accidentals_tbl,notes_tbl,rests_tbl,clefs_tbl]
-
--- > putStrLn$ concatMap (unicode_table_hs . flip unicode_table_block tbl) accidentals_rng_set
-accidentals_rng_set :: [Unicode_Range]
-accidentals_rng_set = [(0x266D,0x266F),(0x1D12A,0x1D133)]
-
--- > putStrLn$ unicode_table_hs (unicode_table_block barlines_rng tbl)
-barlines_rng :: Unicode_Range
-barlines_rng = (0x1D100,0x1D105)
-
--- | UNICODE barline symbols.
---
--- > let r = "𝄀𝄁𝄂𝄃𝄄𝄅" in map (toEnum . fst) barlines_tbl == r
-barlines_tbl :: Unicode_Table
-barlines_tbl =
-  [(0x1D100,"MUSICAL SYMBOL SINGLE BARLINE")
-  ,(0x1D101,"MUSICAL SYMBOL DOUBLE BARLINE")
-  ,(0x1D102,"MUSICAL SYMBOL FINAL BARLINE")
-  ,(0x1D103,"MUSICAL SYMBOL REVERSE FINAL BARLINE")
-  ,(0x1D104,"MUSICAL SYMBOL DASHED BARLINE")
-  ,(0x1D105,"MUSICAL SYMBOL SHORT BARLINE")]
-
--- | UNICODE accidental symbols.
---
--- > let r = "♭♮♯𝄪𝄫𝄬𝄭𝄮𝄯𝄰𝄱𝄲𝄳" in map (toEnum . fst) accidentals_tbl == r
-accidentals_tbl :: Unicode_Table
-accidentals_tbl =
-    [(0x266D,"MUSIC FLAT SIGN")
-    ,(0x266E,"MUSIC NATURAL SIGN")
-    ,(0x266F,"MUSIC SHARP SIGN")
-    ,(0x1D12A,"MUSICAL SYMBOL DOUBLE SHARP")
-    ,(0x1D12B,"MUSICAL SYMBOL DOUBLE FLAT")
-    ,(0x1D12C,"MUSICAL SYMBOL FLAT UP")
-    ,(0x1D12D,"MUSICAL SYMBOL FLAT DOWN")
-    ,(0x1D12E,"MUSICAL SYMBOL NATURAL UP")
-    ,(0x1D12F,"MUSICAL SYMBOL NATURAL DOWN")
-    ,(0x1D130,"MUSICAL SYMBOL SHARP UP")
-    ,(0x1D131,"MUSICAL SYMBOL SHARP DOWN")
-    ,(0x1D132,"MUSICAL SYMBOL QUARTER TONE SHARP")
-    ,(0x1D133,"MUSICAL SYMBOL QUARTER TONE FLAT")]
-
--- > putStrLn$ unicode_table_hs (unicode_table_block notes_rng tbl)
-notes_rng :: Unicode_Range
-notes_rng = (0x1D15C,0x1D164)
-
--- | UNICODE note duration symbols.
---
--- > let r = "𝅜𝅝𝅗𝅥𝅘𝅥𝅘𝅥𝅮𝅘𝅥𝅯𝅘𝅥𝅰𝅘𝅥𝅱𝅘𝅥𝅲" in map (toEnum . fst) notes_tbl == r
-notes_tbl :: Unicode_Table
-notes_tbl =
-    [(0x1D15C,"MUSICAL SYMBOL BREVE")
-    ,(0x1D15D,"MUSICAL SYMBOL WHOLE NOTE")
-    ,(0x1D15E,"MUSICAL SYMBOL HALF NOTE")
-    ,(0x1D15F,"MUSICAL SYMBOL QUARTER NOTE")
-    ,(0x1D160,"MUSICAL SYMBOL EIGHTH NOTE")
-    ,(0x1D161,"MUSICAL SYMBOL SIXTEENTH NOTE")
-    ,(0x1D162,"MUSICAL SYMBOL THIRTY-SECOND NOTE")
-    ,(0x1D163,"MUSICAL SYMBOL SIXTY-FOURTH NOTE")
-    ,(0x1D164,"MUSICAL SYMBOL ONE HUNDRED TWENTY-EIGHTH NOTE")]
-
--- > putStrLn$ unicode_table_hs (unicode_table_block rests_rng tbl)
-rests_rng :: Unicode_Range
-rests_rng = (0x1D13B,0x1D142)
-
--- | UNICODE rest symbols.
---
--- > let r = "𝄻𝄼𝄽𝄾𝄿𝅀𝅁𝅂" in map (toEnum . fst) rests_tbl == r
-rests_tbl :: Unicode_Table
-rests_tbl =
-    [(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")]
-
--- | Augmentation dot.
---
--- > map toEnum [0x1D15E,0x1D16D,0x1D16D] == "𝅗𝅥𝅭𝅭"
-augmentation_dot :: Unicode_Point
-augmentation_dot = (0x1D16D, "MUSICAL SYMBOL COMBINING AUGMENTATION DOT")
-
--- > putStrLn$ unicode_table_hs (unicode_table_block clefs_rng tbl)
-clefs_rng :: Unicode_Range
-clefs_rng = (0x1D11E,0x1D126)
-
--- | UNICODE clef symbols.
---
--- > let r = "𝄞𝄟𝄠𝄡𝄢𝄣𝄤𝄥𝄦" in map (toEnum . fst) clefs_tbl == r
-clefs_tbl :: Unicode_Table
-clefs_tbl =
-    [(0x1D11E,"MUSICAL SYMBOL G CLEF")
-    ,(0x1D11F,"MUSICAL SYMBOL G CLEF OTTAVA ALTA")
-    ,(0x1D120,"MUSICAL SYMBOL G CLEF OTTAVA BASSA")
-    ,(0x1D121,"MUSICAL SYMBOL C CLEF")
-    ,(0x1D122,"MUSICAL SYMBOL F CLEF")
-    ,(0x1D123,"MUSICAL SYMBOL F CLEF OTTAVA ALTA")
-    ,(0x1D124,"MUSICAL SYMBOL F CLEF OTTAVA BASSA")
-    ,(0x1D125,"MUSICAL SYMBOL DRUM CLEF-1")
-    ,(0x1D126,"MUSICAL SYMBOL DRUM CLEF-2")]
-
--- > putStrLn$ unicode_table_hs (unicode_table_block noteheads_rng tbl)
-noteheads_rng :: Unicode_Range
-noteheads_rng = (0x1D143,0x1D15B)
-
--- | UNICODE notehead symbols.
---
--- > let r = "𝅃𝅄𝅅𝅆𝅇𝅈𝅉𝅊𝅋𝅌𝅍𝅎𝅏𝅐𝅑𝅒𝅓𝅔𝅕𝅖𝅗𝅘𝅙𝅚𝅛" in map (toEnum . fst) noteheads_tbl == r
-noteheads_tbl :: Unicode_Table
-noteheads_tbl =
-    [(0x1d143,"MUSICAL SYMBOL X NOTEHEAD")
-    ,(0x1d144,"MUSICAL SYMBOL PLUS NOTEHEAD")
-    ,(0x1d145,"MUSICAL SYMBOL CIRCLE X NOTEHEAD")
-    ,(0x1d146,"MUSICAL SYMBOL SQUARE NOTEHEAD WHITE")
-    ,(0x1d147,"MUSICAL SYMBOL SQUARE NOTEHEAD BLACK")
-    ,(0x1d148,"MUSICAL SYMBOL TRIANGLE NOTEHEAD UP WHITE")
-    ,(0x1d149,"MUSICAL SYMBOL TRIANGLE NOTEHEAD UP BLACK")
-    ,(0x1d14a,"MUSICAL SYMBOL TRIANGLE NOTEHEAD LEFT WHITE")
-    ,(0x1d14b,"MUSICAL SYMBOL TRIANGLE NOTEHEAD LEFT BLACK")
-    ,(0x1d14c,"MUSICAL SYMBOL TRIANGLE NOTEHEAD RIGHT WHITE")
-    ,(0x1d14d,"MUSICAL SYMBOL TRIANGLE NOTEHEAD RIGHT BLACK")
-    ,(0x1d14e,"MUSICAL SYMBOL TRIANGLE NOTEHEAD DOWN WHITE")
-    ,(0x1d14f,"MUSICAL SYMBOL TRIANGLE NOTEHEAD DOWN BLACK")
-    ,(0x1d150,"MUSICAL SYMBOL TRIANGLE NOTEHEAD UP RIGHT WHITE")
-    ,(0x1d151,"MUSICAL SYMBOL TRIANGLE NOTEHEAD UP RIGHT BLACK")
-    ,(0x1d152,"MUSICAL SYMBOL MOON NOTEHEAD WHITE")
-    ,(0x1d153,"MUSICAL SYMBOL MOON NOTEHEAD BLACK")
-    ,(0x1d154,"MUSICAL SYMBOL TRIANGLE-ROUND NOTEHEAD DOWN WHITE")
-    ,(0x1d155,"MUSICAL SYMBOL TRIANGLE-ROUND NOTEHEAD DOWN BLACK")
-    ,(0x1d156,"MUSICAL SYMBOL PARENTHESIS NOTEHEAD")
-    ,(0x1d157,"MUSICAL SYMBOL VOID NOTEHEAD")
-    ,(0x1d158,"MUSICAL SYMBOL NOTEHEAD BLACK")
-    ,(0x1d159,"MUSICAL SYMBOL NULL NOTEHEAD")
-    ,(0x1d15a,"MUSICAL SYMBOL CLUSTER NOTEHEAD WHITE")
-    ,(0x1d15b,"MUSICAL SYMBOL CLUSTER NOTEHEAD BLACK")]
-
--- > map toEnum [0x1D143,0x1D165] == "𝅃𝅥"
-stem :: Unicode_Point
-stem = (0x1D165, "MUSICAL SYMBOL COMBINING STEM")
-
--- > putStrLn$ unicode_table_hs (unicode_table_block dynamics_rng tbl)
-dynamics_rng :: Unicode_Range
-dynamics_rng = (0x1D18C,0x1D193)
-
--- > map (toEnum . fst) dynamics_tbl == "𝆌𝆍𝆎𝆏𝆐𝆑𝆒𝆓"
-dynamics_tbl :: Unicode_Table
-dynamics_tbl =
-    [(0x1d18c,"MUSICAL SYMBOL RINFORZANDO")
-    ,(0x1d18d,"MUSICAL SYMBOL SUBITO")
-    ,(0x1d18e,"MUSICAL SYMBOL Z")
-    ,(0x1d18f,"MUSICAL SYMBOL PIANO")
-    ,(0x1d190,"MUSICAL SYMBOL MEZZO")
-    ,(0x1d191,"MUSICAL SYMBOL FORTE")
-    ,(0x1d192,"MUSICAL SYMBOL CRESCENDO")
-    ,(0x1d193,"MUSICAL SYMBOL DECRESCENDO")]
-
--- > putStrLn$ unicode_table_hs (unicode_table_block articulations_rng tbl)
-articulations_rng :: Unicode_Range
-articulations_rng = (0x1D17B,0x1D18B)
-
--- > putStrLn (map (toEnum . fst) articulations_tbl :: String)
-articulations_tbl :: Unicode_Table
-articulations_tbl =
-    [(0x1d17b,"MUSICAL SYMBOL COMBINING ACCENT")
-    ,(0x1d17c,"MUSICAL SYMBOL COMBINING STACCATO")
-    ,(0x1d17d,"MUSICAL SYMBOL COMBINING TENUTO")
-    ,(0x1d17e,"MUSICAL SYMBOL COMBINING STACCATISSIMO")
-    ,(0x1d17f,"MUSICAL SYMBOL COMBINING MARCATO")
-    ,(0x1d180,"MUSICAL SYMBOL COMBINING MARCATO-STACCATO")
-    ,(0x1d181,"MUSICAL SYMBOL COMBINING ACCENT-STACCATO")
-    ,(0x1d182,"MUSICAL SYMBOL COMBINING LOURE")
-    ,(0x1d183,"MUSICAL SYMBOL ARPEGGIATO UP")
-    ,(0x1d184,"MUSICAL SYMBOL ARPEGGIATO DOWN")
-    ,(0x1d185,"MUSICAL SYMBOL COMBINING DOIT")
-    ,(0x1d186,"MUSICAL SYMBOL COMBINING RIP")
-    ,(0x1d187,"MUSICAL SYMBOL COMBINING FLIP")
-    ,(0x1d188,"MUSICAL SYMBOL COMBINING SMEAR")
-    ,(0x1d189,"MUSICAL SYMBOL COMBINING BEND")
-    ,(0x1d18a,"MUSICAL SYMBOL COMBINING DOUBLE TONGUE")
-    ,(0x1d18b,"MUSICAL SYMBOL COMBINING TRIPLE TONGUE")]
-
--- * Math
-
-ix_set_to_tbl :: Unicode_Table -> [Unicode_Index] -> Unicode_Table
-ix_set_to_tbl tbl ix = zip ix (map (flip T.lookup_err tbl) ix)
-
--- | Unicode dot-operator.
---
--- > dot_operator == '⋅'
-dot_operator :: Char
-dot_operator = toEnum 0x22C5
-
--- | Math symbols outside of the math blocks.
---
--- > putStrLn (unicode_table_hs (ix_set_to_tbl tbl math_plain_ix))
-math_plain_ix :: [Unicode_Index]
-math_plain_ix = [0x00D7,0x00F7]
-
--- > map (toEnum . fst) math_plain_tbl == "×÷"
-math_plain_tbl :: Unicode_Table
-math_plain_tbl = [(0xd7,"MULTIPLICATION SIGN"),(0xf7,"DIVISION SIGN")]
-
--- * Blocks
-
-type Unicode_Block = (Unicode_Range,String)
-
--- > putStrLn$ unicode_table_hs (concatMap (flip unicode_table_block tbl . fst) unicode_blocks)
-unicode_blocks :: [Unicode_Block]
-unicode_blocks =
-    [((0x01B00,0x01B7F),"Balinese")
-    ,((0x02200,0x022FF),"Mathematical Operators")
-    ,((0x025A0,0x025FF),"Geometric Shapes")
-    ,((0x027C0,0x027EF),"Miscellaneous Mathematical Symbols-A")
-    ,((0x027F0,0x027FF),"Supplemental Arrows-A")
-    ,((0x02800,0x028FF),"Braille Patterns")
-    ,((0x02900,0x0297F),"Supplemental Arrows-B")
-    ,((0x02980,0x029FF),"Miscellaneous Mathematical Symbols-B")
-    ,((0x02A00,0x02AFF),"Supplemental Mathematical Operators")
-    ,((0x1D000,0x1D0FF),"Byzantine Musical Symbols")
-    ,((0x1D100,0x1D1FF),"Musical Symbols")
-    ,((0x1D200,0x1D24F),"Ancient Greek Musical Notation")
-    ]
-
--- * BAGUA, EIGHT TRI-GRAMS
-
--- | Bagua tri-grams.
---
--- > putStrLn $ unicode_table_hs (unicode_table_block (fst bagua) tbl)
-bagua :: Unicode_Block
-bagua = ((0x02630,0x02637),"BAGUA")
-
-{- | Table of eight tri-grams.
-
-HEAVEN,乾,Qián,☰,111
-LAKE,兌,Duì,☱,110
-FIRE,離,Lí,☲,101
-THUNDER,震,Zhèn,☳,100
-WIND,巽,Xùn,☴,011
-WATER,坎,Kǎn,☵,010
-MOUNTAIN,艮,Gèn,☶,001
-EARTH,坤,Kūn,☷,000
-
--}
-bagua_tbl :: Unicode_Table
-bagua_tbl =
-  [(0x2630,"TRIGRAM FOR HEAVEN")
-  ,(0x2631,"TRIGRAM FOR LAKE")
-  ,(0x2632,"TRIGRAM FOR FIRE")
-  ,(0x2633,"TRIGRAM FOR THUNDER")
-  ,(0x2634,"TRIGRAM FOR WIND")
-  ,(0x2635,"TRIGRAM FOR WATER")
-  ,(0x2636,"TRIGRAM FOR MOUNTAIN")
-  ,(0x2637,"TRIGRAM FOR EARTH")]
-
--- * YIJING (I-CHING), SIXTY-FOUR HEXAGRAMS
-
--- | Yijing hexagrams in King Wen sequence.
---
--- > putStrLn $ unicode_table_hs (unicode_table_block (fst yijing) tbl)
-yijing :: Unicode_Block
-yijing = ((0x04DC0,0x04DFF),"YIJING")
-
-{- | Yijing hexagrams in King Wen sequence.
-
-䷀,乾,qián,111,111
-䷁,坤,kūn,000,000
-䷂,屯,chún,100,010
-䷃,蒙,méng,010,001
-䷄,需,xū,111,010
-䷅,訟,sòng,010,111
-䷆,師,shī,010,000
-䷇,比,bǐ,000,010
-䷈,小畜,xiǎo chù,111,011
-䷉,履,lǚ,110,111
-䷊,泰,tài,111,000
-䷋,否,pǐ,000,111
-䷌,同人,tóng rén,101,111
-䷍,大有,dà yǒu,111,101
-䷎,謙,qiān,001,000
-䷏,豫,yù,000,100
-䷐,隨,suí,100,110
-䷑,蠱,gŭ,011,001
-䷒,臨,lín,110,000
-䷓,觀,guān,000,011
-䷔,噬嗑,shì kè,100,101
-䷕,賁,bì,101,001
-䷖,剝,bō,000,001
-䷗,復,fù,100,000
-䷘,無妄,wú wàng,100,111
-䷙,大畜,dà chù,111,001
-䷚,頤,yí,100,001
-䷛,大過,dà guò,011,110
-䷜,坎,kǎn,010,010
-䷝,離,lí,101,101
-䷞,咸,xián,001,110
-䷟,恆,héng,011,100
-䷠,遯,dùn,001,111
-䷡,大壯,dà zhuàng,111,100
-䷢,晉,jìn,000,101
-䷣,明夷,míng yí,101,000
-䷤,家人,jiā rén,101,011
-䷥,睽,kuí,110,101
-䷦,蹇,jiǎn,001,010
-䷧,解,xiè,010,100
-䷨,損,sǔn,110,001
-䷩,益,yì,100,011
-䷪,夬,guài,111,110
-䷫,姤,gòu,011,111
-䷬,萃,cuì,000,110
-䷭,升,shēng,011,000
-䷮,困,kùn,010,110
-䷯,井,jǐng,011,010
-䷰,革,gé,101,110
-䷱,鼎,dǐng,011,101
-䷲,震,zhèn,100,100
-䷳,艮,gèn,001,001
-䷴,漸,jiàn,001,011
-䷵,歸妹,guī mèi,110,100
-䷶,豐,fēng,101,100
-䷷,旅,lǚ,001,101
-䷸,巽,xùn,011,011
-䷹,兌,duì,110,110
-䷺,渙,huàn,010,011
-䷻,節,jié,110,010
-䷼,中孚,zhōng fú,110,011
-䷽,小過,xiǎo guò,001,110
-䷾,既濟,jì jì,101,010
-䷿,未濟,wèi jì,010,101
--}
-yijing_tbl :: Unicode_Table
-yijing_tbl =
-  [(0x4dc0,"HEXAGRAM FOR THE CREATIVE HEAVEN")
-  ,(0x4dc1,"HEXAGRAM FOR THE RECEPTIVE EARTH")
-  ,(0x4dc2,"HEXAGRAM FOR DIFFICULTY AT THE BEGINNING")
-  ,(0x4dc3,"HEXAGRAM FOR YOUTHFUL FOLLY")
-  ,(0x4dc4,"HEXAGRAM FOR WAITING")
-  ,(0x4dc5,"HEXAGRAM FOR CONFLICT")
-  ,(0x4dc6,"HEXAGRAM FOR THE ARMY")
-  ,(0x4dc7,"HEXAGRAM FOR HOLDING TOGETHER")
-  ,(0x4dc8,"HEXAGRAM FOR SMALL TAMING")
-  ,(0x4dc9,"HEXAGRAM FOR TREADING")
-  ,(0x4dca,"HEXAGRAM FOR PEACE")
-  ,(0x4dcb,"HEXAGRAM FOR STANDSTILL")
-  ,(0x4dcc,"HEXAGRAM FOR FELLOWSHIP")
-  ,(0x4dcd,"HEXAGRAM FOR GREAT POSSESSION")
-  ,(0x4dce,"HEXAGRAM FOR MODESTY")
-  ,(0x4dcf,"HEXAGRAM FOR ENTHUSIASM")
-  ,(0x4dd0,"HEXAGRAM FOR FOLLOWING")
-  ,(0x4dd1,"HEXAGRAM FOR WORK ON THE DECAYED")
-  ,(0x4dd2,"HEXAGRAM FOR APPROACH")
-  ,(0x4dd3,"HEXAGRAM FOR CONTEMPLATION")
-  ,(0x4dd4,"HEXAGRAM FOR BITING THROUGH")
-  ,(0x4dd5,"HEXAGRAM FOR GRACE")
-  ,(0x4dd6,"HEXAGRAM FOR SPLITTING APART")
-  ,(0x4dd7,"HEXAGRAM FOR RETURN")
-  ,(0x4dd8,"HEXAGRAM FOR INNOCENCE")
-  ,(0x4dd9,"HEXAGRAM FOR GREAT TAMING")
-  ,(0x4dda,"HEXAGRAM FOR MOUTH CORNERS")
-  ,(0x4ddb,"HEXAGRAM FOR GREAT PREPONDERANCE")
-  ,(0x4ddc,"HEXAGRAM FOR THE ABYSMAL WATER")
-  ,(0x4ddd,"HEXAGRAM FOR THE CLINGING FIRE")
-  ,(0x4dde,"HEXAGRAM FOR INFLUENCE")
-  ,(0x4ddf,"HEXAGRAM FOR DURATION")
-  ,(0x4de0,"HEXAGRAM FOR RETREAT")
-  ,(0x4de1,"HEXAGRAM FOR GREAT POWER")
-  ,(0x4de2,"HEXAGRAM FOR PROGRESS")
-  ,(0x4de3,"HEXAGRAM FOR DARKENING OF THE LIGHT")
-  ,(0x4de4,"HEXAGRAM FOR THE FAMILY")
-  ,(0x4de5,"HEXAGRAM FOR OPPOSITION")
-  ,(0x4de6,"HEXAGRAM FOR OBSTRUCTION")
-  ,(0x4de7,"HEXAGRAM FOR DELIVERANCE")
-  ,(0x4de8,"HEXAGRAM FOR DECREASE")
-  ,(0x4de9,"HEXAGRAM FOR INCREASE")
-  ,(0x4dea,"HEXAGRAM FOR BREAKTHROUGH")
-  ,(0x4deb,"HEXAGRAM FOR COMING TO MEET")
-  ,(0x4dec,"HEXAGRAM FOR GATHERING TOGETHER")
-  ,(0x4ded,"HEXAGRAM FOR PUSHING UPWARD")
-  ,(0x4dee,"HEXAGRAM FOR OPPRESSION")
-  ,(0x4def,"HEXAGRAM FOR THE WELL")
-  ,(0x4df0,"HEXAGRAM FOR REVOLUTION")
-  ,(0x4df1,"HEXAGRAM FOR THE CAULDRON")
-  ,(0x4df2,"HEXAGRAM FOR THE AROUSING THUNDER")
-  ,(0x4df3,"HEXAGRAM FOR THE KEEPING STILL MOUNTAIN")
-  ,(0x4df4,"HEXAGRAM FOR DEVELOPMENT")
-  ,(0x4df5,"HEXAGRAM FOR THE MARRYING MAIDEN")
-  ,(0x4df6,"HEXAGRAM FOR ABUNDANCE")
-  ,(0x4df7,"HEXAGRAM FOR THE WANDERER")
-  ,(0x4df8,"HEXAGRAM FOR THE GENTLE WIND")
-  ,(0x4df9,"HEXAGRAM FOR THE JOYOUS LAKE")
-  ,(0x4dfa,"HEXAGRAM FOR DISPERSION")
-  ,(0x4dfb,"HEXAGRAM FOR LIMITATION")
-  ,(0x4dfc,"HEXAGRAM FOR INNER TRUTH")
-  ,(0x4dfd,"HEXAGRAM FOR SMALL PREPONDERANCE")
-  ,(0x4dfe,"HEXAGRAM FOR AFTER COMPLETION")
-  ,(0x4dff,"HEXAGRAM FOR BEFORE COMPLETION")]
diff --git a/Music/Theory/Wyschnegradsky.hs b/Music/Theory/Wyschnegradsky.hs
--- a/Music/Theory/Wyschnegradsky.hs
+++ b/Music/Theory/Wyschnegradsky.hs
@@ -3,13 +3,14 @@
 
 import Data.Char {- base -}
 import Data.List {- list -}
-import Data.List.Split {- split -}
 import Data.Maybe {- base -}
 
-import Music.Theory.List {- hmt -}
-import Music.Theory.Pitch {- hmt -}
-import Music.Theory.Pitch.Spelling.Table {- hmt -}
+import qualified Data.List.Split as Split {- split -}
 
+import qualified Music.Theory.List as List {- hmt -}
+import qualified Music.Theory.Pitch as Pitch {- hmt -}
+import qualified Music.Theory.Pitch.Spelling.Table as Spelling {- hmt -}
+
 -- | In a modulo /m/ system, normalise step increments to be either -1
 -- or 1.  Non steps raise an error.
 --
@@ -27,7 +28,7 @@
 -- > map parse_num_sign ["2+","4-"] == [2,-4]
 parse_num_sign :: (Num n, Read n) => String -> n
 parse_num_sign s =
-    case separate_last s of
+    case List.separate_last s of
       (n,'+') -> read n
       (n,'-') -> negate (read n)
       _ -> error "parse_num_sign"
@@ -46,9 +47,9 @@
 parse_vec :: Num n => Maybe Int -> n -> String -> [n]
 parse_vec n m =
     let f = case n of
-              Just i -> dx_d m . take i . cycle
-              Nothing -> dx_d m
-    in dropRight 1 . f . concatMap (vec_expand . parse_num_sign) . splitOn ","
+              Just i -> List.dx_d m . take i . cycle
+              Nothing -> List.dx_d m
+    in List.dropRight 1 . f . concatMap (vec_expand . parse_num_sign) . Split.splitOn ","
 
 -- | Modulo addition.
 add_m :: Integral a => a -> a -> a -> a
@@ -82,13 +83,13 @@
 seq_group :: Int -> Int -> Seq a -> [[a]]
 seq_group c_div r_div s =
     case s of
-      Circumferential c -> chunksOf c_div c
-      Radial r -> transpose (chunksOf r_div r)
+      Circumferential c -> Split.chunksOf c_div c
+      Radial r -> transpose (Split.chunksOf r_div r)
 
 -- | Printer for pitch-class segments.
 iw_pc_pp :: Integral n => String -> [[n]] -> IO ()
 iw_pc_pp sep =
-    let f = pitch_pp_opt (False,False) . octpc_to_pitch pc_spell_ks . (,) 4
+    let f = Pitch.pitch_pp_opt (False,False) . Pitch.octpc_to_pitch Spelling.pc_spell_ks . (,) 4
     in putStrLn . intercalate sep . map (unwords . map f)
 
 -- * U3
@@ -133,7 +134,7 @@
 -- > let f = parse_vec Nothing 0 in map (\(p,q) -> (f p,f q)) u3_vec_text_rw
 --
 -- > let f (c,r) = putStrLn (unlines ["C: " ++ c,"R: " ++ r])
--- > in mapM_ f (interleave u3_vec_text_iw u3_vec_text_rw)
+-- > mapM_ f (List.interleave u3_vec_text_iw u3_vec_text_rw)
 u3_vec_text_rw :: [(String, String)]
 u3_vec_text_rw =
     [("4+,3-,5+,3-,3+"
@@ -160,7 +161,7 @@
 u3_vec_ix :: Num n => ([[n]],[[n]])
 u3_vec_ix =
     let f (p,q) = [parse_vec Nothing 0 p,parse_vec Nothing 0 q]
-        [c,r] = transpose (map f u3_vec_text_rw)
+        (c,r) = List.firstSecond (transpose (map f u3_vec_text_rw))
     in (c,r)
 
 -- | Radial indices (ie. each /ray/ as an index sequence).
@@ -170,7 +171,7 @@
 u3_ix_radial =
     let (c,r) = u3_vec_ix
         r' = zipWith replicate (map length c) r
-    in zipWith (\p q -> map (add_m 6 p) q) (concat c) (concat r')
+    in zipWith (map . add_m 6) (concat c) (concat r')
 
 -- | Colour names in index sequence.
 u3_clr_nm :: [String]
@@ -207,7 +208,7 @@
     map length .
     group .
     map (normalise_step 6) .
-    d_dx .
+    List.d_dx .
     map u3_ch_ix .
     filter (not . isSpace)
 
@@ -263,7 +264,7 @@
             ,"#c2ba3d","#a2a367"
             ,"#537a77","#203342"
             ,"#84525e","#bc6460"]
-        n = interleave [6,4,2,0,10,8] [5,3,1,11,9,7] :: [Int]
+        n = List.interleave [6,4,2,0,10,8] [5,3,1,11,9,7] :: [Int]
     in map snd (sort (zip n c))
 
 -- | RGB form of colours.
@@ -302,7 +303,7 @@
 
 -- > iw_pc_pp "|" [u11_gen_seq 7 18 [5]]
 u11_gen_seq :: Integral i => i -> Int -> [i] -> [i]
-u11_gen_seq z n = map (`mod` 12) . take n . dx_d z . cycle
+u11_gen_seq z n = map (`mod` 12) . take n . List.dx_d z . cycle
 
 u11_seq_rule :: Integral i => Maybe Int -> [i]
 u11_seq_rule n = u11_gen_seq 0 18 (maybe [-1] (\x -> replicate x (-1) ++ [5]) n)
diff --git a/Music/Theory/Xenakis/S4.hs b/Music/Theory/Xenakis/S4.hs
--- a/Music/Theory/Xenakis/S4.hs
+++ b/Music/Theory/Xenakis/S4.hs
@@ -6,8 +6,6 @@
 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
 
@@ -145,12 +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
@@ -159,7 +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)
 
@@ -169,14 +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
diff --git a/Music/Theory/Xenakis/Sieve.hs b/Music/Theory/Xenakis/Sieve.hs
--- a/Music/Theory/Xenakis/Sieve.hs
+++ b/Music/Theory/Xenakis/Sieve.hs
@@ -6,12 +6,9 @@
 import qualified Data.List as L
 import Music.Theory.List
 
--- | Synonym for 'Integer'
-type I = Integer
-
 -- | A Sieve.
 data Sieve = Empty -- ^ 'Empty' 'Sieve'
-           | L (I,I) -- ^ Primitive 'Sieve' of /modulo/ and /index/
+           | L (Integer, Integer) -- ^ Primitive 'Sieve' of /modulo/ and /index/
            | Union Sieve Sieve -- ^ 'Union' of two 'Sieve's
            | Intersection Sieve Sieve -- ^ 'Intersection' of two 'Sieve's
            | Complement Sieve -- ^ 'Complement' of a 'Sieve'
@@ -50,21 +47,22 @@
 -- | Variant of 'L', ie. 'curry' 'L'.
 --
 -- > l 15 19 == L (15,19)
-l :: I -> I -> Sieve
+l :: Integer -> Integer -> Sieve
 l = curry L
 
 -- | unicode synonym for 'l'.
-(⋄) :: I -> I -> Sieve
+(⋄) :: Integer -> Integer -> Sieve
 (⋄) = l
 
 infixl 3 ∪
 infixl 4 ∩
 infixl 5 ⋄
 
--- | In a /normal/ 'Sieve' /m/ is '>' /i/.
---
--- > normalise (L (15,19)) == L (15,4)
--- > normalise (L (11,13)) == L (11,2)
+{- | In a /normal/ 'Sieve' /m/ is '>' /i/.
+
+> normalise (L (15,19)) == L (15,4)
+> normalise (L (11,13)) == L (11,2)
+-}
 normalise :: Sieve -> Sieve
 normalise s =
     case s of
@@ -74,18 +72,20 @@
       Intersection s0 s1 -> Intersection (normalise s0) (normalise s1)
       Complement s' -> Complement (normalise s')
 
--- | Predicate to test if a 'Sieve' is /normal/.
---
--- > is_normal (L (15,4)) == True
--- > is_normal (L (11,13)) == False
+{- | Predicate to test if a 'Sieve' is /normal/.
+
+> is_normal (L (15,4)) == True
+> is_normal (L (11,13)) == False
+-}
 is_normal :: Sieve -> Bool
 is_normal s = s == normalise s
 
--- | Predicate to determine if an 'I' is an element of the 'Sieve'.
---
--- > map (element (L (3,1))) [1..4] == [True,False,False,True]
--- > map (element (L (15,4))) [4,19 .. 49] == [True,True,True,True]
-element :: Sieve -> I -> Bool
+{- | Predicate to determine if an 'I' is an element of the 'Sieve'.
+
+> map (element (L (3,1))) [1..4] == [True,False,False,True]
+> map (element (L (15,4))) [4,19 .. 49] == [True,True,True,True]
+-}
+element :: Sieve -> Integer -> Bool
 element s n =
     case s of
       Empty -> False
@@ -94,8 +94,11 @@
       Intersection s0 s1 -> element s0 n && element s1 n
       Complement s' -> not (element s' n)
 
--- > take 9 (i_complement [1,3..]) == [0,2..16]
-i_complement :: [I] -> [I]
+{- | 'I' not in set.
+
+> take 9 (i_complement [1,3..]) == [0,2..16]
+-}
+i_complement :: [Integer] -> [Integer]
 i_complement =
     let f x s = case s of
                 [] -> [x ..]
@@ -105,14 +108,15 @@
                           GT -> error "i_complement"
     in f 0
 
--- | Construct the sequence defined by a 'Sieve'.  Note that building
--- a sieve that contains an intersection clause that has no elements
--- gives @_|_@.
---
--- > let {d = [0,2,4,5,7,9,11]
--- >     ;r = d ++ map (+ 12) d}
--- > in take 14 (build (union (map (l 12) d))) == r
-build :: Sieve -> [I]
+{- | Construct the sequence defined by a 'Sieve'.  Note that building
+     a sieve that contains an intersection clause that has no elements
+     gives @_|_@.
+
+> let d = [0,2,4,5,7,9,11]
+> let r = d ++ map (+ 12) d
+> take 14 (build (union (map (l 12) d))) == r
+-}
+build :: Sieve -> [Integer]
 build s =
     let u_f = map head . L.group
         i_f = let g [x,_] = [x]
@@ -125,8 +129,7 @@
          Intersection s0 s1 -> i_f (merge (build s0) (build s1))
          Complement s' -> i_complement (build s')
 
-{- | Variant of 'build' that gives the first /n/ places of the
-  'reduce' of 'Sieve'.
+{- | Variant of 'build' that gives the first /n/ places of the 'reduce' of 'Sieve'.
 
 > buildn 6 (union (map (l 8) [0,3,6])) == [0,3,6,8,11,14]
 > buildn 12 (L (3,2)) == [2,5,8,11,14,17,20,23,26,29,32,35]
@@ -137,117 +140,105 @@
 > buildn 6 (3⋄0 ∪ 4⋄0) == [0,3,4,6,8,9]
 > buildn 8 (5⋄2 ∩ 2⋄0 ∪ 7⋄3) == [2,3,10,12,17,22,24,31]
 > buildn 12 (5⋄1 ∪ 7⋄2) == [1,2,6,9,11,16,21,23,26,30,31,36]
+> buildn 19 (L (3,2) ∪ L (7, 1)) == [1, 2, 5, 8, 11, 14, 15, 17, 20, 22, 23, 26, 29, 32, 35, 36, 38, 41, 43]
+> buildn 19 (3⋄0 ∪ 7⋄0) == [0, 3, 6, 7, 9, 12, 14, 15, 18, 21, 24, 27, 28, 30, 33, 35, 36, 39, 42]
 
 > buildn 10 (3⋄2 ∩ 4⋄7 ∪ 6⋄9 ∩ 15⋄18) == [3,11,23,33,35,47,59,63,71,83]
 
-> let {s = 3⋄2∩4⋄7∩6⋄11∩8⋄7 ∪ 6⋄9∩15⋄18 ∪ 13⋄5∩8⋄6∩4⋄2 ∪ 6⋄9∩15⋄19
->     ;s' = 24⋄23 ∪ 30⋄3 ∪ 104⋄70}
-> in buildn 16 s == buildn 16 s'
+> let s = 3⋄2∩4⋄7∩6⋄11∩8⋄7 ∪ 6⋄9∩15⋄18 ∪ 13⋄5∩8⋄6∩4⋄2 ∪ 6⋄9∩15⋄19
+> let s' = 24⋄23 ∪ 30⋄3 ∪ 104⋄70
+> buildn 16 s == buildn 16 s'
 
 > buildn 10 (24⋄23 ∪ 30⋄3 ∪ 104⋄70) == [3,23,33,47,63,70,71,93,95,119]
 
 > let r = [2,3,4,5,8,9,10,11,14,17,19,20,23,24,26,29,31]
-> in buildn 17 (5⋄4 ∪ 3⋄2 ∪ 7⋄3) == r
+> buildn 17 (5⋄4 ∪ 3⋄2 ∪ 7⋄3) == r
 
 > let r = [0,1,3,6,9,10,11,12,15,16,17,18,21,24,26,27,30]
-> in buildn 17 (5⋄1 ∪ 3⋄0 ∪ 7⋄3) == r
+> buildn 17 (5⋄1 ∪ 3⋄0 ∪ 7⋄3) == r
 
 > let r = [0,2,3,4,6,7,9,11,12,15,17,18,21,22,24,25,27,30,32]
-> in buildn 19 (5⋄2 ∪ 3⋄0 ∪ 7⋄4) == r
+> buildn 19 (5⋄2 ∪ 3⋄0 ∪ 7⋄4) == r
 
 Agon et. al. p.155
 
-> let {a = c (13⋄3 ∪ 13⋄5 ∪ 13⋄7 ∪ 13⋄9)
->     ;b = 11⋄2
->     ;c' = c (11⋄4 ∪ 11⋄8)
->     ;d = 13⋄9
->     ;e = 13⋄0 ∪ 13⋄1 ∪ 13⋄6
->     ;f = (a ∩ b) ∪ (c' ∩ d) ∪ e}
-> in buildn 13 f == [0,1,2,6,9,13,14,19,22,24,26,27,32]
+> let a = c (13⋄3 ∪ 13⋄5 ∪ 13⋄7 ∪ 13⋄9)
+> let b = 11⋄2
+> let c' = c (11⋄4 ∪ 11⋄8)
+> let d = 13⋄9
+> let e = 13⋄0 ∪ 13⋄1 ∪ 13⋄6
+> let f = (a ∩ b) ∪ (c' ∩ d) ∪ e
+> buildn 13 f == [0,1,2,6,9,13,14,19,22,24,26,27,32]
 
 > differentiate [0,1,2,6,9,13,14,19,22,24,26,27,32] == [1,1,4,3,4,1,5,3,2,2,1,5]
 
-> import Music.Theory.Pitch
+> import Music.Theory.Pitch {- hmt -}
 
-> let {n = [0,1,2,6,9,13,14,19,22,24,26,27,32]
->     ;r = "C C𝄲 C♯ D♯ E𝄲 F𝄰 G A𝄲 B C C♯ C𝄰 E"}
-> in unwords (map (pitch_class_pp . pc24et_to_pitch . (`mod` 24)) n) == r
+> let n = [0,1,2,6,9,13,14,19,22,24,26,27,32]
+> let r = "C C𝄲 C♯ D♯ E𝄲 F𝄰 G A𝄲 B C C♯ C𝄰 E"
+> unwords (map (pitch_class_pp . pc24et_to_pitch . (`mod` 24)) n) == r
 
 Jonchaies
 
 > let s = map (17⋄) [0,1,4,5,7,11,12,16]
-> in differentiate (buildn 25 (union s))
+> let r = [1,3,1,2,4,1,4,1,1,3,1,2,4,1,4,1,1,3,1,2,4,1,4,1]
+> differentiate (buildn 25 (union s)) == r
+> let a2 = octpc_to_midi (2,9)
+> let m = scanl (+) a2 r
+> import Music.Theory.Pitch.Spelling.Table {- hmt -}
+> let p = "A2 A#2 C#3 D3 E3 G#3 A3 C#4 D4 D#4 F#4 G4 A4 C#5 D5 F#5 G5 G#5 B5 C6 D6 F#6 G6 B6 C7"
+> unwords (map (pitch_pp_iso . midi_to_pitch pc_spell_sharp) m) == p
 
 Nekuïa
 
-> let s = [24⋄0,14⋄2,22⋄3,31⋄4,28⋄7,29⋄9,19⋄10,25⋄13,24⋄14,26⋄17,23⋄21
->         ,24⋄10,30⋄9,35⋄17,29⋄24,32⋄25,30⋄29,26⋄21,30⋄17,31⋄16]
-> in differentiate (buildn 24 (union s))
+> let s = [24⋄0,14⋄2,22⋄3,31⋄4,28⋄7,29⋄9,19⋄10,25⋄13,24⋄14,26⋄17,23⋄21,24⋄10,30⋄9,35⋄17,29⋄24,32⋄25,30⋄29,26⋄21,30⋄17,31⋄16]
+> let r = [2,1,1,3,2,1,3,1,2,1,4,3,1,4,1,4,1,3,1,4,1,3,1,4,1,4,1,1,3,1,3,1,2,3,1,4,1,4,4,1]
+> differentiate (buildn 41 (union s)) == r
+> let a0 = octpc_to_midi (0,9)
+> let m = scanl (+) a0 r
+> import Music.Theory.Pitch.Spelling.Table {- hmt -}
+> let p = "A0 B0 C1 C#1 E1 F#1 G1 A#1 B1 C#2 D2 F#2 A2 A#2 D3 D#3 G3 G#3 B3 C4 E4 F4 G#4 A4 C#5 D5 F#5 G5 G#5 B5 C6 D#6 E6 F#6 A6 A#6 D7 D#7 G7 B7 C8"
+> unwords (map (pitch_pp_iso . midi_to_pitch pc_spell_sharp) m) == p
 
+> let s = [8⋄0∩3⋄0,2⋄0∩7⋄2,2⋄1∩11⋄3,31⋄4,4⋄3∩7⋄0,29⋄9,19⋄10,25⋄13,8⋄6∩3⋄2,2⋄1∩13⋄4,23⋄21,8⋄2∩3⋄1,2⋄1∩3⋄0∩5⋄4,5⋄2∩7⋄3,29⋄24,32⋄25,2⋄1∩3⋄2∩5⋄4,2⋄1∩13⋄8,2⋄1∩3⋄2∩5⋄2,31⋄16]
+> differentiate (buildn 41 (union s)) == r
+
 Major scale:
 
 > let s = (c(3⋄2) ∩ 4⋄0) ∪ (c(3⋄1) ∩ 4⋄1) ∪ (3⋄2 ∩ 4⋄2) ∪ (c(3⋄0) ∩ 4⋄3)
-> in buildn 7 s == [0,2,4,5,7,9,11]
+> buildn 7 s == [0,2,4,5,7,9,11]
 
 Nomos Alpha:
 
-let {s = (c (13⋄3 ∪ 13⋄5 ∪ 13⋄7 ∪ 13⋄9) ∩ 11⋄2) ∪ (c (11⋄4 ∪ 11⋄8) ∩ 13⋄9) ∪ (13⋄0 ∪ 13⋄1 ∪ 13⋄6)
-    ;r = [0,1,2,6,9,13,14,19,22,24,26,27,32,35,39,40,45,52,53,58,61,65,66,71,78,79,84,87,90,91,92,97]}
-in buildn 32 s == r
-
-/Psappha/ (Flint):
-
-> let {s = union [(8⋄0∪8⋄1∪8⋄7)∩(5⋄1∪5⋄3)
->                ,(8⋄0∪8⋄1∪8⋄2)∩5⋄0
->                ,8⋄3∩(5⋄0∪5⋄1∪5⋄2∪5⋄3∪5⋄4)
->                ,8⋄4∩(5⋄0∪5⋄1∪5⋄2∪5⋄3∪5⋄4)
->                ,(8⋄5∪8⋄6)∩(5⋄2∪5⋄3∪5⋄4)
->                ,8⋄1∩5⋄2
->                ,8⋄6∩5⋄1]
->     ;r = [0,1,3,4,6,8,10,11,12
->          ,13,14,16,17,19,20,22,23,25
->          ,27,28,29,31,33,35,36,37,38]}
-> in buildn 27 s == r
-
-À R. (Hommage à Maurice Ravel) (Squibbs, 1996)
-
-> let {s = union [8⋄0∩(11⋄0∪11⋄4∪11⋄5∪11⋄6∪11⋄10)
->                ,8⋄1∩(11⋄2∪11⋄3∪11⋄6∪11⋄7∪11⋄9)
->                ,8⋄2∩(11⋄0∪11⋄1∪11⋄2∪11⋄3∪11⋄5∪11⋄10)
->                ,8⋄3∩(11⋄1∪11⋄2∪11⋄3∪11⋄4∪11⋄10)
->                ,8⋄4∩(11⋄0∪11⋄4∪11⋄8)
->                ,8⋄5∩(11⋄0∪11⋄2∪11⋄3∪11⋄7∪11⋄9∪11⋄10)
->                ,8⋄6∩(11⋄1∪11⋄3∪11⋄5∪11⋄7∪11⋄8∪11⋄9)
->                ,8⋄7∩(11⋄1∪11⋄3∪11⋄6∪11⋄7∪11⋄8∪11⋄10)]
->     ;r = [0,2,3,4,7,9,10,13,14,16
->          ,17,21,23,25,29,30,32,34,35,38
->          ,39,43,44,47,48,52,53,57,58,59
->          ,62,63,66,67,69,72,73,77,78,82
->          ,86,87]}
-> in buildn 42 s == r
+let s = (c (13⋄3 ∪ 13⋄5 ∪ 13⋄7 ∪ 13⋄9) ∩ 11⋄2) ∪ (c (11⋄4 ∪ 11⋄8) ∩ 13⋄9) ∪ (13⋄0 ∪ 13⋄1 ∪ 13⋄6)
+let r = [0,1,2,6,9,13,14,19,22,24,26,27,32,35,39,40,45,52,53,58,61,65,66,71,78,79,84,87,90,91,92,97]
+buildn 32 s == r
 
 -}
-buildn :: Int -> Sieve -> [I]
+buildn :: Int -> Sieve -> [Integer]
 buildn n = take n . build . reduce
 
--- | Standard differentiation function.
---
--- > differentiate [1,3,6,10] == [2,3,4]
--- > differentiate [0,2,4,5,7,9,11,12] == [2,2,1,2,2,2,1]
+{- | Standard differentiation function.
+
+> differentiate [1,3,6,10] == [2,3,4]
+> differentiate [0,2,4,5,7,9,11,12] == [2,2,1,2,2,2,1]
+-}
 differentiate :: (Num a) => [a] -> [a]
 differentiate x = zipWith (-) (tail x) x
 
--- | Euclid's algorithm for computing the greatest common divisor.
---
--- > euclid 1989 867 == 51
+{- | Euclid's algorithm for computing the greatest common divisor.
+
+> euclid 1989 867 == 51
+-}
 euclid :: (Integral a) => a -> a -> a
 euclid i j =
     let k = i `mod` j
     in if k == 0 then j else euclid j k
 
--- | Bachet De Méziriac's algorithm.
---
--- > de_meziriac 15 4 == 3 && euclid 15 4 == 1
+{- | Bachet De Méziriac's algorithm.
+
+> de_meziriac 15 4 == 3 && euclid 15 4 == 1
+-}
 de_meziriac :: (Integral a) => a -> a -> a
 de_meziriac i j =
     let f t = if (t * i) `mod` j /= 1
@@ -255,12 +246,12 @@
               else t
     in if j == 1 then 1 else f 1
 
--- | Attempt to reduce the 'Intersection' of two 'L' nodes to a
--- singular 'L' node.
---
--- > reduce_intersection (3,2) (4,7) == Just (12,11)
--- > reduce_intersection (12,11) (6,11) == Just (12,11)
--- > reduce_intersection (12,11) (8,7) == Just (24,23)
+{- | Attempt to reduce the 'Intersection' of two 'L' nodes to a singular 'L' node.
+
+> reduce_intersection (3,2) (4,7) == Just (12,11)
+> reduce_intersection (12,11) (6,11) == Just (12,11)
+> reduce_intersection (12,11) (8,7) == Just (24,23)
+-}
 reduce_intersection :: (Integral t) => (t,t) -> (t,t) -> Maybe (t,t)
 reduce_intersection (m1,i1) (m2,i2) =
     let d = euclid m1 m2
@@ -275,20 +266,21 @@
        then Nothing
        else Just (m3,i3)
 
--- | Reduce the number of nodes at a 'Sieve'.
---
--- > reduce (L (3,2) ∪ Empty) == L (3,2)
--- > reduce (L (3,2) ∩ Empty) == L (3,2)
--- > reduce (L (3,2) ∩ L (4,7)) == L (12,11)
--- > reduce (L (6,9) ∩ L (15,18)) == L (30,3)
---
--- > let s = 3⋄2∩4⋄7∩6⋄11∩8⋄7 ∪ 6⋄9∩15⋄18 ∪ 13⋄5∩8⋄6∩4⋄2 ∪ 6⋄9∩15⋄19
--- > in reduce s == (24⋄23 ∪ 30⋄3 ∪ 104⋄70)
---
--- > putStrLn $ sieve_pp (reduce s)
---
--- > let s = 3⋄2∩4⋄7∩6⋄11∩8⋄7 ∪ 6⋄9∩15⋄18 ∪ 13⋄5∩8⋄6∩4⋄2 ∪ 6⋄9∩15⋄19
--- > in reduce s == (24⋄23 ∪ 30⋄3 ∪ 104⋄70)
+{- | Reduce the number of nodes at a 'Sieve'.
+
+> reduce (L (3,2) ∪ Empty) == L (3,2)
+> reduce (L (3,2) ∩ Empty) == L (3,2)
+> reduce (L (3,2) ∩ L (4,7)) == L (12,11)
+> reduce (L (6,9) ∩ L (15,18)) == L (30,3)
+
+> let s = 3⋄2∩4⋄7∩6⋄11∩8⋄7 ∪ 6⋄9∩15⋄18 ∪ 13⋄5∩8⋄6∩4⋄2 ∪ 6⋄9∩15⋄19
+> reduce s == (24⋄23 ∪ 30⋄3 ∪ 104⋄70)
+
+> putStrLn $ sieve_pp (reduce s)
+
+> let s = 3⋄2∩4⋄7∩6⋄11∩8⋄7 ∪ 6⋄9∩15⋄18 ∪ 13⋄5∩8⋄6∩4⋄2 ∪ 6⋄9∩15⋄19
+> reduce s == (24⋄23 ∪ 30⋄3 ∪ 104⋄70)
+-}
 reduce :: Sieve -> Sieve
 reduce s =
     let f g s1 s2 =
@@ -307,3 +299,43 @@
          Intersection (L p) (L q) -> maybe Empty L (reduce_intersection p q)
          Intersection s1 s2 -> f Intersection s1 s2
          Complement s' -> Complement (reduce s')
+
+-- * Literature
+
+psappha_flint_c :: [Sieve]
+psappha_flint_c =
+  let s0 = (8⋄0∪8⋄1∪8⋄7)∩(5⋄1∪5⋄3)
+      s1 = (8⋄0∪8⋄1∪8⋄2)∩5⋄0
+      s2 = 8⋄3∩(5⋄0∪5⋄1∪5⋄2∪5⋄3∪5⋄4)
+      s3 = 8⋄4∩(5⋄0∪5⋄1∪5⋄2∪5⋄3∪5⋄4)
+      s4 = (8⋄5∪8⋄6)∩(5⋄2∪5⋄3∪5⋄4)
+      s5 = 8⋄1∩5⋄2
+      s6 = 8⋄6∩5⋄1
+  in [s0, s1, s2, s3, s4, s5, s6]
+
+{- | /Psappha/ (Flint)
+
+> let r = [0,1,3,4,6,8,10,11,12,13,14,16,17,19,20,22,23,25,27,28,29,31,33,35,36,37,38]
+> buildn 27 psappha_flint == r
+-}
+psappha_flint :: Sieve
+psappha_flint = union psappha_flint_c
+
+a_r_squibbs_c :: [Sieve]
+a_r_squibbs_c =
+  [8⋄0∩(11⋄0∪11⋄4∪11⋄5∪11⋄6∪11⋄10)
+  ,8⋄1∩(11⋄2∪11⋄3∪11⋄6∪11⋄7∪11⋄9)
+  ,8⋄2∩(11⋄0∪11⋄1∪11⋄2∪11⋄3∪11⋄5∪11⋄10)
+  ,8⋄3∩(11⋄1∪11⋄2∪11⋄3∪11⋄4∪11⋄10)
+  ,8⋄4∩(11⋄0∪11⋄4∪11⋄8)
+  ,8⋄5∩(11⋄0∪11⋄2∪11⋄3∪11⋄7∪11⋄9∪11⋄10)
+  ,8⋄6∩(11⋄1∪11⋄3∪11⋄5∪11⋄7∪11⋄8∪11⋄9)
+  ,8⋄7∩(11⋄1∪11⋄3∪11⋄6∪11⋄7∪11⋄8∪11⋄10)]
+
+{- | À R. (Hommage à Maurice Ravel) (Squibbs, 1996)
+
+let r = [0,2,3,4,7,9,10,13,14,16,17,21,23,25,29,30,32,34,35,38,39,43,44,47,48,52,53,57,58,59,62,63,66,67,69,72,73,77,78,82,86,87]
+buildn 42 a_r_squibbs == r
+-}
+a_r_squibbs :: Sieve
+a_r_squibbs = union a_r_squibbs_c
diff --git a/Music/Theory/Z.hs b/Music/Theory/Z.hs
--- a/Music/Theory/Z.hs
+++ b/Music/Theory/Z.hs
@@ -9,7 +9,7 @@
 -- | Z type.
 --
 -- > map z_modulus [z7,z12] == [7,12]
-data Z i = Z {z_modulus :: i}
+newtype Z i = Z {z_modulus :: i}
 
 -- | 'mod' of 'Z'.
 --
@@ -81,7 +81,7 @@
 to_Z z = z_fromInteger z . fromIntegral
 
 from_Z :: (Integral i,Num n) => i -> n
-from_Z i = fromIntegral i
+from_Z = fromIntegral
 
 -- | Universe of 'Z'.
 --
@@ -115,7 +115,7 @@
 z_divMod z p q = (z_div z p q,z_mod z (mod p q))
 
 z_toInteger :: Integral i => Z i -> i -> i
-z_toInteger z = to_Z z
+z_toInteger = to_Z
 
 -- * Z16
 
diff --git a/Music/Theory/Z/Boros_1990.hs b/Music/Theory/Z/Boros_1990.hs
--- a/Music/Theory/Z/Boros_1990.hs
+++ b/Music/Theory/Z/Boros_1990.hs
@@ -15,15 +15,15 @@
 import qualified Music.Theory.Array.Text as T
 import qualified Music.Theory.Combinations as T
 import qualified Music.Theory.Graph.Dot as T
-import qualified Music.Theory.Graph.FGL as T
+import qualified Music.Theory.Graph.Fgl as T
 import qualified Music.Theory.List as T
 import qualified Music.Theory.Set.List as T
 import qualified Music.Theory.Tuple as T
 import qualified Music.Theory.Z as T
 import qualified Music.Theory.Z.Forte_1973 as T
-import qualified Music.Theory.Z.TTO as T
+import qualified Music.Theory.Z.Tto as T
 
--- * UTIL
+-- * Util
 
 singular :: String -> [t] -> t
 singular err l =
@@ -37,9 +37,9 @@
 elem_by :: (t -> t -> Bool) -> t -> [t] -> Bool
 elem_by f e = any (f e)
 
--- * TTO
+-- * Tto
 
-tto_tni_univ :: Integral i => [T.TTO i]
+tto_tni_univ :: 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]]
@@ -51,67 +51,67 @@
 uniq_tni :: Integral i => [i] -> [[i]]
 uniq_tni = nub . all_tni
 
-type PC = Int
-type PCSET = [PC]
-type SC = PCSET
+type Pc = Int
+type Pcset = [Pc]
+type Sc = Pcset
 
 -- > pcset_trs 3 [0,1,9] == [0,3,4]
-pcset_trs :: Int -> PCSET -> PCSET
+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 :: [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 :: Pcset -> Bool
 self_inv p = elem_by set_eq (map (T.z_negate T.z12) p) (all_tn p)
 
 -- | Pretty printer, comma separated.
 --
 -- > pcset_pp [0,3,7,10] == "0,3,7,10"
-pcset_pp :: PCSET -> String
+pcset_pp :: Pcset -> String
 pcset_pp = intercalate "," . map show
 
 -- | Pretty printer, hexadecimal, no separator.
 --
 -- > pcset_pp_hex [0,3,7,10] == "037A"
-pcset_pp_hex :: PCSET -> String
-pcset_pp_hex = map toUpper . concat . map (flip showHex "")
+pcset_pp_hex :: Pcset -> String
+pcset_pp_hex = map toUpper . concatMap (`showHex` "")
 
--- * ATH
+-- * Ath
 
 -- | Forte prime form of the all-trichord hexachord.
 --
 -- > T.sc_name ath == "6-Z17"
 -- > T.sc "6-Z17" == ath
-ath :: PCSET
+ath :: Pcset
 ath = [0,1,2,4,7,8]
 
 -- | Is /p/ an instance of 'ath'.
-is_ath :: PCSET -> Bool
+is_ath :: Pcset -> Bool
 is_ath p = T.z_forte_prime T.z12 p == ath
 
 -- | Table 1, p.20
 --
 -- > length ath_univ == 24
-ath_univ :: [PCSET]
+ath_univ :: [Pcset]
 ath_univ = uniq_tni ath
 
--- | Calculate 'T.TTO' of pcset, which must be an instance of 'ath'.
+-- | Calculate 'T.Tto' of pcset, which must be an instance of 'ath'.
 --
--- > ath_tni [1,2,3,7,8,11] == T.TTO 3 1 True
-ath_tni :: PCSET -> T.TTO PC
+-- > ath_tni [1,2,3,7,8,11] == T.Tto 3 1 True
+ath_tni :: Pcset -> T.Tto Pc
 ath_tni = singular "ath_tni" . filter ((== 1) . T.tto_M) . T.z_tto_rel 5 T.z12 ath
 
 -- | Give label for instance of 'ath', prime forms are written H and inversions h.
 --
 -- > ath_pp [1,2,3,7,8,11] == "h3"
-ath_pp :: PCSET -> String
+ath_pp :: Pcset -> String
 ath_pp p =
     let r = ath_tni p
         h = if T.tto_I r then 'h' else 'H'
@@ -120,51 +120,51 @@
 -- | The twenty three-element subsets of 'ath'.
 --
 -- > length ath_trichords == 20
-ath_trichords :: [PCSET]
+ath_trichords :: [Pcset]
 ath_trichords = T.combinations (3::Int) ath
 
 -- | '\\' of 'ath' and /p/, ie. the pitch classes that are in 'ath' and not in /p/.
 --
 -- > ath_complement [0,1,2] == [4,7,8]
-ath_complement :: PCSET -> PCSET
+ath_complement :: Pcset -> Pcset
 ath_complement p = ath \\ p
 
 -- | /p/ is a pcset, /q/ a sc, calculate pcsets in /q/ that with /p/ form 'ath'.
 --
 -- > ath_completions [0,1,2] (T.sc "3-3") == [[6,7,10],[4,7,8]]
 -- > ath_completions [6,7,10] (T.sc "3-5") == [[1,2,8]]
-ath_completions :: PCSET -> SC -> [PCSET]
+ath_completions :: Pcset -> Sc -> [Pcset]
 ath_completions p q =
     let f z = is_ath (p ++ z)
     in filter f (uniq_tni q)
 
-realise_ath_seq :: [PCSET] -> [[PCSET]]
+realise_ath_seq :: [Pcset] -> [[Pcset]]
 realise_ath_seq sq =
     case sq of
       p:q:sq' -> concatMap (\z -> map (p :) (realise_ath_seq (z : sq'))) (ath_completions p q)
       _ -> [sq]
 
 -- return edges that connect z to nodes at gr in an ATH relation
-ath_gr_extend :: [T.EDGE PCSET] -> PCSET -> [T.EDGE PCSET]
+ath_gr_extend :: [T.Edge Pcset] -> Pcset -> [T.Edge Pcset]
 ath_gr_extend gr c =
     let f x y = if is_ath (x ++ y) then Just (x,y) else Nothing
         g (p,q) = mapMaybe (f c) [p,q]
     in nub (map T.t2_sort (concatMap g gr))
 
-gr_trs :: Int -> [T.EDGE PCSET] -> [T.EDGE PCSET]
+gr_trs :: Int -> [T.Edge Pcset] -> [T.Edge Pcset]
 gr_trs n = let f (p,q) = (pcset_trs n p,pcset_trs n q) in map f
 
--- * TABLES
+-- * Tables
 
 -- > length table_3 == 20
-table_3 :: [((PCSET,SC,T.SC_Name),(PCSET,SC,T.SC_Name))]
+table_3 :: [((Pcset,Sc,T.SC_Name),(Pcset,Sc,T.SC_Name))]
 table_3 =
     let f p = let q = ath_complement p
                   i x = (x,T.z_forte_prime T.z12 x,T.sc_name x)
               in (i p,i q)
     in map f ath_trichords
 
-pp_tbl :: T.TABLE -> [String]
+pp_tbl :: T.Text_Table -> [String]
 pp_tbl = T.table_pp T.table_opt_simple
 
 -- > putStrLn $ unlines $ table_3_md
@@ -176,7 +176,7 @@
     in pp_tbl (hdr : map f table_3)
 
 -- > length table_4 == 10
-table_4 :: [((PCSET,PCSET,T.SC_Name),(PCSET,PCSET,T.SC_Name))]
+table_4 :: [((Pcset,Pcset,T.SC_Name),(Pcset,Pcset,T.SC_Name))]
 table_4 = nub (map T.t2_sort table_3)
 
 -- > putStrLn $ unlines $ table_4_md
@@ -187,7 +187,7 @@
         hdr = ["Trichords","Prime Forms","Forte Numbers"]
     in pp_tbl (hdr : map f table_4)
 
-table_5 :: [(PCSET,Int)]
+table_5 :: [(Pcset,Int)]
 table_5 = T.histogram (map (T.z_forte_prime T.z12) ath_trichords)
 
 -- > putStrLn $ unlines $ table_5_md
@@ -196,7 +196,7 @@
     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 :: [(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
@@ -207,38 +207,38 @@
     let f (p,q,r) = [pcset_pp_hex p,show q,show r]
     in pp_tbl (["SC","#H0","#Hn"] : map f table_6)
 
--- * FIGURES
+-- * Figures
 
-fig_1 :: [T.EDGE PCSET]
+fig_1 :: [T.Edge Pcset]
 fig_1 = map (T.t2_map T.p3_snd) table_4
 
-fig_1_gr :: G.Gr PCSET ()
+fig_1_gr :: G.Gr Pcset ()
 fig_1_gr = T.g_from_edges fig_1
 
 -- > putStrLn $ unlines $ map (unwords . map pcset_pp) fig_2
-fig_2 :: [[PCSET]]
+fig_2 :: [[Pcset]]
 fig_2 =
  let g = G.undir fig_1_gr
      n = G.labNodes g
      n' = filter ((== 2) . G.deg g . fst) n
      c = T.combinations (2::Int) n'
-     p = map (\[lhs,rhs] -> G.esp (fst lhs) (fst rhs) g) c
-     p' = (filter (not . null) p)
- in map (mapMaybe (\x -> lookup x n)) p'
+     p = map (\l -> let (lhs,rhs) = T.firstSecond l in G.esp (fst lhs) (fst rhs) g) c
+     p' = filter (not . null) p
+ in map (mapMaybe (`lookup` n)) p'
 
-fig_3 :: [[T.EDGE PCSET]]
+fig_3 :: [[T.Edge Pcset]]
 fig_3 = map (concatMap (T.adj2 1) . realise_ath_seq) fig_2
 
-fig_3_gr :: [G.Gr PCSET ()]
+fig_3_gr :: [G.Gr Pcset ()]
 fig_3_gr = map T.g_from_edges fig_3
 
-fig_4 :: [[T.EDGE PCSET]]
+fig_4 :: [[T.Edge Pcset]]
 fig_4 =
     let p = concatMap realise_ath_seq fig_2
         q = filter ([0,1,2] `elem`) p
     in map (T.adj2 1) q
 
-fig_5 :: [[T.EDGE PCSET]]
+fig_5 :: [[T.Edge Pcset]]
 fig_5 =
     let c = [0,4,8]
         f gr = case ath_gr_extend gr c of
@@ -249,25 +249,25 @@
 
 -- * Drawing
 
-uedge_set :: Ord v => [T.EDGE v] -> [T.EDGE v]
+uedge_set :: Ord v => [T.Edge v] -> [T.Edge v]
 uedge_set = nub . map T.t2_sort
 
 -- | Self-inversional pcsets are drawn in a double circle, other pcsets in a circle.
-set_shape :: PCSET -> T.DOT_ATTR
+set_shape :: Pcset -> T.Dot_Attr
 set_shape v = ("shape",if self_inv v then "doublecircle" else "circle")
 
-type GR = G.Gr PCSET ()
+type Gr = G.Gr Pcset ()
 
-gr_pp' :: (PCSET -> String) -> T.GR_PP PCSET ()
+gr_pp' :: (Pcset -> String) -> T.Graph_Pp Pcset ()
 gr_pp' f = (\(_,v) -> [set_shape v,("label",f v)],const [])
 
-gr_pp :: T.GR_PP PCSET ()
+gr_pp :: T.Graph_Pp Pcset ()
 gr_pp = gr_pp' pcset_pp
 
 d_fig_1 :: [String]
 d_fig_1 = T.fgl_to_udot [] gr_pp fig_1_gr
 
-d_fig_3_g :: GR
+d_fig_3_g :: Gr
 d_fig_3_g = T.g_from_edges (uedge_set (concat fig_3))
 
 d_fig_3 :: [String]
@@ -276,25 +276,25 @@
 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 :: 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 :: 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_L PCSET PCSET]
+d_fig_5_e :: [T.Edge_Lbl Pcset Pcset]
 d_fig_5_e = map (\(p,q) -> ((p,q),p++q)) (uedge_set (concat fig_5))
 
-d_fig_5_g' :: G.Gr PCSET PCSET
+d_fig_5_g' :: G.Gr Pcset Pcset
 d_fig_5_g' = T.g_from_edges_l d_fig_5_e
 
 d_fig_5' :: [String]
 d_fig_5' =
-    let pp = (\_ -> [("shape","")],\(_,e) -> [("label",ath_pp e)])
+    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'
diff --git a/Music/Theory/Z/Castren_1994.hs b/Music/Theory/Z/Castren_1994.hs
--- a/Music/Theory/Z/Castren_1994.hs
+++ b/Music/Theory/Z/Castren_1994.hs
@@ -11,7 +11,7 @@
 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
+import qualified Music.Theory.Z.Sro as Sro
 
 type Z12 = Int8
 
@@ -20,7 +20,7 @@
 -- > 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]
+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'.
 --
@@ -30,7 +30,7 @@
 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))
+    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
@@ -80,7 +80,7 @@
 -- > 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_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/.
 --
@@ -88,7 +88,7 @@
 -- > 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)))
+ti_subsets x a = filter (`List.is_subset` x) (nub (map sort (Sro.z_sro_ti_related z12 a)))
 
 -- | Trivial run length encoder.
 --
diff --git a/Music/Theory/Z/Clough_1979.hs b/Music/Theory/Z/Clough_1979.hs
--- a/Music/Theory/Z/Clough_1979.hs
+++ b/Music/Theory/Z/Clough_1979.hs
@@ -13,7 +13,7 @@
 transpose_to_zero p =
     case p of
       [] -> []
-      n:_ -> map (+ (negate n)) p
+      n:_ -> map (subtract n) p
 
 -- | Diatonic pitch class (Z7) set to /chord/.
 --
diff --git a/Music/Theory/Z/Drape_1999.hs b/Music/Theory/Z/Drape_1999.hs
--- a/Music/Theory/Z/Drape_1999.hs
+++ b/Music/Theory/Z/Drape_1999.hs
@@ -11,8 +11,8 @@
 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
+import Music.Theory.Z.Sro
+import Music.Theory.Z.Tto
 
 -- | Cardinality filter
 --
@@ -145,7 +145,7 @@
 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)
+    in concatMap (is !!)
 
 -- | Degree of intersection.
 --
@@ -218,7 +218,7 @@
 -}
 frg_pp :: Integral i => [i] -> String
 frg_pp =
-    let f = unwords . map (\p -> T.bracket ('[',']') p)
+    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
 
@@ -310,7 +310,7 @@
 issb :: Integral i => [i] -> [i] -> [String]
 issb p q =
     let k = length q - length p
-        f = any id . map (\x -> z_forte_prime z12 (p ++ x) == q) . z_tto_ti_related z12
+        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.
@@ -360,7 +360,7 @@
 > 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 :: 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.
@@ -381,15 +381,15 @@
 > rsg 5 z12 [0,1,2,3] [11,6,1,4] == sros "r1T4MI r1RT1M"
 
 -}
-rsg :: Integral i => i -> Z i -> [i] -> [i] -> [SRO i]
-rsg m z x y = filter (\o -> z_sro_apply z o x == y) (z_sro_univ (length x) m z)
+rsg :: Integral i => i -> Z i -> [i] -> [i] -> [Sro i]
+rsg = z_sro_rel
 
 -- | Subsets.
 --
 -- > cf [4] (sb z12 [sc "6-32",sc "6-8"]) == [[0,2,3,5],[0,1,3,5],[0,2,3,7],[0,2,4,7],[0,2,5,7]]
 sb :: Integral i => Z i -> [[i]] -> [[i]]
 sb z xs =
-    let f p = all id (map (\q -> has_sc z q p) xs)
+    let f p = all (\q -> has_sc z q p) xs
     in filter f scs
 
 {- | scc = set class completion
@@ -416,24 +416,24 @@
     ,"complement"
     ,"multiplication-by-five-transform"]
 
--- | (PCSET,TTO,FORTE-PRIME)
-type SI i = ([i],TTO i,[i])
+-- | (Pcset,Tto,Forte-Prime)
+type Si i = ([i],Tto i,[i])
 
 -- | Calculator for si.
 --
--- > si_calc z12 [0,5,3,11]
-si_calc :: Integral i => [i] -> (SI i,[i],[Int],SI i,SI i)
+-- > 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:_ = rs 5 z12 x_f 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 z12 [0,5,3,11]
+-- > 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) =
@@ -516,13 +516,13 @@
 >>> 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]
+> 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]
+> sro (Z.Sro 0 False 4 False True) [1,5,6] == [3,11,10]
 
 >>> echo 156 | pct sro T4  | pct sro T0I
 732
@@ -535,8 +535,8 @@
 > 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 o = z_sro_apply z o
+sro :: Integral i => Z i -> Sro i -> [i] -> [i]
+sro = z_sro_apply
 
 {- | tmatrix
 
diff --git a/Music/Theory/Z/Drape_1999/Cli.hs b/Music/Theory/Z/Drape_1999/Cli.hs
new file mode 100644
--- /dev/null
+++ b/Music/Theory/Z/Drape_1999/Cli.hs
@@ -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)
diff --git a/Music/Theory/Z/Forte_1973.hs b/Music/Theory/Z/Forte_1973.hs
--- a/Music/Theory/Z/Forte_1973.hs
+++ b/Music/Theory/Z/Forte_1973.hs
@@ -2,6 +2,7 @@
 --   Yale University Press, New Haven, 1973.
 module Music.Theory.Z.Forte_1973 where
 
+import Data.Bifunctor {- base -}
 import Data.List {- base -}
 import Data.Maybe {- base -}
 
@@ -10,7 +11,7 @@
 
 import Music.Theory.Unicode {- hmt -}
 import Music.Theory.Z {- hmt -}
-import Music.Theory.Z.SRO {- hmt -}
+import Music.Theory.Z.Sro {- hmt -}
 
 -- * Prime form
 
@@ -55,6 +56,7 @@
 
 > 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]))
@@ -366,7 +368,7 @@
 sc_table_unicode :: Num n => SC_Table n
 sc_table_unicode =
     let f = map (\c -> if c == '-' then non_breaking_hypen else c)
-    in map (\(nm,pc) -> (f nm,pc)) sc_table
+    in map (first f) sc_table
 
 -- | Lookup name of prime form of set class.  It is an error for the
 -- input not to be a forte prime form.
diff --git a/Music/Theory/Z/Morris_1974.hs b/Music/Theory/Z/Morris_1974.hs
--- a/Music/Theory/Z/Morris_1974.hs
+++ b/Music/Theory/Z/Morris_1974.hs
@@ -2,13 +2,15 @@
 -- /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 -}
 
--- | 'L.msum' '.' 'map' 'return'.
+-- | 'msum' '.' 'map' 'return'.
 --
 -- > L.observeAll (fromList [1..7]) == [1..7]
-fromList :: L.MonadPlus m => [a] -> m a
-fromList = L.msum . map return
+fromList :: MonadPlus m => [a] -> m a
+fromList = msum . map return
 
 -- | Interval from /i/ to /j/ in modulo-/n/.
 --
@@ -21,16 +23,16 @@
 -- > map (length . L.observeAll . all_interval_m) [4,6,8,10] == [2,4,24,288]
 -- > [0,1,3,2,9,5,10,4,7,11,8,6] `elem` L.observeAll (all_interval_m 12)
 -- > length (L.observeAll (all_interval_m 12)) == 3856
-all_interval_m :: L.MonadLogic m => Int -> m [Int]
+all_interval_m :: (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]
-                    L.guard (i `notElem` p)
-                    let j:_ = p
+                    guard (i `notElem` p)
+                    let j = head p
                         m = int_n n i j
-                    L.guard (m `notElem` q)
+                    guard (m `notElem` q)
                     recur (k + 1) (i : p) (m : q)
     in recur 1 [0] []
 
diff --git a/Music/Theory/Z/Read_1978.hs b/Music/Theory/Z/Read_1978.hs
--- a/Music/Theory/Z/Read_1978.hs
+++ b/Music/Theory/Z/Read_1978.hs
@@ -11,7 +11,7 @@
 
 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 -}
+import qualified Music.Theory.Z.Sro as Sro {- hmt -}
 
 -- | Coding.
 type Code = Word64
@@ -29,7 +29,7 @@
 
 -- | Pretty printer for 'Bit_Array'.
 bit_array_pp :: Bit_Array -> String
-bit_array_pp = map intToDigit . map fromEnum
+bit_array_pp = map (intToDigit . fromEnum)
 
 -- | Parse PP of 'Bit_Array'.
 --
@@ -79,7 +79,7 @@
 -- | 'bit_array_to_code' of 'set_to_bit_array'.
 --
 -- > 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])
+-- > 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 = bit_array_to_code . set_to_bit_array z
 
@@ -92,7 +92,7 @@
         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))
+        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.
@@ -163,6 +163,6 @@
 -- > 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
+    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))
diff --git a/Music/Theory/Z/SRO.hs b/Music/Theory/Z/SRO.hs
deleted file mode 100644
--- a/Music/Theory/Z/SRO.hs
+++ /dev/null
@@ -1,214 +0,0 @@
--- | 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 Text.Parsec.String 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 -> P.GenParser Char () (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
-
--- * 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))
diff --git a/Music/Theory/Z/Sro.hs b/Music/Theory/Z/Sro.hs
new file mode 100644
--- /dev/null
+++ b/Music/Theory/Z/Sro.hs
@@ -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))
diff --git a/Music/Theory/Z/TTO.hs b/Music/Theory/Z/TTO.hs
deleted file mode 100644
--- a/Music/Theory/Z/TTO.hs
+++ /dev/null
@@ -1,148 +0,0 @@
--- | 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 Text.Parsec.String 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 -> P.GenParser Char () (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
diff --git a/Music/Theory/Z/Tto.hs b/Music/Theory/Z/Tto.hs
new file mode 100644
--- /dev/null
+++ b/Music/Theory/Z/Tto.hs
@@ -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
diff --git a/README b/README
deleted file mode 100644
--- a/README
+++ /dev/null
@@ -1,21 +0,0 @@
-hmt - haskell music theory
---------------------------
-
-[haskell](http://haskell.org/) music theory
-
-related:
-
-- [hmt-diagrams](?t=hmt-diagrams)
-- [hmt-texts](?t=hmt-texts)
-
-## cli
-
-[csv-midi](?t=hmt&e=md/csv-midi.md),
-[db](?t=hmt&e=md/db.md),
-[gl](?t=hmt&e=md/gl.md),
-[obj](?t=hmt&e=md/obj.md),
-[pct](?t=hmt&e=md/pct.md),
-[ply](?t=hmt&e=md/ply.md),
-[scala](?t=hmt&e=md/scala.md)
-
-© [rohan drape](http://rohandrape.net/), 2006-2020, [gpl](http://gnu.org/copyleft/).
diff --git a/README.md b/README.md
new file mode 100644
--- /dev/null
+++ b/README.md
@@ -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/).
diff --git a/hmt.cabal b/hmt.cabal
--- a/hmt.cabal
+++ b/hmt.cabal
@@ -1,118 +1,96 @@
+cabal-version:     2.4
 Name:              hmt
-Version:           0.18
+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, 2006-2020
+Copyright:         Rohan Drape, 2006-2022
 Author:            Rohan Drape
 Maintainer:        rd@rohandrape.net
 Stability:         Experimental
 Homepage:          http://rohandrape.net/t/hmt
-Tested-With:       GHC == 8.6.5
+Tested-With:       GHC == 9.2.4
 Build-Type:        Simple
-Cabal-Version:     >= 1.10
 
-Data-files:        README
+Data-files:        README.md
                    data/csv/mnd/*.csv
                    data/dot/euler/*.dot
                    data/scl/*.scl
 
 Library
-  Build-Depends:   aeson,
-                   array,
+  Build-Depends:   array,
                    base >= 4.9 && < 5,
                    bytestring,
                    colour,
                    containers,
+                   data-memocombinators,
                    data-ordlist,
                    directory,
                    fgl,
                    filepath,
-                   hsc3 == 0.18.*,
+                   hmt-base == 0.20.*,
                    lazy-csv,
                    logict,
                    multiset-comb,
                    parsec,
-                   permutation,
                    primes,
                    process,
                    random,
                    safe,
                    split,
+                   strict,
                    text,
                    time
   Default-Language:Haskell2010
   GHC-Options:     -Wall -fwarn-tabs
-  Exposed-modules: Music.Theory.Array
-                   Music.Theory.Array.Cell_Ref
-                   Music.Theory.Array.CSV
-                   Music.Theory.Array.CSV.Midi.MND
-                   Music.Theory.Array.CSV.Midi.SKINI
+  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.Text
-                   Music.Theory.Bits
+                   Music.Theory.Array.Square
                    Music.Theory.Bjorklund
                    Music.Theory.Block_Design.Johnson_2007
                    Music.Theory.Braille
-                   Music.Theory.Byte
                    Music.Theory.Clef
-                   Music.Theory.Combinations
                    Music.Theory.Contour.Polansky_1992
-                   Music.Theory.DB.Common
-                   Music.Theory.DB.CSV
-                   Music.Theory.DB.JSON
-                   Music.Theory.DB.Plain
-                   Music.Theory.Directory
+                   Music.Theory.Db.Cli
+                   Music.Theory.Db.Common
+                   Music.Theory.Db.Csv
+                   Music.Theory.Db.Plain
                    Music.Theory.Duration
                    Music.Theory.Duration.Annotation
-                   Music.Theory.Duration.CT
+                   Music.Theory.Duration.ClickTrack
+                   Music.Theory.Duration.Hollos2014
                    Music.Theory.Duration.Name
                    Music.Theory.Duration.Name.Abbreviation
-                   Music.Theory.Duration.RQ
-                   Music.Theory.Duration.RQ.Division
-                   Music.Theory.Duration.RQ.Tied
+                   Music.Theory.Duration.Rq
+                   Music.Theory.Duration.Rq.Division
+                   Music.Theory.Duration.Rq.Tied
                    Music.Theory.Duration.Sequence.Notate
                    Music.Theory.Dynamic_Mark
-                   Music.Theory.Either
-                   Music.Theory.Enum
-                   Music.Theory.Function
                    Music.Theory.Gamelan
                    Music.Theory.Graph.Deacon_1934
                    Music.Theory.Graph.Dot
-                   Music.Theory.Graph.FGL
-                   Music.Theory.Graph.IO
+                   Music.Theory.Graph.Fgl
                    Music.Theory.Graph.Johnson_2014
-                   Music.Theory.Graph.LCF
-                   Music.Theory.Graph.OBJ
-                   Music.Theory.Graph.PLY
-                   Music.Theory.Graph.Type
                    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.IO
                    Music.Theory.Key
-                   Music.Theory.List
-                   Music.Theory.Map
-                   Music.Theory.Math
-                   Music.Theory.Math.Convert
-                   Music.Theory.Math.Convert.FX
+                   Music.Theory.List.Logic
+                   Music.Theory.Math.Convert.Fx
                    Music.Theory.Math.Nichomachus
-                   Music.Theory.Math.OEIS
+                   Music.Theory.Math.Oeis
                    Music.Theory.Math.Prime
-                   Music.Theory.Maybe
                    Music.Theory.Meter.Barlow_1987
                    Music.Theory.Metric.Buchler_1998
                    Music.Theory.Metric.Morris_1980
                    Music.Theory.Metric.Polansky_1996
-                   Music.Theory.Monad
-                   Music.Theory.Opt
-                   Music.Theory.Ord
                    Music.Theory.Parse
-                   Music.Theory.Permutations
                    Music.Theory.Permutations.List
                    Music.Theory.Permutations.Morris_1984
                    Music.Theory.Pitch
@@ -127,35 +105,33 @@
                    Music.Theory.Pitch.Spelling.Table
                    Music.Theory.Random.I_Ching
                    Music.Theory.Random.Jones_1981
-                   Music.Theory.Read
                    Music.Theory.Set.List
                    Music.Theory.Set.Set
-                   Music.Theory.Show
-                   Music.Theory.String
                    Music.Theory.Tempo_Marking
                    Music.Theory.Tiling.Canon
                    Music.Theory.Tiling.Johnson_2004
                    Music.Theory.Tiling.Johnson_2009
                    Music.Theory.Time.Bel1990.R
-                   Music.Theory.Time.Duration
-                   Music.Theory.Time.Notation
+                   Music.Theory.Time.KeyKit
+                   Music.Theory.Time.KeyKit.Basic
+                   Music.Theory.Time.KeyKit.Parser
                    Music.Theory.Time.Seq
                    Music.Theory.Time_Signature
-                   Music.Theory.Tuple
                    Music.Theory.Tuning
                    Music.Theory.Tuning.Alves_1997
-                   Music.Theory.Tuning.DB
-                   Music.Theory.Tuning.DB.Alves
-                   Music.Theory.Tuning.DB.Gann
-                   Music.Theory.Tuning.DB.Microtonal_Synthesis
-                   Music.Theory.Tuning.DB.Riley
-                   Music.Theory.Tuning.DB.Werckmeister
-                   Music.Theory.Tuning.EFG
-                   Music.Theory.Tuning.ET
+                   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.Graph.Iset
+                   Music.Theory.Tuning.Hs
                    Music.Theory.Tuning.Load
                    Music.Theory.Tuning.Meyer_1929
                    Music.Theory.Tuning.Midi
@@ -166,15 +142,16 @@
                    Music.Theory.Tuning.Polansky_1990
                    Music.Theory.Tuning.Rosenboom_1979
                    Music.Theory.Tuning.Scala
+                   Music.Theory.Tuning.Scala.Cli
+                   Music.Theory.Tuning.Scala.Functions
                    Music.Theory.Tuning.Scala.Interval
-                   Music.Theory.Tuning.Scala.KBM
+                   Music.Theory.Tuning.Scala.Kbm
                    Music.Theory.Tuning.Scala.Meta
                    Music.Theory.Tuning.Scala.Mode
                    Music.Theory.Tuning.Sethares_1994
                    Music.Theory.Tuning.Syntonic
                    Music.Theory.Tuning.Type
                    Music.Theory.Tuning.Wilson
-                   Music.Theory.Unicode
                    Music.Theory.Wyschnegradsky
                    Music.Theory.Xenakis.S4
                    Music.Theory.Xenakis.Sieve
@@ -183,6 +160,7 @@
                    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
@@ -191,9 +169,9 @@
                    Music.Theory.Z.Morris_1987.Parse
                    Music.Theory.Z.Rahn_1980
                    Music.Theory.Z.Read_1978
-                   Music.Theory.Z.TTO
-                   Music.Theory.Z.SRO
+                   Music.Theory.Z.Tto
+                   Music.Theory.Z.Sro
 
 Source-Repository  head
-  Type:            darcs
-  Location:        http://rohandrape.net/sw/hmt
+  Type:            git
+  Location:        https://gitlab.com/rd--/hmt