Cubocta filling space?

On Thu, 28 Oct 1999, Paul Hahn wrote:
> . . . you can't take the cuboctahedron and no
> other shape and fill space with it.

On Fri, 29 Oct 1999, Paul Hahn wrote:
> . . . the 7-limit diamond can be used to fill
> the lattice, and a lot of really weird pitchsets can be derived if you
> don't care how small the intervals represented by the unison vectors
> actually are.

Casual readers may wonder how this can be so, since the 7-limit diamond
looks like a cubocta in the triangulated 3-D lattice. This is left as
an exercise for the reader. 8-)>

However, I will offer a set of unison vectors that indicate how the
13-note scale formed by the 7-limit diamond can be used to tesselate the
lattice (this constitutes an existence proof for the second statement
above):

| -1 2 1 |
| 1 3 0 | = 13.
| 4 -1 0 |

Note that only one of these "unison vectors" is actually smaller than
any of the scale steps involved. (1 3 0) is actually almost as far from
being a comma as possible, in the region between a fifth (/fourth) and a
tritone.

--pH <manynote@library.wustl.edu> http://library.wustl.edu/~manynote
O
/\ "Well, so far, every time I break he runs out.
-\-\-- o But he's gotta slip up sometime . . . "

>However, I will offer a set of unison vectors that indicate how the
>13-note scale formed by the 7-limit diamond can be used to tesselate the
>lattice . . .

Oh, now I get it. Boy do I feel like an idiot!