Higher primes
A while back I made an edit on 181edo, saying it has less than 30% error on most prime harmonics up to 137. You removed this info, giving the edit summary "don't bombard the readers with random prime numbers. 30% unsigned error isn't even special." There is a similar section on the page for 43edo, which goes as follows:
Although not consistent, 43edo performs quite well in very high prime limits. It has unambiguous mappings for all prime harmonics up to 113 (after which the demands on its pitch resolution finally become too great), with the sole exceptions of 23, 71, 89, and 103, making a great Ringer scale.
Here, prime 41 with 37.5% relative error is considered "unambiguous". Four missing primes in the 113-limit isn't really too special with this rather relaxed bound. You may want to do something about this section, though maybe more can be kept as 43edo is smaller than 181.--Overthink (talk) 22:52, 12 January 2026 (UTC)
- Originally, this part read:
Although not consistent, it performs quite decently in very high limits. It has unambiguous mappings for all prime harmonics up to 64 [61], with the sole exceptions of 23 and, perhaps, 41.
- Then some editor was being crazy about it cuz four exceptions are no sole exceptions. But I don't think I'm gonna remove that entirely. Rather, I'm moving it to a higher-limit JI subsection of the approximation to JI section to hopefully declutter the theory section.
2187/1250
I’m planning to draft a page for 2187/1250 in my userspace since it’s a 5-limit ratio closely approximating 7/4, but I think I should name it something. Something like 5-limit harmonic-esque seventh or something referencing the ragismic temperament since it’s 4375/4374 below 7/4. Do you have any name suggestions? hotcrystal0 19:12, 14 January 2026 (UTC)
Generator counts
I'm planning to start another chord page draft at User:Overthink/Chords of pajara (not yet created as of the time this is written). The issue is that it's not as simple to give a chord by generator counts, as there's a half-octave period in pajara. The page Unidec/Chords uses a val, but it is quite messy. I propose the following solution: The half-octave is taken as the period, and the generator is a perfect fifth. Intervals reachable by stacking fifths are just written with a number; for example, 1–3/2–12/7 would be "0–1–3". An interval that requires stacking fifths from the half-octave would be written with "T" (for tritone) before the number of fifths stacked; for example, 1–6/5–3/2 would be written as "0–T3–1". Maybe it would be better to give an "R" (for root) before intervals reachable by stacking fifths, so that 1–6/5–3/2 would be "R0–T3–R1", which is more readable. I'm also not too sure if the fifth should be the generator or the semitone instead.--Overthink (talk) 01:28, 20 January 2026 (UTC)
- I have to say I'm influenced by hkm's usage of an apostrophe to denote an offset by a period, so in that scheme, 1–6/5–3/2 can be written as "0–'3–1". I feel it looks fairly clean, not too intrusive, at least for temps with a semi-octave period. I think the generator should be taken as the fifth, not the semitone, cuz it's easier to think of the temp as two chains of fifths offset by a semi-octave. —FloraC (talk) 09:29, 20 January 2026 (UTC)
[-37 0 0 0 0 10⟩
Does there exist a page for the [-37 0 0 0 0 10⟩ comma, or the difference between 10 13/8s and 7 octaves? hotcrystal0 16:24, 20 January 2026 (UTC)