Talk:Marvel: Difference between revisions

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:: --[[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)

@@ Line 201: / Line 201: @@
 :: --[[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)