Eikosany as ball in Wilson lattice

If L is an odd number, we may call a product of odd numbers up through
L, 3^e3 5^e5 ... L^el, a Wilson product. These do not represent pitch
classes when L>7, because of the lack of unique factorization.
However, you can put a symmetrical A_n lattice structure on them,
which makes the Wilson products into a lattice, where the L-limit
consonaces are the closest products to the unison, and are all at the
same distance. This means, of course, we would count 9/7 as a
consonance, but not 3^2/7, and would regard 9/3^2 as a comma.

This, according to Paul, is Wilson's point of view, and if we adopt
it, the Eikosany is a deep hole, whose center is 3^(1/2) 5^(1/2)
7^(1/2) 9^(1/2) 11^(1/2). This does not extend far enough to involve
the 9/3^2 comma, for ball scales of larger radius we will have
multiple Wilson products corresponding to a single pitch class, and
will have "scales" where some of the scale steps are 9/3^2 or 3^2/9.

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:

> This, according to Paul, is Wilson's point of view, and if we adopt
> it, the Eikosany is a deep hole, whose center is 3^(1/2) 5^(1/2)
> 7^(1/2) 9^(1/2) 11^(1/2).

Moreover, the holes of the lattice and CPS are, in any dimension, two
different ways of getting the same thing, which I can prove. I'd be
interested to know where all this lattice stuff Paul found is from.