Talk:The Riemann zeta function and tuning: Difference between revisions
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::: Well, to be specific, I didn't say that zeta integral was intended to account for octave-tempering, I said I believed it corresponded to robustness of detuning the octave so that it seems to me ''more reasonable'' to consider the pure-octaves tunings for zeta integral equal temperaments than zeta peak equal temperaments. This can be demonstrated pretty directly by noting that the zeta integer peaks are meaningfully different from the zeta peaks. --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 20:27, 14 April 2025 (UTC) | ::: Well, to be specific, I didn't say that zeta integral was intended to account for octave-tempering, I said I believed it corresponded to robustness of detuning the octave so that it seems to me ''more reasonable'' to consider the pure-octaves tunings for zeta integral equal temperaments than zeta peak equal temperaments. This can be demonstrated pretty directly by noting that the zeta integer peaks are meaningfully different from the zeta peaks. --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 20:27, 14 April 2025 (UTC) | ||
:::: Zeta integral and zeta peak integer are different metrics; ''zeta peak integer'' refers to the value of zeta at the pure-octave EDO while ''zeta integral'' refers to the integral/area under the curve between two zeros, which is only definable at s = 1/2 (assuming RH) because that's where the zeros are; similarly zeta gap refers to the distance between the two zeros adjoining the peak. Are you referring to peak integer edos instead? In that case the list is still on the working page. | :::: Zeta integral and zeta peak integer are different metrics; ''zeta peak integer'' refers to the value of zeta at the pure-octave EDO while ''zeta integral'' refers to the integral/area under the curve between two zeros, which is only definable at s = 1/2 (assuming RH) because that's where the zeros are; similarly zeta gap refers to the distance between the two zeros adjoining the peak (normalized in some way?) and is therefore also specific to s = 1/2. Are you referring to peak integer edos instead? In that case the list is still on the working page. | ||
:::: [[User:Lériendil|Lériendil]] ([[User talk:Lériendil|talk]]) 22:52, 14 April 2025 (UTC) | :::: [[User:Lériendil|Lériendil]] ([[User talk:Lériendil|talk]]) 22:52, 14 April 2025 (UTC) | ||