Properly support chord inversions

While I did change a lot of functionality, I also ran `elm-format` across the
codebase, which makes these changes a bit noisy.

Here is the TL;DR:
- Properly support chord inversions
- Ensure that the piano styling changes dynamically when I change the variables
  like `naturalWidth`
- Add start and end notes to define the size of the piano and which chords we
  create
- Support elm-format and run it across entire project
- Debug Misc.comesBefore
- Introduce a ChordInspector and debugger

TODO: Ensure that we only generate chords where all of the notes can be rendered
on the displayed keys.

TODO: Add preferences panel, so that I can do things like "Practice blues chords
in C and E with chord substitutions."

1 files changed, 1118 insertions, 196 deletions

diff --git a/website/sandbox/chord-drill-sergeant/src/Theory.elm b/website/sandbox/chord-drill-sergeant/src/Theory.elm
index 9e84aeac4c4e..4dc4c3e511e8 100644
--- a/website/sandbox/chord-drill-sergeant/src/Theory.elm
+++ b/website/sandbox/chord-drill-sergeant/src/Theory.elm
@@ -1,8 +1,10 @@
 module Theory exposing (..)
 
 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".
 
@@ -13,102 +15,259 @@ 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
+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 NoteClass = 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
-              | Whole
-              | MajorThird
-              | MinorThird
-
-{-| A bundle of notes which are usually, but not necessarily harmonious. -}
+letters of notes. For instance C2, C3, C4 are all instances of C.
+-}
+type NoteClass
+    = 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
-  , chordPosition : ChordPosition
-  }
+    { 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
-               | Major7
-               | MajorDominant7
-               | Minor
-               | Minor7
-               | MinorDominant7
-               | Augmented
-               | Augmented7
-               | Diminished
-               | Diminished7
+may cause more problems than it solves.
+-}
+type ChordType
+    = Major
+    | 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 ChordPosition = First
-                   | Second
-                   | Third
-                   | Fourth
+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. -}
+chords that harmonize with one another.
+-}
 type alias Key =
-  { noteClass : NoteClass
-  , mode : Mode
-  }
+    { noteClass : NoteClass
+    , 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,
+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
+better idea of the extent of this project.
+-}
+type Mode
+    = BluesMode
+    | MajorMode
+    | MinorMode
+
+
+scaleDegree : Int -> Key -> NoteClass
+scaleDegree which { noteClass } =
+    case noteClass of
+        _ ->
+            C
+
 
 {-| Returns the Note in the cental octave of the piano for a given
-NoteClass. For example, C4 -- or "middle C" -- for C. -}
+NoteClass. For example, C4 -- or "middle C" -- for C.
+-}
 noteInCentralOctave : NoteClass -> Note
 noteInCentralOctave noteClass =
     case noteClass 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
+        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 note that is one half step away from `note` in the direction,
 `dir`.
@@ -117,155 +276,918 @@ Maybe.
 -}
 halfStep : StepDirection -> Note -> Maybe Note
 halfStep dir note =
-  case dir of
-    Up   -> Misc.comesAfter note allNotes
-    Down -> Misc.comesBefore note allNotes
+    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 Interval
+intervalsForMode : Mode -> List IntervalVector
 intervalsForMode mode =
-  case mode of
-    MajorMode -> [Whole, Whole, Half, Whole, Whole, Whole, Half]
-    MinorMode -> [Whole, Half, Whole, Whole, Half, Whole, Whole]
-    BluesMode -> [MinorThird, Whole, Half, Half, MinorThird]
-
-{-| Return a list of the intervals the comprise a chord -}
-intervalsForChordType : ChordType -> List Interval
-intervalsForChordType chordType =
-  case chordType of
-    Major          -> [MajorThird, MinorThird]
-    Major7         -> [MajorThird, MinorThird, MajorThird]
-    MajorDominant7 -> [MajorThird, MinorThird, MajorThird, MinorThird]
-    Minor          -> [MinorThird, MajorThird]
-    Minor7         -> [MinorThird, MajorThird, MajorThird]
-    MinorDominant7 -> [MinorThird, MajorThird, MajorThird, MinorThird]
-    Augmented      -> [MajorThird, MajorThird]
-    Augmented7     -> [MajorThird, MajorThird, Whole]
-    Diminished     -> [MinorThird, MinorThird]
-    Diminished7    -> [MinorThird, MinorThird, MinorThird]
-
-{-| Return the note in the direction, `dir`, away from `note` `s` intervals -}
-step : StepDirection -> Interval -> Note -> Maybe Note
-step dir s note =
-  let
-    doHalfStep = halfStep dir
-  in
-    case s of
-      Half ->
-          doHalfStep note
-      Whole ->
-          doHalfStep note
-              |> Maybe.andThen doHalfStep
-      MinorThird ->
-          doHalfStep note
-              |> Maybe.andThen doHalfStep
-              |> Maybe.andThen doHalfStep
-      MajorThird ->
-          doHalfStep note
-              |> Maybe.andThen doHalfStep
-              |> Maybe.andThen doHalfStep
-              |> Maybe.andThen doHalfStep
-
-{-| Returns a list of all of the notes up from a give `note`.
-
-In the case where applying all of the steps would result in running off of the
-edge of the piano, this function returns a Maybe. -}
-applySteps : List Interval -> Note -> Maybe (List Note)
+    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, Half ]
+
+        MinorMode ->
+            List.map up [ Whole, Half, Whole, Whole, Half, Whole, Whole ]
+
+        BluesMode ->
+            List.map up [ MinorThird, Whole, Half, Half, MinorThird ]
+
+
+{-| Return a list of the intervals the comprise 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 ]
+
+        -- 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 -> applySteps 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.
+
+-}
+applySteps : List IntervalVector -> Note -> Maybe (List Note)
 applySteps steps note =
     doApplySteps steps note [] |> Maybe.map List.reverse
 
-doApplySteps : List Interval -> Note -> List Note -> Maybe (List Note)
+
+doApplySteps : List IntervalVector -> Note -> List Note -> Maybe (List Note)
 doApplySteps steps note result =
     case steps of
-        [] -> Just (note::result)
-        s::rest ->
-            case step Up s note of
-                Just x -> doApplySteps rest x (note::result)
-                Nothing -> Nothing
+        [] ->
+            Just (note :: result)
+
+        s :: rest ->
+            case step s note of
+                Just x ->
+                    doApplySteps rest x (note :: result)
+
+                Nothing ->
+                    Nothing
+
 
-{-| Return the NoteClass for a given note. -}
+{-| Return the KeyClass for a given `note`.
+-}
+keyClass : Note -> KeyClass
+keyClass note =
+    if isNatural note then
+        Natural
+
+    else
+        Accidental
+
+
+{-| Return the NoteClass for a given note.
+-}
 classifyNote : Note -> NoteClass
 classifyNote note =
-    if List.member note [C1, C2, C3, C4, C5, C6, C7, C8] then
+    if List.member note [ C1, C2, C3, C4, C5, C6, C7, C8 ] then
         C
-    else if List.member note [C_sharp1, C_sharp2, C_sharp3, C_sharp4, C_sharp5, C_sharp6, C_sharp7] then
+
+    else if List.member note [ C_sharp1, C_sharp2, C_sharp3, C_sharp4, C_sharp5, C_sharp6, C_sharp7 ] then
         C_sharp
-    else if List.member note [D1, D2, D3, D4, D5, D6, D7] then
+
+    else if List.member note [ D1, D2, D3, D4, D5, D6, D7 ] then
         D
-    else if List.member note [D_sharp1, D_sharp2, D_sharp3, D_sharp4, D_sharp5, D_sharp6, D_sharp7] then
+
+    else if List.member note [ D_sharp1, D_sharp2, D_sharp3, D_sharp4, D_sharp5, D_sharp6, D_sharp7 ] then
         D_sharp
-    else if List.member note [E1, E2, E3, E4, E5, E6, E7] then
+
+    else if List.member note [ E1, E2, E3, E4, E5, E6, E7 ] then
         E
-    else if List.member note [F1, F2, F3, F4, F5, F6, F7] then
+
+    else if List.member note [ F1, F2, F3, F4, F5, F6, F7 ] then
         F
-    else if List.member note [F_sharp1, F_sharp2, F_sharp3, F_sharp4, F_sharp5, F_sharp6, F_sharp7] then
+
+    else if List.member note [ F_sharp1, F_sharp2, F_sharp3, F_sharp4, F_sharp5, F_sharp6, F_sharp7 ] then
         F_sharp
-    else if List.member note [G1, G2, G3, G4, G5, G6, G7] then
+
+    else if List.member note [ G1, G2, G3, G4, G5, G6, G7 ] then
         G
-    else if List.member note [G_sharp1, G_sharp2, G_sharp3, G_sharp4, G_sharp5, G_sharp6, G_sharp7] then
+
+    else if List.member note [ G_sharp1, G_sharp2, G_sharp3, G_sharp4, G_sharp5, G_sharp6, G_sharp7 ] then
         G_sharp
-    else if List.member note [A1, A2, A3, A4, A5, A6, A7] then
+
+    else if List.member note [ A1, A2, A3, A4, A5, A6, A7 ] then
         A
-    else if List.member note [A_sharp1, A_sharp2, A_sharp3, A_sharp4, A_sharp5, A_sharp6, A_sharp7] then
+
+    else if List.member note [ A_sharp1, A_sharp2, A_sharp3, A_sharp4, A_sharp5, A_sharp6, A_sharp7 ] then
         A_sharp
+
     else
         B
 
-{-| Return a list of the notes that comprise a `chord` -}
+
+{-| Return a list of the notes that comprise a `chord`
+-}
 notesForChord : Chord -> Maybe (List Note)
-notesForChord {note, chordType} =
-    case applySteps (intervalsForChordType chordType) note of
-        Nothing -> Nothing
-        Just notes -> Just <| note::notes
+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` -}
+{-| Return the scale for a given `key`
+-}
 notesForKey : Key -> List Note
-notesForKey {noteClass, mode} =
-    let origin = noteInCentralOctave noteClass
-    in case applySteps (intervalsForMode mode) origin of
-           -- We should never hit the Nothing case here.
-           Nothing -> []
-           Just scale -> scale
-
-{-| Return a list of all of the notes that we know about. -}
-allNotes : List Note
-allNotes =
-  [ 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
-  ]
-
-{-| Return a list of all of the chords that we know about. -}
-allChords : List Chord
-allChords =
-  let notes = allNotes
-      chordTypes = [ Major
-                   , Major7
-                   , MajorDominant7
-                   , Minor
-                   , Minor7
-                   , MinorDominant7
-                   , Augmented
-                   , Augmented7
-                   , Diminished
-                   , Diminished7
-                   ]
-      chordPositions = [ First
-                       , Second
-                       , Third
-                       , Fourth
-                       ] in
+notesForKey { noteClass, mode } =
+    let
+        origin =
+            noteInCentralOctave noteClass
+    in
+    case applySteps (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 =
+    case classifyNote note of
+        C ->
+            False
+
+        C_sharp ->
+            True
+
+        D ->
+            False
+
+        D_sharp ->
+            True
+
+        E ->
+            False
+
+        F ->
+            False
+
+        F_sharp ->
+            True
+
+        G ->
+            False
+
+        G_sharp ->
+            True
+
+        A ->
+            False
+
+        A_sharp ->
+            True
+
+        B ->
+            False
+
+
+{-| Return true if `note` is a white key.
+-}
+isNatural : Note -> Bool
+isNatural note =
+    note |> isAccidental |> not
+
+
+{-| 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 =
+    [ 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
+    ]
+        |> List.Extra.dropWhile ((/=) start)
+        |> List.Extra.takeWhile ((/=) end)
+
+
+{-| 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 : Note -> Note -> List Chord
+allChords start end =
+    let
+        notes =
+            notesFromRange start end
+
+        chordTypes =
+            [ Major
+            ]
+
+        chordInversions =
+            [ Root
+            , First
+            ]
+    in
     notes
-    |> List.Extra.andThen (\note -> chordTypes
-    |> List.Extra.andThen (\chordType -> chordPositions
-    |> List.Extra.andThen (\chordPosition -> [{ note = note
-                                             , chordType = chordType
-                                             , chordPosition = chordPosition
-                                             }])))
+        |> List.Extra.andThen
+            (\note ->
+                chordTypes
+                    |> List.Extra.andThen
+                        (\chordType ->
+                            chordInversions
+                                |> List.Extra.andThen
+                                    (\chordInversion ->
+                                        [ { note = note
+                                          , chordType = chordType
+                                          , chordInversion = chordInversion
+                                          }
+                                        ]
+                                    )
+                        )
+            )
+
+
+{-| Serialize a human-readable format of `note`.
+-}
+viewNote : Note -> String
+viewNote note =
+    case note of
+        C1 ->
+            "C1"
+
+        C_sharp1 ->
+            "C♯/D♭1"
+
+        D1 ->
+            "D1"
+
+        D_sharp1 ->
+            "D♯/E♭1"
+
+        E1 ->
+            "E1"
+
+        F1 ->
+            "F1"
+
+        F_sharp1 ->
+            "F♯/G♭1"
+
+        G1 ->
+            "G1"
+
+        G_sharp1 ->
+            "G♯/A♭1"
+
+        A1 ->
+            "A1"
+
+        A_sharp1 ->
+            "A♯/B♭1"
+
+        B1 ->
+            "B1"
+
+        C2 ->
+            "C2"
+
+        C_sharp2 ->
+            "C♯/D♭2"
+
+        D2 ->
+            "D2"
+
+        D_sharp2 ->
+            "D♯/E♭2"
+
+        E2 ->
+            "E2"
+
+        F2 ->
+            "F2"
+
+        F_sharp2 ->
+            "F♯/G♭2"
+
+        G2 ->
+            "G2"
+
+        G_sharp2 ->
+            "G♯/A♭2"
+
+        A2 ->
+            "A2"
+
+        A_sharp2 ->
+            "A♯/B♭2"
+
+        B2 ->
+            "B2"
+
+        C3 ->
+            "C3"
+
+        C_sharp3 ->
+            "C♯/D♭3"
+
+        D3 ->
+            "D3"
+
+        D_sharp3 ->
+            "D♯/E♭3"
+
+        E3 ->
+            "E3"
+
+        F3 ->
+            "F3"
+
+        F_sharp3 ->
+            "F♯/G♭3"
+
+        G3 ->
+            "G3"
+
+        G_sharp3 ->
+            "G♯/A♭3"
+
+        A3 ->
+            "A3"
+
+        A_sharp3 ->
+            "A♯/B♭3"
+
+        B3 ->
+            "B3"
+
+        C4 ->
+            "C4"
+
+        C_sharp4 ->
+            "C♯/D♭4"
+
+        D4 ->
+            "D4"
+
+        D_sharp4 ->
+            "D♯/E♭4"
+
+        E4 ->
+            "E4"
+
+        F4 ->
+            "F4"
+
+        F_sharp4 ->
+            "F♯/G♭4"
+
+        G4 ->
+            "G4"
+
+        G_sharp4 ->
+            "G♯/A♭4"
+
+        A4 ->
+            "A4"
+
+        A_sharp4 ->
+            "A♯/B♭4"
+
+        B4 ->
+            "B4"
+
+        C5 ->
+            "C5"
+
+        C_sharp5 ->
+            "C♯/D♭5"
+
+        D5 ->
+            "D5"
+
+        D_sharp5 ->
+            "D♯/E♭5"
+
+        E5 ->
+            "E5"
+
+        F5 ->
+            "F5"
+
+        F_sharp5 ->
+            "F♯/G♭5"
+
+        G5 ->
+            "G5"
+
+        G_sharp5 ->
+            "G♯/A♭5"
+
+        A5 ->
+            "A5"
+
+        A_sharp5 ->
+            "A♯/B♭5"
+
+        B5 ->
+            "B5"
+
+        C6 ->
+            "C6"
+
+        C_sharp6 ->
+            "C♯/D♭6"
+
+        D6 ->
+            "D6"
+
+        D_sharp6 ->
+            "D♯/E♭6"
+
+        E6 ->
+            "E6"
+
+        F6 ->
+            "F6"
+
+        F_sharp6 ->
+            "F♯/G♭6"
+
+        G6 ->
+            "G6"
+
+        G_sharp6 ->
+            "G♯/A♭6"
+
+        A6 ->
+            "A6"
+
+        A_sharp6 ->
+            "A♯/B♭6"
+
+        B6 ->
+            "B6"
+
+        C7 ->
+            "C7"
+
+        C_sharp7 ->
+            "C♯/D♭7"
+
+        D7 ->
+            "D7"
+
+        D_sharp7 ->
+            "D♯/E♭7"
+
+        E7 ->
+            "E7"
+
+        F7 ->
+            "F7"
+
+        F_sharp7 ->
+            "F♯/G♭7"
+
+        G7 ->
+            "G7"
+
+        G_sharp7 ->
+            "G♯/A♭7"
+
+        A7 ->
+            "A7"
+
+        A_sharp7 ->
+            "A♯/B♭7"
+
+        B7 ->
+            "B7"
+
+        C8 ->
+            "C8"
+
+
+inspectChord : Chord -> String
+inspectChord { note, chordType, chordInversion } =
+    viewNote note
+        ++ " "
+        ++ (case chordType of
+                Major ->
+                    "major"
+
+                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"
+           )
+        ++ " "
+        ++ (case chordInversion of
+                Root ->
+                    "root position"
+
+                First ->
+                    "1st inversion"
+
+                Second ->
+                    "2nd inversion"
+           )
+
+
+viewChord : Chord -> String
+viewChord { note, chordType, chordInversion } =
+    viewNoteClass (classifyNote note)
+        ++ " "
+        ++ (case chordType of
+                Major ->
+                    "major"
+
+                Major7 ->
+                    "major 7th"
+
+                MajorDominant7 ->
+                    "major dominant 7th"
+
+                Minor ->
+                    "minor"
+
+                MinorMajor7 ->
+                    "minor 7th"
+
+                MinorDominant7 ->
+                    "minor dominant 7th"
+
+                Augmented ->
+                    "augmented"
+
+                AugmentedDominant7 ->
+                    "augmented 7th"
+
+                Diminished ->
+                    "diminished"
+
+                DiminishedDominant7 ->
+                    "diminished 7th"
+
+                DiminishedMajor7 ->
+                    "diminished major 7th"
+           )
+        ++ " "
+        ++ (case chordInversion of
+                Root ->
+                    "root position"
+
+                First ->
+                    "1st inversion"
+
+                Second ->
+                    "2nd inversion"
+           )
+
+
+{-| Serialize a human-readable format of `noteClass`.
+-}
+viewNoteClass : NoteClass -> String
+viewNoteClass noteClass =
+    case noteClass 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"