Just Intonation and general tuning headache

Hi!
So I was trying to write a very simple exercise to train myself to sing just intervals. I created a custom tonality, 1200 octave divisions, with cent values correlating to C JI. Then I wrote one bar in this intonation with a C+E chord, then a bar in normal 12EDO with the same chord, the idea being to train myself to hear the difference between the two E’s. But upon playing I could hear that the C itself was not the same between the two tonalities After a bit of head-scratching realised that this is because at least the way I had it set up, although Dorico correctly plays the intervals of this C JI, it seems to still begins calculating the cent values from A=440, so C in this Tonality won’t correspond to C in 12EDO C Major.
How would I go about creating a Just Intoned C Major scale with C=261, without changing the general tuning in the playback options, so the tuning of this C remains consistent when I alternate between C major in JI and 12 EDO?

Hi @yoyokoko without wanting to put a dampener on you, I’d say that Dorico is not the right tool for the job in this case. Have you investigated Scala:

https://www.huygens-fokker.org/scala/

Many hardware and VST synths accept Scala tunings.

I know this is not the answer you were hoping for, but Dorico, while supporting custom tonality systems, does not seem to me to be well fitted to your task. I’d be interested to hear if people have had success with this - happy to be proved wrong!

Good question! I have done some work in the Ben Johnston system, but I’ve been lucky to be working with music based on A=440 (so I know C is therefore 15.64 cents higher than standard pitch).

I doubt that this specific thing can be done within one Dorico file with proper notation. For your exercise purposes, I guess you could create compensating accidentals, to “fake” J.I. in E.T. or vice-versa. But that defeats the purpose of the notation. Or just accept that A is the common pitch and go from there.

To the Team: This is a persistent issue with J.I. in particular. One has to choose a reference pitch, and in practice it is more often C than A. Would it be possible to someday provide that option in the Edit Tonality System dialog? (With C chosen, the list of divisions would start and end with C instead of A.) Currently the only way I know to make C the standard pitch in J.I. is to lower the pitch of A to 436 in Playback Options.

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Thanks Andro. Just getting into the whole multiple-tunings thing and wasn’t aware of Scala. Very helpful.

Thanks Mark. So looks like only awkward workarounds for now.
I hope Dorico will expand it’s alternate-tonalities functionality in the future.
Allowing one to designate a primary note which all intervals are calculated from would be great.

If you’re interested, here is a little file using the Helmholtz Ellis Just Intonation accidentals from plainsound.org, which combines JI and 12tet and seems to do what you’re asking for. (In HEJI, the natural sign with the horizontal bar on top plays equal temperament.)

You can play each staff individually by clicking in its staff (not on a note). If you play the top two staves together, they sound fine; if you play all three, the E’s sound out of tune, because of the pure 5:4 ratio for the major third. Is this what you’re looking for?

For me, what is weird here is that the HEJI C and 12tet C, to me, sound practically identical; and if we are indeed working from A 440, they shouldn’t, from what I understand. Maybe they are a tiny bit different? If there is a difference it’s subtle; but I have noticed differences between HEJI/12tet pitches in other projects of mine.

HarmonicSeries-Gesualdo-JohnstonLattice.dorico (735.3 KB)

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Many thanks for this Stephen!

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btw, correcting a mistake in my original post, I meant C=264Hz, not 201

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It’s because the first bar of the file is playing in the same HE Cents JI system. Select the first note, select 12-EDO and add another open key sig. Then when you select notes in the different bars you can see the tonality system change in the panel, and also hear the differences.

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Thanks Mark! I thought I had set the first bar to 12tet, but I was mistaken. After fixing that, there is definitely slow beating on the middle C and E when I play the top two staves together; not so much on the G, at least to my ear.