2020-04-11 11:45:42 +02:00
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module Theory exposing (..)
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import List.Extra
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import Maybe.Extra
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import Misc
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2020-04-12 17:43:34 +02:00
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2020-04-11 11:45:42 +02:00
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{-| Notes are the individuals sounds that we use to create music. Think: "do re
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mi fa so la ti do".
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Note: Technically a "C-sharp" is also a "D-flat", but I will model accidentals
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(i.e. sharps and flats) as sharps and represent the ambiguity when I render the
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underlying state of the application.
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Note: There are "notes" like A, B, D-flat, and then there are notes like "middle
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C", also denoted in scientific pitch notation as C4. I'm unsure of what to call
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each of these, and my application does not model scientific pitch notation yet,
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2020-04-12 17:43:34 +02:00
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so these non-scientific pitch denote values are "notes" for now.
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-}
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type Note
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= C1
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| C_sharp1
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| D1
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| D_sharp1
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| E1
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| F1
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| F_sharp1
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| G1
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| G_sharp1
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| A1
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| A_sharp1
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| B1
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| C2
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| C_sharp2
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| D2
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| D_sharp2
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| E2
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| F2
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| F_sharp2
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| G2
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| G_sharp2
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| A2
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| A_sharp2
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| B2
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| C3
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| C_sharp3
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| D3
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| D_sharp3
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| E3
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| F3
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| F_sharp3
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| G3
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| G_sharp3
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| A3
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| A_sharp3
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| B3
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| C4
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| C_sharp4
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| D4
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| D_sharp4
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| E4
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| F4
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| F_sharp4
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| G4
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| G_sharp4
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| A4
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| A_sharp4
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| B4
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| C5
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| C_sharp5
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| D5
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| D_sharp5
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| E5
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| F5
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| F_sharp5
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| G5
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| G_sharp5
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| A5
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| A_sharp5
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| B5
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| C6
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| C_sharp6
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| D6
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| D_sharp6
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| E6
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| F6
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| F_sharp6
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| G6
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| G_sharp6
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| A6
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| A_sharp6
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| B6
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| C7
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| C_sharp7
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| D7
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| D_sharp7
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| E7
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| F7
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| F_sharp7
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| G7
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| G_sharp7
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| A7
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| A_sharp7
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| B7
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| C8
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2020-04-12 00:11:04 +02:00
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{-| I alluded to this concept in the Note type's documentation. These are the
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letters of notes. For instance C2, C3, C4 are all instances of C.
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-}
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type NoteClass
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= C
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| C_sharp
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| D
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| D_sharp
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| E
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| F
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| F_sharp
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| G
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| G_sharp
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| A
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| A_sharp
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| B
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{-| Encode whether you are traversing "up" or "down" intervals
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-}
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type StepDirection
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= Up
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| Down
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{-| One can measure the difference between between notes using intervals.
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-}
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type Interval
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= Half
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| NHalves Int
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| Whole
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| MajorThird
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| MinorThird
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| PerfectFifth
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| AugmentedFifth
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| DiminishedFifth
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| MajorSeventh
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| DominantSeventh
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{-| Add direction to a distance on the piano.
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-}
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type alias IntervalVector =
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{ interval : Interval
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, direction : StepDirection
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}
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{-| A bundle of notes which are usually, but not necessarily harmonious.
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-}
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Prefer type alias to type
Elm reminds me of Haskell. In fact, I'm using `haskell-mode` (for now) in Emacs
to write my Elm code, and it works reliably. I'm not writing a Haskell app, but
if I were, I would define my application Model with the following Haskell code:
```haskell
data Model = Model { whitelistedChords :: [Theory.Chord]
, selectedChord :: Theory.Chord
, isPaused :: Bool
, tempo :: Int
}
```
When I first modelled my application state, I did something similar. After
reading more Elm examples of SPAs, I see that people prefer using type aliases
to define records. As far as I know, you cannot do this in Haskell; I believe
all types are "tagged" (something about "nominal typing" comes to mind). Anyhow,
Elm isn't Haskell; Haskell has cool features like type classes; Elm has cool
features like human-readable error messages and exhaustiveness checking for
cases. I love Haskell, and I love Elm, and you didn't ask.
Anyhow, this commit refactors my records as type aliases instead of types. I
think the resulting code is more readable and ergonomic.
2020-04-11 17:50:02 +02:00
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type alias Chord =
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{ note : Note
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, chordType : ChordType
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, chordInversion : ChordInversion
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}
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{-| Many possible chords exist. This type encodes the possibilities. I am
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tempted to model these in a more "DRY" way, but I worry that this abstraction
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may cause more problems than it solves.
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-}
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type ChordType
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= Major
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| Major7
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| MajorDominant7
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| Minor
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| MinorMajor7
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| MinorDominant7
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| Augmented
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| AugmentedDominant7
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| Diminished
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| DiminishedDominant7
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| DiminishedMajor7
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{-| On a piano, a triad can be played three ways. As a rule-of-thumb, The number
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of ways a pianist can play a chord is equal to the number of notes in the chord
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itself.
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-}
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type ChordInversion
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= Root
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| First
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| Second
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{-| Whether a given note is a white key or a black key.
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-}
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type KeyClass
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= Natural
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| Accidental
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{-| Songs are written in one or more keys, which define the notes and therefore
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chords that harmonize with one another.
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-}
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Prefer type alias to type
Elm reminds me of Haskell. In fact, I'm using `haskell-mode` (for now) in Emacs
to write my Elm code, and it works reliably. I'm not writing a Haskell app, but
if I were, I would define my application Model with the following Haskell code:
```haskell
data Model = Model { whitelistedChords :: [Theory.Chord]
, selectedChord :: Theory.Chord
, isPaused :: Bool
, tempo :: Int
}
```
When I first modelled my application state, I did something similar. After
reading more Elm examples of SPAs, I see that people prefer using type aliases
to define records. As far as I know, you cannot do this in Haskell; I believe
all types are "tagged" (something about "nominal typing" comes to mind). Anyhow,
Elm isn't Haskell; Haskell has cool features like type classes; Elm has cool
features like human-readable error messages and exhaustiveness checking for
cases. I love Haskell, and I love Elm, and you didn't ask.
Anyhow, this commit refactors my records as type aliases instead of types. I
think the resulting code is more readable and ergonomic.
2020-04-11 17:50:02 +02:00
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type alias Key =
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{ noteClass : NoteClass
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, mode : Mode
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}
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2020-04-11 11:45:42 +02:00
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{-| We create "scales" by enumerating the notes of a given key. These keys are
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defined by the "tonic" note and the "mode". I thought about including Ionian,
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Dorian, Phrygian, etc., but in the I would like to avoid over-abstracting this
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early on, so I'm going to err on the side of overly concrete until I have a
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better idea of the extent of this project.
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-}
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type Mode
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= BluesMode
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| MajorMode
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| MinorMode
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scaleDegree : Int -> Key -> NoteClass
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scaleDegree which { noteClass } =
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case noteClass of
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_ ->
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C
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{-| Returns the Note in the cental octave of the piano for a given
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NoteClass. For example, C4 -- or "middle C" -- for C.
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-}
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noteInCentralOctave : NoteClass -> Note
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noteInCentralOctave noteClass =
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case noteClass of
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C ->
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C4
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C_sharp ->
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C_sharp4
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D ->
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D4
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D_sharp ->
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D_sharp4
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E ->
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E4
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F ->
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F4
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F_sharp ->
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F_sharp4
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G ->
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G4
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G_sharp ->
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G_sharp4
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A ->
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A4
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A_sharp ->
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A_sharp4
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B ->
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B4
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2020-04-12 00:11:04 +02:00
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2020-04-12 20:20:00 +02:00
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{-| Return the human-readable version of a chord inversion.
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-}
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inversionName : ChordInversion -> String
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inversionName inversion =
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case inversion of
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Root ->
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"Root"
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First ->
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"First"
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Second ->
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"Second"
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2020-04-11 11:45:42 +02:00
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{-| Return the note that is one half step away from `note` in the direction,
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`dir`.
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In the case of stepping up or down from the end of the piano, this returns a
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Maybe.
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-}
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2020-04-12 00:11:04 +02:00
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halfStep : StepDirection -> Note -> Maybe Note
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halfStep dir note =
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let
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everyNote =
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notesFromRange C2 C8
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in
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case dir of
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Up ->
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Misc.comesAfter note everyNote
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Down ->
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Misc.comesBefore note everyNote
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2020-04-12 00:11:04 +02:00
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2020-04-11 11:45:42 +02:00
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{-| Return a list of steps to take away from the root note to return back to the
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root note for a given mode.
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-}
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intervalsForMode : Mode -> List IntervalVector
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intervalsForMode mode =
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let
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up x =
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{ direction = Up, interval = x }
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down x =
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{ direction = Down, interval = x }
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in
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case mode of
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MajorMode ->
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List.map up [ Whole, Whole, Half, Whole, Whole, Whole, Half ]
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MinorMode ->
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List.map up [ Whole, Half, Whole, Whole, Half, Whole, Whole ]
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BluesMode ->
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List.map up [ MinorThird, Whole, Half, Half, MinorThird ]
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{-| Return a list of the intervals the comprise a chord. Each interval measures
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the distance away from the root-note of the chord.
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-}
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intervalsForChordType : ChordType -> ChordInversion -> List IntervalVector
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intervalsForChordType chordType chordInversion =
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let
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up x =
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{ direction = Up, interval = x }
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down x =
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{ direction = Down, interval = x }
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in
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case ( chordType, chordInversion ) of
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-- Major
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( Major, Root ) ->
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[ up MajorThird, up PerfectFifth ]
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( Major, First ) ->
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[ down (NHalves 5), down (NHalves 8) ]
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( Major, Second ) ->
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[ down (NHalves 5), up MajorThird ]
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-- Major7
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( Major7, Root ) ->
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[ up MajorThird, up PerfectFifth, up MajorSeventh ]
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( Major7, First ) ->
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down Half :: intervalsForChordType Major chordInversion
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( Major7, Second ) ->
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down Half :: intervalsForChordType Major chordInversion
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-- MajorDominant7
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( MajorDominant7, Root ) ->
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up DominantSeventh :: intervalsForChordType Major chordInversion
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( MajorDominant7, First ) ->
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down Whole :: intervalsForChordType Major chordInversion
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( MajorDominant7, Second ) ->
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down Whole :: intervalsForChordType Major chordInversion
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-- Minor
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( Minor, Root ) ->
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[ up MinorThird, up PerfectFifth ]
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|
|
( 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)
|
2020-04-11 11:45:42 +02:00
|
|
|
applySteps steps note =
|
2020-04-12 00:11:04 +02:00
|
|
|
doApplySteps steps note [] |> Maybe.map List.reverse
|
|
|
|
|
2020-04-12 17:43:34 +02:00
|
|
|
|
|
|
|
doApplySteps : List IntervalVector -> Note -> List Note -> Maybe (List Note)
|
2020-04-12 00:11:04 +02:00
|
|
|
doApplySteps steps note result =
|
|
|
|
case steps of
|
2020-04-12 17:43:34 +02:00
|
|
|
[] ->
|
|
|
|
Just (note :: result)
|
|
|
|
|
|
|
|
s :: rest ->
|
|
|
|
case step s note of
|
|
|
|
Just x ->
|
|
|
|
doApplySteps rest x (note :: result)
|
|
|
|
|
|
|
|
Nothing ->
|
|
|
|
Nothing
|
|
|
|
|
2020-04-12 00:11:04 +02:00
|
|
|
|
2020-04-12 17:43:34 +02:00
|
|
|
{-| 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.
|
|
|
|
-}
|
2020-04-12 00:11:04 +02:00
|
|
|
classifyNote : Note -> NoteClass
|
|
|
|
classifyNote note =
|
2020-04-12 17:43:34 +02:00
|
|
|
if List.member note [ C1, C2, C3, C4, C5, C6, C7, C8 ] then
|
2020-04-12 00:11:04 +02:00
|
|
|
C
|
2020-04-12 17:43:34 +02:00
|
|
|
|
|
|
|
else if List.member note [ C_sharp1, C_sharp2, C_sharp3, C_sharp4, C_sharp5, C_sharp6, C_sharp7 ] then
|
2020-04-12 00:11:04 +02:00
|
|
|
C_sharp
|
2020-04-12 17:43:34 +02:00
|
|
|
|
|
|
|
else if List.member note [ D1, D2, D3, D4, D5, D6, D7 ] then
|
2020-04-12 00:11:04 +02:00
|
|
|
D
|
2020-04-12 17:43:34 +02:00
|
|
|
|
|
|
|
else if List.member note [ D_sharp1, D_sharp2, D_sharp3, D_sharp4, D_sharp5, D_sharp6, D_sharp7 ] then
|
2020-04-12 00:11:04 +02:00
|
|
|
D_sharp
|
2020-04-12 17:43:34 +02:00
|
|
|
|
|
|
|
else if List.member note [ E1, E2, E3, E4, E5, E6, E7 ] then
|
2020-04-12 00:11:04 +02:00
|
|
|
E
|
2020-04-12 17:43:34 +02:00
|
|
|
|
|
|
|
else if List.member note [ F1, F2, F3, F4, F5, F6, F7 ] then
|
2020-04-12 00:11:04 +02:00
|
|
|
F
|
2020-04-12 17:43:34 +02:00
|
|
|
|
|
|
|
else if List.member note [ F_sharp1, F_sharp2, F_sharp3, F_sharp4, F_sharp5, F_sharp6, F_sharp7 ] then
|
2020-04-12 00:11:04 +02:00
|
|
|
F_sharp
|
2020-04-12 17:43:34 +02:00
|
|
|
|
|
|
|
else if List.member note [ G1, G2, G3, G4, G5, G6, G7 ] then
|
2020-04-12 00:11:04 +02:00
|
|
|
G
|
2020-04-12 17:43:34 +02:00
|
|
|
|
|
|
|
else if List.member note [ G_sharp1, G_sharp2, G_sharp3, G_sharp4, G_sharp5, G_sharp6, G_sharp7 ] then
|
2020-04-12 00:11:04 +02:00
|
|
|
G_sharp
|
2020-04-12 17:43:34 +02:00
|
|
|
|
|
|
|
else if List.member note [ A1, A2, A3, A4, A5, A6, A7 ] then
|
2020-04-12 00:11:04 +02:00
|
|
|
A
|
2020-04-12 17:43:34 +02:00
|
|
|
|
|
|
|
else if List.member note [ A_sharp1, A_sharp2, A_sharp3, A_sharp4, A_sharp5, A_sharp6, A_sharp7 ] then
|
2020-04-12 00:11:04 +02:00
|
|
|
A_sharp
|
2020-04-12 17:43:34 +02:00
|
|
|
|
2020-04-12 00:11:04 +02:00
|
|
|
else
|
|
|
|
B
|
2020-04-11 11:45:42 +02:00
|
|
|
|
2020-04-12 17:43:34 +02:00
|
|
|
|
|
|
|
{-| Return a list of the notes that comprise a `chord`
|
|
|
|
-}
|
2020-04-12 00:11:04 +02:00
|
|
|
notesForChord : Chord -> Maybe (List Note)
|
2020-04-12 17:43:34 +02:00
|
|
|
notesForChord { note, chordType, chordInversion } =
|
|
|
|
intervalsForChordType chordType chordInversion
|
|
|
|
|> List.map (\interval -> step interval note)
|
|
|
|
|> Maybe.Extra.combine
|
|
|
|
|> Maybe.map (\notes -> note :: notes)
|
|
|
|
|
2020-04-11 11:45:42 +02:00
|
|
|
|
2020-04-12 17:43:34 +02:00
|
|
|
{-| Return the scale for a given `key`
|
|
|
|
-}
|
2020-04-11 11:45:42 +02:00
|
|
|
notesForKey : Key -> List Note
|
2020-04-12 17:43:34 +02:00
|
|
|
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)
|
|
|
|
|
|
|
|
|
2020-04-12 20:20:00 +02:00
|
|
|
{-| 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
|
|
|
|
, Major7
|
|
|
|
, MajorDominant7
|
|
|
|
, Minor
|
|
|
|
, MinorMajor7
|
|
|
|
, MinorDominant7
|
|
|
|
, Augmented
|
|
|
|
, AugmentedDominant7
|
|
|
|
, Diminished
|
|
|
|
, DiminishedDominant7
|
|
|
|
, DiminishedMajor7
|
|
|
|
]
|
|
|
|
|
|
|
|
|
2020-04-12 17:43:34 +02:00
|
|
|
{-| 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`.
|
|
|
|
-}
|
2020-04-12 20:20:00 +02:00
|
|
|
allChords : Note -> Note -> List ChordInversion -> List Chord
|
|
|
|
allChords start end chordInversions =
|
2020-04-12 17:43:34 +02:00
|
|
|
let
|
|
|
|
notes =
|
|
|
|
notesFromRange start end
|
|
|
|
|
|
|
|
chordTypes =
|
2020-04-12 20:20:00 +02:00
|
|
|
allChordTypes
|
2020-04-12 17:43:34 +02:00
|
|
|
in
|
2020-04-11 11:45:42 +02:00
|
|
|
notes
|
2020-04-12 17:43:34 +02:00
|
|
|
|> 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"
|