Talk:The Riemann zeta function and tuning: Difference between revisions
correction |
add extra explanation for why i believe the adjustment is correct |
||
| Line 120: | Line 120: | ||
:: --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 21:19, 16 April 2025 (UTC) | :: --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 21:19, 16 April 2025 (UTC) | ||
::: I've been trying to figure out how to make it more clear why I believe that the alteration is correct. So it seems like it must be correct to think of cosine as being a function that gives a reward or punishment in the -1 to 1 range so that confirms it is in some sense directly related to the step size. The question is rather whether multiplying by ''x'' is for sure the right adjustment to make it absolute. The reason I believe it is correct is because of how we expect the relative and absolute scoring function to behave w.r.t. contorted systems. Consider 53edo which is very strong in the 5-limit, so that its 5-limit mapping is preserved for quite a few multiples. The cosine will consider 53''x''-edo as having underlying relative errors as ''x'' times as off, and in the absolute sense this corresponds to the maximum offness being 1/''x'' the size. Therefore, if we want to adjust for the fact that we are judging with a -1 to 1 range for harmonics that can only be up to 1/''x'' as off, isn't the correct adjustment necessarily to multiply by ''x''? --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 15:42, 17 April 2025 (UTC) | |||