Interval Vectors

The work I am doing with musical set theory and interval vectors can be summarized:

1. Studying hexachords, pentachords, and their configuration in
different S(5,6,12) Steiner systems, and the M12 group (the
symmetry group of S(5,6,12), in particular a certain double
Steiner System.

2. Studying the interval vector values in a pure way, and the
use of inversion (mirror image), complementation, M5 symmetry
(swapping 1,5) and "modified" M5 symmetry (swapping 2,4)

Since M5 can be found holding even elements fixed and changing odds by +6, it can also be found by holding odd elements fixed and changing
even by +6. Using interval vectors then, we would have 0->6 which
we can throw out because 0 isn't in the vector (only 1 to 11 or 1 to
6) So that will send 2->8 (4), 4->10 (2) and that's it.

3. Complementation, ends up being tied up with 2,4 swapping in
the pentad diagrams, because complementary hexads get sandwiched
between rows that are 1,5 swappable. etc. In fact, every block
of four rows each has 1,5 and 2,4 swapping, except three where
Z-related pentads alter this (or extra symmetry)

That's kind of a summary, and a starting point for a spinoff newsgroup.

PGH