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Message: 6477 Date: Tue, 22 Jan 2002 22:11:19 Subject: Re: deeper analysis of Schoenberg unison-vectors 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: > > > > > Have you ever considered the [34, 54, 79, 96] version of twintone? > > >You mentioned playing with someone who had a 34-et guitar, I think. > > > The 34-tET version of twintone? It's better than 12, but much worse > > than 22. > > Depends on what you are using the 7-limit stuff to do, I would think--it is sweeter so far as the 5-limit goes. Then we're talking diaschismic, not twintone. Or if they're the same thing, we need another word for "paultone".
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Message: 6478 Date: Wed, 23 Jan 2002 10:32:54 Subject: Re: hemiennealimmal / MIRACLE Partch? (was: A top 20 11-limit ...)) From: monz > From: jonszanto <jonszanto@xxxxx.xxx> > To: <tuning-math@xxxxxxxxxxx.xxx> > Sent: Tuesday, January 22, 2002 4:25 PM > Subject: [tuning-math] Re: hemiennealimmal / MIRACLE Partch? (was: A top 20 11-limit ...) > > > --- In tuning-math@y..., "monz" <joemonz@y...> wrote: > > Well ... there are two available: > > Nope, there's more, and you probably will find the last very useable: > Richard Kassel has a big book, MUSA 9, that is a complete > transcription, analysis, history, and background on Barstow (the > piece, not the town). He uses the 1968 version, but I believe the > entire thing is translated into Johnston notation complete with > harmonic analysis. Thanks, Jon! I know Richard, but didn't know about this! Unfortunately, as with Hackbarth's transcription of _Daphne_, anyone wanting to analyze Partch's music must first learn how to decode Johnston's notation ... and that ain't the easiest thing to do. My suggestion is to start with this: An examination of * And, BTW, I had speculated on the MIRACLE-Partch connection last summer, and drew some inferences from an examination of what Partch said in _Genesis_ about various ETs and other tunings: An examination of * -monz _________________________________________________________ Do You Yahoo!? Get your free @yahoo.com address at Yahoo! Mail Setup *
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Message: 6479 Date: Wed, 23 Jan 2002 20:21:08 Subject: Re: new Dictionary entry: "torsion" From: paulerlich > --- In tuning-math@y..., "monz" <joemonz@y...> wrote: > > > > new Dictionary entry: "torsion" > > > > Definitions of tuning terms: torsion, (c) 2002 by Joe Monzo * > > > > > > Feedback appreciated. > > > > (and thanks for the helpful criticisms, Paul) Monz, this might be confusing because even the 12-tone Duodene can be split in this way (into two augmented scale PBs a 9:8 apart) and yet it does not possess torsion. The key point is that some unison vector (or combination thereof, depending on how you define UV) is an integer power (or multiple, in cents) of some interval within the block. In the particular example, the "unison vector" in question goes from one corner of the block to the opposite corner, and is the syntonic comma squared.
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Message: 6481 Date: Wed, 23 Jan 2002 20:42:11 Subject: Re: twintone, paultone (was something about schoenberg From: clumma >I'm trying to keep track of these at ><Catalogue of linear temperaments *>. I'd seen this before, but only now taken the time to read it thoroughly. All I can say is, "Thank you, thank you, thank you, thank you, thank you, Graham!". -Carl
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Message: 6482 Date: Wed, 23 Jan 2002 12:47:52 Subject: Re: new Dictionary entry: "torsion" From: monz > From: paulerlich <paul@xxxxxxxxxxxxx.xxx> > To: <tuning-math@xxxxxxxxxxx.xxx> > Sent: Wednesday, January 23, 2002 12:21 PM > Subject: [tuning-math] Re: new Dictionary entry: "torsion" > > > --- In tuning-math@y..., "monz" <joemonz@y...> wrote: > > > > new Dictionary entry: "torsion" > > > > Definitions of tuning terms: torsion, (c) 2002 by Joe Monzo * > > > > > Monz, this might be confusing because even the 12-tone Duodene can be > split in this way (into two augmented scale PBs a 9:8 apart) and yet > it does not possess torsion. The key point is that some unison vector > (or combination thereof, depending on how you define UV) is an > integer power (or multiple, in cents) of some interval within the > block. In the particular example, the "unison vector" in question > goes from one corner of the block to the opposite corner, and is the > syntonic comma squared. Try it now. I included Paul's post verbatim under my description of the "classic example", but also changed a bit in the first paragraph (i.e., the actual definition part). Is that first paragraph good enough now? -monz _________________________________________________________ Do You Yahoo!? Get your free @yahoo.com address at Yahoo! Mail Setup *
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Message: 6483 Date: Wed, 23 Jan 2002 20:50:50 Subject: Re: new Dictionary entry: "torsion" From: paulerlich --- In tuning-math@y..., "monz" <joemonz@y...> wrote: > > > From: paulerlich <paul@s...> > > To: <tuning-math@y...> > > Sent: Wednesday, January 23, 2002 12:21 PM > > Subject: [tuning-math] Re: new Dictionary entry: "torsion" > > > > > > --- In tuning-math@y..., "monz" <joemonz@y...> wrote: > > > > > > new Dictionary entry: "torsion" > > > > > > Definitions of tuning terms: torsion, (c) 2002 by Joe Monzo * > > > > > > > > > Monz, this might be confusing because even the 12-tone Duodene can be > > split in this way (into two augmented scale PBs a 9:8 apart) and yet > > it does not possess torsion. The key point is that some unison vector > > (or combination thereof, depending on how you define UV) is an > > integer power (or multiple, in cents) of some interval within the > > block. In the particular example, the "unison vector" in question > > goes from one corner of the block to the opposite corner, and is the > > syntonic comma squared. > > > Try it now. > > I included Paul's post verbatim under my description of the > "classic example", but also changed a bit in the first paragraph > (i.e., the actual definition part). Is that first paragraph > good enough now? I don't see the change as addressing my objection above in any way. Do you?
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Message: 6484 Date: Wed, 23 Jan 2002 20:54:18 Subject: Re: new Dictionary entry: "torsion" From: paulerlich --- In tuning-math@y..., "paulerlich" <paul@s...> wrote: > --- In tuning-math@y..., "monz" <joemonz@y...> wrote: > > > > > From: paulerlich <paul@s...> > > > To: <tuning-math@y...> > > > Sent: Wednesday, January 23, 2002 12:21 PM > > > Subject: [tuning-math] Re: new Dictionary entry: "torsion" > > > > > > > > > --- In tuning-math@y..., "monz" <joemonz@y...> wrote: > > > > > > > > new Dictionary entry: "torsion" > > > > > > > > Definitions of tuning terms: torsion, (c) 2002 by Joe Monzo * > > > > > > > > > > > > > Monz, this might be confusing because even the 12-tone Duodene > can be > > > split in this way (into two augmented scale PBs a 9:8 apart) and > yet > > > it does not possess torsion. The key point is that some unison > vector > > > (or combination thereof, depending on how you define UV) is an > > > integer power (or multiple, in cents) of some interval within the > > > block. In the particular example, the "unison vector" in question > > > goes from one corner of the block to the opposite corner, and is > the > > > syntonic comma squared. > > > > > > Try it now. > > > > I included Paul's post verbatim under my description of the > > "classic example", but also changed a bit in the first paragraph > > (i.e., the actual definition part). Is that first paragraph > > good enough now? > > I don't see the change as addressing my objection above in any way. > Do you? Sorry, Monz, I didn't hit refresh. Well, the definition now is quite incorrect even as a description (let alone a definition), as you can see by comparing what you say with the example you give. "Torsion describes a condition where a set of pitch-classes appears to create a periodicity-block, when in reality that apparent periodicity-block is actually composed of two or more (call it n) identical smaller periodicity-blocks, each exactly 1/n as large as the apparent one, whose pitch-classes are separated by some interval which acts as a unison-vector and which is an integer power of an interval included within the actual smaller periodicity-block itself." You won't find sets of pitch classes separated by such an interval.
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Message: 6487 Date: Wed, 23 Jan 2002 13:37:06 Subject: Re: new Dictionary entry: "torsion" From: monz > From: paulerlich <paul@xxxxxxxxxxxxx.xxx> > To: <tuning-math@xxxxxxxxxxx.xxx> > Sent: Wednesday, January 23, 2002 12:54 PM > Subject: [tuning-math] Re: new Dictionary entry: "torsion" > > --- In tuning-math@y..., "monz" <joemonz@y...> wrote: > > > new Dictionary entry: "torsion" > > > > Definitions of tuning terms: torsion, (c) 2002 by Joe Monzo * > > > Well, the definition now is quite incorrect even as a description > (let alone a definition), as you can see by comparing what you say > with the example you give. > > "Torsion describes a condition where a set of pitch-classes appears > to create a periodicity-block, when in reality that apparent > periodicity-block is actually composed of two or more (call it n) > identical smaller periodicity-blocks, each exactly 1/n as large as > the apparent one, whose pitch-classes are separated by some interval > which acts as a unison-vector and which is an integer power of an > interval included within the actual smaller periodicity-block itself." > > You won't find sets of pitch classes separated by such an interval. ACK!! OK, I don't have time to do anything else now. You guys hash out how this definition should be corrected, and I'll change it when I read your follow-up posts later tonight. -monz _________________________________________________________ Do You Yahoo!? Get your free @yahoo.com address at Yahoo! Mail Setup *
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Message: 6491 Date: Wed, 23 Jan 2002 22:33:07 Subject: Re: Proposed dictionary entry: torsion From: paulerlich --- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote: > torsion > > Torsion describes a condition wherein an independent set of n unison vectors (<uvector.htm>) fails to define a periodicity block of dimension n, because of the existence of torsion elements, meaning intervals which are not products of the proposed set of unison vectors, but some power of which are. > > Torsion may be tested by forming the n by n+1 matrix whose rows correspond to the unison vectors, and calculating the gcd (<Access Denied *>) of the minors (<Access Denied *>) > of the matrix. If the rows are linearly independent but the gcd is not one, we have torsion. > > The term comes from mathematical usage, see > <Access Denied *>. This is awesome!! Should you say "field of unison vectors" or "ring of unison vectors" or some such as opposed to "set of unison vectors" above? The idea is to eliminate the ambiguity that arises from the two usages of "unison vector" that you brought up -- a member of the basis for the kernel, or a member of the kernel. P.S. An early example of torsion: Yahoo groups: /tuning/message/9694 * Kees' corrections: Yahoo groups: /tuning/message/9757 *
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Message: 6494 Date: Wed, 23 Jan 2002 00:59:43 Subject: Re: Heuristic? From: paulerlich --- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote: > --- In tuning-math@y..., "paulerlich" <paul@s...> wrote: > > > Why? This is not the heuristic for complexity we're looking at here -- > > it's the heuristic for error! > > So small values of your heuristuc applied to 5-limit commas should >correspond to good 5-limit temperaments, and larger values to not-so- >good? One heuristic, |n-d|/(d*log(d)), gives you the the "error" component of goodness, while another, log(d), gives you the "gens"/"complexity" component. Please look again at Yahoo groups: /tuning-math/message/2491 * You'll need to use "Expand Messages".
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Message: 6496 Date: Wed, 23 Jan 2002 23:00:47 Subject: Re: Proposed dictionary entry: torsion From: paulerlich --- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote: > --- In tuning-math@y..., "paulerlich" <paul@s...> wrote: > > > Should you say "field of unison vectors" or "ring of unison vectors" > > or some such as opposed to "set of unison vectors" above? > > You could say "group generated by the unison vectors", but I >thought I made it clear with "set" that I was talking about a basis >for the kernel, not the kernel itself. Well then your definition doesn't seem to work, because if the basis is the diesis and the schisma, the syntonic comma squared is in the kernel, but not in the basis.
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Message: 6497 Date: Wed, 23 Jan 2002 01:25:30 Subject: Re: new Dictionary entry: "torsion" From: paulerlich --- In tuning-math@y..., "monz" <joemonz@y...> wrote: > > new Dictionary entry: "torsion" > > Definitions of tuning terms: torsion, (c) 2002 by Joe Monzo * > > > Feedback appreciated. > > (and thanks for the helpful criticisms, Paul) > > > > -monz Why hyphenate periodicity-block? You don't hyphenate vacuum-cleaner, do you?
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