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]

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

Transpose by n.

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

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

Invert about n.

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

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

Composition of invert about 0 and tn.

tni 4 [1,5,6] == [3,10,11]
(invert 0 . tn  4) [1,5,6] == [2,3,7]

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

Modulo 12 multiplication

mn 11 [0,1,4,9] == invert 0 [0,1,4,9]

m5 :: [Z12] -> [Z12]

M5, ie. mn 5.

m5 [0,1,3] == [0,3,5]

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

T-related sets of p.

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

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

T/I-related set of p.

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