I have a problem. Since Arabic and Persian music are notated as 24-EDO, I investigate any little theory I can find about 24-EDO harmony. Even though I know more precise intonation information about Arabic and Persian music than what is notated - I just can't help myself. That in mind, here's an intruiging piece in 24-EDO by Gustavo Martins: https://www.youtube.com/watch?v=8loy6AAhgCQ
That's not a famous composer you'll recognize. It's someone on the xenharmonic discord.
Let's analyze the harmony of the piece. In another source, Gustavo writes that the song uses this scale:
[C, Dd, D#, Fd, Ft, G, Ad, A#, Bt, C] : [0, 3, 6, 9, 11, 14, 17, 20, 23, 24]
And maybe it does, but his music is notated with Eb instead of D# sometimes, and Bb instead of A#, so I'm already a little worried.
I started analyzing his chords from the sheet music in the video. At first I was assuming that accidentals carry through the measure unless another accidental appears on the same pitch class, but then I noticed he has a lot of extra accidentals if that were the case. But if I don't do that, then I think there are notes from outside the scale. So I might have to play along with the audio to verify if his notation matches his audio.
Until I do that, here are some chords that I read off the sheet music:
[C, Eb, Ft, Ad]
[Dd, Fd, Ad]
[Ft, Ad, C, Eb, G]
[C, Eb, G, Bb]
[Dd, Ft, Ad]
...
Let's look his theory for a bit while I'm stalled on analyzing the piece.
Suppose you start with a rank-2 diminished seventh chord:
[C, Eb, Gb, Bbb]
All of these notes are separated by 3\12-EDO, like a minor third. Gustavo interlaces this with a nother diminished second chord that is 3\24-steps higher.
We could write this as
[C#t, Et, Gt, Bd]
or
[Dd, Fd, Abd, Cbd]
Putting the two chords together, Gustavo writes the interleaved dim7 scales as
[C, Dd, D#, Fd, F#, Gt, A, Bd] - Scale 1
But he doesn't use this. He copies it and raises it by a 2\24-EDO semitone,
[C#, Dt, E, Ft, G, Ad, Bt] - Scale 2
And then takes the first four notes from Scale 1 and the last five notes from Scale 2, giving
[C, Dd, D#, Fd] + [Ft, G, Ad, Bt]
which he calls the microtonal minor scale. This sure looks insane, but he made nice music with it, so I'm going to keep working with it for a while, I guess.
...
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