... Oh dear! You're really testing us aren't you? _SUB_harmonic series, ratios of 23, and tempering (albeit by ratios). ... The above notation is quite...
... I'd prefer to go with )|( as the 7:11 comma since it only involves a 0.55 cent schisma. I feel that a 3 flag symbol for something under 10 cents could not...
... There ... for ... be ... a ... choice ... Now that I've more time to look at this, I would say definitely 94, for two reasons: 1) If you're including the...
... 11:14 ... ratio in ... ratios ... I don't ... rather ... I think by now that we would agree that it would be the 5 comma plus 5' comma (or "schisma")...
... I don't ... notation. The ... Peppermint ... that ... out ... comma ... and 494 ... seems ... places ... a 0.55 ... cents ... Agreed, but I would call it...
... Me too. But some prefer RMS error, and some minimax beating, both of which favour something closer to 50-ET in the 5-limit. Perhaps what we should do is...
... I've been thinking this over while in the process of answering other things. I'm not familiar with the problems of notating some of the esoteric ETs, for...
Hi George, ... Everything I said should apply to any instrument. I used keyboarding as a 'worst-case' example. ... That was a bad choice of terminology. The...
... Let's take meantone for an example. If we define the three linear functions u1 = x - l2(3) u2 = 4x - 4 - l2(5) u3 = 3x -4 - l2(5/3) using "l2" to mean log...
Minimax generators can also be calculated with Scala by the "calculate/minimax" command. It shows the least squares optimum at the same time, so you don't need...
... 31. ... get ... not ... of which ... Since the 5-limit optimal generator size depends on the optimizing method, then it's a tossup between 31 and 50. I...
... It turns out this is so high because of round off error. I redid the calculation using 100 digits of accuracy, and got: p=2 7/26 comma meantone p=4 7/26...
... To this you may add p=3 (7+sqrt(11))/38 comma meantone, .271490126 comma, a little flatter than the rest of them, but still far from 1/3 comma. If you want...
... The issue that I raise is: how many different notations can you expect a person to learn? ... Of course. ... Okay, but only as long as the music is written...
... Why not 7':11' if it is 11' - 7' ? But see my alternative suggestion below. ... I'll just note that neither of us have answered the above yet, in case the ...
... Frankly I think "minimax" is a silly term. I prefer to call it the max-absolute (MA) generator. Obviously we're trying to minimise the error measure in...
... One rather rough and ready rule along these lines would be to pick the last division which occurs as a denominator of a convergent for both the rms and...
... No, but it might make sense to say that for meantones that are on the 1/3-comma side of golden meantone (or some such boundary) a 50-ET-based notation may...
... As many as he needs to play the music he wants to. Since learning septimal notation gives access to 300 years of Western music, the potential payoff for...
... Here's one that comes close, but instead decides that the 81-et is right for the 5-limit. Has anyone even proposed using it? For this definition, we...
... This method works fine as a way of choosing an et for a temperament for computer music purposes, but is a little over the top as a way to define a notation...
... That sounds like an excellent idea! ... As a matter of fact there is a sagittal notation that agrees with 118, 171 and 289 and is also compatible with 53...
Notice that this sagittal notation for schismic depends only on the temperament's mapping from generators to primes and not on any particular range of...
At 02:32 AM 4/01/2003 +0000, wallyesterpaulrus ... OK. I admit defeat on the acronym. But I'd still prefer to call it max-absolute rather than minimax. ... --...
Here's my latest suggestion regarding symbolising the 5'-comma (5-schisma) up and down: Make them separate symbols. Like an accent mark on a character but...
"Poptimal" is short for "p-optimal". The p here is a real variable p>=2, which is what analysts normally use when discussing these Holder type normed linear...
I think I actually followed most of that, and what's more, found it very interesting. Thanks. But with regard to sagittal notation for these temperaments, some...
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