12-edo's approximation to the 5th harmonic (a.k.a. 4th overtone) is 14 cents sharp, not flat -- it's at 400 cents plus two octaves, whereas the 5th harmonic is at 386 cents plus two octaves.
I admit to being unfamiliar with unequal temperaments. As a jazz player they seems like a complete bummer to me, as I love to transpose on a whim and don't want the intervallic structure to depend on what key I'm in.
Yeah, I had a sign error in my head there (unequal major thirds are the relatively flat ones).
I know that there is some unequal tempered jazz out there from very early recordings, and I assume they thought the different character of the keys added extra character and possibly some extra "grunge," but it would be interesting to compare the improvisational style to equal tempered jazz.
I know of at least one person who's very fond of a 12-tone JI scale she came up with, which she happily plays in every key. She tattooed it onto her arm.
I've played in 58-edo, which to me is basically indistinguishable from JI. It's just a little too big to use comfortably on the Lumatone. I can use it on the monome comfortably, but the monome doesn't have velocity sensitivity, which for me is a deal killer. On the Lumatone the biggest I feel comfortable playing is 46-edo. Fortunately, 46-edo sounds incredible.
It doesn't have the best approximation to 5/4 -- it's 5 cents sharp -- but that error goes in the same direction as the error in 12-edo that we're used to, so (because we're all used to 12-edo) it sounds world better than, say, the 5/4 that 41-edo gives you, which is 6 cents flat.
I admit to being unfamiliar with unequal temperaments. As a jazz player they seems like a complete bummer to me, as I love to transpose on a whim and don't want the intervallic structure to depend on what key I'm in.