RE: [tuning] RE: re: Bizarre periodicity blocks found in 5 dimens ions

I wrote,

>>Although the 20-tone 13-limit periodicity blocks turned out to be double
>>10-tone ones, this 11-limit one is not:

Carl wrote,

>But that one does seem to approximate 20-tET.

Exactly.

>Question is, is the original
>idea correct -- that all periodicity blocks (or perhaps only those with
>unison vectors smaller than their smallest 2nd) approximate N-tET? Or
>don't we know yet?

Obviously, the original idea is not correct (if you define N as the
determinant of the matrix of unison vector exponents), as proved by those
13-limit double 10-tET periodicity blocks.

Wait a minute Carl.

You wrote,

>Question is, is the original
>idea correct -- that all periodicity blocks (or perhaps only those with
>unison vectors smaller than their smallest 2nd) approximate N-tET? Or
>don't we know yet?

In a sense, the weird periodicity block I found had "seconds" of 441:440 and
540:539 -- these are smaller than some of the unison vectors. So maybe the
"original idea" (if you can formulate it precisely) is correct after all.