View source for Talk:Schismic–commatic 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 <s>Syntonic-Pythagorean</s> ''(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. <small>unsigned contribution by: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]], 6:18, 8 July 2024 (UTC)</small>

: 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. --[[User:Aura|Aura]] ([[User talk: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. [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk: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. [[User:FloraC|FloraC]] ([[User talk: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.  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 19:16, 30 July 2024 (UTC)

== 5-limit gracecordial ==
This restriction should not be canonical as both 113 & 125 and 149 & 161 are viable extensions and the optimum is around 137edo. Now there are "biscordial" and "triscordial" (idk why the ''s''), I think the restriction of gracecordial can be called ''monocordial''. —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 12:08, 24 April 2026 (UTC)