Music.Theory.Z.SRO

Serial (ordered) pitch-class operations on Z.

Documentation

tn :: (Integral i, Functor f) => i -> i -> f i -> f i

Transpose p by n.

tn 5 4 [0,1,4] == [4,0,3]
tn 12 4 [1,5,6] == [5,9,10]

invert :: (Integral i, Functor f) => i -> i -> f i -> f i

Invert p about n.

invert 5 0 [0,1,4] == [0,4,1]
invert 12 6 [4,5,6] == [8,7,6]
invert 12 0 [0,1,3] == [0,11,9]

tni :: (Integral i, Functor f) => i -> i -> f i -> f i

Composition of invert about 0 and tn.

tni 5 1 [0,1,3] == [1,0,3]
tni 12 4 [1,5,6] == [3,11,10]
(invert 12 0 . tn  12 4) [1,5,6] == [7,3,2]

mn :: (Integral i, Functor f) => i -> i -> f i -> f i

Modulo multiplication.

mn 12 11 [0,1,4,9] == tni 12 0 [0,1,4,9]

t_related :: (Integral i, Functor f) => i -> f i -> [f i]

T-related sequences of p.

length (t_related 12 [0,3,6,9]) == 12

ti_related :: (Eq (f i), Integral i, Functor f) => i -> f i -> [f i]

T/I-related sequences of p.

length (ti_related 12 [0,1,3]) == 24
length (ti_related 12 [0,3,6,9]) == 24
ti_related 12 [0] == map return [0..11]

rti_related :: Integral i => i -> [i] -> [[i]]

R/T/I-related sequences of p.

length (rti_related 12 [0,1,3]) == 48
length (rti_related 12 [0,3,6,9]) == 24

Sequence operations

tn_to :: Integral a => a -> a -> [a] -> [a]

Variant of tn, transpose p so first element is n.

tn_to 12 5 [0,1,3] == [5,6,8]
map (tn_to 12 0) [[0,1,3],[1,3,0],[3,0,1]]

invert_ix :: Integral i => i -> Int -> [i] -> [i]

Variant of invert, inverse about nth element.

map (invert_ix 12 0) [[0,1,3],[3,4,6]] == [[0,11,9],[3,2,0]]
map (invert_ix 12 1) [[0,1,3],[3,4,6]] == [[2,1,11],[5,4,2]]

tmatrix :: Integral i => i -> [i] -> [[i]]

The standard t-matrix of p.

tmatrix 12 [0,1,3] == [[0,1,3]
                      ,[11,0,2]
                      ,[9,10,0]]