Music.Theory.Z12.TTO

Pitch-class set (unordered) operations on Z12.

Documentation

pcset :: Integral a => [a] -> [Z12]

Map to pitch-class and reduce to set.

pcset [1,13] == [1]

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

Transpose by n.

tto_tn 4 [1,5,6] == [5,9,10]
tto_tn 4 [0,4,8] == [0,4,8]

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

Invert about n.

tto_invert 6 [4,5,6] == [6,7,8]
tto_invert 0 [0,1,3] == [0,9,11]

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

Composition of invert about 0 and tn.

tto_tni 4 [1,5,6] == [3,10,11]
(tto_invert 0 . tto_tn 4) [1,5,6] == [2,3,7]

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

Modulo 12 multiplication

tto_mn 11 [0,1,4,9] == tto_invert 0 [0,1,4,9]

tto_m5 :: [Z12] -> [Z12]

M5, ie. mn 5.

tto_m5 [0,1,3] == [0,3,5]

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

T-related sets of p.

length (tto_t_related [0,1,3]) == 12
tto_t_related [0,3,6,9] == [[0,3,6,9],[1,4,7,10],[2,5,8,11]]

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

T/I-related set of p.

length (tto_ti_related [0,1,3]) == 24
tto_ti_related [0,3,6,9] == [[0,3,6,9],[1,4,7,10],[2,5,8,11]]