Add Pitch.Hz module for working with musical pitches in Hertz

haskMus.cabal

@@ -29,6 +29,7 @@ library
         Pitch.Parser
         Pitch.Pitch
         Pitch.QuasiQuoter
+        Pitch.Hz
         Rtm.Common
         Rtm.Parser
         Rtm.QuasiQuoter

src/Pitch/Hz.hs

@@ -0,0 +1,33 @@
+module Pitch.Hz where
+
+-- | The Pitch.Hz module provides types and functions to work with musical pitches in terms of semitones and Hertz.
+
+-- `newtype` wrappers for `Semitone` and `Hz` provide type safety.
+newtype Semitone = Semitone {unSemitone :: Double} deriving (Show, Eq, Num, Ord)
+newtype Hz = Hz {unHz :: Double} deriving (Show, Eq, Num, Ord)
+
+-- Standard pitch (A4) definition in Hertz.
+pitchStandard :: Hz
+pitchStandard = Hz 440.0
+
+-- Convert a `Semitone` or `Double` representing semitones to `Hz`.
+-- Works for both integral and fractional semitones.
+semitoneToHz :: Double -> Hz
+semitoneToHz n = pitchStandard * Hz (2 ** (n / 12.0))
+
+-- Convert a frequency in `Hz` to its equivalent in semitones relative to `pitchStandard`.
+-- Calculated using the logarithm base 2.
+hzToDouble :: Hz -> Double
+hzToDouble (Hz hz) = 12.0 * logBase 2 (hz / unHz pitchStandard)
+
+-- Use `hzToDouble` to convert Hz to `Semitone`.
+hzToSemitone :: Hz -> Semitone
+hzToSemitone = Semitone . hzToDouble
+
+-- Directly retrieve the underlying `Double` from a `Semitone`.
+semitoneToDouble :: Semitone -> Double
+semitoneToDouble (Semitone n) = n
+
+-- Wrap a `Double` as a `Semitone`.
+doubleToSemitone :: Double -> Semitone
+doubleToSemitone = Semitone