Talk:Marvel: Difference between revisions

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--[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 22:52, 15 January 2025 (UTC)

A clarification on why the 7-limited 25-odd-limit is important to analyse for marvel: it is the smallest odd-limit which introduces a tempered equivalence within the interval set of the odd-limit other than the trivial [[~]][[16/15]][[~]][[15/14]], and the 25-odd-limit has significantly higher tuning fidelity than anything in the 9-odd-limit; the square root of 25/9 is 5/3, so the tuning fidelity required is almost double even if we use the very forgiving (nonstrict) "square root of the odd-limit" as a weighting for cent error, and is almost thrice otherwise, or even more if you are concerned with pure dyadic convincingness. Therefore, an optimized marvel tuning must clearly tune closer to [[32/25]] than to [[9/7]], because there is no good reason that the musically useful augmented fifth [[~]][[25/16]] should be discarded as a target given how naturally marvel extends a 5-limit lattice into the 7-limit, giving rise to things like the [[marveldene]]. There is also [[~][[28/25]][[~]][[9/8]] in the 7-limited 25-odd-limit but the usefulness of that seems more dubious, but it does show why ideally prime 3 should be tuned flat, hence systems like 72edo and 84edo.

(I think the one thing I do agree with though is that 16/15 is obviously undertempered in 53edo, but it seems to come about as a result of other considerations so I'm not fully sure it can be evaded because only a single 3 and 5 are involved. If you ask me, the smallest edo that is obviously "more optimized" (in terms of tuning) than 53edo for marvel is [[125edo]], its tuning profile looks about exactly correct as far as I ca tell. But that is over double the notes! I wouldn't dare add a single note more because already there is a lot of inconsistencies in higher 7-limited odd-limits as I've shown; I'll elaborate a little in the next (and final) post.)

--[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 23:42, 15 January 2025 (UTC)

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 --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 22:52, 15 January 2025 (UTC)
+A clarification on why the 7-limited 25-odd-limit is important to analyse for marvel: it is the smallest odd-limit which introduces a tempered equivalence within the interval set of the odd-limit other than the trivial [[~]][[16/15]][[~]][[15/14]], and the 25-odd-limit has significantly higher tuning fidelity than anything in the 9-odd-limit; the square root of 25/9 is 5/3, so the tuning fidelity required is almost double even if we use the very forgiving (nonstrict) "square root of the odd-limit" as a weighting for cent error, and is almost thrice otherwise, or even more if you are concerned with pure dyadic convincingness. Therefore, an optimized marvel tuning must clearly tune closer to [[32/25]] than to [[9/7]], because there is no good reason that the musically useful augmented fifth [[~]][[25/16]] should be discarded as a target given how naturally marvel extends a 5-limit lattice into the 7-limit, giving rise to things like the [[marveldene]]. There is also [[~][[28/25]][[~]][[9/8]] in the 7-limited 25-odd-limit but the usefulness of that seems more dubious, but it does show why ideally prime 3 should be tuned flat, hence systems like 72edo and 84edo.
+(I think the one thing I do agree with though is that 16/15 is obviously undertempered in 53edo, but it seems to come about as a result of other considerations so I'm not fully sure it can be evaded because only a single 3 and 5 are involved. If you ask me, the smallest edo that is obviously "more optimized" (in terms of tuning) than 53edo for marvel is [[125edo]], its tuning profile looks about exactly correct as far as I ca tell. But that is over double the notes! I wouldn't dare add a single note more because already there is a lot of inconsistencies in higher 7-limited odd-limits as I've shown; I'll elaborate a little in the next (and final) post.)
+--[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 23:42, 15 January 2025 (UTC)