Absolute.hs

{-# LANGUAGE GeneralizedNewtypeDeriving #-}

-------------------------------------------------------------------------------------
-- |
-- Copyright   : (c) Hans Hoglund 2012
--
-- License     : BSD-style
--
-- Maintainer  : hans@hanshoglund.se
-- Stability   : experimental
-- Portability : portable
--
-- Absolute representation of loudness, or dynamics.
--
-- The canonical loudness representation is 'Amplitude'. For conversion, see 'HasAmplitude'.
--
-------------------------------------------------------------------------------------

module Music.Dynamics.Absolute (
        Amplitude(..),
        Decibel,
        Bel,
        HasAmplitude(..),
        decibel,
        bel,
) where

import Data.Maybe
import Data.Either
import Data.Semigroup
import Control.Monad
import Control.Applicative

-- |
-- Amplitude level, where @0@ is silent and @1@ is peak.
--
newtype Amplitude = Amplitude { getAmplitude :: Double }
    deriving (Read, Show, Eq, Enum, Num, Ord, Fractional, Floating, Real, RealFrac)

-- |
-- A logarithmic representation of amplitude such that
--
-- >
-- > x * 10 = amplitude (bel x + 1)
--
newtype Bel = Bel { getBel :: Amplitude }
    deriving (Read, Show, Eq, Enum, Num, Ord, Fractional, Floating, Real, RealFrac)

-- |
-- A logarithmic representation of amplitude such that
--
-- >
-- > x * 10 = amplitude (decibel x + 10)
--
newtype Decibel = Decibel { getDecibel :: Amplitude }
    deriving (Read, Show, Eq, Enum, Num, Ord, Fractional, Floating, Real, RealFrac)

instance Semigroup Amplitude    where (<>) = (*)
instance Semigroup Decibel      where (<>) = (+)
instance Semigroup Bel          where (<>) = (+)

instance Monoid Amplitude       where { mempty  = 1 ; mappend = (*) }
instance Monoid Decibel         where { mempty  = 0 ; mappend = (+) }
instance Monoid Bel         where { mempty  = 0 ; mappend = (+) }

class HasAmplitude a where
    amplitude :: a -> Amplitude

instance HasAmplitude Amplitude where
    amplitude = id

instance HasAmplitude Decibel where
    amplitude (Decibel f)   = (10/1) ** (f / 10)

instance HasAmplitude Bel where
    amplitude (Bel f)       = (10/1) ** (f / 1)

decibel :: HasAmplitude a => a -> Decibel
decibel a = Decibel $ logBase (10/1) (amplitude a) * 10

bel :: HasAmplitude a => a -> Bel
bel a = Bel $ logBase (10/1) (amplitude a) * 1