hmt-0.15: Haskell Music Theory

Safe Haskell | None
Language | Haskell98

Music.Theory.Z12.SRO

Contents

- Sequence operations

Description

Serial (ordered) pitch-class operations on `Z12`.

Synopsis

- tn :: Z12 -> [Z12] -> [Z12]
- invert :: Z12 -> [Z12] -> [Z12]
- tni :: Z12 -> [Z12] -> [Z12]
- mn :: Z12 -> [Z12] -> [Z12]
- m5 :: [Z12] -> [Z12]
- t_related :: [Z12] -> [[Z12]]
- ti_related :: [Z12] -> [[Z12]]
- rti_related :: [Z12] -> [[Z12]]
- tmi_related :: [Z12] -> [[Z12]]
- rtmi_related :: [Z12] -> [[Z12]]
- rrtmi_related :: [Z12] -> [[Z12]]
- tn_to :: Z12 -> [Z12] -> [Z12]
- invert_ix :: Int -> [Z12] -> [Z12]
- tmatrix :: [Z12] -> [[Z12]]

# Documentation

tn :: Z12 -> [Z12] -> [Z12] Source #

Transpose p by n.

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

invert :: Z12 -> [Z12] -> [Z12] Source #

Invert p about n.

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

tni :: Z12 -> [Z12] -> [Z12] Source #

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] Source #

Modulo 12 multiplication

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

m5 :: [Z12] -> [Z12] Source #

M5, ie. `mn` `5`.

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

t_related :: [Z12] -> [[Z12]] Source #

T-related sequences of p.

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

ti_related :: [Z12] -> [[Z12]] Source #

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]] Source #

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]] Source #

T/M/I-related sequences of p.

rtmi_related :: [Z12] -> [[Z12]] Source #

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

rrtmi_related :: [Z12] -> [[Z12]] Source #

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

# Sequence operations

tn_to :: Z12 -> [Z12] -> [Z12] Source #

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

    tn_to 5 [0,1,3] == [5,6,8]
    map (tn_to 0) [[0,1,3],[1,3,0],[3,0,1]] == [[0,1,3],[0,2,11],[0,9,10]]

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

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]] Source #

The standard t-matrix of p.

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