```module Music.Theory.Pitch where

import Data.Function

type PitchClass = Integer
type Octave = Integer

data Note_T = C | D | E | F | G | A | B
deriving (Eq, Ord, Enum, Bounded, Show)

data Alteration_T = DoubleFlat
| ThreeQuarterToneFlat | Flat | QuarterToneFlat
| Natural
| QuarterToneSharp | Sharp | ThreeQuarterToneSharp
| DoubleSharp
deriving (Eq, Ord, Enum, Show)

data Pitch = Pitch { note :: Note_T
, alteration :: Alteration_T
, octave :: Octave }
deriving (Eq, Show)

instance Ord Pitch where
compare = pitch_compare

note_to_pc :: Note_T -> Integer
note_to_pc n =
case n of
C -> 0
D -> 2
E -> 4
F -> 5
G -> 7
A -> 9
B -> 11

alteration_to_diff :: Alteration_T -> Integer
alteration_to_diff a =
case a of
DoubleFlat -> -2
Flat -> -1
Natural -> 0
Sharp -> 1
DoubleSharp -> 2
_ -> error "alteration_to_diff: quarter tone"

alteration_to_fdiff :: Alteration_T -> Double
alteration_to_fdiff a =
case a of
ThreeQuarterToneFlat -> -1.5
QuarterToneFlat -> -0.5
QuarterToneSharp -> 0.5
ThreeQuarterToneSharp -> 1.5
_ -> fromIntegral (alteration_to_diff a)

pitch_to_octpc :: Pitch -> (Octave, PitchClass)
pitch_to_octpc = midi_to_octpc . pitch_to_midi

pitch_to_midi :: Pitch -> Integer
pitch_to_midi (Pitch n a o) =
let a' = alteration_to_diff a
n' = note_to_pc n
in 12 + o * 12 + n' + a'

pitch_to_fmidi :: Pitch -> Double
pitch_to_fmidi (Pitch n a o) =
let a' = alteration_to_fdiff a
o' = fromIntegral o
n' = fromIntegral (note_to_pc n)
in 12 + o' * 12 + n' + a'

pitch_to_pc :: Pitch -> PitchClass
pitch_to_pc = snd . pitch_to_octpc

pitch_compare :: Pitch -> Pitch -> Ordering
pitch_compare = compare `on` pitch_to_octpc

octpc_to_pitch :: (Octave, PitchClass) -> Pitch
octpc_to_pitch (o,pc) =
let (n,a) = case pc of
0 -> (C,Natural)
1 -> (C,Sharp)
2 -> (D,Natural)
3 -> (E,Flat)
4 -> (E,Natural)
5 -> (F,Natural)
6 -> (F,Sharp)
7 -> (G,Natural)
8 -> (A,Flat)
9 -> (A,Natural)
10 -> (B,Flat)
11 -> (B,Natural)
_ -> error ("octpc_to_pitch: " ++ show pc)
in Pitch n a o

octpc_nrm :: (Octave, PitchClass) -> (Octave, PitchClass)
octpc_nrm (o,pc) =
if pc > 11
then octpc_nrm (o+1,pc-12)
else if pc < 0
then octpc_nrm (o-1,pc+12)
else (o,pc)

octpc_trs :: Integer -> (Octave, PitchClass) -> (Octave, PitchClass)
octpc_trs n (o,pc) = octpc_nrm (o,pc+n)

octpc_to_midi :: (Octave, PitchClass) -> Integer
octpc_to_midi (o,pc) = 60 + ((o - 4) * 12) + pc

midi_to_octpc :: Integer -> (Octave, PitchClass)
midi_to_octpc n = (n - 12) `divMod` 12

pitch_edit_octave :: (Integer -> Integer) -> Pitch -> Pitch
pitch_edit_octave f (Pitch n a o) = Pitch n a (f o)

note_t_transpose :: Note_T -> Int -> Note_T
note_t_transpose x n =