Talk:20567edo

14 inconsistent pairs

I'm not sure of the notability given that, to be clear. —FloraC (talk) 09:37, 31 January 2026 (UTC)

The no-61 81-odd limit has a colossal number of intervals, 1288 to be exact. This behemoth consistently approximates 1260 of those (97.82%). Is there a smaller edo that approximates such a huge odd-limit, within some reasonable restrictions? The only one I can think about is 1600edo with the 45-odd-limit (424 intervals), on which only 39/25; 50/39 fail (99.53%) --Eufalesio (talk) 12:27, 2 February 2026 (UTC)

I'm not convinced that the percentage of consistently mapped intervals in an odd limit is a useful metric to start with, and imo odd limits stop being useful way before 81, in addition to the fact that 20567 is a giant mega-edo that is already noted to be consistent in the 57-odd-limit. Besides, you can eliminate 4 inconsistently mapped interval pairs and get an even higher percentage if you set the limit to 79, so I still don't see a reason to specifically note the 14 inconsistent pairs in the 81-odd-limit, I'm afraid. —FloraC (talk) 17:46, 2 February 2026 (UTC)

Percentage helps, but I've noticed that absolute number of consistent interval pairs are more important. You raise a good point that there are "only" 10 inconsistent pairs with the 79-odd-limit, but that's only a 0.55% decrease from the 81-odd-limit. At what point does an edo's odd-limit have too many inconsistencies to be definitely not usable? And add to that, what consistency denominations are truly useful?

I would say in this case, no-61 81-odd-limit is a good point to stop. You can do fine without one specific super high prime, add 4 more to add more bang to your buck, the rest of the primes beyond 79 are badly approximated, and, it ends in a power of 3. Glazing? Possibly. But, this edo is already very niche, so selling it as an even higher limit beast will help fortify the image in its niche substantially. Besides, this glazing is not entirely baseless.