Music.Theory.Z12.TTO

Description

Pitch-class set (unordered) operations on `Z12`.

Synopsis

# Documentation

pcset :: Integral a => [a] -> [Z12]Source

Map to pitch-class and reduce to set.

``` pcset [1,13] == [1]
```

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

Transpose by n.

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

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

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

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

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]Source

Modulo 12 multiplication

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

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

M5, ie. `mn` `5`.

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

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

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]]Source

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]]
```