Combination product set

This is an expert page. It either assumes experience with xen theory or involves fairly technical procedures.

A combination product set (CPS) is a scale generated by the following means:

1. A set S of n intervals is the starting point.
2. All the combinations of k elements of the set are obtained, and their products taken.
3. These are combined into a set, and then all of the elements of that set are divided by one of them (which one is arbitrary; if a canonical choice is required, the smallest element could be used).
4. The resulting elements are octave-reduced and sorted in ascending order, resulting in an octave period of a periodic scale (the usual sort of scale, in other words) which we may call CPS(S, k).