Ambitus.hs

{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE MultiParamTypeClasses #-}

------------------------------------------------------------------------------------
-- |
-- Copyright   : (c) Hans Hoglund, Edward Lilley 2012–2014
--
-- License     : BSD-style
--
-- Maintainer  : hans@hanshoglund.se
-- Stability   : experimental
-- Portability : non-portable (TF,GNTD)
--
-- Musical ambitus, or pitch ranges.
--
-------------------------------------------------------------------------------------

module Music.Pitch.Ambitus where

import Data.Interval hiding (Interval, interval)
import qualified Data.Interval as I
import Control.Lens

-- | An ambitus is a closed interval (in the mathematical sense).
-- 
-- Also known as /range/ or /tessitura/, this type can be used to restrict the
-- range of a melody, chord or other pitch container.
-- 
-- It is also used in @music-parts@ to represent the range of instruments.
-- 
newtype Ambitus a = Ambitus { getAmbitus :: (I.Interval a) }

instance Wrapped (Ambitus a) where
  type Unwrapped (Ambitus a) = I.Interval a
  _Wrapped' = iso getAmbitus Ambitus
instance Rewrapped (Ambitus a) (Ambitus b)

instance (Show a, Num a, Ord a) => Show (Ambitus a) where
  show a = show (a^.from ambitus) ++ "^.ambitus"

ambitus :: (Num a, Ord a) => Iso' (a, a) (Ambitus a)
ambitus = iso toA unA . _Unwrapped
  where
    toA = (\(m, n) -> (I.<=..<=) (Finite m) (Finite n))
    unA a = case (I.lowerBound a, I.upperBound a) of
      (Finite m, Finite n) -> (m, n)