Wrong playback of microtonal enharmonics

The tonality system I’ve specified is for 22 equal divisions of the octave. In this tuning, quarter-tone sharp is defined as identical to diatonic semitone sharp, ie. E-quarter-tone-sharp = F, and A-quarter-tone-sharp = B flat. (The pitch delta of quarter-tone is 1; sharps and flats are 3 steps up or down.) Dorico plays these back correctly when I input the notes in the two spellings. It also gives the correct alternative enharmonic spelling, if I input the notes and then press Alt+ or Alt-. However, in this latter case, the playback is no longer correct. In the enclosed example, the first two chords were entered manually. The first chord was entered by inputting the notes of the C major chord, and then transposing the chord up a quarter-tone by pressing Shift-Alt-Up_arrow. The playback of the first two chords is correct. They are enharmonically equivalent, so the same chord is heard twice. The third chord was input by inputting a D-flat major chord and then pressing Alt-. Dorico does give the correct enharmonic equivalent, ie. C-major-quarter-tone-sharp, but the playback is not correct. It does not play A-flat/G-quarter-tone-sharp nor F/E-quarter-tone-sharp as unisons, although it correctly plays D-flat/C-quarter-tone-sharp as a unison.

Is this a bug? Or is Dorico altogether unable to handle enharmonic spellings and their playback in microtonal tonality systems, and if so, is this being looked into?
22edo enharmonics.dorico.zip (566 KB)

Enharmonics are tricky in microtonal music, I think; if you get the same sounding result by manually entering the pitches, I am already impressed! Asking for the Alt+ and Alt- shortcuts to work here seems like a big ask to me, especially since this is probably a pretty esoteric situation. Nevertheless it’s good to know, and thanks for sharing the file. It would be interesting to see what the team does with this - it could be an issue of somehow “generalizing” the enharmonic shortcut.

Something tangentially related happened to me in January, when I was making parts for a piece in Helmholtz Ellis just intonation (HEJI). I had a score in C with three transposing instruments (clarinet, saxophone and horn); but even with 12,000 divisions of the octave, I did not have equal-tempered major 2nds, major 6ths, or perfect 5ths, so I couldn’t hit the “Transpose” button! I had to make those parts by hand, so to speak, in a separate score layout.

In 24-equal Dorico works perfectly, though. It transposes correctly with Shift-Alt-Arrow and flips the enharmonic spelling with Alt-plus/minus, and the playback is correct. If I select E-quarter-tone sharp and press Alt-plus, Dorico correctly changes the spelling to F-quarter-tone-flat and plays it back as the same pitch, which it is. I thought it might have trouble with the 3/4-step intervals, as it does in my 22-equal example, but in 24-equal those come out right, too. So if I have G-three-quarters-sharp and I press Alt-plus, Dorico changes it to A-quarter-tone-flat and plays it correctly, ie. the same pitch.

I suppose Dorico has trouble when the diatonic semitones EF and BC are defined as only 1 step. In 24edo the diatonic scale (from A) is 4244244 while in 22edo it’s 4144144. This shouldn’t happen, though, given that 24edo works. Perhaps it is indeed a bug.

Yes, transposing instruments are a problem in microtonal notation and in HEJI. It’s a subject that’s been discussed with the Dorico team, and I hope it’s going to be improved in the future.

Thanks - that is excellent news about 24tet working with enharmonics, I’ve never tried it.

The pitches of the first and last chords are not the same, internally. The E quarter-tone sharp in the first chord, for example, has a pitch of 710/11, while the E quarter-tone sharp in the third chord has a pitch of 65. I’m not sure exactly why that is, but we’ll look into it.

It could be a fractional rounding error due to an intermediate calculation’s resolution. I plan my JI systems in Excel and unwanted substation of one fraction for another is a pain.

The difference between 710/11 and 715/11 (or 1420/22 and 1430/22 since we are in 22EDO) seems a bit big for a rounding error!

Thank you for looking into this, Daniel. It would be great to have the enharmonic flip working in microtonal tunings.

You’re right, but I’ve been tied up in excel when it has substituted one for another before further calculation blows up the difference.