Music.Pitch.Equal

Generic equal temperament pitch.

Use the type-level numbers from type-unary to construct an temperement dividing the octave in any number of steps. Common cases such as 6-TET (whole-tones), 12-TET (half-tones) and 24-TET (quarter-tones) are provided for convenience.

Equal temperament

data Equal a

Instances

Eq (Equal a)

IsNat a => Num (Equal a)

Ord (Equal a)

Show (Equal a)

IsNat a => Monoid (Equal a)

IsNat a => Semigroup (Equal a)

IsNat a => VectorSpace (Equal a)

IsNat a => AdditiveGroup (Equal a)

type Scalar (Equal a) = Equal a

toEqual :: IsNat a => Int -> Equal a

 Create an equal-temperament value.

fromEqual :: IsNat a => Equal a -> Int

Extract an equal-temperament value.

equalToRatio :: IsNat a => Equal a -> Double

Convert an equal-temeperament value to a frequency ratio.

>>> equalToRatio (7 :: Equal12)
1.4983070768766815

>>> equalToRatio (4 :: Equal12)
1.2599210498948732

size :: IsNat a => Equal a -> Int

Size of this type (value not evaluated).

>>> size (undefined :: Equal N2)
2

>>> size (undefined :: Equal N12)
12

cast :: (IsNat a, IsNat b) => Equal a -> Equal b

Safely cast a tempered value to another size.

>>> cast (1 :: Equal12) :: Equal24
2 :: Equal24

>>> cast (8 :: Equal12) :: Equal6
4 :: Equal6

>>> (2 :: Equal12) + cast (2 :: Equal24)
3 :: Equal12

Synonyms

type Equal6 = Equal N6

type Equal12 = Equal N12

type Equal17 = Equal N17

type Equal24 = Equal N24

type Equal36 = Equal N36

Extra type-level naturals

type N20 = N10 :*: N2

type N30 = N10 :*: N3

type N17 = N10 :+: N7

type N24 = N20 :+: N4

type N36 = N30 :+: N6