music-pitch-1.3: src/Music/Pitch/Relative.hs

{-# LANGUAGE
    GeneralizedNewtypeDeriving,
    FlexibleInstances,
    DeriveFunctor,
    TypeFamilies,
    StandaloneDeriving,
    OverloadedStrings,
    DeriveFoldable #-}

-------------------------------------------------------------------------------------
-- |
-- Copyright   : (c) Hans Hoglund 2012
--
-- License     : BSD-style
--
-- Maintainer  : hans@hanshoglund.se
-- Stability   : experimental
-- Portability : portable
--
-- Provides overloaded pitch literals.
--
-------------------------------------------------------------------------------------

module Music.Pitch.Relative (
    module Music.Pitch.Relative.Accidental,
    module Music.Pitch.Relative.Interval,
    module Music.Pitch.Relative.Name,
    module Music.Pitch.Relative.Number,
    module Music.Pitch.Relative.Pitch,
    module Music.Pitch.Relative.Quality,
    module Music.Pitch.Relative.Semitones,
)
where

import Data.Maybe
import Data.Either
import Data.Semigroup
import Data.VectorSpace
import Data.AffineSpace
import Control.Monad
import Control.Applicative
import Music.Pitch.Absolute hiding (Octaves(..), octaves)
import Music.Pitch.Literal
import qualified Data.List as List

import Music.Pitch.Relative.Semitones
import Music.Pitch.Relative.Accidental
import Music.Pitch.Relative.Quality
import Music.Pitch.Relative.Name
import Music.Pitch.Relative.Number
import Music.Pitch.Relative.Pitch
import Music.Pitch.Relative.Interval


{-  
    Some terminology:                                           
        
        newtype Pitch = (PitchClass, Semitones)
            For example (E, Natural)
            We write [c,cs,db..] for [(C, Natural), (C, Sharp), (D, Flat)..]
        
        newtype Interval = (Number, Semitones)
            For example (Augmented, IV)
        
        Interval is the relative representation of pitch 
        
        Pitch is an affine space with Interval as the difference type
            c           .+^ major third = e
            major third ^+^ major third = augmentedFifth
        

        Pitch addition and enhamonic equivalence:



        
        Semitones is the smallest musical unit (Semitones in Western music)
        
        The `semitones` function retrieves the number of Semitones in a pitch, for example
            semitones :: Interval -> Semitones
            semitones major third = 4

        Note that semitones is surjetive. We can define a non-deterministic function `intervals`
            intervals :: Semitones -> [Interval]
            intervals 4 = [majorThird, diminishedFourth]
        Law
            map semitones (intervals a) = replicate n a    for all n > 0
        Lemma
            map semitones (intervals a)
        

        isHemitonic   [1,2,2] = True
        isHemitonic   [2,2,2] = False
        isCohemitonic [1,1,2] = True
        isCohemitonic [1,2,1] = False
        isTritonic ...
        
        A Scale is a [Semitones], for example [2,2,1,2,2,2,1]
            From this we can derive       [2,4,5,7,9,11,12]
        A Scale is a function (Number -> Interval)
        A Scale is a function (Number -> Semitones)

    Tonal
        isConsonance :: Interval -> Bool
        isPerfectConsonance :: Interval -> Bool
        isImperfectConsonance :: Interval -> Bool
        isDissonance :: Interval -> Bool
        isDissonance :: Interval -> Bool
        isHemitonic :: Interval -> Bool
        isTritonic :: Interval -> Bool

        isSemitone :: Interval -> Bool
        isSemitone :: Interval -> Bool
        isLeap :: Interval -> Bool
        isSimple :: Interval -> Bool
        isCompound :: Interval -> Bool
        
        -- TODO simplify etc
        isMelodicDissonance :: Interval -> Bool


    "Post-tonal"
    
        Messiaen
        
        mode1 = [2,2,2,2,2]
        mode2 = [1,2, 1,2, 1,2, 1,2]
        mode3 = [2,1,1, 2,1,1, 2,1,1]
        mode4 = [1,1,3,1,   1,1,3,1]
        mode5 = [1,4,1,     1,4,1]
        mode6 = [2,2,1,1,   2,2,1,1]
        mode7 = [1,1,1,2,1, 1,1,1,2,1]


-   Old stuff>



-- Semitone is an enumerated associated type
type family Semitone a :: *
type family Alteration a :: *

-- A scale is a function :: Semitone a -> a
newtype Scale a = Scale { getScale :: [Semitone a] } 
-- Eq, Show

semitone :: Scale a -> Semitone a -> a
semitone = undefined


semitone (Scale xs) p = xs !! (fromIntegral p `mod` length xs)


fromSemitone :: (Num a, Ord a, Integral b, Num c) => Scale a -> b -> c
fromSemitone (Scale xs) p = fromIntegral $ fromMaybe (length xs - 1) $ List.findIndex (>= fromIntegral p) xs

scaleFromSemitones :: Num a => [a] -> Scale a
scaleFromSemitones = Scale . accum
    where
        accum = snd . List.mapAccumL add 0
        add a x = (a + x, a + x)

-- numberOfSemitones :: Scale a -> Int
numberOfSemitones = length . getScale

major :: Num a => Scale a
major = scaleFromSemitones [0,2,2,1,2,2,2,1]

naturalMinor :: Num a => Scale a
naturalMinor = scaleFromSemitones [0,2,1,2,2,1,2,2]

harmonicMinor :: Num a => Scale a                     
harmonicMinor = scaleFromSemitones [0,2,1,2,2,1,3,1]

-}


-- or' :: (t -> Bool) -> (t -> Bool) -> t -> Bool
-- or' p q x = p x || q x

-- replicate' n = replicate (fromIntegral n)