Re: [tuning] Re: great explanation [periodicity block]

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 . . .