> import Music.Theory

$ sro T4 156
59A

> tn 4 [1,5,6]

$ sro T4I 156
3BA

> tni 4 [1,5,6]

$ echo 156 | sro T4  | sro T0I
732

> let f n = invert 0 . tn n
> in f 4 [1,5,6]

$ pcom pcseg iseg 01549 | pcom iseg icseg | pcom icseg icset
145

> (set . map ic . int) [0,1,5,4,9]

$ pcom pcseg pcset 01549 | pcom pcset sc | pcom sc icv | pcom icv icset
1345

> import Data.Maybe

> let icv_icset x = let f x y = if x > 0 then Just y else Nothing
>                   in catMaybes (zipWith f x [1..6])
> in (icv_icset . icv . forte_prime) [0,1,5,4,9]

Allen Forte "The Basic Interval Patterns" JMT 17/2 (1973):234-272

$ function bip { pcom pcseg iseg $ | pcom iseg icseg | nrm -r }
$ bip 0t95728e3416
11223344556
$

> bip [0,10,9,5,7,2,8,11,3,4,1,6]

$ pg 5-Z17 | bip | sort -u > 5-Z17.bip ; \
  pg 5-Z37 | bip | sort -u > 5-Z37.bip ; \
  comm 5-Z17.bip 5-Z37.bip -1 -2 | wc -l
16
$

> import Data.List

> let f = nub . map bip . permutations . sc
> in f "5-Z17" `intersect` f "5-Z37"

$ cat ../db.sh
for sc in $(fl -c $1)
do
  pg $sc | bip | sort -u > $sc
done
$ sh ../db.sh 4
$ ls
4-1   4-12  4-16  4-19  4-21  4-24  4-27  4-4   4-7   4-Z15
4-10  4-13  4-17  4-2   4-22  4-25  4-28  4-5   4-8   4-Z29
4-11  4-14  4-18  4-20  4-23  4-26  4-3   4-6   4-9
$

> let { s = filter ((== 4) . length) scs
>     ; x = map permutations s }
> in zip (map sc_name s) (map (set . (map bip)) x)

$ cat view.sh
for i in $(fl -c $1 | pg | bip | sort -u)
do
  echo $i":" $(grep -l $i * | sort -t '-' +1  -n | tr "\n" " ")
done
$ sh view.sh 4
111: 4-1
112: 4-1 4-2 4-3
113: 4-1 4-3 4-4 4-7
...
$

> let { n = 4
>     ; s = filter ((== n) . length) scs
>     ; x = map permutations s
>     ; z = zip (map sc_name s) (map (set . (map bip)) x)
>     ; f b (s, bs) = if b `elem` bs then Just s else Nothing
>     ; g b = catMaybes (map (f b) z)
>     ; a = set (map bip (concat x)) }
> in zip a (map g a)

$ cyc <  ~/src/pct/lib/scs | epmq \
> "in cset 89" "is icset 12" "hasnt icseg 11" | scdb
7-34    ascending melodic minor collection
7-35    diatonic collection (d)
8-28    octotonic collection (Messiaen Mode II)
$

> let { cyc xs = xs ++ [head xs]
>     ; a = filter (\p -> length p `elem` [8,9]) (map cyc scs)
>     ; b = filter (\p -> set (int p) == [1,2]) a
>     ; c = filter (\p -> not ([1,1] `isInfixOf` int p)) b }
> in map sc_name c

$ epmq < ~/src/pct/lib/univ "in cset 6" "in pcset 579t024" \
> "has sc 5-35" "hasnt sc 2-6" "notin pcset 024579e"
02579A
$

> let { a = cf [6] (powerset [0..11])
>     ; b = filter (is_superset [0,2,4,5,7,9,10]) a
>     ; c = filter (`has_sc` (sc "5-35")) b
>     ; d = filter (not . (`has_sc` (sc "2-6"))) c }
> in filter (not . is_superset [0,2,4,5,7,9,11]) d

$ echo 024579 | sro RT4I
79B024

> sro (SRO 0 True 4 False True) [0,2,4,5,7,9]

$ sro T4I 156
3BA

> sro (SRO 0 False 4 False True) [1,5,6]

$ echo 156 | sro T0I | sro T4
3BA

> import Control.Arrow

> let { i = SRO 0 False 0 False True
>     ; t4 = SRO 0 False 4 False False }
> in (sro i >>> sro t4) [1,5,6]

$ echo 156 | sro T4  | sro T0I
732

> let { i = SRO 0 False 0 False True
>     ; t4 = SRO 0 False 4 False False }
> in (sro i . sro t4) [1,5,6]

$ rsg 156 3BA
T4I

> rsg [1,5,6] [3,11,10]

$ rsg 0123 05t3
T0M

> rsg [0,1,2,3] [0,5,10,3]

$ rsg 0123 4e61
RT1M

> rsg [0,1,2,3] [4,11,6,1]

$ echo e614 | rsg 0123
r3RT1M

note: pct uses right rotation rotation.

> rsg [0,1,2,3] [11,6,1,4]

> sro (SRO 1 True 1 True False) [0,1,2,3]

> sro (SRO 1 False 4 True True) [0,1,2,3]

T0 = T0M1; Tn = TnM1
I = MB; TnI = TnMB,
M = M5; TnM = TnM5,
MI = IM = M7 = MBM5; TnMI = TnM7

> mn 11 [0,1,4,9] == tni 0 [0,1,4,9]

$ se -c5 123
12333
12233
12223
11233
11223
11123
$

> se 5 [1,2,3]

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

> ici_c [1,2,3]

> ici [1,2,3]

> cgg [[0],[1,11],[2,10],[3,9],[4,8],[5,7],[6]]

$ se -c5 1245 | pg | ici | pcom iseg sc | \
  sort -u | epmq "in cset 6" | wc -l
42
$

> let { a = se 5 [1,2,4,5]
>     ; b = concatMap permutations a
>     ; c = concatMap ici b
>     ; d = map (forte_prime . dx_d 0) c
>     ; e = nub d
>     ; f = cf [6] e }
> in length f

$ cg -r3 0159
015
019
059
159
$

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

$ cmpl 02468t
13579B
$

> cmpl [0,2,4,6,8,10]

$ cyc 056
0560
$

> cyc [0,5,6]

$ dim 016
T1d
T1m
T0o
$

> dim [0,1,6]

$ dis 24
1256
$

> dis [2,4]

$ echo 024579e | doi 6 | sort -u
024579A
024679B
$ echo 01234 | doi 2 7-35 | sort -u
13568AB
$

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

> doi 2 (sc "7-35") [0,1,2,3,4]

$ spsc 4-11 4-12
5-26[02458]
$ spsc 3-11 3-8
4-27[0258]
4-Z29[0137]
$ spsc `fl 3`
6-Z17[012478]
$

> spsc [sc "4-11", sc "4-12"]

> spsc [sc "3-11", sc "3-8"]

> spsc (cf [3] scs)

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

> ess [2,3,10] [0,1,6,4,3,2,5]

$ echo 22341 | icf
22341
$

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

$ icseg 013265e497t8
12141655232
$

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

$ imb -c34 024579 | pfmt
024 245 457 579
0245 2457 4579
$

> imb [3,4] [0,2,4,5,7,9]

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

> issb (sc "3-7") (sc "6-32")

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

> set (mxs [0,2,4,5,7,9] [6,4,2])

$ nrm 0123456543210
0123456
$

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

$ pi 0236 12
0236
6320
532B
B235
$

> pci [0,2,3,6] [1,2]

$ rs 0123 e614
T1M
$ rs 0123 641e
T1M
$ rs 0123 641e416
T1M
$

> rs [0,1,2,3] [6,4,1,11]

$ sb 6-32 6-8 | fn | pfmt
1-1
2-1 2-2 2-3 2-4 2-5
3-2 3-4 3-6 3-7 3-9 3-11
4-10 4-11 4-14 4-22 4-23
5-23
$ for i in `cat ~/src/pct/lib/scs | cf 6 | fn` ; \
  do echo $i >> LIST ; sb $i | cf 3 | wc -l >> LIST ; done
$

> map sc_name (sb [sc "6-32", sc "6-8"])

> let f p = let xs = cf [3] (sb [p]) 
>           in (sc_name p, length xs)
> in map f (cf [6] scs)

$ echo 024579 | sro RT4I
79B024

> sro (rnrtnmi "RT4I") [0,2,4,5,7,9]