Talk:Tenney–Euclidean metrics: Difference between revisions

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 : 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)