Talk:Tenney-Euclidean metrics
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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 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?
--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. 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 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.
- 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.
- - Sintel (talk) 12:49, 10 April 2022 (UTC)
- I think it's best to talk to Mike Battaglia about this. He protected the page without giving a reason (normally no page – besides main – of a wiki is protected). --Xenwolf (talk) 06:25, 12 April 2022 (UTC)
- Hopefully Mike's FB post answers part of this (hopefully this link works too). FloraC (talk) 13:04, 12 April 2022 (UTC)