Talk:The Riemann zeta function and tuning: Difference between revisions

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 – [[User:Sintel|Sintel🎏]] ([[User_talk:Sintel|talk]]) 16:23, 13 April 2025 (UTC)
+: Re: "When we talk about how well an equal temperament (ET) approximates just intonation, we're essentially asking: "How accurately can this system represent the harmonic series?""
+: I believe this is wrong/misleading. The reason the list of EDOs given by zeta records is so sparse is because it measures only pure relative error and doesn't care whether you are looking at 2edo or 2000edo. It's fundamentally not fair to characterise it as "how accurately it can represent"; it's "how tone-efficiently it can represent for its size, with no other considerations". I've shown you get a lot more interesting EDOs/ETs if you multiply the resulting score by the size of the EDO/ET, and yet more if you consider things that, while not record peaks, are still better than one of the best of ''n'' previous peaks (where I suggest ''n'' = 3 as recovering almost all interesting tuning info). --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 18:56, 14 April 2025 (UTC)