Music.Theory.Z12.SRO

Serial (ordered) pitch-class operations on Z12.

Documentation

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

Transpose p by n.

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

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

Invert p about n.

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

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

Composition of invert about 0 and tn.

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

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

Modulo 12 multiplication

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

m5 :: [Z12] -> [Z12]

M5, ie. mn 5.

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

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

T-related sequences of p.

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

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

T/I-related sequences of p.

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

rti_related :: [Z12] -> [[Z12]]

R/T/I-related sequences of p.

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

tmi_related :: [Z12] -> [[Z12]]

T/M/I-related sequences of p.

rtmi_related :: [Z12] -> [[Z12]]

R/T/M/I-related sequences of p.

rrtmi_related :: [Z12] -> [[Z12]]

r/R/T/M/I-related sequences of p.

Sequence operations

tn_to :: Z12 -> [Z12] -> [Z12]

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

 tn_to 5 [0,1,3] == [5,6,8]

invert_ix :: Int -> [Z12] -> [Z12]

Variant of invert, inverse about nth element.

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

tmatrix :: [Z12] -> [[Z12]]

The standard t-matrix of p.

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