> ----- 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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