[tuning-math] agreeing without understanding (was: questions about Graham's matrices)

> From: Paul Erlich <paul@stretch-music.com>
> To: <tuning-math@yahoogroups.com>
> Sent: Thursday, June 28, 2001 10:45 PM
> Subject: [tuning-math] Re: questions about Graham's matrices
>
>
> --- In tuning-math@y..., "monz" <joemonz@y...> wrote:
>
> > But I'm glad to see that somehow we managed to agree on this,
> > without understanding each other! Cool.
> >
> Yes, and I think it's a very important point.

I agree. We were both frustrated that we couldn't understand
each other, in both cases, but it turns out that we were
thinking basically the same thing all along.

> Rather than the basis being 3, 5, 7, it could just as
> easily be, say, 5/4, 6/5, 7/6, or any other basis that
> spans the 3D lattice (though consonant intervals are
> somewhat preferable here).

Sure, these are all good. But I was thinking along the
lines of, say, an axis representing a meantone generator,
such as (3/2)/((81/80)^(1/4)) , for example.

This is why, a few months back, I was so interested in
Regener's work. It seems to be along these lines...
transformations of ratio-space.

-monz
http://www.monz.org
"All roads lead to n^0"

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com

--- In tuning-math@y..., "monz" <joemonz@y...> wrote:
>
> Sure, these are all good. But I was thinking along the
> lines of, say, an axis representing a meantone generator,
> such as (3/2)/((81/80)^(1/4)) , for example.

Well that, of course, would be the _right_ way to plot meantone
tunings. Which is what I was trying to tell you while grudgingly
figuring out for you how to plot meantone on the usual (3,5) axes
using fractional exponents.