Talk:Marvel: Difference between revisions

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::::: I understand and can sympathize about your frustration in the XA Discord. Thanks for the detailed explanation. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 16:23, 18 January 2025 (UTC)

=== Continued discussion of odd-limit complexity weighting ===

"if each individual case were impractical, they'd prolly not magically combine to something practical" to be honest I don't see why not; if the same EDO appears in the sequence for multiple tonality diamonds you're interested in (both simple and complex), how is it flawed to pick that EDO as your tuning of interest for trying out/further investigation? (This is especially true if you investigate different punishment strategies and it generally keeps appearing, because that ensures a more diverse sample of philosophies for tuning agreeing on the same tuning.)

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:: I wanted to elaborate on something I said a little: "It doesn't seem like the answer could be less sensitive than this, but it's admittedly a strange answer I'd like more justification for". The weird thing about using the square-root of the odd-limit was when I used the most contentious interval I accepted the tempering of as psychoacoustically convincing (which is the ~3/2 and ~4/3 in 7edo), then the implied bounds for all the odd-limits seem to match my experience with a suspicious degree of accuracy, recognising, for example, that [[80edo]]'s very off [[~]][[15/13]] is tempered with basically exactly as much damage as I can accept for harmonically-contextualised purposes.

:: "Becuz I also take account of harmonic significance and frequency of use" I think this is maybe where the disagreement is arising from. I fundamentally don't agree that you can weight in this way; you can't say "because I use 3/2 often, therefore 3/2 is the most important to have low error on", because that disregards the tuning fidelity required for more complex intervals. It doesn't matter how infrequently you use something; if you do use it, then having it be too damaged will have consequences in its sound (specifically its capability of concordance) so you either do or don't care about whether it concords. Plus, if you wanted to adopt that philosophy then ironically [[53edo]] is ''definitely'' optimal for marvel, because it cares first and foremost about 2-limit, then 3-limit, then 5-limit, then 7-limit, then 11-limit, ''strictly'' in that order, which is exactly the proposed frequency falloff you are advocating for. So by your own reasoning, it should be the best tuning for it, because it tunes primes better the smaller they are. Discarding it due to the uneven tuning of the full 9-odd-limit is indirectly an admission of complexity weighting, at which point you can't avoid the fact that more complex intervals need to be tuned better to concord. How much better is up to debate ofc, but it's definitely not unweighted for the reasons I gave.

:: "Becuz I also take account of harmonic significance and frequency of use" I think this is maybe where the disagreement is arising from. I fundamentally don't agree that you can weight in this way; you can't say "because I use 3/2 often, therefore 3/2 is the most important to have low error on", because that disregards the tuning fidelity required for more complex intervals as well as disregards that your 3/2 may already be good enough for every practical purpose (which is especially likely if you look at larger odd-limits including composite odds because of the frequency of 3 appearing in the factorisation). It doesn't matter how infrequently you use something; if you do use it, then having it be too damaged will have consequences in its sound (specifically its capability of concordance) so you either do or don't care about whether it concords. Plus, if you wanted to adopt that philosophy then ironically [[53edo]] is ''definitely'' optimal for marvel, because it cares first and foremost about 2-limit, then 3-limit, then 5-limit, then 7-limit, then 11-limit, ''strictly'' in that order, which is exactly the proposed frequency falloff you are advocating for. So by your own reasoning, it should be the best tuning for it, because it tunes primes better the smaller they are. Discarding it due to the uneven tuning of the full 9-odd-limit is indirectly an admission of complexity weighting, at which point you can't avoid the fact that more complex intervals need to be tuned better to concord. How much better is up to debate ofc, but it's definitely not unweighted for the reasons I gave.

:: --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 17:32, 20 January 2025 (UTC)

::: I don't think I've misunderstood. I specifically meant that when you pick a limit, you care about that limit (which includes smaller limits) and do not care about any intervals outside of it. For example when you pick 25 as a limit, you absolutely don't care about intervals of 27. That doesn't happen in reality cuz if I care about 25 so much that I put it at the local peak of the weighting curve, I have no reason to completely dismiss 27.

::: Next you said: "I just don't see what the point of targeting more complex harmonies at all is in that case." My answer is: it's not granted that there should be a point of targeting more complex harmonies. The worth of it is something that needs proof. I've been holding that the objectively best thus optimal and recommendable weighting curve is where you don't have to choose a target, and where it just does the rolloff for you.

::: Note that looking at multiple sequences and counting the times an edo appears isn't the same as interpolating the scores of the edo across limits. Interpolation would make some sense, actually, since that can translate to a configuration of the weighting curve. Counting the times cannot. It implies a completely different mindset, which I've described. You care about a limit and specifically not any intervals outside of it, and then you care about a larger limit which defies your previous choice. Then you care about yet another larger limit which defies your previous two choices. Now I don't think this is utterly wrong, but it's a new, opaque metric layered on the old metric. Same problem as POTE, if that means something to you. You could say there's some sort of "black magic" that somehow makes it close enough to what you want, but as I said it doesn't translate to or represent a realistic scenario. Generally you have a scenario in your mind and find a mathematical model for it. I find it hard to believe in if a model doesn't correspond to a scenario.

::: I'll keep holding that the optimal tuning should take account of harmonic significance and frequency of use. First, I disagree that it disregards the tuning fidelity required for more complex intervals. It just trades that against the other concerns which are just as pressing if not more so. Second, by frequency I do imply probability, cuz frequency is the expected value of use/unuse of the interval. If you're not sure you're gonna use a certain complex interval like once in a hundred chords then giving it a high weight is a waste of optimization resource. So it's not that either I care or don't care about whether it concords. More like I care, but the amount of care is in a way proportional to its harmonic significance and frequeny of use.

::: 53edo is clearly undertempered cuz it trades simple 7-odd-limit concords in favor of complex 25-odd-limit wolves. It might score better in wilson metrics than tenney cuz wilson is where 9 is simpler than 7, but 25 is still more complex than both 7 and 9, in addition to the fact recognized by euclidean metrics that trading 25 for 7 in marvel is more efficient use of optimization resource in the same way as trading 3 for 5 is in meantone. Ftr, here's the BE-optimal GPV sequence for septimal marvel:

::: 10, 12, 19, 31, 41, 53, 72, 125, 197.

::: For undecimal marvel:

::: 10, 12e, 19, 22, 31, 41, 53, 72, 125, 166, 197e, 269ce, 435cce.

::: [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 11:01, 21 January 2025 (UTC)

:::: There is a reason that counting the times is way better than building in interpolation in the way you suggest. It's because of the tuning fidelity issue. If I build in a weighting curve, then I am algorithmically giving permission for the most complex harmonies to be the most off, which I've argued is objectively the wrong choice if you want to target those harmonies. By contrast, by not having a falloff I am ensuring that if those harmonies are too off, the rest of the tuning better be worth the sacrifice in the tuning fidelity where it's most needed. This allows systems that are biased to simpler harmonies appear. I've expressed that already I'm not sure if weighting proportional to the square root of the odd-limit is too forgiving for complex harmonies, but some strange edos can start appearing if you bias too strongly for large odd-limits. For example, using proportional to the odd-limit implies [[67edo]] is a lower-absolute-error system for the [[17-odd-limit]] than [[58edo]], which I suspect is happening because of the sharp 11 and 13 of 58edo being punished more strongly as a result, which I don't find convincing. --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 15:59, 21 January 2025 (UTC)

::::: You've already given permission for whatever intervals beyond the limit you specify to be the most off. You've already allowed, by specifying the 25-odd-limit, intervals of 27 to be the most off, which is "objectively the wrong choice" by your logic. So I don't get what you're insisting. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 10:10, 2 February 2025 (UTC)

@@ Line 167: / Line 167: @@
 ::::: I understand and can sympathize about your frustration in the XA Discord. Thanks for the detailed explanation. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 16:23, 18 January 2025 (UTC)
+=== Continued discussion of odd-limit complexity weighting ===
 "if each individual case were impractical, they'd prolly not magically combine to something practical" to be honest I don't see why not; if the same EDO appears in the sequence for multiple tonality diamonds you're interested in (both simple and complex), how is it flawed to pick that EDO as your tuning of interest for trying out/further investigation? (This is especially true if you investigate different punishment strategies and it generally keeps appearing, because that ensures a more diverse sample of philosophies for tuning agreeing on the same tuning.)
@@ Line 196: / Line 198: @@
 :: I wanted to elaborate on something I said a little: "It doesn't seem like the answer could be less sensitive than this, but it's admittedly a strange answer I'd like more justification for". The weird thing about using the square-root of the odd-limit was when I used the most contentious interval I accepted the tempering of as psychoacoustically convincing (which is the ~3/2 and ~4/3 in 7edo), then the implied bounds for all the odd-limits seem to match my experience with a suspicious degree of accuracy, recognising, for example, that [[80edo]]'s very off [[~]][[15/13]] is tempered with basically exactly as much damage as I can accept for harmonically-contextualised purposes.
-:: "Becuz I also take account of harmonic significance and frequency of use" I think this is maybe where the disagreement is arising from. I fundamentally don't agree that you can weight in this way; you can't say "because I use 3/2 often, therefore 3/2 is the most important to have low error on", because that disregards the tuning fidelity required for more complex intervals. It doesn't matter how infrequently you use something; if you do use it, then having it be too damaged will have consequences in its sound (specifically its capability of concordance) so you either do or don't care about whether it concords. Plus, if you wanted to adopt that philosophy then ironically [[53edo]] is ''definitely'' optimal for marvel, because it cares first and foremost about 2-limit, then 3-limit, then 5-limit, then 7-limit, then 11-limit, ''strictly'' in that order, which is exactly the proposed frequency falloff you are advocating for. So by your own reasoning, it should be the best tuning for it, because it tunes primes better the smaller they are. Discarding it due to the uneven tuning of the full 9-odd-limit is indirectly an admission of complexity weighting, at which point you can't avoid the fact that more complex intervals need to be tuned better to concord. How much better is up to debate ofc, but it's definitely not unweighted for the reasons I gave.
+:: "Becuz I also take account of harmonic significance and frequency of use" I think this is maybe where the disagreement is arising from. I fundamentally don't agree that you can weight in this way; you can't say "because I use 3/2 often, therefore 3/2 is the most important to have low error on", because that disregards the tuning fidelity required for more complex intervals as well as disregards that your 3/2 may already be good enough for every practical purpose (which is especially likely if you look at larger odd-limits including composite odds because of the frequency of 3 appearing in the factorisation). It doesn't matter how infrequently you use something; if you do use it, then having it be too damaged will have consequences in its sound (specifically its capability of concordance) so you either do or don't care about whether it concords. Plus, if you wanted to adopt that philosophy then ironically [[53edo]] is ''definitely'' optimal for marvel, because it cares first and foremost about 2-limit, then 3-limit, then 5-limit, then 7-limit, then 11-limit, ''strictly'' in that order, which is exactly the proposed frequency falloff you are advocating for. So by your own reasoning, it should be the best tuning for it, because it tunes primes better the smaller they are. Discarding it due to the uneven tuning of the full 9-odd-limit is indirectly an admission of complexity weighting, at which point you can't avoid the fact that more complex intervals need to be tuned better to concord. How much better is up to debate ofc, but it's definitely not unweighted for the reasons I gave.
 :: --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 17:32, 20 January 2025 (UTC)
+::: I don't think I've misunderstood. I specifically meant that when you pick a limit, you care about that limit (which includes smaller limits) and do not care about any intervals outside of it. For example when you pick 25 as a limit, you absolutely don't care about intervals of 27. That doesn't happen in reality cuz if I care about 25 so much that I put it at the local peak of the weighting curve, I have no reason to completely dismiss 27.
+::: Next you said: "I just don't see what the point of targeting more complex harmonies at all is in that case." My answer is: it's not granted that there should be a point of targeting more complex harmonies. The worth of it is something that needs proof. I've been holding that the objectively best thus optimal and recommendable weighting curve is where you don't have to choose a target, and where it just does the rolloff for you.
+::: Note that looking at multiple sequences and counting the times an edo appears isn't the same as interpolating the scores of the edo across limits. Interpolation would make some sense, actually, since that can translate to a configuration of the weighting curve. Counting the times cannot. It implies a completely different mindset, which I've described. You care about a limit and specifically not any intervals outside of it, and then you care about a larger limit which defies your previous choice. Then you care about yet another larger limit which defies your previous two choices. Now I don't think this is utterly wrong, but it's a new, opaque metric layered on the old metric. Same problem as POTE, if that means something to you. You could say there's some sort of "black magic" that somehow makes it close enough to what you want, but as I said it doesn't translate to or represent a realistic scenario. Generally you have a scenario in your mind and find a mathematical model for it. I find it hard to believe in if a model doesn't correspond to a scenario.
+::: I'll keep holding that the optimal tuning should take account of harmonic significance and frequency of use. First, I disagree that it disregards the tuning fidelity required for more complex intervals. It just trades that against the other concerns which are just as pressing if not more so. Second, by frequency I do imply probability, cuz frequency is the expected value of use/unuse of the interval. If you're not sure you're gonna use a certain complex interval like once in a hundred chords then giving it a high weight is a waste of optimization resource. So it's not that either I care or don't care about whether it concords. More like I care, but the amount of care is in a way proportional to its harmonic significance and frequeny of use.
+::: 53edo is clearly undertempered cuz it trades simple 7-odd-limit concords in favor of complex 25-odd-limit wolves. It might score better in wilson metrics than tenney cuz wilson is where 9 is simpler than 7, but 25 is still more complex than both 7 and 9, in addition to the fact recognized by euclidean metrics that trading 25 for 7 in marvel is more efficient use of optimization resource in the same way as trading 3 for 5 is in meantone. Ftr, here's the BE-optimal GPV sequence for septimal marvel:
+::: 10, 12, 19, 31, 41, 53, 72, 125, 197.
+::: For undecimal marvel:
+::: 10, 12e, 19, 22, 31, 41, 53, 72, 125, 166, 197e, 269ce, 435cce.
+::: [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 11:01, 21 January 2025 (UTC)
+:::: There is a reason that counting the times is way better than building in interpolation in the way you suggest. It's because of the tuning fidelity issue. If I build in a weighting curve, then I am algorithmically giving permission for the most complex harmonies to be the most off, which I've argued is objectively the wrong choice if you want to target those harmonies. By contrast, by not having a falloff I am ensuring that if those harmonies are too off, the rest of the tuning better be worth the sacrifice in the tuning fidelity where it's most needed. This allows systems that are biased to simpler harmonies appear. I've expressed that already I'm not sure if weighting proportional to the square root of the odd-limit is too forgiving for complex harmonies, but some strange edos can start appearing if you bias too strongly for large odd-limits. For example, using proportional to the odd-limit implies [[67edo]] is a lower-absolute-error system for the [[17-odd-limit]] than [[58edo]], which I suspect is happening because of the sharp 11 and 13 of 58edo being punished more strongly as a result, which I don't find convincing. --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 15:59, 21 January 2025 (UTC)
+::::: You've already given permission for whatever intervals beyond the limit you specify to be the most off. You've already allowed, by specifying the 25-odd-limit, intervals of 27 to be the most off, which is "objectively the wrong choice" by your logic. So I don't get what you're insisting. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 10:10, 2 February 2025 (UTC)