90edo Diaschismic

I have posted some music in the past that uses 34edo, a tuning system that has very good approximations for conventional intervals like perfect fifths and major thirds. But 34edo does not temper out the syntonic comma 81:80; instead it tempers out the diaschisma 2048:2025. The diagram above is a tonnetz diagram for diaschismic tuning of the conventional 12 notes of a piano.

Conventional music, in the Palestrina - Wagner tradition, is built on tempering the syntonic comma, which is the foundation of meantone tunings. The tonnetz diagram for meantone tuning looks quite different:

There is a spectrum of meantone tunings, where the flatness of the perfect fifth is traded against the sharpness of the major third. 31edo, or quarter comma meantone, are at one end of the spectrum, where the major thirds are quite precise while the perfect fifth is rather flat. It occurred to me that the same sort of spectrum should exist for diaschismic tunings.

Perfect fifths are a bit sharper than just, in diaschismic tunings. There are two wolf fifths, D-A and Ab-Eb in the tonnetz diagram. These are flat, to make for the sharpness of most of the fifths. As the fifths are sharpened, most of the major thirds get flatter. When the fifths get to around 707 cents (versus the just fifth of 702 cents), the major thirds become just, at 386 cents. There are wolf major thirds in this tuning though, such as A-C# in the tonnetz diagram, that sharpen as the fifths sharpen.

It turns out that 90edo has fifths that are close to the value needed to make the major thirds very exact... so of course I had to see what it sounded like: 90edo scale 12.