u/hazenut

An abstract art style (??) depiction of just intonation triads. Created for myself in search of tonalities, or pure amusement :P

There are two flavors of it, one includes all ordinary triads with complexity abc<N, the other also includes all "utonality triads" whose complexity is defined as lcm(abc)^3/(abc)<N. Obviously the second one is more complete but they mostly contain pairs of mirrored triads which causes more clutters.

You can see for every triad there is a solid marker and a hollow marker. If the solid marker is much larger than the hollow marker it is strongly otonal while if the inverse is true it is strongly utonal.

When complexity limit increases one can observe some interesting structures to emerge. There are larger still plots (N>8000000) but are too large to upload :)

Source code (also svg and larger N versions)

So after experimenting and playing on a lot of edos, I declare that I fall in love with the sound of 53edo. But it has a glaring problem(or feature): it's not meantone. But my music has diatonic backbone and the comma pumps irks me a lot. Did anyone had success dealing with the syntonic comma?

Other edos I had tried and my feeling about them:

31edo: perfect in paper, sweet sounding but can get boring fast. It's bit sterile because its very JI sound. Also I want to do 13-limit and tiny melodic inflections ~20-30c which it's not capable of.

41edo: perfect in paper but turned out everything sounds inexplicably a bit off to me. Also the syntonic comma is even more pronounced which makes diatonic melodies very angular.

43edo: if not for the bad 7/4 and horrible 7/6 I am almost sold, but tridecimal feeling is spot on, and melodic step size is near optimal by ear(27.9c)

50edo/81edo/212edo: golden meantone series, adequate 13-limit, expanded palette compared to 31edo. I was close to declare that golden meantone is the best meantone before I found out it kinds of lacks of zest compared to 43edo. There is downside that diatonic being too mellow.

72edo: With the step size being small, I can sort of just use zarlino for diatonic and won't feel angular at all. Problem is, it's difficult to get out of 12edo chain, and generally sound similar to 12edo due to its beating patterns for a lot of its intervals.

It's a pity there is no good meantone tuning in the comma-level range (supports interval of size 20-30c) or did I miss something? On the other hand, 53edo sounds absolutely gorgeous. If only I can tame the comma, hehe.

All just intonation triads (within complexity and cent limit) in a graph

taming the comma and feeling about edos