User:Godtone/zeta: Difference between revisions

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We can be confident in their notability because the larger entries appear in a wide range of odd-limits (19 thru 123) according to [[User:Godtone/optimal edo sequences|the <code>optimal_edo_sequence</code>s for those odd-limits]]. (You can calculate them yourself by using my [[User:Godtone#My_Python_3_code|copyleft Python 3 code]] (which needs no dependencies).)

Specifically, an equal temperament is included if it does better than the 10th-best-scoring equal temperament so far*, and the below details both what is added to the sequence and the top 9 at any given point. These can mostly be thought of as corresponding to [[edo]]s with the exception of 39 equal temperament, because 39edo is close to a zeta valley so that it isn't meaningfully considered in-tune by zeta without the 3.8{{cent}} flat [[~~2/1|~~octave]] that zeta recommends.

Specifically, an equal temperament is included if it does better than the 10th-best-scoring equal temperament so far*, and the below details both what is added to the sequence and the top 9 at any given point. These can mostly be thought of as corresponding to [[edo]]s with the exception of 39 equal temperament, because 39edo is close to a zeta valley so that it isn't meaningfully considered in-tune by zeta without the 3.8{{cent}} flat [[octave]] that zeta recommends.

<nowiki>*</nowiki> For this reason, we start the list at 10et (corresponding to 10edo) because all previous equal temperaments' inclusion is unsurprising. (The first to be excluded is 18et, corresponding to [[18edo]] being close to a zeta valley.)

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 We can be confident in their notability because the larger entries appear in a wide range of odd-limits (19 thru 123) according to [[User:Godtone/optimal edo sequences|the <code>optimal_edo_sequence</code>s for those odd-limits]]. (You can calculate them yourself by using my [[User:Godtone#My_Python_3_code|copyleft Python 3 code]] (which needs no dependencies).)
-Specifically, an equal temperament is included if it does better than the 10th-best-scoring equal temperament so far*, and the below details both what is added to the sequence and the top 9 at any given point. These can mostly be thought of as corresponding to [[edo]]s with the exception of 39 equal temperament, because 39edo is close to a zeta valley so that it isn't meaningfully considered in-tune by zeta without the 3.8{{cent}} flat [[2/1|octave]] that zeta recommends.
+Specifically, an equal temperament is included if it does better than the 10th-best-scoring equal temperament so far*, and the below details both what is added to the sequence and the top 9 at any given point. These can mostly be thought of as corresponding to [[edo]]s with the exception of 39 equal temperament, because 39edo is close to a zeta valley so that it isn't meaningfully considered in-tune by zeta without the 3.8{{cent}} flat [[octave]] that zeta recommends.
 <nowiki>*</nowiki> For this reason, we start the list at 10et (corresponding to 10edo) because all previous equal temperaments' inclusion is unsurprising. (The first to be excluded is 18et, corresponding to [[18edo]] being close to a zeta valley.)