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]]

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.

>>> 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]]

ciseg :: [Z12] -> [Z12]

Cyclic interval segment.

cmpl :: [Z12] -> [Z12]

Synonynm for complement.

>>> cmpl 02468t
13579B

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

cyc :: [a] -> [a]

Form cycle.

>>> cyc 056
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.

>>> 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.

>>> dis 24
1256

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

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

Degree of intersection.

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

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

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

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

fn :: [Z12] -> String

Forte name.

has_ess :: [Z12] -> [Z12] -> Bool

p has_ess q is true iff p can embed q in sequence.

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

Embedded segment search.

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

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

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.

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

Interval cycle filter.

>>> echo 22341 | icf
22341

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

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

Interval class set to interval sets.

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

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

ici_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.

>>> 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.

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

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

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

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

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

Matrix search.

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

 S.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.

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

Pitch-class invariances (called pi at pct).

>>> pi 0236 12
0236
6320
532B
B235

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

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

Relate sets.

>>> rs 0123 641e
T1M

 import Music.Theory.Z12.Morris_1987.Parse
 rs [0,1,2,3] [6,4,1,11] == [(rnrtnmi "T1M",[1,6,11,4])
                            ,(rnrtnmi "T4MI",[4,11,6,1])]

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

Relate segments.

>>> rsg 156 3BA
T4I

 rsg [1,5,6] [3,11,10] == [rnrtnmi "T4I",rnrtnmi "r1RT4MI"]

>>> rsg 0123 05t3
T0M

 rsg [0,1,2,3] [0,5,10,3] == [rnrtnmi "T0M",rnrtnmi "RT3MI"]

>>> rsg 0123 4e61
RT1M

 rsg [0,1,2,3] [4,11,6,1] == [rnrtnmi "T4MI",rnrtnmi "RT1M"]

>>> echo e614 | rsg 0123
r3RT1M

 rsg [0,1,2,3] [11,6,1,4] == [rnrtnmi "r1T4MI",rnrtnmi "r1RT1M"]

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

Subsets.

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

Super set-class.

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

 spsc [sc "4-11", sc "4-12"] == ["5-26"]

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

 spsc [sc "3-11", sc "3-8"] == ["4-27","4-Z29"]

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

 spsc (cf [3] scs) == ["6-Z17"]