[tuning-math] better than ratios (was: Re: Hypothesis revisited)

> ----- Original Message -----
> From: Paul Erlich <paul@stretch-music.com>
> To: <tuning-math@yahoogroups.com>
> Sent: Monday, June 25, 2001 4:27 AM
> Subject: [tuning-math] Re: Hypothesis revisited
>
>
> --- In tuning-math@y..., "D.Stearns" <STEARNS@C...> wrote:
>
> > (Incidentally, I think the 135/128 "major chroma" is a
> > chromatic unison vector of the so-called miracle generator at
> > two-dimensions; with 34171875/33554432 being the commatic unison
> > vector if the generator is taken to a 10- or 11-tone MOS.)
>
> I see the MIRACLE scales as needing three or four unison vectors
> each, since they live in a 7- or 11-limit lattice (i.e., they're
> 3D or 4D).

For the benefit of anyone else who (like me) got lost in this
thread, Dan's commatic unison vector is a 5-limit one, expressible
in prime-factor notation (much better, I think) as 2^-25 * 3^7 * 5^6,
or [-25 7 6] (which is how Graham writes it).

Dan's chromatic unison vector (also 5-limit) is 2^-7 * 3^2 * 5^1
= [-7 2 1].

So much better than ratios...

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

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