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Message: 10353 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 * > > > > 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 Date: Sat, 21 Feb 2004 03:51:03 Subject: cool voronoi/delaunay applet From: Paul Erlich Voronoi/Delaunay Applet *
Message: 10356 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 *
Message: 10360 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/ * <*> 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 *
Message: 10363 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 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 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 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 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 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) > > Manuel That'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 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) > > Manuel The 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 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 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 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: 10374 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 1201.4675 I 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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