Talk:Schismic–Pythagorean equivalence continuum

Add option for Syntonic-Schismic equivalence continuum?

Wouldn't it be good to have a k = n - 1 option to equate this to a Syntonic-Pythagorean (edit: typo -- meant to put Syntonic-Schismic or Schismic-Syntonic) equivalence continuum, the same way the syntonic-chromatic equivalence continuum has a k = n - 2 option? This is because the Pythagorean comma will not be directly relevant for most temperaments that are not multiples of 12EDO, but the syntonic comma has wide relevance, both as a comma and as a musical interval in its own right. unsigned contribution by: Lucius Chiaraviglio, 6:18, 8 July 2024 (UTC)

For what it's worth, the Pythagorean comma not only has relevance as the difference between, say, C# and Db, but it has functions as a musical interval in its own right, much like the syntonic comma. That said, I can see what you're talking about otherwise. --Aura (talk) 14:36, 8 July 2024 (UTC)

I can see what you're saying about the Pythagorean comma as a musical interval in its own right (basically a negative Diesis) for an extended Pythagorean tuning (or at least something REALLY CLOSE like 53EDO -- I don't think something not quite so close like 41EDO would be close enough). But for non-Pythagorean tunings and non-multiples of 12EDO, the Syntonic comma is far more likely to be relevant. Lucius Chiaraviglio (talk) 19:20, 30 July 2024 (UTC)

Syntonic-commatic/Pythagorean is not k = n - 1 but m s.t. 1/m + 1/n = 1 as is already documented. I suppose you mean schismic-syntonic? Tbh I never find that k = n - 2 of syntonic-chromatic useful at all. You'd better ask Godtone, who proposed that. I for one think the most important of these temps is that the interval class of 3 is split into n or m parts. FloraC (talk) 12:10, 9 July 2024 (UTC)

Oops, typo. You're right -- I meant to put Syntonic-Schismic or Schismic-Syntonic. Fixing this in the title and in my original comment. Lucius Chiaraviglio (talk) 19:16, 30 July 2024 (UTC)