WIP: Pitches, Voicings, and Lead Sheets Brainstorm

src/Brainstorm.hs

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+-- Placeholder code
+newtype Note = Note {getN :: Int}
+newtype Interval = Interval {getI :: Int}
+newtype Chord = Chord {getC :: Int}
+
+
+-- | We might wanna make a type class of things convertible
+-- to a frequency value. For this simple type, it's just the one field.
+--
+-- All of these datatypes are also places where we can return distances
+-- given 2 values. For pitch, we can return 3 types of distances; for MIDI, 2;
+-- for frequencies, 1.
+--
+-- Frequency as a number of hertz.
+newtype Frequency = Frequency {hertz :: Int}
+
+-- | Smart constructor for frequency, checks for i > 0.
+frequencyFrom :: Int -> Frequency
+frequencyFrom i = undefined
+
+-- | A MIDI note has a number.
+newtype MIDI = MIDI {getNum :: Int}
+
+-- | Smart constructor for MIDI notes, checks for 0 <= i < 128.
+midiFrom :: Int -> Maybe MIDI
+midiFrom = undefined
+
+-- | Convert a MIDI to a frequency.
+midiToFreq :: MIDI -> Frequency
+midiToFreq = undefined
+
+-- | Transpose a MIDI note by some amount. We could also use intervals here if needed.
+transposeM :: MIDI -> Int -> MIDI
+transposeM = undefined
+
+-- | Pitch in scientific pitch notation (SPN)
+data Pitch = Pitch {getNote :: Note, octave :: Int}
+
+-- | Smart constructor for Pitch
+pitchFrom :: Note -> Int -> Pitch
+pitchFrom = undefined
+
+-- | Convert pitch to a MIDI
+pitchToMIDI :: Pitch -> MIDI
+pitchToMIDI = undefined
+
+-- | Convert pitch to a frequency
+pitchToFreq :: Pitch -> Frequency
+pitchToFreq = midiToFreq . pitchToMIDI
+
+-- | Transpose a pitch by some interval. We could also use integers here if needed.
+transposeP :: Pitch -> Interval -> Pitch
+transposeP = undefined
+
+-- | Convert MIDI to the simplest possible pitches (i.e. using the fewest accidentals)
+midiToPitches :: MIDI -> [Pitch]
+midiToPitches = undefined
+
+-- | A chord with a bass note (not the best name, but hey) that can be specified or not
+data ChordWithBass = ChordWithBass {getChord :: Chord,
+                                    getBass :: Maybe Note}
+
+-- | Checks whether the voicing is in root position (i.e. bass note is chord root)
+isRootPosition :: ChordWithBass -> Bool
+isRootPosition = undefined
+
+-- | A voicing is a chord with a bass note potentially specified, and a list of pitches.
+data Voicing = Voicing {getCWB :: ChordWithBass,
+                        getPitches :: [Pitch]}
+
+-- | Smart constructor for voicings.
+voicingFrom :: ChordWithBass -> [Pitch] -> Maybe Voicing
+voicingFrom = undefined
+
+-- | There will be a number of such functions for different voicing strategies.
+generateVoicing :: ChordWithBass -> [Pitch]
+generateVoicing = undefined
+
+-- | Given two voicings, returns the voice leading distance between them in half steps.
+voiceLeadingDistance :: Voicing -> Voicing -> Int
+voiceLeadingDistance = undefined
+
+-- | Given a voicing and a chord we want to reach, find the voicing with the minimum voice leading distance.
+voiceLeadFromTo :: Voicing -> ChordWithBass -> Voicing
+voiceLeadFromTo = undefined
+
+newtype Progression = Progression {getChords :: [ChordWithBass]}
+
+-- | Given a chord progression and an initial voicing, voice lead each successive chord
+-- to minimize voice leading distance from the previous one.
+progressionToVoicings :: Progression -> Voicing -> [Voicing]
+progressionToVoicings = undefined
+
+-- | Tritone sub an entire progression by subbing each individual chord.
+-- We can come up with a number of different substitutions that operate on
+-- the whole progression rather than just individual chords.
+tritoneSub :: Progression -> Progression
+tritoneSub = undefined
+
+-- | Given a progression, a number of beats per bar, and a list of
+-- durations (in number of beats), i.e. one duration per chord in progression,
+-- we can create a lead sheet datatype.
+data LeadSheet = LeadSheet {getProg :: Progression,
+                            getMeter :: Int,
+                            getDurations :: [Int]}
+