doubling phenomenon (also, transposing notes by unison vectors)

>>I know I could stand to understand better what happens to a block when
>>notes are transposed by unison vectors -- an issue raised in the gentle
>>introduction series but never fully explored. What do you think of an
>>"excursion" on that, Paul?
>
>Well, that is what the existing "excursion" is about -- in a special case.

Really? I had a feeling the two were related (or rather, questions about
what happens when notes are transposed by unison vectors came up when I was
thinking about the doubling phenomenon). Perhaps you could clarify.

>So a small interval within the periodicity block is not sufficient (but
>of course it is necessary) to establish a periodicity within the
>periodicity.
>
>I wonder, is there a necessary condition that we can establish?

I wish I had better tools to work with blocks, but could the doubling
phenomenon be caused when one unison vector more closely approximates one
of the unit vectors (i.e. 3:2) than it does the unison? And in general,
what happens when you build blocks by, say, approximating a unison on one
axis, and approximating the unit vector of the first axis on the second?

-Carl