module Theory exposing (..) import Array exposing (Array) import Dict exposing (Dict) import List.Extra import Maybe.Extra import Misc {-| Notes are the individuals sounds that we use to create music. Think: "do re mi fa so la ti do". Note: Technically a "C-sharp" is also a "D-flat", but I will model accidentals (i.e. sharps and flats) as sharps and represent the ambiguity when I render the underlying state of the application. Note: There are "notes" like A, B, D-flat, and then there are notes like "middle C", also denoted in scientific pitch notation as C4. I'm unsure of what to call each of these, and my application does not model scientific pitch notation yet, so these non-scientific pitch denote values are "notes" for now. -} type Note = C1 | C_sharp1 | D1 | D_sharp1 | E1 | F1 | F_sharp1 | G1 | G_sharp1 | A1 | A_sharp1 | B1 | C2 | C_sharp2 | D2 | D_sharp2 | E2 | F2 | F_sharp2 | G2 | G_sharp2 | A2 | A_sharp2 | B2 | C3 | C_sharp3 | D3 | D_sharp3 | E3 | F3 | F_sharp3 | G3 | G_sharp3 | A3 | A_sharp3 | B3 | C4 | C_sharp4 | D4 | D_sharp4 | E4 | F4 | F_sharp4 | G4 | G_sharp4 | A4 | A_sharp4 | B4 | C5 | C_sharp5 | D5 | D_sharp5 | E5 | F5 | F_sharp5 | G5 | G_sharp5 | A5 | A_sharp5 | B5 | C6 | C_sharp6 | D6 | D_sharp6 | E6 | F6 | F_sharp6 | G6 | G_sharp6 | A6 | A_sharp6 | B6 | C7 | C_sharp7 | D7 | D_sharp7 | E7 | F7 | F_sharp7 | G7 | G_sharp7 | A7 | A_sharp7 | B7 | C8 {-| I alluded to this concept in the Note type's documentation. These are the letters of notes. For instance C2, C3, C4 are all instances of C. -} type PitchClass = C | C_sharp | D | D_sharp | E | F | F_sharp | G | G_sharp | A | A_sharp | B {-| Encode whether you are traversing "up" or "down" intervals -} type StepDirection = Up | Down {-| One can measure the difference between between notes using intervals. -} type Interval = Half | NHalves Int | Whole | MajorThird | MinorThird | PerfectFifth | AugmentedFifth | DiminishedFifth | MajorSeventh | DominantSeventh {-| Add direction to a distance on the piano. -} type alias IntervalVector = { interval : Interval , direction : StepDirection } {-| A bundle of notes which are usually, but not necessarily harmonious. -} type alias Chord = { note : Note , chordType : ChordType , chordInversion : ChordInversion } {-| Many possible chords exist. This type encodes the possibilities. I am tempted to model these in a more "DRY" way, but I worry that this abstraction may cause more problems than it solves. -} type ChordType = Major | Sus2 | Sus4 | Major7 | MajorDominant7 | Minor | MinorMajor7 | MinorDominant7 | Augmented | AugmentedDominant7 | Diminished | DiminishedDominant7 | DiminishedMajor7 {-| On a piano, a triad can be played three ways. As a rule-of-thumb, The number of ways a pianist can play a chord is equal to the number of notes in the chord itself. -} type ChordInversion = Root | First | Second {-| Whether a given note is a white key or a black key. -} type KeyClass = Natural | Accidental {-| Songs are written in one or more keys, which define the notes and therefore chords that harmonize with one another. -} type alias Key = { pitchClass : PitchClass , mode : Mode } {-| We create "scales" by enumerating the notes of a given key. These keys are defined by the "tonic" note and the "mode". I thought about including Ionian, Dorian, Phrygian, etc., but in the I would like to avoid over-abstracting this early on, so I'm going to err on the side of overly concrete until I have a better idea of the extent of this project. -} type Mode = BluesMode | MajorMode | MinorMode type alias NoteMetadata = { note : Note , label : String , pitchClass : PitchClass , natural : Bool } {-| An integer representing which note in a given scale to play. -} type alias ScaleDegree = Int {-| Returns the Note in the cental octave of the piano for a given PitchClass. For example, C4 -- or "middle C" -- for C. -} noteInCentralOctave : PitchClass -> Note noteInCentralOctave pitchClass = case pitchClass of C -> C4 C_sharp -> C_sharp4 D -> D4 D_sharp -> D_sharp4 E -> E4 F -> F4 F_sharp -> F_sharp4 G -> G4 G_sharp -> G_sharp4 A -> A4 A_sharp -> A_sharp4 B -> B4 {-| Return the human-readable version of a chord inversion. -} inversionName : ChordInversion -> String inversionName inversion = case inversion of Root -> "Root" First -> "First" Second -> "Second" {-| Return the human-readable version of a chord type. -} chordTypeName : ChordType -> String chordTypeName chordType = case chordType of Major -> "major" Sus2 -> "suspended 2" Sus4 -> "suspended 4" Major7 -> "major 7th" MajorDominant7 -> "major dominant 7th" Minor -> "minor" MinorMajor7 -> "minor major 7th" MinorDominant7 -> "minor dominant 7th" Augmented -> "augmented" AugmentedDominant7 -> "augmented dominant 7th" Diminished -> "diminished" DiminishedDominant7 -> "diminished dominant 7th" DiminishedMajor7 -> "diminished major 7th" {-| Return the note that is one half step away from `note` in the direction, `dir`. In the case of stepping up or down from the end of the piano, this returns a Maybe. -} halfStep : StepDirection -> Note -> Maybe Note halfStep dir note = let everyNote = notesFromRange C2 C8 in case dir of Up -> Misc.comesAfter note everyNote Down -> Misc.comesBefore note everyNote {-| Return a list of steps to take away from the root note to return back to the root note for a given mode. -} intervalsForMode : Mode -> List IntervalVector intervalsForMode mode = let up x = { direction = Up, interval = x } down x = { direction = Down, interval = x } in case mode of MajorMode -> List.map up [ Whole, Whole, Half, Whole, Whole, Whole ] MinorMode -> List.map up [ Whole, Half, Whole, Whole, Half, Whole ] BluesMode -> List.map up [ MinorThird, Whole, Half, Half, MinorThird ] {-| Return a list of the intervals that a chord. Each interval measures the distance away from the root-note of the chord. -} intervalsForChordType : ChordType -> ChordInversion -> List IntervalVector intervalsForChordType chordType chordInversion = let up x = { direction = Up, interval = x } down x = { direction = Down, interval = x } in case ( chordType, chordInversion ) of -- Major ( Major, Root ) -> [ up MajorThird, up PerfectFifth ] ( Major, First ) -> [ down (NHalves 5), down (NHalves 8) ] ( Major, Second ) -> [ down (NHalves 5), up MajorThird ] -- Sus2 ( Sus2, Root ) -> [ up Whole, up PerfectFifth ] ( Sus2, First ) -> [ down (NHalves 10), down (NHalves 5) ] ( Sus2, Second ) -> [ down (NHalves 5), up Whole ] -- Sus4 ( Sus4, Root ) -> [ up (NHalves 5), up PerfectFifth ] ( Sus4, First ) -> [ down (NHalves 7), down (NHalves 5) ] ( Sus4, Second ) -> [ down (NHalves 5), up (NHalves 5) ] -- Major7 ( Major7, Root ) -> [ up MajorThird, up PerfectFifth, up MajorSeventh ] ( Major7, First ) -> down Half :: intervalsForChordType Major chordInversion ( Major7, Second ) -> down Half :: intervalsForChordType Major chordInversion -- MajorDominant7 ( MajorDominant7, Root ) -> up DominantSeventh :: intervalsForChordType Major chordInversion ( MajorDominant7, First ) -> down Whole :: intervalsForChordType Major chordInversion ( MajorDominant7, Second ) -> down Whole :: intervalsForChordType Major chordInversion -- Minor ( Minor, Root ) -> [ up MinorThird, up PerfectFifth ] ( Minor, First ) -> [ down (NHalves 5), down (NHalves 9) ] ( Minor, Second ) -> [ down (NHalves 5), up MinorThird ] -- MinorMajor7 ( MinorMajor7, Root ) -> up MajorSeventh :: intervalsForChordType Minor chordInversion ( MinorMajor7, First ) -> down Half :: intervalsForChordType Minor chordInversion ( MinorMajor7, Second ) -> down Half :: intervalsForChordType Minor chordInversion -- MinorDominant7 ( MinorDominant7, Root ) -> up DominantSeventh :: intervalsForChordType Minor chordInversion ( MinorDominant7, First ) -> down Whole :: intervalsForChordType Minor chordInversion ( MinorDominant7, Second ) -> down Whole :: intervalsForChordType Minor chordInversion -- Augmented ( Augmented, Root ) -> [ up MajorThird, up AugmentedFifth ] ( Augmented, First ) -> [ down (NHalves 8), down (NHalves 4) ] ( Augmented, Second ) -> [ down (NHalves 4), up MajorThird ] -- AugmentedDominant7 ( AugmentedDominant7, Root ) -> up DominantSeventh :: intervalsForChordType Augmented chordInversion ( AugmentedDominant7, First ) -> down Whole :: intervalsForChordType Augmented chordInversion ( AugmentedDominant7, Second ) -> down Whole :: intervalsForChordType Augmented chordInversion -- Diminished ( Diminished, Root ) -> [ up MinorThird, up DiminishedFifth ] ( Diminished, First ) -> [ down (NHalves 6), down (NHalves 9) ] ( Diminished, Second ) -> [ down (NHalves 6), up MinorThird ] -- DiminishedDominant7 ( DiminishedDominant7, Root ) -> up DominantSeventh :: intervalsForChordType Diminished chordInversion ( DiminishedDominant7, First ) -> down Whole :: intervalsForChordType Diminished chordInversion ( DiminishedDominant7, Second ) -> down Whole :: intervalsForChordType Diminished chordInversion -- DiminishedMajor7 ( DiminishedMajor7, Root ) -> up MajorSeventh :: intervalsForChordType Diminished chordInversion ( DiminishedMajor7, First ) -> down Half :: intervalsForChordType Diminished chordInversion ( DiminishedMajor7, Second ) -> down Half :: intervalsForChordType Diminished chordInversion {-| Return the note in the direction, `dir`, away from `note` `s` intervals -} step : IntervalVector -> Note -> Maybe Note step { direction, interval } note = let doStep int = step { direction = direction, interval = int } in case interval of Half -> halfStep direction note NHalves n -> List.repeat n { direction = direction , interval = Half } |> (\x -> walkNotes x note) |> Maybe.andThen (List.reverse >> List.head) Whole -> note |> doStep Half |> Maybe.andThen (doStep Half) MinorThird -> note |> doStep Whole |> Maybe.andThen (doStep Half) MajorThird -> note |> doStep Whole |> Maybe.andThen (doStep Whole) PerfectFifth -> note |> doStep MajorThird |> Maybe.andThen (doStep MinorThird) AugmentedFifth -> note |> doStep PerfectFifth |> Maybe.andThen (doStep Half) DiminishedFifth -> note |> doStep MajorThird |> Maybe.andThen (doStep Whole) MajorSeventh -> note |> doStep PerfectFifth |> Maybe.andThen (doStep MajorThird) DominantSeventh -> note |> doStep PerfectFifth |> Maybe.andThen (doStep MinorThird) {-| Returns a list of all of the notes away from a give `note`. - The 0th element is applied to `note`. - The 1st element is applied to the result of the previous operation. - The 2nd element is applied to the result of the previous operation. - and so on...until all of the `steps` are exhausted. In the case where applying any of the steps would result in running off of either edge of the piano, this function returns a Nothing. -} walkNotes : List IntervalVector -> Note -> Maybe (List Note) walkNotes steps note = doWalkNotes steps note [] |> Maybe.map List.reverse {-| Recursive helper for `walkNotes`. -} doWalkNotes : List IntervalVector -> Note -> List Note -> Maybe (List Note) doWalkNotes steps note result = case steps of [] -> Just (note :: result) s :: rest -> case step s note of Just x -> doWalkNotes rest x (note :: result) Nothing -> Nothing {-| Return the KeyClass for a given `note`. -} keyClass : Note -> KeyClass keyClass note = if isNatural note then Natural else Accidental {-| Return the PitchClass for a given note. -} classifyNote : Note -> PitchClass classifyNote note = note |> getNoteMetadata |> .pitchClass {-| Return a list of the notes that comprise a `chord` -} notesForChord : Chord -> Maybe (List Note) notesForChord { note, chordType, chordInversion } = intervalsForChordType chordType chordInversion |> List.map (\interval -> step interval note) |> Maybe.Extra.combine |> Maybe.map (\notes -> note :: notes) {-| Return the scale for a given `key`. -} notesForKey : Key -> List Note notesForKey { pitchClass, mode } = let origin = noteInCentralOctave pitchClass in case walkNotes (intervalsForMode mode) origin of -- We should never hit the Nothing case here. Nothing -> [] Just scale -> scale {-| Return true if `note` is a black key. -} isAccidental : Note -> Bool isAccidental note = note |> isNatural |> not {-| Return true if `note` is a white key. -} isNatural : Note -> Bool isNatural note = note |> getNoteMetadata |> .natural {-| Return a list of all of the notes that we know about. Only return the notes within the range `start` and `end`. -} notesFromRange : Note -> Note -> List Note notesFromRange start end = noteMetadata |> Array.toList |> List.map .note |> List.Extra.dropWhile ((/=) start) |> List.Extra.takeWhile ((/=) end) {-| Return a list of all of the chord inversions about which we know. -} allInversions : List ChordInversion allInversions = [ Root, First, Second ] {-| Return a list of all of the chord types about which we know. -} allChordTypes : List ChordType allChordTypes = [ Major , Sus2 , Sus4 , Major7 , MajorDominant7 , Minor , MinorMajor7 , MinorDominant7 , Augmented , AugmentedDominant7 , Diminished , DiminishedDominant7 , DiminishedMajor7 ] {-| Return a list of all of the key modes about which we know. -} allModes : List Mode allModes = [ MajorMode, MinorMode, BluesMode ] {-| Return a list of all of the keys about which we know. -} allKeys : List Key allKeys = allPitchClasses |> List.Extra.andThen (\pitchClass -> allModes |> List.Extra.andThen (\mode -> [ { pitchClass = pitchClass , mode = mode } ] ) ) {-| Return an array of every note on a piano. Note: Currently this piano has 85 keys, but modern pianos have 88 keys. I would prefer to have 88 keys, but it's not urgent. -} noteMetadata : Array NoteMetadata noteMetadata = Array.fromList [ { note = A1, label = "A1", pitchClass = A, natural = True } , { note = A_sharp1, label = "A♯/B♭1", pitchClass = A_sharp, natural = False } , { note = B1, label = "B1", pitchClass = B, natural = True } , { note = C1, label = "C1", pitchClass = C, natural = True } , { note = C_sharp1, label = "C♯/D♭1", pitchClass = C_sharp, natural = False } , { note = D1, label = "D1", pitchClass = D, natural = True } , { note = D_sharp1, label = "D♯/E♭1", pitchClass = D_sharp, natural = False } , { note = E1, label = "E1", pitchClass = E, natural = True } , { note = F1, label = "F1", pitchClass = F, natural = True } , { note = F_sharp1, label = "F♯/G♭1", pitchClass = F_sharp, natural = False } , { note = G1, label = "G1", pitchClass = G, natural = True } , { note = G_sharp1, label = "G♯/A♭1", pitchClass = G, natural = False } , { note = A2, label = "A2", pitchClass = A, natural = True } , { note = A_sharp2, label = "A♯/B♭2", pitchClass = A_sharp, natural = False } , { note = B2, label = "B2", pitchClass = B, natural = True } , { note = C2, label = "C2", pitchClass = C, natural = True } , { note = C_sharp2, label = "C♯/D♭2", pitchClass = C_sharp, natural = False } , { note = D2, label = "D2", pitchClass = D, natural = True } , { note = D_sharp2, label = "D♯/E♭2", pitchClass = D_sharp, natural = False } , { note = E2, label = "E2", pitchClass = E, natural = True } , { note = F2, label = "F2", pitchClass = F, natural = True } , { note = F_sharp2, label = "F♯/G♭2", pitchClass = F_sharp, natural = False } , { note = G2, label = "G2", pitchClass = G, natural = True } , { note = G_sharp2, label = "G♯/A♭2", pitchClass = G, natural = False } , { note = A3, label = "A3", pitchClass = A, natural = True } , { note = A_sharp3, label = "A♯/B♭3", pitchClass = A_sharp, natural = False } , { note = B3, label = "B3", pitchClass = B, natural = True } , { note = C3, label = "C3", pitchClass = C, natural = True } , { note = C_sharp3, label = "C♯/D♭3", pitchClass = C_sharp, natural = False } , { note = D3, label = "D3", pitchClass = D, natural = True } , { note = D_sharp3, label = "D♯/E♭3", pitchClass = D_sharp, natural = False } , { note = E3, label = "E3", pitchClass = E, natural = True } , { note = F3, label = "F3", pitchClass = F, natural = True } , { note = F_sharp3, label = "F♯/G♭3", pitchClass = F_sharp, natural = False } , { note = G3, label = "G3", pitchClass = G, natural = True } , { note = G_sharp3, label = "G♯/A♭3", pitchClass = G, natural = False } , { note = A4, label = "A4", pitchClass = A, natural = True } , { note = A_sharp4, label = "A♯/B♭4", pitchClass = A_sharp, natural = False } , { note = B4, label = "B4", pitchClass = B, natural = True } , { note = C4, label = "C4", pitchClass = C, natural = True } , { note = C_sharp4, label = "C♯/D♭4", pitchClass = C_sharp, natural = False } , { note = D4, label = "D4", pitchClass = D, natural = True } , { note = D_sharp4, label = "D♯/E♭4", pitchClass = D_sharp, natural = False } , { note = E4, label = "E4", pitchClass = E, natural = True } , { note = F4, label = "F4", pitchClass = F, natural = True } , { note = F_sharp4, label = "F♯/G♭4", pitchClass = F_sharp, natural = False } , { note = G4, label = "G4", pitchClass = G, natural = True } , { note = G_sharp4, label = "G♯/A♭4", pitchClass = G, natural = False } , { note = A5, label = "A5", pitchClass = A, natural = True } , { note = A_sharp5, label = "A♯/B♭5", pitchClass = A_sharp, natural = False } , { note = B5, label = "B5", pitchClass = B, natural = True } , { note = C5, label = "C5", pitchClass = C, natural = True } , { note = C_sharp5, label = "C♯/D♭5", pitchClass = C_sharp, natural = False } , { note = D5, label = "D5", pitchClass = D, natural = True } , { note = D_sharp5, label = "D♯/E♭5", pitchClass = D_sharp, natural = False } , { note = E5, label = "E5", pitchClass = E, natural = True } , { note = F5, label = "F5", pitchClass = F, natural = True } , { note = F_sharp5, label = "F♯/G♭5", pitchClass = F_sharp, natural = False } , { note = G5, label = "G5", pitchClass = G, natural = True } , { note = G_sharp5, label = "G♯/A♭5", pitchClass = G, natural = False } , { note = A6, label = "A6", pitchClass = A, natural = True } , { note = A_sharp6, label = "A♯/B♭6", pitchClass = A_sharp, natural = False } , { note = B6, label = "B6", pitchClass = B, natural = True } , { note = C6, label = "C6", pitchClass = C, natural = True } , { note = C_sharp6, label = "C♯/D♭6", pitchClass = C_sharp, natural = False } , { note = D6, label = "D6", pitchClass = D, natural = True } , { note = D_sharp6, label = "D♯/E♭6", pitchClass = D_sharp, natural = False } , { note = E6, label = "E6", pitchClass = E, natural = True } , { note = F6, label = "F6", pitchClass = F, natural = True } , { note = F_sharp6, label = "F♯/G♭6", pitchClass = F_sharp, natural = False } , { note = G6, label = "G6", pitchClass = G, natural = True } , { note = G_sharp6, label = "G♯/A♭6", pitchClass = G, natural = False } , { note = A7, label = "A7", pitchClass = A, natural = True } , { note = A_sharp7, label = "A♯/B♭7", pitchClass = A_sharp, natural = False } , { note = B7, label = "B7", pitchClass = B, natural = True } , { note = C7, label = "C7", pitchClass = C, natural = True } , { note = C_sharp7, label = "C♯/D♭7", pitchClass = C_sharp, natural = False } , { note = D7, label = "D7", pitchClass = D, natural = True } , { note = D_sharp7, label = "D♯/E♭7", pitchClass = D_sharp, natural = False } , { note = E7, label = "E7", pitchClass = E, natural = True } , { note = F7, label = "F7", pitchClass = F, natural = True } , { note = F_sharp7, label = "F♯/G♭7", pitchClass = F_sharp, natural = False } , { note = G7, label = "G7", pitchClass = G, natural = True } , { note = G_sharp7, label = "G♯/A♭7", pitchClass = G, natural = False } , { note = C8, label = "C8", pitchClass = C, natural = True } ] {-| Mapping of note data to commonly needed metadata for that note. -} getNoteMetadata : Note -> NoteMetadata getNoteMetadata note = case Array.get (noteAsNumber note) noteMetadata of Just metadata -> metadata -- This case should never hit, so we just return C1 to appease the -- compiler. Nothing -> getNoteMetadata C1 {-| Return the numeric representation of `note` to ues when comparing two notes. -} noteAsNumber : Note -> Int noteAsNumber note = let result = noteMetadata |> Array.toList |> List.indexedMap Tuple.pair |> Misc.find (\( _, x ) -> x.note == note) in case result of Nothing -> 0 Just ( i, _ ) -> i {-| Return true if all of the notes that comprise `chord` can be played on a piano whose keys begin at `start` and end at `end`. -} chordWithinRange : Note -> Note -> Chord -> Bool chordWithinRange start end chord = case notesForChord chord of Just notes -> let nums = List.map noteAsNumber notes lo = List.minimum nums |> Maybe.withDefault (noteAsNumber start) hi = List.maximum nums |> Maybe.withDefault (noteAsNumber end) in lo >= noteAsNumber start && hi < noteAsNumber end Nothing -> False {-| Return a list of all of the pitch classes that we know about. -} allPitchClasses : List PitchClass allPitchClasses = [ C , C_sharp , D , D_sharp , E , F , F_sharp , G , G_sharp , A , A_sharp , B ] {-| Return a list of all of the chords that we know about. Only create chords from the range of notes delimited by the range `start` and `end`. -} allChords : { start : Note , end : Note , inversions : List ChordInversion , chordTypes : List ChordType , pitchClasses : List PitchClass } -> List Chord allChords { start, end, inversions, chordTypes, pitchClasses } = let notes = notesFromRange start end |> List.filter (\note -> List.member (classifyNote note) pitchClasses) in notes |> List.Extra.andThen (\note -> chordTypes |> List.Extra.andThen (\chordType -> inversions |> List.Extra.andThen (\inversion -> [ { note = note , chordType = chordType , chordInversion = inversion } ] ) ) ) |> List.filter (chordWithinRange start end) {-| Return a human-readable format of `note`. -} viewNote : Note -> String viewNote note = note |> getNoteMetadata |> .label {-| Return a human-readable format of `chord`. -} viewChord : Chord -> String viewChord { note, chordType, chordInversion } = viewPitchClass (classifyNote note) ++ " " ++ chordTypeName chordType ++ " " ++ inversionName chordInversion ++ " position" {-| Return a human-readable format of `pitchClass`. -} viewPitchClass : PitchClass -> String viewPitchClass pitchClass = case pitchClass of C -> "C" C_sharp -> "C♯/D♭" D -> "D" D_sharp -> "D♯/E♭" E -> "E" F -> "F" F_sharp -> "F♯/G♭" G -> "G" G_sharp -> "G♯/A♭" A -> "A" A_sharp -> "A♯/B♭" B -> "B" viewMode : Mode -> String viewMode mode = case mode of MajorMode -> "major" MinorMode -> "minor" BluesMode -> "blues" {-| Return the human-readable format of `key`. -} viewKey : Key -> String viewKey { pitchClass, mode } = viewPitchClass pitchClass ++ " " ++ viewMode mode {-| Returns a pairing of a scale-degree to the type of chord at that scale degree. -} practiceChordsForMode : Mode -> Dict ScaleDegree ChordType practiceChordsForMode mode = case mode of MajorMode -> Dict.fromList [ ( 1, Major ) , ( 2, Minor ) , ( 3, Minor ) , ( 4, Major ) , ( 5, Major ) , ( 6, Minor ) , ( 7, Diminished ) ] MinorMode -> Dict.fromList [ ( 1, Minor ) , ( 2, Diminished ) , ( 3, Major ) , ( 4, Minor ) , ( 5, Minor ) , ( 6, Major ) , ( 7, Major ) ] BluesMode -> Dict.fromList [ ( 1, MajorDominant7 ) -- While many refer to the blues progression as a I-IV-V, the IV -- chord is really a MajorDominant7 made from the third scale -- degree. , ( 3, MajorDominant7 ) , ( 5, MajorDominant7 ) ] {-| Returns a list of chords for a particular `key`. -} chordsForKey : Key -> List Chord chordsForKey key = let chords = practiceChordsForMode key.mode in notesForKey key |> List.indexedMap (\i note -> case Dict.get (i + 1) chords of Nothing -> Nothing Just chordType -> Just (allInversions |> List.Extra.andThen (\inversion -> [ { note = note , chordType = chordType , chordInversion = inversion } ] ) ) ) |> Maybe.Extra.values |> List.concat