--- In tuning-math@y..., "monz" <joemonz@y...> wrote:

> Can someone explain what's going on here, and what candidates
> may be found for unison-vectors by extending the 11-limit system,
> in order to define a 12-tone periodicity-block? Thanks.

See if this helps;

We can extend the set {33/32,64/63,81/80,45/44} to an 11-limit notation in
various ways, for instance

<56/55,33/32,65/63,81/80,45/44>^(-1) = [h7,h12,g7,-h2,h5]

where g7 differs from h7 by g7(7)=19. Using this, we find the corresponding
block is

(56/55)^n (33/32)^round(12n/7) (64/63)^n (81/80)^round(-2n/12)
(45/44)^round(5n/7), or 1-9/8-32/27-4/3-3/2-27/16-16/9; the Pythagorean scale.
We don't need anything new to find a 12-note scale; we get

1--16/15--9/8--32/27--5/4--4/3--16/11--3/2--8/5--5/3--19/9--15/8

or variants, the variants coming from the fact that 12 is even, by using 12
rather than 7 in the denominator.