harmoniask

Exploring jazz music theory with Haskell.

Harmoniask is a little project to embed elements of Jazz music into Haskell, such as chords, substitutions, standard harmonic sequences and so on.

As a standalone application, it can read a text file containing sequences of chords and output it in a MIDI file, possibly using alternative tunings (eg. Pythagoric, Werckmeister...). Note however that not every MIDI player support the MTS (Midi Tuning Standard) for alternative tunings.

How to install

git clone
stack build

Some examples

A simple chord, both in its abstract and concrete representations:

λ> majTriad
Chord [Unison,ThirdMaj,Fifth]

λ> realizeChord majTriad 60 -- 60 = Middle C
[60,64,67]

Constructing chords via combinators:

λ> addOnTop SeventhMin majTriad 
Chord [Unison,ThirdMaj,Fifth,SeventhMin]

Constructing more complex chords:

λ> x_9b = 
	addOnTop SeventhMin |> 
	addOnTop NinthMaj   |> 
	alter NinthMaj Flat |> 
	remove Fifth

λ> x_9b majTriad 
Chord [Unison,ThirdMaj,SeventhMin,NinthMin]

λ> realizeChord (x_9b majTriad) 60 
[60,64,70,72]

Some simple Sequence (sequence of chords that stays inside a tonality):

λ> v_i = Sequence [Fifth, Unison] [x_7 majTriad, x_maj7 majTriad]
Sequence [Fifth,Unison] 
         [Chord [Unison,ThirdMaj,Fifth,SeventhMin]
		 ,Chord [Unison,ThirdMaj,Fifth,SeventhMaj]]	

λ> realizeSeq 60 v_i
[[67,71,74,77],[60,64,67,71]] -- G7 | Cmaj7

Some Sequence combinators:

λ> ii_v_i = Sequence 
            [SecondMaj, Fifth, Unison]
            [x_7 minTriad, x_7 majTriad, x_maj7 majTriad]

λ> ii_v_tritone = (removeLastSeq |>>| tritoneSub)
λ> ii_v_tritone ii_v_i
Sequence [SecondMaj,SecondMin] 
	     [Chord [Unison,ThirdMin,Fifth,SeventhMin], 
		  Chord [Unison,ThirdMaj,Fifth,SeventhMin]]
		  
λ> realizeSeq 60 $ ii_v_tritone ii_v_i
[[62,65,69,72],[61,65,68,71]] -- D-7 | Db7

Realizing a Sequence while trying to reduce the distance between the notes of subsequent chords:

λ> realizeSeqCompact 60 ii_v_i
[[62,65,69,72], -- D-7
 [62,65,67,71], -- G7, 2nd inversion
 [60,64,67,71]] -- Cmaj7

Creating Harmonys, a collection of sequences in different tonalities:

circleFifths :: Harmony
circleFifths = Harmony intervals sequences
	where intervals = concat $ replicate 6 [Up Fourth, Down Fifth]
	sequences       = replicate 12 ii_v_i

λ> circleFifths
Harmony 
	[Up Fourth, Down Fifth, Up Fourth, Down Fifth...] 
	[Sequence [SecondMaj,Fifth,Unison] 
	          [Chord [Unison,ThirdMin,Fifth,SeventhMin],
			   Chord [Unison,ThirdMaj,Fifth,SeventhMin],
			   Chord [Unison,ThirdMaj,Fifth,SeventhMaj]],
     Sequence [SecondMaj,Fifth,Unison] 
	          [Chord [Unison,ThirdMin,Fifth,SeventhMin],
			   Chord [Unison,ThirdMaj,Fifth,SeventhMin],
			   Chord [Unison,ThirdMaj,Fifth,SeventhMaj]],
     Sequence ... ... ... ]

Exporting to a Midi file:

λ> examplePitches = realizeHarmonyWith (noteToMidi C) realizeSeqCompact circleFifths
λ> exampleTrack = makeTrack (MidiOptions 120 Nothing Nothing) examplePitches
λ> writeMidiFile "examples/out.mid" $ createMidiFile $ exampleTrack

Here is the result.