Talk:The Riemann zeta function and tuning: Difference between revisions
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: Also, I'm not convinced that zeta integral is a useless metric to the point of not including it because it represents how well an equal temperament does when detuned so that it is a "peak" in a more general sense. In other words, because of this property, I firmly believe the zeta integral list makes more sense to think of as a "zeta EDO list" than the zeta peak list. You could say taking the values at the EDOs makes the most sense but after consideration of how zeta works/behaves, allowing octave tempering can be seen as a method of accounting for the "tendency" of an equal temperament (whether it generally tunes primes sharp or flat), hence resulting in only favouring systems that tend close to just. --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 19:01, 14 April 2025 (UTC) | : Also, I'm not convinced that zeta integral is a useless metric to the point of not including it because it represents how well an equal temperament does when detuned so that it is a "peak" in a more general sense. In other words, because of this property, I firmly believe the zeta integral list makes more sense to think of as a "zeta EDO list" than the zeta peak list. You could say taking the values at the EDOs makes the most sense but after consideration of how zeta works/behaves, allowing octave tempering can be seen as a method of accounting for the "tendency" of an equal temperament (whether it generally tunes primes sharp or flat), hence resulting in only favouring systems that tend close to just. --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 19:01, 14 April 2025 (UTC) | ||
:: Ok, it could be made more clear that it's a relative error measurement. It's there in the intro but not in the derivation. To be honest I wouldn't read that much into the "intuitive explanation" section, there's a lot of details that I'm skipping over deliberately. | |||
:: As for your second point, I don't personally believe integral or gap lists are that meaningful, if only because they depend on the choice of sigma = 1/2. But currently the plan is the leave the main lists as they are right now, so the integral list would be included. Also, the general sharp/flat tendency is taken into account already by taking non-integer peaks, so I do agree that restricting to integers is not that interesting. | |||
:: – [[User:Sintel|Sintel🎏]] ([[User_talk:Sintel|talk]]) 20:08, 14 April 2025 (UTC) | |||