# Pct

> import Control.Arrow
> import Data.Function
> import Data.List
> import Data.Maybe
> import Music.Theory.Parse
> import Music.Theory.Pct
> import Music.Theory.Permutations
> import Music.Theory.PitchClass
> import Music.Theory.Prime
> import Music.Theory.Table
> import Music.Theory.Set

This file illustrates equivalent expressions in pct and hmt terms.

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

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

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

> let icv_icset x = let f x y = if x > 0 then Just y else Nothing
>                   in catMaybes (zipWith f x [1..6])
> in (icv_icset . icv . forte_prime) [0,1,5,4,9] == [1,3,4,5]

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

> let f g = sort (g [1..4])
> in f permutations_l == f permutations

> let f = nub . map bip . permutations . sc
> in length (f "5-Z17" `intersect` f "5-Z37") == 16

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

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

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

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

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

> let {cyc xs = xs ++ [head xs]
>     ;a = filter (\p -> length p `elem` [8,9]) (map cyc scs)
>     ;b = filter (\p -> set (int p) == [1,2]) a
>     ;c = filter (\p -> not ([1,1] `isInfixOf` int p)) b}
> in map sc_name c == ["7-34","7-35","8-28"]

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

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

    $ echo 156 | sro T0I | sro T4
    3BA

> let {i = SRO 0 False 0 False True
>     ;t4 = SRO 0 False 4 False False}
> in (sro i >>> sro t4) [1,5,6] == [3,11,10]

    $ echo 156 | sro T4  | sro T0I
    732

> let {i = SRO 0 False 0 False True
>     ;t4 = SRO 0 False 4 False False}
> in (sro i . sro t4) [1,5,6] == [7,3,2]

Note that pct uses right rotation rotation.

> sro (SRO 1 True 1 True False) [0,1,2,3] == [11,6,1,4]
> sro (SRO 1 False 4 True True) [0,1,2,3] == [11,6,1,4]

    I = MB; TnI = TnMB,

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

    MI = IM = M7 = MBM5; TnMI = TnM7

> sro (rnrtnmi "T0MI") [0,1,4,9] == mn 7 [0,1,4,9]

    T0 = T0M1; Tn = TnM1
    M = M5; TnM = TnM5,

    $ se -c5 123
    12333
    12233
    12223
    11233
    11223
    11123

> se 5 [1,2,3]

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

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

> let {a = 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 == 42

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

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

    $ rs 0123 e614
    T1M
    $ rs 0123 641e416
    T1M

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

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

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