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Message: 10350 - Contents - Hide Contents Date: Sat, 21 Feb 2004 03:24:12 Subject: Re: JIP From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote:> /root/tentop.htm * [with cont.] (Wayb.) > > If the JIP is not a point in the original space it operates on, then > it probably shouldn't be referred to as a point.It's a vector in a normed vector space, and these are sometimes called points if you are thinking of the geometry involved. Rather, it seems to> measure pitch, so why not refer to it as PITCH or something?I did call it SIZE, which I recall you didn't like. Anyway, I don't think your remark makes much sense--it's just as much a point as something in the Tenney space.

Message: 10351 - Contents - Hide Contents Date: Sat, 21 Feb 2004 03:25:35 Subject: Re: Who's Val, anyway? From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote:> I sympathize with the confusion over the term "Val". You have named > its dual after our friend Monz. Graham's approach has always been, I > think, to work with these directly, so why not refer to them with the > term "Breed" (which happens to be descriptive as well!)?Either that, or we could get Graham to change his name to Val.

Message: 10353 - Contents - Hide Contents Date: Sat, 21 Feb 2004 03:30:55 Subject: Re: JIP From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote:> --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> > wrote: >> /root/tentop.htm * [with cont.] (Wayb.) >>>> If the JIP is not a point in the original space it operates on, > then>> it probably shouldn't be referred to as a point. >> It's a vector in a normed vector space, and these are sometimes > called points if you are thinking of the geometry involved.Thinking about the geometry involved, I understand that for any given value returned by JIP, there is an n-1 dimensional hyperplane in Tenney space.>> Rather, it seems to >> measure pitch, so why not refer to it as PITCH or something? >> I did call it SIZE, which I recall you didn't like. Anyway, I don't > think your remark makes much sense--it's just as much a point as > something in the Tenney space.I'm smiling, but I don't think there's any hope of us ever writing a paper together. So does it measure pitch or not?

Message: 10355 - Contents - Hide Contents Date: Sat, 21 Feb 2004 03:51:03 Subject: cool voronoi/delaunay applet From: Paul Erlich Voronoi/Delaunay Applet * [with cont.] (Wayb.)

Message: 10356 - Contents - Hide Contents Date: Sat, 21 Feb 2004 05:13:55 Subject: poincare duality From: Paul Erlich I think Mathworld could use your help with this one, Gene: Poincar Duality -- from MathWorld * [with cont.]

Message: 10357 - Contents - Hide Contents Date: Sat, 21 Feb 2004 07:26:20 Subject: Re: JIP From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote:> So does it measure pitch or not?It maps monzos to pitches.

Message: 10358 - Contents - Hide Contents Date: Sat, 21 Feb 2004 07:34:35 Subject: Re: poincare duality From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote:> I think Mathworld could use your help with this one, Gene: > > Poincar Duality -- from MathWorld * [with cont.]It's a little succinct, isn't it? Actually, if I did write something it would be for Wikipedia. I started out thinking about adding something on the Riemann-Siegel zeta function, just so I could refer to it, and ended up deciding that some more important special functions were missing. So I added the Jacobi theta function and defined Jacobi and Weierstrass elliptic functions in terms of it, just as I always thought was the best method, added a Dedekind eta function, a j invariant, and a Dirichlet eta function. In all of which I managed to lose sight of my original goal of relevance to music, but the encyclopedia is much improved in the area of special functions relevant to number theory.

Message: 10359 - Contents - Hide Contents Date: Sat, 21 Feb 2004 07:53:39 Subject: Re: poincare duality From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote:> I think Mathworld could use your help with this one, Gene: > > Poincar Duality -- from MathWorld * [with cont.]By the way, there's a discussion of this page Exterior power - Wikipedia, the free encyclopedia * [with cont.] (Wayb.) = Exterior power - Wikipedia, the free encyclopedia * [with cont.] (Wayb.) on the corresponding talk page ("discuss this page.") I was thinking of writing something on the wedge product which could actually be understandable by non-mathematicians, and Charles was not too keen on the idea. However, I see that immediately afterward he moved material from the Grassmann algebra page to this one, giving it an entire new introductory section, and thereby making it more concrete, just as we had discussed. I'd be interested if people here could tell me if it makes any sense to them, and how much. ________________________________________________________________________ ________________________________________________________________________ ------------------------------------------------------------------------ Yahoo! Groups Links <*> To visit your group on the web, go to: Yahoo groups: /tuning-math/ * [with cont.] <*> To unsubscribe from this group, send an email to: tuning-math-unsubscribe@xxxxxxxxxxx.xxx <*> Your use of Yahoo! Groups is subject to: Yahoo! Terms of Service * [with cont.] (Wayb.)

Message: 10360 - Contents - Hide Contents Date: Mon, 23 Feb 2004 03:07:03 Subject: Re: JIP From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote:> --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> > wrote: >>> So does it measure pitch or not? >> It maps monzos to pitches.So when it operates on monzos (which would seem to be the understood role of a functional in Tenney space), it returns the pitch. This seems like a basic thing you'd want to inform the reader of . . . ________________________________________________________________________ ________________________________________________________________________ ------------------------------------------------------------------------ Yahoo! Groups Links <*> To visit your group on the web, go to: Yahoo groups: /tuning-math/ * [with cont.] <*> To unsubscribe from this group, send an email to: tuning-math-unsubscribe@xxxxxxxxxxx.xxx <*> Your use of Yahoo! Groups is subject to: Yahoo! Terms of Service * [with cont.] (Wayb.)

Message: 10363 - Contents - Hide Contents Date: Tue, 24 Feb 2004 16:48:09 Subject: creepy numbers From: Paul Erlich Though it's not tuning-related, I thought Gene or someone might be able to "explain" this strange phenomenon: (999999/127000)^2 = 62.00000000006200 . . . . ?

Message: 10364 - Contents - Hide Contents Date: Tue, 24 Feb 2004 18:13:42 Subject: Re: non-1200: Tenney/heuristic meantone temperament From: Manuel Op de Coul Paul wrote on 5 Jan:>Now, for all primes r, >If p contains any factors of r, the r-rungs in the lattice (which >have length log2(r)) are shrunk from >cents(r) >to >cents(r) - log2(r)*cents(p/q)/log2(p*q). >If q contains any factors of 2, they are instead stretched to >cents(r) + log2(r)*cents(p/q)/log2(p*q).Sorry for being so behind. I noticed that this TOP tempering can be easily done with Scala. First you need to set the prime weights to the reciprocal of their log2, like this: SET HARMCONST 2 1.0 SET HARMCONST 3 0.69092975 SET HARMCONST 5 0.43067656 SET HARMCONST 7 0.35620719 etc., primes not in the comma don't have to be set of course. Then do PROJECT/TEMPER/WEIGHTED <comma(s)>>No, it's simply limited to temperaments of codimension 1.It doesn't have to be, the above command takes any number of commas and tempers them out simultaneously. I'll make an extra option for the PROJECT/TEMPER command so that the SET HARMCONSTs can be omitted. Manuel

Message: 10365 - Contents - Hide Contents Date: Tue, 24 Feb 2004 17:25:41 Subject: Re: non-1200: Tenney/heuristic meantone temperament From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx "Manuel Op de Coul" <manuel.op.de.coul@e...> wrote:> > Paul wrote on 5 Jan:>> Now, for all primes r, >> If p contains any factors of r, the r-rungs in the lattice (which >> have length log2(r)) are shrunk from >> cents(r) >> to >> cents(r) - log2(r)*cents(p/q)/log2(p*q). >> If q contains any factors of 2, they are instead stretched to >> cents(r) + log2(r)*cents(p/q)/log2(p*q). >> Sorry for being so behind. I noticed that this TOP tempering > can be easily done with Scala. First you need to set the prime > weights to the reciprocal of their log2, like this: > > SET HARMCONST 2 1.0 > SET HARMCONST 3 0.69092975 > SET HARMCONST 5 0.43067656 > SET HARMCONST 7 0.35620719 > etc., primes not in the comma don't have to be set of course. > > Then do PROJECT/TEMPER/WEIGHTED <comma(s)> Huh!>> No, it's simply limited to temperaments of codimension 1. >> It doesn't have to be, the above command takes any number of > commas and tempers them out simultaneously.Really?? Wow. What do you get for 5-limit 12-equal TOP?

Message: 10366 - Contents - Hide Contents Date: Tue, 24 Feb 2004 19:00:44 Subject: Re: non-1200: Tenney/heuristic meantone temperament From: Manuel Op de Coul>Really?? Wow. What do you get for 5-limit 12-equal TOP?(1195.378, 1894.637, 2797.035) Manuel

Message: 10367 - Contents - Hide Contents Date: Tue, 24 Feb 2004 19:06:31 Subject: Re: non-1200: Tenney/heuristic meantone temperament From: Manuel Op de Coul Not sure that you expected that answer though. If I temper out the syntonic comma and the schisma the result is better: (1200.051, 1901.874, 2785.782) Manuel

Message: 10368 - Contents - Hide Contents Date: Tue, 24 Feb 2004 18:29:28 Subject: Re: non-1200: Tenney/heuristic meantone temperament From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx "Manuel Op de Coul" <manuel.op.de.coul@e...> wrote:>>> Really?? Wow. What do you get for 5-limit 12-equal TOP? >> (1195.378, 1894.637, 2797.035) > > ManuelThat's not correct. For one thing, it's not equal! 1195.378/12 = 99.6148 1894.637/19 = 99.7177 2797.035/28 = 99.8941 For another thing, the diesis doesn't vanish: <1195.378 1894.637 2797.035|7 0 -3> = -23.459

Message: 10369 - Contents - Hide Contents Date: Tue, 24 Feb 2004 18:33:03 Subject: Re: non-1200: Tenney/heuristic meantone temperament From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx "Manuel Op de Coul" <manuel.op.de.coul@e...> wrote:> > Not sure that you expected that answer though. > If I temper out the syntonic comma and the schisma the > result is better: > > (1200.051, 1901.874, 2785.782) > > ManuelThe syntonic comma isn't being tempered out at all here: <1200.051 1901.874 2785.782|-4 4 -1> = 21.51 And this certainly isn't an equal temperament!

Message: 10370 - Contents - Hide Contents Date: Tue, 24 Feb 2004 18:44:01 Subject: Re: non-1200: Tenney/heuristic meantone temperament From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx "Manuel Op de Coul" <manuel.op.de.coul@e...> wrote:> It doesn't have to be, the above command takes any number of > commas and tempers them out simultaneously.So at best, there seems to be an error in this procedure.

Message: 10371 - Contents - Hide Contents Date: Tue, 24 Feb 2004 21:23:50 Subject: Re: non-1200: Tenney/heuristic meantone temperament From: Manuel Op de Coul>That's not correct. For one thing, it's not equal!Yes, sorry, I forgot again how to use my own program! The code is correct, but I gave it the wrong parameters. It should have been (1200.6171 1900.9770 2801.4398). Step is 100.051421. Manuel

Message: 10372 - Contents - Hide Contents Date: Tue, 24 Feb 2004 21:52:47 Subject: Re: non-1200: Tenney/heuristic meantone temperament From: Manuel Op de Coul 31-equal TOP is this, identical for 5-limit and 7-limit: (1201.6366 1899.3611 2790.8979 3372.3350) Manuel

Message: 10373 - Contents - Hide Contents Date: Tue, 24 Feb 2004 22:03:00 Subject: Re: non-1200: Tenney/heuristic meantone temperament From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Manuel Op de Coul" <manuel.op.de.coul@e...> wrote:> > 31-equal TOP is this, identical for 5-limit and 7-limit: > (1201.6366 1899.3611 2790.8979 3372.3350)I get 1201.4675 ________________________________________________________________________ ________________________________________________________________________ ------------------------------------------------------------------------ Yahoo! Groups Links <*> To visit your group on the web, go to: Yahoo groups: /tuning-math/ * [with cont.] <*> To unsubscribe from this group, send an email to: tuning-math-unsubscribe@xxxxxxxxxxx.xxx <*> Your use of Yahoo! Groups is subject to: Yahoo! Terms of Service * [with cont.] (Wayb.)

Message: 10374 - Contents - Hide Contents Date: Wed, 25 Feb 2004 18:22:00 Subject: Re: non-1200: Tenney/heuristic meantone temperament From: Manuel Op de Coul Gene wrote:>> 31-equal TOP is this, identical for 5-limit and 7-limit: >> (1201.6366 1899.3611 2790.8979 3372.3350)>I get 1201.4675I don't see how that can be correct. Your twelfth will be 1899.094. Then (1901.955 - 1899.094) / (1201.4675 - 1200.0) = 1.95 which is not log2(3)/log2(2) = 1.585. Manuel

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