Refactor Hz and Semitone types

src/Pitch/Hz.hs

@@ -3,31 +3,56 @@ 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)
+newtype Semitone = Semitone {unSemitone :: Double} deriving (Eq, Num, Ord)
+newtype Hz = Hz {unHz :: Double} deriving (Eq, Num, Ord)
 
--- Standard pitch (A4) definition in Hertz.
+instance Show Semitone where
+  show (Semitone n) = show n <> " Semitone(s)"
+
+instance Show Hz where
+  show (Hz hz) = show hz <> " Hz"
+
+
+-- | Standard pitch (A4) definition in Hertz.
+-- 
+-- >>> pitchStandard
+-- 440.0 Hz
 pitchStandard :: Hz
 pitchStandard = Hz 440.0
 
--- Convert a `Semitone` or `Double` representing semitones to `Hz`.
+-- | Convert a `Semitone` or `Double` representing semitones to `Hz`.
 -- Works for both integral and fractional semitones.
+--
+-- >>> semitoneToHz 12
+-- 880.0 Hz
 semitoneToHz :: Double -> Hz
 semitoneToHz n = pitchStandard * Hz (2 ** (n / 12.0))
 
--- Convert a frequency in `Hz` to its equivalent in semitones relative to `pitchStandard`.
+-- | Convert a frequency in `Hz` to its equivalent in semitones relative to `pitchStandard`.
 -- Calculated using the logarithm base 2.
+--
+-- >>> hzToDouble (Hz 880.0)
+-- 12.0
 hzToDouble :: Hz -> Double
 hzToDouble (Hz hz) = 12.0 * logBase 2 (hz / unHz pitchStandard)
 
--- Use `hzToDouble` to convert Hz to `Semitone`.
+-- | Use `hzToDouble` to convert Hz to `Semitone`.
+--
+-- >>> hzToSemitone (Hz 880.0)
+-- Semitone {unSemitone = 12.0}
 hzToSemitone :: Hz -> Semitone
 hzToSemitone = Semitone . hzToDouble
 
--- Directly retrieve the underlying `Double` from a `Semitone`.
+-- | Directly retrieve the underlying `Double` from a `Semitone`.
+--
+-- >>> semitoneToDouble (Semitone 12.0)
+-- 12.0
 semitoneToDouble :: Semitone -> Double
 semitoneToDouble (Semitone n) = n
 
--- Wrap a `Double` as a `Semitone`.
+-- | Wrap a `Double` as a `Semitone`.
+--
+-- >>> doubleToSemitone 12.0
+-- Semitone {unSemitone = 12.0}
 doubleToSemitone :: Double -> Semitone
 doubleToSemitone = Semitone