old cross sets

To make a cross set, transpose the scale by each of its own degrees. Paul
E. noticed that this produces structures with scaling symmetry on the
lattice. Try a triad on the triangular lattice to see what I mean. I'm not
sure about more than one iteration. I think I tried a triad of triads and
it didn't work...

Cross sets never have more than ((n^2)/2 + 1) notes, where n is the number
of notes in the seed scale. This gets fairly economical at higher limits;
the 15-limit cross set has only 33 notes. That means you can have harmonics
8-16 as your scale (if you like harmonic scales as I do), and modulate to
every key with only 33 pitches. Of course, you can't modulate to every key
of every key, but it isn't too shabby with perfect 15-limit consonance and
33 notes.

-C.