Talk:The Riemann zeta function and tuning: Difference between revisions
m →Reworking page: clarify what i meant about zeta integral being significant (or at least why i think it's significant) |
concern about replacing the page |
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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) | ||
=== General concern about edit strategy === | |||
I generally am opposed to simply replacing a page that has had many small contributions over a long period of time and which has existed mostly unchanged unless that page is clearly very bad to the point of being hard to salvage without essentially rewriting it completely. I believed that the [[Father–3 equivalence continuum]] was bad enough to warrant this strategy (I wanted to replace it with what is currently located at [[Father–3 equivalence continuum/Godtone's approach]], but in retrospect I should've tried moving the former to a sub-page as my intent wasn't deletion). I don't believe the zeta page is bad enough. The issues I believe that page has that I don't believe the zeta page has are: | |||
* Lacking clear motivation as to why you'd want to make certain choices. Gene's derivation does not lack this and I just went through the effort of making explicit some things that might be non-obvious. | |||
* Comprehensibility: even for a math-intimidated reader, the result is ultimately in edo lists of one kind or another, which IMO ''are'' accessible, given they stand out as lists of clickable numbers, and given you aren't required to understand all parts of a derivation to make use of the result. (For example, I don't understand the very last steps in Gene's derivation, but I understand them as being a mathematical exercise of showing equivalence so that it's in a sense a trivial (but important to work out for rigor) detail.) By contrast, the rational points at which temperaments are located in the continuum don't correspond to anything obvious unless you already know what sort of relation it's supposed to have. | |||
Having said this, I don't understand the other derivations well enough to comment on their comprehensibility or well-motivatedness (which probably reflects badly on them TBH). | |||
Point being, as a wiki, I believe the purpose is above all to document. To document well should not be a reason for replacing what many had previously collectively agreed was worth documenting through incremental changes. Therefore I believe it's much more productive to bring up specific sections of the zeta page that might be in dire need of change/replacement, rather than replacing the whole page outright. (Unless I've misunderstood how much or what [[User:Sintel/Zeta_working_page]] is supposed to replace exactly?) | |||
--[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 21:27, 14 April 2025 (UTC) | |||