Talk:Marvel: Difference between revisions

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:::: --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 18:23, 17 January 2025 (UTC)

::::: You said: "I highly recommend looking at multiple <code>optimal_edo_sequence</code>s". To this I had answered: "Altho you measured a variety of odd limits to seemingly give results for a variety of use cases, if each individual case were impractical, they'd prolly not magically combine to something practical."

::::: Say I have a 50% probability of using intervals of 27 (cuz I can't know what chords I'm gonna use before composing), you believe I can extract something useful from your 25- and 27-odd-limit results by interpolating them or some other means. I mean, no. Your 25-odd-limit result is based on 100% for 25 and 0% for 27, and your 27-odd-limit result is based on 100% for 27. Neither is realistic. I'd much prefer a result that takes accounts of how much probability/frequency these intervals appear, and generally it's a rapidly decreasing probability/frequency with increasing complexity. If I use 27, I'll be using it like once in 100 times I use 3, 5, 7, and 9; I'll be using it like once in 10 times I use 15 and 21; and I might as well just insert 35 instead. So once in 100 times a chord is out of tune is generally not as bad as not tuning the rest 99 chords well. Simplicity weighting is just natural in these scenarios. Even equal weighting looks alright. I absolutely don't recommend complexity weighting and I have no idea how you got to complexity squared or even the fourth. You know it's absurd and I do too. In fact the paradox I raised happens with all complexity weighting. You start with infinite weight for the octaves. Then you have a valley. It grows to a peak at the limit, after which it's zero. We're staring at a zigzag when a function on the harmonic series is supposed to be smooth.

::::: You said: "Many of the best temperaments equating two intervals want ''both'' of the interpretations to be usable so that you can use the ambiguity for new progressions not possible in JI". The complex intervals we discussed (25/16, 75/64, etc.) can all be made evident by stacking simpler intervals, so even if the 25/16 is tuned to pure 14/9 (or even flat of 14/9), its identity is evident if you approach it by two steps of 5/4. That's also the most sane approach. I'm not saying you should use those intervals like that; I just mean those intervals can use those extra supports. In a way the tuning requirement of 25/16 is already covered by that of 5/4, so that's another reason I don't believe in complexity weighting.

::::: On the topic of duplicates in the tonality diamonds, you're right I won't trust the results more if you include them. I've said I don't think there's an objectively right answer and that I believe it only reflects personal artistic choices. I've said I don't like having this extra variable compared to the simplicity of prime-based/all-interval metrics.

::::: 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)

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 :::: --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 18:23, 17 January 2025 (UTC)
+::::: You said: "I highly recommend looking at multiple <code>optimal_edo_sequence</code>s". To this I had answered: "Altho you measured a variety of odd limits to seemingly give results for a variety of use cases, if each individual case were impractical, they'd prolly not magically combine to something practical."
+::::: Say I have a 50% probability of using intervals of 27 (cuz I can't know what chords I'm gonna use before composing), you believe I can extract something useful from your 25- and 27-odd-limit results by interpolating them or some other means. I mean, no. Your 25-odd-limit result is based on 100% for 25 and 0% for 27, and your 27-odd-limit result is based on 100% for 27. Neither is realistic. I'd much prefer a result that takes accounts of how much probability/frequency these intervals appear, and generally it's a rapidly decreasing probability/frequency with increasing complexity. If I use 27, I'll be using it like once in 100 times I use 3, 5, 7, and 9; I'll be using it like once in 10 times I use 15 and 21; and I might as well just insert 35 instead. So once in 100 times a chord is out of tune is generally not as bad as not tuning the rest 99 chords well. Simplicity weighting is just natural in these scenarios. Even equal weighting looks alright. I absolutely don't recommend complexity weighting and I have no idea how you got to complexity squared or even the fourth. You know it's absurd and I do too. In fact the paradox I raised happens with all complexity weighting. You start with infinite weight for the octaves. Then you have a valley. It grows to a peak at the limit, after which it's zero. We're staring at a zigzag when a function on the harmonic series is supposed to be smooth.
+::::: You said: "Many of the best temperaments equating two intervals want ''both'' of the interpretations to be usable so that you can use the ambiguity for new progressions not possible in JI". The complex intervals we discussed (25/16, 75/64, etc.) can all be made evident by stacking simpler intervals, so even if the 25/16 is tuned to pure 14/9 (or even flat of 14/9), its identity is evident if you approach it by two steps of 5/4. That's also the most sane approach. I'm not saying you should use those intervals like that; I just mean those intervals can use those extra supports. In a way the tuning requirement of 25/16 is already covered by that of 5/4, so that's another reason I don't believe in complexity weighting.
+::::: On the topic of duplicates in the tonality diamonds, you're right I won't trust the results more if you include them. I've said I don't think there's an objectively right answer and that I believe it only reflects personal artistic choices. I've said I don't like having this extra variable compared to the simplicity of prime-based/all-interval metrics.
+::::: 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)