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.

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.)

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--[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 23:51, 15 January 2025 (UTC)

: Consistency is irrelevant for multirank temps. I'm sure I've related this to you many times. If you care about efficiency, the most efficient way to use these temps is always to only take the notes closest to the tonic on the lattice. None of the larger edos is "too many notes" if you're using the same scale/block in the lattice as they only differ by intonation.

: I strongly disagree about the metric you use to derive the "optimal edo sequence" and I've said this a few times too. I know you spent lots of time on it but first of all pls stop citing it as if it was some kind of objective metric. I've been skeptical about any claims involving taking average values from these diamonds. There's lots of open questions, like how you choose intervals from a tonality diamond. A tonality diamond has duplicate, unreduced intervals, e.g. for 3/2 there's 6/4, 9/6, and so on. Did you include these, reduced or unreduced? I guess you didn't, but why not? To be fair I don't think there's an answer to the best practice. The choices one makes here only represent how they see it and not others.

: For those reasons, I think metrics based on tonality diamonds are more questionable than prime-based/all-interval optimization schemes, and you can still give complex intervals more weight in these schemes. It's just that all complexity weighting faces the paradox that a growing weight suddenly plunges to zero at the edge of the limit, plus that tuning the octave pure no longer makes sense cuz if tuning sensitivity grows with complexity, the octave is supposed to be the least sensitive to mistuning.

: 105-odd-limit makes no sense for marvel as 25/16 is already conflated with 14/9. If I may propose an odd limit to look at, I'd say 21. But again I certainly won't recommend the metric you used. The very point of these temps is to trade high-odd-limit low-prime-limit intervals for low-odd-limit high-prime-limit intervals, in this case high-odd-limit HC5 intervals for low-odd-limit HC7 intervals. Your metric favors intervals like 75/64 over 7/6 which is a huge failure in assessing optimal tunings. They are the same one note in the temp and when playing it, no one cares it's out of tune from 75/64 as much as from 7/6. Similar story for 25/16 vs 14/9, or 32/25 vs 9/7 (ofc 25/16 isn't totally discarded: it's normally targeted more than for example 75/64; I just strongly disagree it should take priority over 14/9).

: As for the larger edos, they don't differ that much. I'm considering random readers here. It's best to offer them a number of choices without judging too much cuz they can judge by themselves. For 240edo specifically I think its tuning profile falls into the fuzzy optimal region as it has a flat 3, flat 5, and sharp 7, tuned pretty evenly out. Whether it's strictly optimal by certain criteria doesn't matter much.

: [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 08:27, 16 January 2025 (UTC)

@@ Line 85: / Line 85: @@
 --[[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.
+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.)
@@ Line 101: / Line 101: @@
 --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 23:51, 15 January 2025 (UTC)
+: Consistency is irrelevant for multirank temps. I'm sure I've related this to you many times. If you care about efficiency, the most efficient way to use these temps is always to only take the notes closest to the tonic on the lattice. None of the larger edos is "too many notes" if you're using the same scale/block in the lattice as they only differ by intonation.
+: I strongly disagree about the metric you use to derive the "optimal edo sequence" and I've said this a few times too. I know you spent lots of time on it but first of all pls stop citing it as if it was some kind of objective metric. I've been skeptical about any claims involving taking average values from these diamonds. There's lots of open questions, like how you choose intervals from a tonality diamond. A tonality diamond has duplicate, unreduced intervals, e.g. for 3/2 there's 6/4, 9/6, and so on. Did you include these, reduced or unreduced? I guess you didn't, but why not? To be fair I don't think there's an answer to the best practice. The choices one makes here only represent how they see it and not others.
+: For those reasons, I think metrics based on tonality diamonds are more questionable than prime-based/all-interval optimization schemes, and you can still give complex intervals more weight in these schemes. It's just that all complexity weighting faces the paradox that a growing weight suddenly plunges to zero at the edge of the limit, plus that tuning the octave pure no longer makes sense cuz if tuning sensitivity grows with complexity, the octave is supposed to be the least sensitive to mistuning.
+: 105-odd-limit makes no sense for marvel as 25/16 is already conflated with 14/9. If I may propose an odd limit to look at, I'd say 21. But again I certainly won't recommend the metric you used. The very point of these temps is to trade high-odd-limit low-prime-limit intervals for low-odd-limit high-prime-limit intervals, in this case high-odd-limit HC5 intervals for low-odd-limit HC7 intervals. Your metric favors intervals like 75/64 over 7/6 which is a huge failure in assessing optimal tunings. They are the same one note in the temp and when playing it, no one cares it's out of tune from 75/64 as much as from 7/6. Similar story for 25/16 vs 14/9, or 32/25 vs 9/7 (ofc 25/16 isn't totally discarded: it's normally targeted more than for example 75/64; I just strongly disagree it should take priority over 14/9).
+: As for the larger edos, they don't differ that much. I'm considering random readers here. It's best to offer them a number of choices without judging too much cuz they can judge by themselves. For 240edo specifically I think its tuning profile falls into the fuzzy optimal region as it has a flat 3, flat 5, and sharp 7, tuned pretty evenly out. Whether it's strictly optimal by certain criteria doesn't matter much.
+: [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 08:27, 16 January 2025 (UTC)