Talk:The Riemann zeta function and tuning: Difference between revisions
m →Top 20 (and top 10) zeta edos: forgot to sign |
m →Alternate list based on unmodified zeta function: correction as per updating of list to top 10 and as per more stuff being added to that page |
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=== Alternate list based on unmodified zeta function === | === Alternate list based on unmodified zeta function === | ||
Here's a list based purely on unmodified zeta, in case someone proves the alteration is wrong (though I'd still be interested in an "absolute" version of the list that includes an equal temperament if it's better than the 3rd-best-scorer so far). Because there's no accounting for the size of the equal temperament, I'm giving equal temperaments a lot of chances to appear to try to account for this bias, so that an equal temperament appears if it's better than the | Here's a list based purely on unmodified zeta, in case someone proves the alteration is wrong (though I'd still be interested in an "absolute" version of the list that includes an equal temperament if it's better than the 3rd-best-scorer so far). Because there's no accounting for the size of the equal temperament, I'm giving equal temperaments a lot of chances to appear to try to account for this bias, so that an equal temperament appears if it's better than the 10th-best-scorer so far. The other reason I give so many chances is that the resulting list is very similar and also surprisingly high-quality. | ||
Take a look at [[User:Godtone/zeta]] and compare edos you're unsure about to [[User:Godtone/optimal_edo_sequences]] by looking for number of occurrences. | Take a look at [[User:Godtone/zeta#Top 10]] and compare edos you're unsure about to [[User:Godtone/optimal_edo_sequences]] by looking for number of occurrences. | ||
A rather strange recurring theme is 60edo is liked by zeta a surprising amount, but looking at its low- and high-limit tuning profile it doesn't seem that remarkable to me. (A strange coincidence is some time ago I had a dream that this was a good edo. That doesn't happen often at all (dreaming about edos, let alone a specific one being good; the dream said its 11-limit was good; maybe that's true in the sense that the high errors of 5, 7 and 11 can easily cancel each-other out in ratios or composites, since zeta doesn't obey a val). Also happens to be significant as the simplest way to represent fourth-order ambiguities in my theory of functional harmony which I derived from first principles starting from [[Ringer scale]]s (especially Perfect Ringer scales), so that (other than the 12edo intervals) it represents the most xenmelodically nontrivial categories available (which correspond to areas of nontrivial harmony).) | A rather strange recurring theme is 60edo is liked by zeta a surprising amount, but looking at its low- and high-limit tuning profile it doesn't seem that remarkable to me. (A strange coincidence is some time ago I had a dream that this was a good edo. That doesn't happen often at all (dreaming about edos, let alone a specific one being good; the dream said its 11-limit was good; maybe that's true in the sense that the high errors of 5, 7 and 11 can easily cancel each-other out in ratios or composites, since zeta doesn't obey a val). Also happens to be significant as the simplest way to represent fourth-order ambiguities in my theory of functional harmony which I derived from first principles starting from [[Ringer scale]]s (especially Perfect Ringer scales), so that (other than the 12edo intervals) it represents the most xenmelodically nontrivial categories available (which correspond to areas of nontrivial harmony).) | ||