Talk:Riemann zeta function: Difference between revisions
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::: – [[User:Sintel|Sintel🎏]] ([[User_talk:Sintel|talk]]) 23:04, 14 April 2025 (UTC) | ::: – [[User:Sintel|Sintel🎏]] ([[User_talk:Sintel|talk]]) 23:04, 14 April 2025 (UTC) | ||
== Criticisms of | == Criticisms of and possible improvements to new list == | ||
If anyone doesn't think these lists are high-quality enough I first encourage naming a bunch of EDOs you don't think should be included in the list (note that 39edo isn't included in any list because it's 39et that's included, as 39edo is near a zeta valley), and then discussing how to improve it. I agree that there are a few ETs in the extended list that seem out of place, and that it seems to get slightly more dubious as we look at larger ETs. Therefore one fix is instead of looking at the absolute error (multiplying by the ET) we could still take tone-efficiency into account by multiplying by the square-root of the ET, but this is harder to motivate beyond "a balance between only caring about relative error (efficiency) and only caring about absolute error (tuning damage)", so it sort of implicates the inclusion of the latter list as a prerequisite so we have something to compare to. Another alteration is trying to improve the extended list. For example, we could include all ETs that do better than the second-best ''record-setter'' rather than the second-best ''scorer'', so that we have a bound that is more forgiving than "second-best scorer" without including too many ETs as "better than third-best scorer" might be judged to do. This is again harder to motivate, but if we take both of these alterations as a given, the list is extremely high-quality. Again, {{nowrap| ''s'' {{=}} 1/2}} and {{nowrap| ''s'' {{=}} 1}} give the same results thru 311et, with the only difference being that {{nowrap| ''s'' {{=}} 1/2}} includes 37et and 121et. The resulting sequence is: | If anyone doesn't think these lists are high-quality enough I first encourage naming a bunch of EDOs you don't think should be included in the list (note that 39edo isn't included in any list because it's 39et that's included, as 39edo is near a zeta valley), and then discussing how to improve it. I agree that there are a few ETs in the extended list that seem out of place, and that it seems to get slightly more dubious as we look at larger ETs. Therefore one fix is instead of looking at the absolute error (multiplying by the ET) we could still take tone-efficiency into account by multiplying by the square-root of the ET, but this is harder to motivate beyond "a balance between only caring about relative error (efficiency) and only caring about absolute error (tuning damage)", so it sort of implicates the inclusion of the latter list as a prerequisite so we have something to compare to. Another alteration is trying to improve the extended list. For example, we could include all ETs that do better than the second-best ''record-setter'' rather than the second-best ''scorer'', so that we have a bound that is more forgiving than "second-best scorer" without including too many ETs as "better than third-best scorer" might be judged to do. This is again harder to motivate, but if we take both of these alterations as a given, the list is extremely high-quality. Again, {{nowrap| ''s'' {{=}} 1/2}} and {{nowrap| ''s'' {{=}} 1}} give the same results thru 311et, with the only difference being that {{nowrap| ''s'' {{=}} 1/2}} includes 37et and 121et. The resulting sequence is: | ||