Just Intonation and general tuning headache

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)