Tuning-Math Digests messages 6803 - 6827

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Message: 6803

Date: Tue, 6 May 2003 16:10:07

Subject: Re: Doing 12-equal within 133-et

From: Manuel Op de Coul

Carl asked:
>Does the .scl format support stretch/compression?
>IIRC the last pitch line is taken as the interval
>of equivalence, so instead of 2/1, we could give
>a cents value of 1197?

Yes indeed!

Manuel


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Message: 6806

Date: Thu, 8 May 2003 11:50:51

Subject: Re: Doing 12-equal within 133-et

From: Manuel Op de Coul

Gene wrote:
>What would be really interesting would be allowing the cents values to
>occur in any order.

Doesn't it?

>By the way, I read somewhere that Scala can produce Csound score
>files. How is that done?

There's an example in cmd\cs-demo.cmd.
Or maybe easier if you have a midi file that you want to
convert to a tuned Csound score is to use midi2cs by
Rüdiger Borrmann. There's a tip about it in tips.par.

Manuel


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Message: 6808

Date: Mon, 12 May 2003 14:12:32

Subject: Re: how come i never saw this before?

From: Carl Lumma

>http://www.musikwissenschaft.uni-mainz.de/ *
>Musikinformatik/schriftenreihe/nr45/scale.pdf

You're mentioned, with a link to sonic arts.  You didn't know it?
 
>btw, what makes much more sense to me is to do multidimensional
>scaling based on a rationalization of the *interval matrix*, not
>the pitch matrix

Indeed.

>i've posted such multidimensional scaling results years ago.

You did?

>better yet would be to simply use the harmonic entropies of the
>intervals, which i think i did in a few posts as well.

You're referring to the minimum pairwise entropy posts?  Those
were awesome.

Harmonic entropy sort of makes the idea of rationalizing a scale
irrelevant.  On the other hand, starting with a *temperament*,
it's useful to have a method for snapping it to the lattice in a
simple way, as in TM reduction.  There's sooo much publishable
on tuning-math . . . . . 
 
>hmm, i'm getting an idea for a movie . . .

Cooool.

-C.


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Message: 6810

Date: Mon, 12 May 2003 14:52:07

Subject: Re: how come i never saw this before?

From: Carl Lumma

>> >better yet would be to simply use the harmonic entropies of the
>> >intervals, which i think i did in a few posts as well.
>> 
>> You're referring to the minimum pairwise entropy posts?
>
>no, just multidimensional scaling solutions.

How should I go about finding those posts?

>> Harmonic entropy sort of makes the idea of rationalizing a scale
>> irrelevant.  On the other hand, starting with a *temperament*,
>> it's useful to have a method for snapping it to the lattice in a
>> simple way, as in TM reduction.
>
>yeah but then you break a lot of the consonant connections. which 
>makes this whole "rationalization" business look pretty unhealthy to 
>me.

Sure.

-C.


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Message: 6816

Date: Wed, 14 May 2003 12:06:24

Subject: Re: Efficicency and ambiguity

From: Manuel Op de Coul

>If I'm understanding Eytan Agmon's paper "Numbers and the Western
>Tone-System", he is interested in MOS in an equal temperament which
>are efficent and have at most one ambiguous interval.

Not at most, exactly one. So your examples don't qualify.

Manuel


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Message: 6823

Date: Thu, 15 May 2003 12:26:27

Subject: Re: Efficicency and ambiguity

From: Manuel Op de Coul

>> why on earth should there be exactly one ambiguous interval? it seems 
>> to me that musical academia has been staring for too long at its 7-
>> out-of-12-equal navel.

>> these? what are these?

>MOS of size (n+1)/2 within an n-et, such that n is odd and 2/n is the
>generator.

Yeah, those have no ambiguous interval, leaving only the even n with
exactly one ambiguous interval.

Manuel


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