TallKite

: For 11-limit, consider a chain of neutral 3rds centered on the unison: m3-hd5-m7-n2-P4-n6-P1-n3-P5-n7-M2-hA4-M6 where hd = half-dim and hA = half-aug. Consider the 6 intervals hd5-n2-n6-n3-n7-hA4. Coldly suspended seems to mean the central part of this chain. Warmly suspended seems to mean the further away parts. Except hd5 = 16/11 gets its own category. Again, this might be because 3/2 is so powerful, 16/11 sounds more like a very flat 3/2 than an interval in its own right. Note that there's a small comma 243/242 which tends to blur the difference between 11-over and 11-under.

: So your categories seem to correspond to various regions of the lattice, which makes sense to me. Not sure I understand the positive/negative classification. Personally I loosely classify imperfect intervals as supermajor-major-neutral-minor-subminor, 5ths as superperfect-perfect-halfdim-dim-(subdim) and 4ths as (superaug)-aug-halfaug-perfect-subperfect. So basically 5-limit and deviations from there, very 31-edo-like. One could add submajor, superminor, superperfect 4th, etc. to get it down to 3-limit, very 41-edo-like. If you sharpen the 5th, then in the 3-limit chain of 5ths major sounds like supermajor and minor sounds subminor. If you flatten it, you get submajor and superminor, and if you flatten a lot, neutral. Is that the logic behind positive/negative? If so, that might be a better way to describe it, rather than referring to edos. Also note that to get 11/8 and 16/11, you are presumably flattening the 5th by a quartertone. This makes the major 2nd sound minor, and the major 3rd sound diminished! --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 07:23, 2 August 2021 (UTC)