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lattices of Schoenberg's rational implications   Message List  
Reply | Forward Message #2848 of 17519 |
Re: lattices of Schoenberg's rational implications

--- In tuning-math@y..., "paulerlich" <paul@s...> wrote:

However, I think the only reality for Schoenberg's
> system is a tuning where there is ambiguity, as defined by the kernel
> <33/32, 64/63, 81/80, 225/224>. BTW, is this Minkowski-reduced?

Nope. The honor belongs to <22/21, 33/32, 36/35, 50/49>.
Mon Jan 21, 2002 3:20 am

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genewardsmith
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Forward 		Message #2848 of 17519 |
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... _________________________________________________________ Do You Yahoo!? Get your free @yahoo.com address at http://mail.yahoo.com... 		monz
joemonz@...
Send Email 		Jul 18, 2001
9:17 am

... It's pretty clear that Schoenberg's theory implies a 12-tone periodicity block....
Paul Erlich
paul@...
Send Email 		Jul 19, 2001
8:44 pm

I was looking again at the post I sent here regarding the math of Schoenberg's tuning ideas: http://groups.yahoo.com/group/tuning-math/messages/516?expand=1 I...
monz
joemonz
Offline Send Email 		Dec 25, 2001
11:43 pm

... See if this helps; We can extend the set {33/32,64/63,81/80,45/44} to an 11-limit notation in various ways, for instance ...
genewardsmith
Offline Send Email 		Dec 26, 2001
8:27 am

... This should be 16/9 rather than 19/9, of course....
genewardsmith
Offline Send Email 		Dec 26, 2001
8:31 am

Help! I set up an Excel spreadsheet to calculate the notes of a periodicity-block according to Gene's formula as expressed here: > Message 2164 > From:...
monz
joemonz
Offline Send Email 		Jan 20, 2002
9:09 pm

... This determinant is why. In my example, the determinant had an absolute value of 1, and so we get what I call a "notation", meaning every 11-limit interval...
genewardsmith
Offline Send Email 		Jan 20, 2002
10:09 pm

... _________________________________________________________ Do You Yahoo!? Get your free @yahoo.com address at http://mail.yahoo.com...
monz
joemonz
Offline Send Email 		Jan 20, 2002
10:23 pm

... Forget it. I don't know why you want to bother with Gene's "notation" here. The "notation" would allow you to specify just ratios unambiguously. However, I...
paulerlich
Offline Send Email 		Jan 21, 2002
2:12 am

... However, I think the only reality for Schoenberg's ... Nope. The honor belongs to <22/21, 33/32, 36/35, 50/49>....
genewardsmith
Offline Send Email 		Jan 21, 2002
3:20 am

... kernel ... Awesome. So this suggests a more compact Fokker parallelepiped as "Schoenberg PB" -- here are the results of placing it in different positions...
paulerlich
Offline Send Email 		Jan 21, 2002
3:48 am

returning to an old subject ... during a big discussion i instigated concerning possible periodicity-blocks which might describe Schoenberg's 1911 12-tET...
monz
joemonz
Offline Send Email 		Apr 24, 2004
9:45 am

Gene, Paul, Graham, > Message 2850 > From: "paulerlich" <paul@s...> > Date: Sun Jan 20, 2002 10:48 pm > Subject: Re: lattices of Schoenberg's rational...
monz
joemonz
Offline Send Email 		Jan 21, 2002
11:31 am
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