source file: m1443.txt
Date: Thu, 11 Jun 1998 05:20:54 -0500 (CDT)

Subject: Re: Fokker's Matrices

From: Paul Hahn <Paul-Hahn@library.wustl.edu>

On Wed, 10 Jun 1998, Graham Breed wrote:
> >You can generate any damn ET you want this way, although sometimes the
> >unisons/commas chosen to vanish aren't very small.
> 
> Correct me if I'm wrong, but Fokker used octave invariant matrices.
> That means you can't use them to define 88CET, for example.

Sorry.  I should have said you can derive any _integral_ ET this
way--but note that the interval divided by the integral doesn't have to
be an octave.  So you can derive the Bohlen-Pierce scale, for example,
by working in the 5-7 plane and assuming tritave equivalence when you
generate your intervals and choose your unison vectors.

On Wed, 10 Jun 1998, Paul H. Erlich wrote:
> What if you add the restriction that the resulting ET can have no better
> approximations of the just intervals than the ones represented by one
> step along the axes? I guess I had that in the back of my mind when I
> asked the above questions.

I'm having difficulty imagining an ET like this--can you give me an
example of such an ET, and then I'll try Fokker's method on it?

--pH <manynote@lib-rary.wustl.edu> http://library.wustl.edu/~manynote
    O
   /\        "Churchill? Can he run a hundred balls?"
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