Music.Theory.Z12.SRO

Contents

Description

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

Synopsis

# Documentation

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

Transpose p by n.

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

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

``` 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]
```

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]]
```