Talk:Tenney–Euclidean metrics: Difference between revisions

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+== simple badness / relative error ==
+In the "TE logflat badness" section it says, "If we define S(A) to be the simple badness (relative error) of A" but I can't figure out what this refers to. It might be [[Tenney-Euclidean_temperament_measures#TE_simple_badness|TE simple badness]] but it might also be [[relative error]]. Does anyone know which, and could they link it up?
+Also, isn't it kind of weird that we have this page for Tenney-Euclidian metrics, but also a page for Tenney-Euclidian temperament measures? What's the diff?
+--[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 00:27, 28 April 2021 (UTC)
+: It's TE simple badness aka relative error ''of a temperament''. It's not the relative error of a single interval.
+: It seems again, the TE temperament measures are about temperaments whereas TE metrics are about intervals. And I do agree the section on logflat badness should go to TE temperament measures page. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 07:53, 28 April 2021 (UTC)
+== logflat derivation ==
+I'd like to have some derivation of the 'flatness' of logflat badness. After some research it seems to be related to what is known as simultaneous diophantine approximations. A theorem + proof for the rank-1 case can be found in "An Introduction to the Theory of Numbers" by Hardy and Wright, theorem 200 in the 4th edition. I have no idea how this works for higher rank, except that the formula seems like it should be mu = r/(d-r).
+In this [https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10079.html discussion on the tuning list] Gene said:
+: I discovered it via a convoluted derivation. It's simple enough that there is probably a way of looking at it which makes it obvious, but I havn't given the matter a lot of thought.
+: I started out from the vals, where I had something derived from the theory of multiple diophantine approximation. Then putting vals together led me to the exponent, which turned out to have a simple formula. I think I may have posted something on it which was fairly indigestible when that happened.
+Which doesn't really help.
+- [[User:Sintel|Sintel]] ([[User talk:Sintel|talk]]) 15:27, 25 March 2022 (UTC)
+: Good news, I found a derivation in Y. Bugeaud et al. "On transfer inequalities in Diophantine approximation, II", https://arxiv.org/abs/0811.2102
+: I also request to unprotect this page. Just to clean up a bit, and move the logflat stuff to [[Tenney-Euclidean temperament measures]].
+: - [[User:Sintel|Sintel]] ([[User talk:Sintel|talk]]) 12:49, 10 April 2022 (UTC)
+:: I can move the part in question, but protection is a policy, unfortunately. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 15:55, 11 April 2022 (UTC)
+::: I think it's best to talk to [[User:Mike Battaglia|Mike Battaglia]] about this. He protected the page without giving a reason (normally no page – besides main – of a wiki is protected). --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 06:25, 12 April 2022 (UTC)
+:::: Hopefully [https://www.facebook.com/groups/xenwiki/permalink/3046365965629387/ Mike's FB post] answers part of this (hopefully this link works too). [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 13:04, 12 April 2022 (UTC)