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Message: 4425 - Contents - Hide Contents Date: Fri, 29 Mar 2002 04:00:18 Subject: Re: Decatonics From: paulerlich --- In tuning-math@y..., Carl Lumma <carl@l...> wrote:>> The criterion I've used the most is Rothenberg's "propriety," >> which is equivalent essentially to Balzano's "coherence," >> So he agrees with us.i thought you objected to calling it *rothenberg* propriety . . . isn't that the whole point?>> I have considerable doubt about JI in nature. Most sounds in >> nature are nonharmonic, if only because the oscillators and resonators >> are complex 3-D structures instead of ideal 1-D strings and air columns. >> It takes considerable effort to train the voice to make harmonic timbres,did john really write this? john?>> and the vocal quality is decidedly un-natural, whether in relation to >> speech or the usual singing voice.this is completely backwards -- i wonder if john got this from the nutty professor. harmonic sounds are the ones that sound most natural and most vocal!
Message: 4428 - Contents - Hide Contents Date: Fri, 29 Mar 2002 04:35:44 Subject: Re: Decatonics From: paulerlich --- In tuning-math@y..., Carl Lumma <carl@l...> wrote:>>>> The criterion I've used the most is Rothenberg's "propriety," >>>> which is equivalent essentially to Balzano's "coherence," >>>>>> So he agrees with us. >>>> i thought you objected to calling it *rothenberg* propriety . . . >> isn't that the whole point? >> No, Rothenberg did coin the term propriety,so then what's the problem?> and a scale is > either proper or not, and IIRC is is the same as Balzano > coherence. It's just that R. doesn't use it to eliminate > scales,so what? i don't get what you were yelling at me about! i was just saying exactly the same thing you're saying here -- that it's the same as balzano coherence. balzano (and some of his followers) *do* use it to eliminate scales, and *that's* what i was responding to.
Message: 4429 - Contents - Hide Contents Date: Fri, 29 Mar 2002 20:10:21 Subject: Re: Decatonics From: genewardsmith --- In tuning-math@y..., Carl Lumma <carl@l...> wrote:> If I'm right about the terms convex and connected, they > only apply to periodicity blocks.They apply to JI scales, block or not, and to tempered scales with a specified defining mapping of primes.
Message: 4430 - Contents - Hide Contents Date: Fri, 29 Mar 2002 05:04:41 Subject: Re: Decatonics From: paulerlich --- In tuning-math@y..., Carl Lumma <carl@l...> wrote:> ...and in the past, you've used this argument to say that > 'propriety doesn't matter', which is true but incomplete, > since it assumes the strictest possible definition for the > term "propriety".point well taken. so i'm agreeing with you that balzano shouldn't be so strict about 'coherence' (though of course there are far worse problems with balzano's theory).
Message: 4431 - Contents - Hide Contents Date: Fri, 29 Mar 2002 13:34:38 Subject: Re: Decatonics From: Carl Lumma>> >f I'm right about the terms convex and connected, they >> only apply to periodicity blocks. >>They apply to JI scales, block or not, and to tempered scales with >a specified defining mapping of primes.Howabout harmonics 8-16. I'm guessing it's 15-limit connected, but is it convex? Is the entry for val in monz's tuning dictionary the only version there is? I searched the archives for "val definition" and yahoo returned what looks like an or search. I tried "val and definition" and got the same results. A search for "val" returned about 1 out of 3 messages. -Carl
Message: 4432 - Contents - Hide Contents Date: Fri, 29 Mar 2002 07:29:47 Subject: Re: A common notation for JI and ETs From: dkeenanuqnetau --- In tuning-math@y..., "gdsecor" <gdsecor@y...> wrote:> i--- In tuning-math@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:>> --- In tuning-math@y..., "gdsecor" <gdsecor@y...> wrote:> Considering that the semantics of the notation have already put us > past the 19 limit, that 217 is not 23-limit consistent, and that 311 > is such an excellent division, I'd say let's go for it! > I guess I just have a knack for finding useful commas (even before I > start looking for them). Are you ready for the next one? It's a > honey: 20735:20736 (5*11*13*29:2^8*3^4, ~0.083 cents). And it turns > out that we don't need any new flags to get the 29 factor: its > defining interval is 256:261 (2^8:3^2*29, ~33.487 cents), and the > convex left flag that we already have (715:729) is ~33.571 cents.256:261 is also the 29-comma I had settled on. That's awesome! But don't forget that the convex left flag also has the meaning 45056:45927 (2^12*11:3^8*7) from its use in combination with the convex right flag to give the large 11-comma 704:729 (what I've taken to abbreviating as the 11'-comma. Fortunately this still differs by less than 0.5 c (5103:5104) from the 29-comma.> As long as we are going for a higher prime limit that will almost > certainly require an additional kind of flag, perhaps that will > present an opportunity to de-confuse the situation a bit, but that > remains to be seen. > > Here's something to keep in mind as we raise the prime limit. I am > sure that there are quite a few people who would think that making a > notation as versatile as this one promises to get is overkill.I personally think primes beyond 11 are of very limited use musically, but I know there are people who claim to have sucessfully used up to 31.> I > think that such a criticism is valid only if its complexity makes it > more difficult to do the simpler things. Let's try to keep it simple > for the ET's under 100 (as I believe we have been able to do so far), > keeping the advanced features in reserve for the power-JI composer > who wants a lot of prime numbers.I totally agree. I think we can take the 11-limit (at least the semantics) as set in stone now. sL 80:81 21.51 c sR 54:55 31.77 c xL 45056:45927 33.15 c xR 63:64 27.26 c And the 13-limit is set in stone in so far as it uses no new flags but gives the existing ones additional meanings. sL 65536:66339 21.08 c 6/311-ET sR 22113:22528 32.19 c 8/311-ET xL 715:729 33.57 c 9/311-ET xR 64:65 26.84 c 7/311-ET But I think we're still free to fiddle around with 17, 19, 23, 29, 31 with the proviso that we introduce no more than one new flag as we introduce each new prime in order. One thing that annoys me is that the 23-comma that works so well re no-new-flags (16384:16767) is not necessarily the most useful one. I prefer 729:736 since it spans the same number of fifths (-6 instead of +6) and is smaller by a pythagorean comma. The 31-comma I favour is 243:248 (3^5:2^3*31) 35.26 c. We have a bunch of commas between 20 and 35 cents which can correspond to a single flag. It really seems to me that the 17-comma (8.73 c) should be represented by something noticeably smaller. Using a concave flag goes some of the way, but maybe not small enough. And certainly the 19-comma (3.38 c) should be represented by something fairly insignificant in size, being 1/7th to 1/10th the size of the others and 1/3rd the size of the 17-comma. What if we make the 19-comma just a blob on the end of the shaft. Neither right nor left but able to be combined with any flags. Then maybe we can get from 19 to 31 with only the two concave flags. What if we leave concave-left as 2176:2187 (the 17-comma) but make concave-right 19683:19840, so that we have: vL 2176:2187 8.73 c 3/311-ET vR 19683:19840 13.75 c 3/311-ET sL+vR 243:248 35.26 c 9/311-ET By the way, I think that two straight left flags, one above the other on the same shaft, is the best thing for two 5-commas. And do we really need the 17'-comma, 4096:4131 (14.73 c)? The above doesn't give us all the steps of 311-ET from 1 to 17, but I don't think that matters. We don't need to actually be able to notate 311-ET. The gaps are 2, 5 and 15 steps (and 12 if you don't accept my suggestion for two 5-commas).> If we build everything in from the > start and do it right, then there will be no need to revise it later > and upset a few people in the process. Indeed. > Believe it or not, the logic behind 5a) is pretty solid, while it is > 5b) that is a bit contrived. ... > So > with a little bit of creativity I can still get what I had (and > really want) in 72; the same thing can be done in 43-ET. This is the > only bit of trickery that I have found any need for in divisions > below 100.Yes. I follow that. Sounds ok.> As you noted, it is nice that, given the way that we are developing > the symbols, this notation will allow the composer to make the > decision whether to use a single-symbol approach or a single-symbols- > with-sharp-and-flat approach. And the musical marketplace could > eventually make a final decision between the two. So while we can > continue to debate this point, we are under no pressure or obligation > to come to an agreement on it. Agreed.
Message: 4433 - Contents - Hide Contents Date: Fri, 29 Mar 2002 08:08:58 Subject: Re: Euler and harmonic entropy From: genewardsmith --- In tuning-math@y..., "paulerlich" <paul@s...> wrote:> i wish this were euler's actual ranking method, but of course he went > even further (off the deep end) with his final formulae for GS.It's been a while since I read Euler; I got this from a paper by van der Pol in the 1946 Music Review, on "Music and the Elementary Theory of Numbers," which perhaps I should report on. I was going through old stuff at my mother's, and I found this, which van der Pol had sent Dick Lehmer and I acquired after he died. I also found copies of the paper I mentioned from the 80s, which I shall resurrect--it seems it was turned down by a couple of dubious characters named Chalmers and Balzano.
Message: 4434 - Contents - Hide Contents Date: Fri, 29 Mar 2002 08:15:10 Subject: Re: Decatonics From: genewardsmith --- In tuning-math@y..., Carl Lumma <carl@l...> wrote:> This isn't right. Both John and I independently made the mistake > that CS was equivalent to *strict* propriety in 1999, forgetting > that there are improper scales which are CS.Are either of these equivalent to the epimorphic property? Are there implications either way?
Message: 4435 - Contents - Hide Contents Date: Fri, 29 Mar 2002 08:18:40 Subject: Re: Hermite normal form From: genewardsmith --- In tuning-math@y..., "paulerlich" <paul@s...> wrote:> --- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:>> Do you want this if half-fourth doesn't work? Hermite form seems to >> allow twin meantone and schismic, and half-fifth meantome and >> schismic, but not the half-fourth versions.> that seems bizarre. is there an intuitive explanation of why this > should be the case?It leads off with positive elements in each column.
Message: 4436 - Contents - Hide Contents Date: Fri, 29 Mar 2002 18:41:10 Subject: Re: Digest Number 331 From: Carl Lumma>they may contain more noise, but do an fft (or anything like that) >and you won't find a systematic significant deviation of the partials >from a harmonic series, in one direction or the other.Do you know of any web site where they did this? Would there be any point in having the boys over on the main list run some stuff through their latest? -Carl
Message: 4437 - Contents - Hide Contents Date: Fri, 29 Mar 2002 00:25:28 Subject: Re: Decatonics From: paulerlich --- In tuning-math@y..., Carl Lumma <carl@l...> wrote:>> sorry -- just force of habit (acquired from john chalmers, i >> believe). so who did introduce the terms 'proper' and 'improper' >> in this context, if not rothenberg? >> I'm not sure. I've seen it around the list(s) on occasion, and > complained bitterly every time. :)i think we should ask john chalmers. look at his post of Tue Apr 19 09:04:34 1994 about 90% of the way down here, where he mentions balzano coherence: arranged--that's a valid insight. The number ... * [with cont.] (Wayb.) he didn't really get wilson's 'constant structures' right so maybe he's mistaken on 'Rothenberg's "propriety"' as well?
Message: 4438 - Contents - Hide Contents Date: Fri, 29 Mar 2002 02:03:00 Subject: Re: Decatonics From: Carl Lumma>> >his isn't right. Both John and I independently made the mistake >> that CS was equivalent to *strict* propriety in 1999, forgetting >> that there are improper scales which are CS. >>Are either of these equivalent to the epimorphic property? Are there >implications either way?I was hoping you could tell me. I've read the defs. for epimorphic and val in monz's dictionary, but I had problems with val. I thought you knew what all this stuff was. Maybe an example. The diatonic scale: in 1/3-comma meantone is strictly proper and CS in 12-et is proper but not strictly so, not CS in Pythagorean tuning is improper and CS In general: SP -> CS, but no other relation exists. Manuel, I think there's a bug in Scala 1.8 (are you still maintaining it?), Pythag 7, 2/1, 0, 3/2, 0, normalize sort show data -> Rothenberg stability = 1.000000 = 1 -Carl
Message: 4439 - Contents - Hide Contents Date: Fri, 29 Mar 2002 10:41:47 Subject: Re: Hermite normal form version of "25 best" From: genewardsmith --- In tuning-math@y..., "paulerlich" <paul@s...> wrote:> again, i'm wondering why you're not putting these in order of g_w.Because sorting a list of commas by size and then computing from that is easier.
Message: 4440 - Contents - Hide Contents Date: Fri, 29 Mar 2002 18:52:22 Subject: Re: Digest Number 331 From: Carl Lumma>sure -- or we could ask francois, as he's apparantly done plenty of >analyses on human voices. i'm quite confident we won't find human >voices with statistically significantly stretched or contracted >partials relative to the harmonic series -- the vocal folds simply >have no way of vibrating in such a manner.Why does it have to be stretched or contracted? What about random differences on each partial, say of over 10 cents? Is such a thing possible? -Ca.
Message: 4441 - Contents - Hide Contents Date: Fri, 29 Mar 2002 10:45 +0 Subject: Re: Decatonics From: graham@xxxxxxxxxx.xx.xx Carl:>> When I read Balzano's paper, incoherency was indeed equivalent to >> propriety. Paul:> me too. so graham, what gives?I don't know about Balzano, but what Mark describes here:>> This is inconsistent with my rule ii: it contains segments of 3 and > more >> adjacent PCs >> >> 0 1 2, 4 5 6 7, 9 10 11 12, etc >> >> So it will show up as intervallically inchoerent (as defined by > Balzano).is not propriety. The fifth-generated pentatonic in 7-equal is 0 1 3 4 5 7. That has 3, 4 and 5 as adjacent pitch classes. But it's proper 0 1 3 4 5 7 1 2 1 1 2 3 3 2 3 3 4 4 4 4 5 5 6 5 6 6 7 7 7 7 7 Perhaps "intervallic coherence" is different to plain old "coherence"? Although that still doesn't cover the second rule (i) at the bottom of page 94 of Mark's paper. *cough* Graham
Message: 4442 - Contents - Hide Contents Date: Fri, 29 Mar 2002 10:47:06 Subject: Re: Decatonics From: genewardsmith --- In tuning-math@y..., Carl Lumma <carl@l...> wrote:> I thought you knew what all this stuff was. Ha!Maybe an example.> The diatonic scale: > > in 1/3-comma meantone is strictly proper and CS > in 12-et is proper but not strictly so, not CS > in Pythagorean tuning is improper and CSAll of the above are epimorphic. I think of scales in terms of the properties epimorphic, convex, and connected.
Message: 4443 - Contents - Hide Contents Date: Fri, 29 Mar 2002 15:39:00 Subject: Re: Decatonics From: manuel.op.de.coul@xxxxxxxxxxx.xxx Carl wrote:>Manuel, I think there's a bug in Scala 1.8 (are you still >maintaining it?), >Pythag >7, 2/1, 0, 3/2, 0, >normalize >sort >show data -> Rothenberg stability = 1.000000 = 1You're correct, it was solved in the 2.x version. Still maintaining it, I should make an update soon. Manuel
Message: 4444 - Contents - Hide Contents Date: Fri, 29 Mar 2002 07:37:47 Subject: Re: Rothenberg propriety From: John Chalmers I haven't followed all this thread, but Rothenberg does not throw out scales just because they are improper, he merely claims that they are perceived differently and behave differently in composition. He also specifically states in another section that there is a listener-dependent threshold for interval perception. Hence, if one doesn't hear melodic intervals as different if they vary in span by a comma or less, then the impropriety of the diatonic in pythagorean tuning would not be noticeable. This is an example of categorical perception and his theory is primarily a theory of perception. Balzano's coherency and Rothenberg propriety are the same. B apparently came upon the idea independently, but does acknowledge Rothenberg more or less obliquely in one of his papers. As for CS, can someone email me an example of an improper one? --John
Message: 4445 - Contents - Hide Contents Date: Fri, 29 Mar 2002 17:15:00 Subject: Re: Rothenberg propriety From: manuel.op.de.coul@xxxxxxxxxxx.xxx>As for CS, can someone email me an example of an improper one?For example 3 1 1 3 or 0.0 450.0 600.0 750.0 1200.0 cents. Manuel
Message: 4446 - Contents - Hide Contents Date: Sat, 30 Mar 2002 05:39:50 Subject: Re: 31-limit microtemperament challenge (was: _The_ 31-limit temperament?) From: genewardsmith --- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:> There will always be 31-limit temperaments for each dimension up to > pi(31)=11 such that they have a basis consisting of commas no larger that half a cent, there will never be one such that all the commas are less than half a cent.Well...except for in codimension 1, with one comma!
Message: 4447 - Contents - Hide Contents Date: Sat, 30 Mar 2002 06:08:27 Subject: Re: Digest Number 331 From: paulerlich --- In tuning-math@y..., Carl Lumma <carl@l...> wrote:>> sure -- or we could ask francois, as he's apparantly done plenty of >> analyses on human voices. i'm quite confident we won't find human >> voices with statistically significantly stretched or contracted >> partials relative to the harmonic series -- the vocal folds simply >> have no way of vibrating in such a manner. >> Why does it have to be stretched or contracted? What about random > differences on each partial, say of over 10 cents?sure. you can add that to my statement, if you wish.
Message: 4448 - Contents - Hide Contents Date: Sat, 30 Mar 2002 06:12:03 Subject: Re: Hermite normal form version of "25 best" From: paulerlich --- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:> --- In tuning-math@y..., "paulerlich" <paul@s...> wrote:>> --- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote: >>>> Because sorting a list of commas by size and then computing from >>> that is easier. >>>> why is that easier than sorting by the size of the numbers in the >> commas (which is my heuristic approximation for g_w)? >> Because the comma is what I use to compute g_w, not the other way >around.huh? let me try this again. forget g_w. if the comma is what you're starting from, why can't you sort by the size of the numbers in the comma, instead of the size of the comma?>I would need to write more code to do it your way, and it doesn't >seem to matter much, given that anyone can arrange things any way >they like.true -- i'm just being anal in that i don't like wading through all kinds of complicated temperaments before even seeing schismic.
Message: 4449 - Contents - Hide Contents Date: Sat, 30 Mar 2002 06:13:07 Subject: Re: 31-limit microtemperament challenge (was: _The_ 31-limit temperament?) From: paulerlich --- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:> --- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote: >>> There will always be 31-limit temperaments for each dimension up to >> pi(31)=11 such that they have a basis consisting of commas nolarger that half a cent, there will never be one such that all the commas are less than half a cent.> > Well...except for in codimension 1, with one comma!you got me there!
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