Talk:Superpyth-22 equivalence continuum

Suggested rename and re-parametrization

This should be renamed and re-parametrized to superpyth-22 equivalence continuum:

Temperaments in the continuum

n	Temperament	Comma
		Ratio	Monzo
0	22 & 22c		[35 -22⟩
1	Quasisuper	8388608/7971615	[23 -13 -1⟩
2	Diaschismic	2048/2025	[11 -4 -2⟩
3	Porcupine	250/243	[1 -5 3⟩
4	Comic	5120000/4782969	[13 -14 4⟩
…	…	…	…
∞	Superpyth	20480/19683	[12 -9 1⟩

Or doing it backwards, the quasisuper-22 equivalence continuum:

Temperaments in the continuum

n	Temperament	Comma
		Ratio	Monzo
0	22 & 22c		[35 -22⟩
1	Superpyth	20480/19683	[12 -9 1⟩
2	Diaschismic	2048/2025	[11 -4 -2⟩
3	22 & 29c		[34 -17 -3⟩
…	…	…	…
∞	Quasisuper	8388608/7971615	[23 -13 -1⟩

Or maybe we should call it superpyth-quasisuper based on the two "order-1" temperaments?

FloraC (talk) 08:21, 16 April 2023 (UTC)

Update: I've found some simple rules to follow:

1. n = 0 should correspond to a 3-limit comma (or in general, the comma that's independent of the last prime).
2. n = 1 should correspond to 1 or -1 in the next prime, and the comma should be smaller than that of n = 0. That seems to narrow the number of candidates down to 2. As we set one of them as n = 1, the other would be n = inf and vice versa.
3. As we decide which is n = 1 and which n = inf, we should try to keep the just value of n greater than 2. We might wanna present both tables in the page, one by n, and the other would be n/(n + 1).

So in this case the answer seems to be superpyth-22. Superpyth is also the smaller comma, as expected.

FloraC (talk) 08:35, 16 April 2023 (UTC)

Honestly, you probably know more about this than I do, so I think we should go with your idea. You can move the page and implement your idea if you want. I mainly just wanted to see the hyper-accurate temperaments that can be extracted from 22-edo. I created this page to extend your idea of equivalence continua to 22-edo, a somewhat accurate temperament for 7-limit.

--Royalmilktea (talk) 06:59, 9 May 2023 (UTC)