Music.Theory.Z12.Drape_1999

Haskell implementations of pct operations. See http://slavepianos.org/rd/t/pct.

Documentation

cf :: Integral n => [n] -> [[a]] -> [[a]]

Cardinality filter

cf [0,3] (cg [1..4]) == [[1,2,3],[1,2,4],[1,3,4],[2,3,4],[]]

cgg :: [[a]] -> [[a]]

Combinatorial sets formed by considering each set as possible values for slot.

cgg [[0,1],[5,7],[3]] == [[0,5,3],[0,7,3],[1,5,3],[1,7,3]]
let n = "01" in cgg [n,n,n] == ["000","001","010","011","100","101","110","111"]

cg :: [a] -> [[a]]

Combinations generator, ie. synonym for powerset.

sort (cg [0,1,3]) == [[],[0],[0,1],[0,1,3],[0,3],[1],[1,3],[3]]

cg_r :: Integral n => n -> [a] -> [[a]]

Powerset filtered by cardinality.

>>> pct cg -r3 0159
015
019
059
159

cg_r 3 [0,1,5,9] == [[0,1,5],[0,1,9],[0,5,9],[1,5,9]]

chn_t0 :: Int -> [Z12] -> [[Z12]]

Chain pcsegs.

>>> echo 024579 | pct chn T0 3 | sort -u
579468 (RT8M)
579A02 (T5)

chn_t0 3 [0,2,4,5,7,9] == [[5,7,9,10,0,2],[5,7,9,4,6,8]]

>>> echo 02457t | pct chn T0 2
7A0135 (RT5I)
7A81B9 (RT9MI)

chn_t0 2 [0,2,4,5,7,10] == [[7,10,0,1,3,5],[7,10,8,1,11,9]]

ciseg :: [Z12] -> [Z12]

Cyclic interval segment.

>>> echo 014295e38t76 | pct cisg
13A7864529B6

ciseg [0,1,4,2,9,5,11,3,8,10,7,6] == [1,3,10,7,8,6,4,5,2,9,11,6]

cmpl :: [Z12] -> [Z12]

Synonynm for complement.

>>> pct cmpl 02468t
13579B

cmpl [0,2,4,6,8,10] == [1,3,5,7,9,11]

cyc :: [a] -> [a]

Form cycle.

>>> echo 056 | pct cyc
0560

cyc [0,5,6] == [0,5,6,0]

d_nm :: Integral a => [a] -> Maybe Char

Diatonic set name. d for diatonic set, m for melodic minor set, o for octotonic set.

dim :: [Z12] -> [(Z12, [Z12])]

Diatonic implications.

dim_nm :: [Z12] -> [(Z12, Char)]

Variant of dim that is closer to the pct form.

>>> pct dim 016
T1d
T1m
T0o

dim_nm [0,1,6] == [(1,'d'),(1,'m'),(0,'o')]

dis :: Integral t => [Int] -> [t]

Diatonic interval set to interval set.

>>> pct dis 24
1256

dis [2,4] == [1,2,5,6]

doi :: Int -> [Z12] -> [Z12] -> [[Z12]]

Degree of intersection.

>>> echo 024579e | pct doi 6 | sort -u
024579A
024679B

let p = [0,2,4,5,7,9,11]
in doi 6 p p == [[0,2,4,5,7,9,10],[0,2,4,6,7,9,11]]

>>> echo 01234 | pct doi 2 7-35 | sort -u
13568AB

doi 2 (T.sc "7-35") [0,1,2,3,4] == [[1,3,5,6,8,10,11]]

fn :: [Z12] -> String

Forte name.

frg_cyc :: T6 [[Z12]]

Z12 cycles.

frg :: [Z12] -> T6 [String]

Fragmentation of cycles.

ic_cycle_vector :: [Z12] -> T6 [Int]

ic_cycle_vector_pp :: T6 [Int] -> String

Pretty printer for ic_cycle_vector.

let r = "IC cycle vector: <1> <22> <111> <1100> <5> <000000>"
in ic_cycle_vector_pp (ic_cycle_vector [0,2,4,5,7,9]) == r

frg_hdr :: [String]

frg_pp :: [Z12] -> String

Fragmentation of cycles.

>>> pct frg 024579
Fragmentation of 1-cycle(s):  [0-2-45-7-9--]
Fragmentation of 2-cycle(s):  [024---] [--579-]
Fragmentation of 3-cycle(s):  [0--9] [-47-] [25--]
Fragmentation of 4-cycle(s):  [04-] [-59] [2--] [-7-]
Fragmentation of 5-cycle(s):  [05------4927]
Fragmentation of 6-cycle(s):  [0-] [-7] [2-] [-9] [4-] [5-]
IC cycle vector: <1> <22> <111> <1100> <5> <000000>

putStrLn $ frg_pp [0,2,4,5,7,9]

ess :: [Z12] -> [Z12] -> [[Z12]]

Embedded segment search.

>>> echo 23A | pct ess 0164325
2B013A9
923507A

ess [0,1,6,4,3,2,5] [2,3,10] == [[9,2,3,5,0,7,10],[2,11,0,1,3,10,9]]

has_sc_pf :: Integral a => ([a] -> [a]) -> [a] -> [a] -> Bool

Can the set-class q (under prime form algorithm pf) be drawn from the pcset p.

has_sc :: [Z12] -> [Z12] -> Bool

Can the set-class q be drawn from the pcset p.

let d = [0,2,4,5,7,9,11] in has_sc d (complement d) == True
has_sc [] [] == True

icf :: (Num a, Eq a) => [[a]] -> [[a]]

Interval cycle filter.

>>> echo 22341 | pct icf
22341

icf [[2,2,3,4,1]] == [[2,2,3,4,1]]

ici :: Num t => [Int] -> [[t]]

Interval class set to interval sets.

>>> pct ici -c 123
123
129
1A3
1A9

ici_c [1,2,3] == [[1,2,3],[1,2,9],[1,10,3],[1,10,9]]

ici_c :: [Int] -> [[Int]]

Interval class set to interval sets, concise variant.

ici_c [1,2,3] == [[1,2,3],[1,2,9],[1,10,3],[1,10,9]]

icseg :: [Z12] -> [Z12]

Interval-class segment.

>>> pct icseg 013265e497t8
12141655232

icseg [0,1,3,2,6,5,11,4,9,7,10,8] == [1,2,1,4,1,6,5,5,2,3,2]

iseg :: [Z12] -> [Z12]

Interval segment (INT).

imb :: Integral n => [n] -> [a] -> [[[a]]]

Imbrications.

let r = [[[0,2,4],[2,4,5],[4,5,7],[5,7,9]]
        ,[[0,2,4,5],[2,4,5,7],[4,5,7,9]]]
in imb [3,4] [0,2,4,5,7,9] == r

issb :: [Z12] -> [Z12] -> [String]

issb gives the set-classes that can append to p to give q.

>>> pct issb 3-7 6-32
3-7
3-2
3-11

issb (T.sc "3-7") (T.sc "6-32") == ["3-2","3-7","3-11"]

mxs :: [Z12] -> [Z12] -> [[Z12]]

Matrix search.

>>> pct mxs 024579 642 | sort -u
6421B9
B97642

T.set (mxs [0,2,4,5,7,9] [6,4,2]) == [[6,4,2,1,11,9],[11,9,7,6,4,2]]

nrm :: Ord a => [a] -> [a]

Normalize.

>>> pct nrm 0123456543210
0123456

nrm [0,1,2,3,4,5,6,5,4,3,2,1,0] == [0,1,2,3,4,5,6]

nrm_r :: Ord a => [a] -> [a]

Normalize, retain duplicate elements.

pci :: [Int] -> [Z12] -> [[Z12]]

Pitch-class invariances (called pi at pct).

>>> pct pi 0236 12
pcseg 0236
pcseg 6320
pcseg 532B
pcseg B235

pci [1,2] [0,2,3,6] == [[0,2,3,6],[5,3,2,11],[6,3,2,0],[11,2,3,5]]

rs :: [Z12] -> [Z12] -> [(TTO Z12, [Z12])]

Relate sets (TnMI).

>>> pct rs 0123 641e
T1M

rs [0,1,2,3] [6,4,1,11] == [(Z.tto_parse "T1M",[1,6,11,4])
                           ,(Z.tto_parse "T4MI",[4,11,6,1])]

rs1 :: [Z12] -> [Z12] -> Maybe (TTO Z12)

rsg :: [Z12] -> [Z12] -> [SRO Z12]

Relate segments.

>>> pct rsg 156 3BA
T4I

rsg [1,5,6] [3,11,10] == [Z.sro_parse "T4I",Z.sro_parse "r1RT4MI"]

>>> pct rsg 0123 05t3
T0M

rsg [0,1,2,3] [0,5,10,3] == [Z.sro_parse "T0M",Z.sro_parse "RT3MI"]

>>> pct rsg 0123 4e61
RT1M

rsg [0,1,2,3] [4,11,6,1] == [Z.sro_parse "T4MI",Z.sro_parse "RT1M"]

>>> echo e614 | pct rsg 0123
r3RT1M

rsg [0,1,2,3] [11,6,1,4] == [Z.sro_parse "r1T4MI",Z.sro_parse "r1RT1M"]

sb :: [[Z12]] -> [[Z12]]

Subsets.

scc :: [Z12] -> [Z12] -> [[Z12]]

scc = set class completion

>>> pct scc 6-32 168
35A
49B
3AB
34B

scc (Z12.sc "6-32") [1,6,8] == [[3,5,10],[4,9,11],[3,10,11],[3,4,11]]

si_hdr :: [String]

type SI = ([Z12], TTO Z12, [Z12])

si_raw :: [Z12] -> (SI, [Z12], [Int], SI, SI)

si_raw_pp :: [Z12] -> [String]

si :: [Z12] -> [String]

Set information.

putStr $ unlines $ si [0,5,3,11]

spsc :: [[Z12]] -> [[Z12]]

Super set-class.

>>> pct spsc 4-11 4-12
5-26[02458]

spsc [Z12.sc "4-11",Z12.sc "4-12"] == [[0,2,4,5,8]]

>>> pct spsc 3-11 3-8
4-27[0258]
4-Z29[0137]

spsc [Z12.sc "3-11",Z12.sc "3-8"] == [[0,2,5,8],[0,1,3,7]]

>>> pct spsc `pct fl 3`
6-Z17[012478]

spsc (cf [3] Z12.scs) == [[0,1,2,4,7,8]]

sra :: [Z12] -> [[Z12]]

sra = stravinsky rotational array

>>> echo 019BA7 | pct sra
019BA7
08A96B
021A34
0B812A
0923B1
056243

let r = [[0,1,9,11,10,7],[0,8,10,9,6,11],[0,2,1,10,3,4]
       ,[0,11,8,1,2,10],[0,9,2,3,11,1],[0,5,6,2,4,3]]
in sra [0,1,9,11,10,7] == r

sro :: SRO Z12 -> [Z12] -> [Z12]

Serial operation.

>>> echo 156 | pct sro T4
59A

sro (Z.sro_parse "T4") [1,5,6] == [5,9,10]

>>> echo 024579 | pct sro RT4I
79B024

sro (Z.SRO 0 True 4 False True) [0,2,4,5,7,9] == [7,9,11,0,2,4]

>>> echo 156 | pct sro T4I
3BA

sro (Z.sro_parse "T4I") [1,5,6] == [3,11,10]
sro (Z.SRO 0 False 4 False True) [1,5,6] == [3,11,10]

>>> echo 156 | pct sro T4  | pct sro T0I
732

(sro (Z.sro_parse "T0I") . sro (Z.sro_parse "T4")) [1,5,6] == [7,3,2]

>>> echo 024579 | pct sro RT4I
79B024

sro (Z.sro_parse "RT4I") [0,2,4,5,7,9] == [7,9,11,0,2,4]

tics :: [Z12] -> [Int]

Vector indicating degree of intersection with inversion at each transposition.

tics [0,2,4,5,7,9] == [3,2,5,0,5,2,3,4,1,6,1,4]
map tics Z12.scs

tmatrix :: [Z12] -> [[Z12]]

tmatrix

>>> pct tmatrix 1258

1258 0147 9A14 67A1

tmatrix [1,2,5,8] == [[1,2,5,8],[0,1,4,7],[9,10,1,4],[6,7,10,1]]

trs :: [Z12] -> [Z12] -> [[Z12]]

trs = transformations search. Search all RTnMI of p for q.

>>> echo 642 | pct trs 024579 | sort -u
531642
6421B9
642753
B97642

let r = [[5,3,1,6,4,2],[6,4,2,1,11,9],[6,4,2,7,5,3],[11,9,7,6,4,2]]
in sort (trs [0,2,4,5,7,9] [6,4,2]) == r

trs_m :: [Z12] -> [Z12] -> [[Z12]]