... Surely not -- it means the more complex a temperament the lower its badness. ... You would? ... He's right, with a caveat that there isn't always a single...
Hi Carl and thanks for your reply! ... Really? I thought it was something like error*complexity^something. ... What about nonoctave ETs? Wouldn't it be more...
... Oh sorry, that was supposed to be *, not /. ... Yes, it's on my list. ... I remember that. ... Didn't Paul say to minimize the 2nd biggest error, etc. in...
... As I just wrote to Graham, I meant * instead of /, but I think you're right, the ^something goes on complexity, and it's the number of primes - 1. ... ...
... Actually that's for linear temperaments, which used to be rank 1 I think. For ETs it would have been primes - 0. But now that linear temperaments are...
... I don't know what Paul said, but I certainly prefer to avoid complicating definitions. In this case, the second mapping looks better to me. It has a...
... I do mention this in my errors and complexities thing http://www.microtonal.co.uk/primerr.pdf The point is, there isn't an obvious way of comparing...
... But is there something wrong in using e.g. the reciprocal of the step size as a complexity measure? If not, my question then becomes: How to change the...
... If you're happy with it I don't think there are any snakes lurking. It's just nice to have a complexity that doesn't depend on the tuning. Graham...
... I try to answer this myself with help from http://tonalsoft.com/enc/b/badness.aspx So is max tenney-weighted error/step size^(3/2) correct for 5-limit?...
Let me try to remember what I wrote the first time I replied to this... ... Oh dear, I can barely understand TOP, let alone TOP-RMS. Do you really have...
... I can barely understand TOP, let alone TOP-RMS. Do you really have good generalizations of TOP for various average error measures? Like with TOP-RMS,...
... I have one variant for a different type of average, the RMS, and variants for octave equivalent approximations. There's no analogy that I can prove to...
... I assume you can calculate the TOP-RMS damage of a tuning. Have you then checked the Tenney-weighted RMS errors of some chords to see if any are greater? ...
... I don't see anything searching my tuning-math archive either. But I did come across Paul saying something about you 'cleverly reducing the steps necessary'...
... He says "For an ET, just stretch so that the weighted errors of the most upward-biased prime and most downward-biased prime are equal in magnitude and...
... Of course there are chords that are going to have higher error than the average. The TOP-RMS is vaguely correlated with the Tenney-weighted error of an...
... Thanks Gene, when the error is Tenney-weighted, the sequence of 5-limit ETs of decreasing badness is 1, 12, 53, 4296,... Of meantone ETs 12-equal has the...
... Badness is a tough tradeoff to make. 12 is not very many tones. It's hard to be non- ad hoc because one composer's delight is another's monstrosity. By...
... e*c^(pi(p)/(pi(p)-1)). ... Hi Carl, ... Yes, I know. My remark above implies that. ... Actually I would prefer something weaker! I would like to have a...
... I think 31 is the poptimal meantone. Maybe Gene'll be a long to explain it. Otherwise, how non-ad hoc do you want? I've found error*complexity is easy to...
... Sorry, I read this backwards (and hence incorrectly) upon replying. ... I'd expect an infinite number of ETs to temper out any comma. How does it work as...
... explain it. Hi Graham, I remember it being 81 for 5-limit. ... Ironically enough non-ad hocness is pretty subjective. At least no coefficients, please! ......
... No problem! ... You are right of course. But if we require that the best approximations of primes in the ET are the same as given by its mapping then I...
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