Talk:The Riemann zeta function and tuning: Difference between revisions
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I can say with confidence that every EDO >= 111 (except maybe 121) deserves to be here, though it's sad that {{EDOs| 48, 50, 56, 106, 113, 137, 149, 161, 193, 202, 229, 239, 248, 277 }} (which I mention as being present in the extended list I added) are missed (which also very much deserve to be there). | I can say with confidence that every EDO >= 111 (except maybe 121) deserves to be here, though it's sad that {{EDOs| 48, 50, 56, 106, 113, 137, 149, 161, 193, 202, 229, 239, 248, 277 }} (which I mention as being present in the extended list I added) are missed (which also very much deserve to be there). | ||
The way I am judging is looking how many occurrences there are of that EDO in the <code>optimal_edo_sequence</code>s for odd-limits 23 thru 123. For EDOs 72 or smaller it's possible to evaluate manually fairly easily, so that this is mainly for larger EDOs, because EG it's not obvious that 106et would be performant. Some EDOs like 190 appear very rarely by this metric, but as 190 has about the same score as 193 (so that IIRC zeta slightly prefers 190 to 193) it seems worth including. Examples of large EDOs present in none of these zeta lists discusssed so far but appearing abundantly in the <code>optimal_edo_sequence</code>s for odd-limits 23 thru 123 are [[181edo]] and [[258edo]], where the former is notably only two off from [[183edo]]. 181 and 183 appear the same number of times (25), where ~half of the time only one of the two appear and the other ~half both appear. An example of a medium EDO that appears in a variety of altered zeta EDO lists but which hasn't appeared any of these is [[62edo]], which appears in the <code>optimal_edo_sequence</code> for every odd-limit 19 thru 77 except 27, as well as in the 93-, 95- and 97-odd-limit. | The way I am judging is looking how many occurrences there are of that EDO in the <code>optimal_edo_sequence</code>s for odd-limits 23 thru 123. For EDOs 72 or smaller it's possible to evaluate manually fairly easily, so that this is mainly for larger EDOs, because EG it's not obvious that 106et would be performant. Some EDOs like 190 appear very rarely by this metric, but as 190 has about the same score as 193 (so that IIRC zeta slightly prefers 190 to 193) it seems worth including. Examples of large EDOs present in none of these zeta lists discusssed so far but appearing abundantly in the <code>optimal_edo_sequence</code>s for odd-limits 23 thru 123 are [[181edo]] and [[258edo]], where the former is notably only two off from [[183edo]]. 181 and 183 appear the same number of times (25), where ~half of the time only one of the two appear and the other ~half both appear. An example of a medium EDO that appears in a variety of altered zeta EDO lists but which hasn't appeared in any of these is [[62edo]], which appears in the <code>optimal_edo_sequence</code> for every odd-limit 19 thru 77 except 27, as well as in the 93-, 95- and 97-odd-limit. | ||
To my eye, the only EDOs that seem out of place in the extended list that I documented are {{EDOs| 38, 39, 45, 60, 96, 176, 212 }}, which I suspected intuitively, but confirmed via checking number of occurrences in the <code>optimal_edo_sequence</code>s for odd-limits 19 thru 123: 38 has one appearance (39-odd-limit), 39 has zero (though that one's unfair cuz it's not octave-tempered but zeta tells us it really should be), 45 has zero, 60 has two (31- and 33-odd-limit), 96 has zero, 176 has zero and 212 has zero. But for some reason, zeta prefers 60et over 63et generally speaking. | To my eye, the only EDOs that seem out of place in the extended list that I documented are {{EDOs| 38, 39, 45, 60, 96, 176, 212 }}, which I suspected intuitively, but confirmed via checking number of occurrences in the <code>optimal_edo_sequence</code>s for odd-limits 19 thru 123: 38 has one appearance (39-odd-limit), 39 has zero (though that one's unfair cuz it's not octave-tempered but zeta tells us it really should be), 45 has zero, 60 has two (31- and 33-odd-limit), 96 has zero, 176 has zero and 212 has zero. But for some reason, zeta prefers 60et over 63et generally speaking. | ||
--[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 18:10, 16 April 2025 (UTC) | --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 18:10, 16 April 2025 (UTC) | ||