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Message: 6901 Date: Mon, 16 Jun 2003 15:16:44 Subject: Re: Fried Alaska From: Carl Lumma >>>>and for any given brat, you can get arbitrarily close to JI. >>> >>>Oh yeah? Then brats are nonsense, I say. >> >>wha??? > >At the least it means we'd need to consider the error as well >as the brat -- brats alone would not be reliable. Ironically, you use this sort of reasoning against prime limit all the time. -Carl
Message: 6903 Date: Mon, 16 Jun 2003 15:52:12 Subject: Re: Fried Alaska From: Carl Lumma >> >At the least it means we'd need to consider the error as well >> >as the brat -- brats alone would not be reliable. >> >> Ironically, you use this sort of reasoning against prime limit >> all the time. > >you're replying to yourself here. Yeah... >what sort of reasoning? let's see the analogy fleshed out. There are ratios of low prime limit that are quite dissonant. There are chords indistinguishable from just with very high brats. I dunno, the sort of reasoning that looks at the function over the pitch continuum and sees if there are anomalies. -Carl
Message: 6905 Date: Mon, 16 Jun 2003 16:24:36 Subject: Re: Fried Alaska From: Carl Lumma >i thought were were talking about well-temperaments with low, >but rational, brats? We were, but I suggested we compare bare chords instead of temperaments, because that's what the assumption about the larger tunings is based on. >you obviously don't care what the brat is for any chord close enough >to just -- it's the significantly tempered ones where brats may or >may not be meaningful. Apparently so. >also, it's not the lowness of the brat, it's the simplicity of t Right; I've just been saying lowness. By simplicity, don't we mean something like the Van Eck widths? -Carl
Message: 6906 Date: Mon, 16 Jun 2003 16:27:16 Subject: Re: Fried Alaska From: Carl Lumma >>you obviously don't care what the brat is for any chord close enough >>to just -- it's the significantly tempered ones where brats may or >>may not be meaningful. > >Apparently so. Also, if we replace "just" with "interval x" in Gene's statement, brats are completely useless without some sort of tolerance adjustment, like we use for odd limit. -Carl
Message: 6908 Date: Mon, 16 Jun 2003 19:21:27 Subject: Re: Fried Alaska From: Carl Lumma >> By simplicity, don't we mean something like the Van Eck widths? > >That's tough to answer without knowing what a Van Eck width is, I found gcdb by the way, but have no idea how it works. The Van Eck width of ratio Ri is log(R(i-1))-log(R(i+1)), where Ri is, say, the ith ratio in a Farey series of order n. Unfortunately, I guess these widths just shrink to nothing as n goes to infinity. The harmonic entropy based on them, however, converges to a finite value. >but the rules of simplicity are these: > >(1) q and -q, 1/q, and -1/q are equally simple. In particular, 0 and >infinity are equally simple. > >(2) To judge how simple q is, you need to look at how simple 5/(3-2q) >and (3-2q)/5q are as well. > >(3) Low numerators and denominators are better than high ones; >bearing in mind that infinity = 1/0 counts as low. Since we have no idea what's supposed to make one brat better than another, I suppose this is fine. -Carl
Message: 6917 Date: Tue, 17 Jun 2003 13:42:54 Subject: Re: harmonic entropy (was: Re: Fried Alaska) From: Carl Lumma >Why is there such a list? Rather than ask a question like that, why not accept it with the rest of these miserable lists, and go there, where I've already forwarded this thread, so as to commingle it with the extremely valuable archives there? -Carl
Message: 6919 Date: Tue, 17 Jun 2003 14:18:02 Subject: that name again is harmonic_entropy From: Carl Lumma For those of you following along at home... Yahoo groups: /harmonic_entropy/ * -C.
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