Hi Paul,

Moving this to tuning-math seemed wise--hope you don't mind!

<<Hmm? Those would be the stepsizes for the 12-tone scale in this

series, not the whole series, correct?>>

Right, following the expansion or contraction rules will walk you up

and back in the series. So the stepsizes for the 22-tone scale in this

series would be 81/80 128/125 25/24, and the 2D UVs would be 3125/3072

and 2048/2025.

--Dan Stearns

--- In tuning-math@y..., "D.Stearns" <STEARNS@C...> wrote:

> <<Hmm? Those would be the stepsizes for the 12-tone scale in this

> series, not the whole series, correct?>>

>

> Right, following the expansion or contraction rules will walk you up

> and back in the series. So the stepsizes for the 22-tone scale in

this

> series would be 81/80 128/125 25/24, and the 2D UVs would be

3125/3072

> and 2048/2025.

There's probably one more, if you take a look at the lattice.

Why don't you make a quick-and-dirty periodicity-revealing lattice

for the 12- and 22-tone scales that result in the "Tribonacci" system?

Right--the 250/243 "major chroma". I think I can do this without the

lattice, in fact that's the whole point!

----- Original Message -----

From: "paulerlich" <paul@stretch-music.com>

To: <tuning-math@yahoogroups.com>

Sent: Wednesday, December 19, 2001 8:44 PM

Subject: [tuning-math] [tuning] Re: great explanation [periodicity

block]

> --- In tuning-math@y..., "D.Stearns" <STEARNS@C...> wrote:

>

> > <<Hmm? Those would be the stepsizes for the 12-tone scale in this

> > series, not the whole series, correct?>>

> >

> > Right, following the expansion or contraction rules will walk you

up

> > and back in the series. So the stepsizes for the 22-tone scale in

> this

> > series would be 81/80 128/125 25/24, and the 2D UVs would be

> 3125/3072

> > and 2048/2025.

>

> There's probably one more, if you take a look at the lattice.

>

> Why don't you make a quick-and-dirty periodicity-revealing lattice

> for the 12- and 22-tone scales that result in the "Tribonacci"

system?

>

>

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--- In tuning-math@y..., "D.Stearns" <STEARNS@C...> wrote:

> Right--the 250/243 "major chroma". I think I can do this without the

> lattice, in fact that's the whole point!

Well seeing it on a lattice would convince us of this . . .