Combination product set
From Xenharmonic Reference
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:
- A set S of n intervals (usually odd harmonics) is the starting point.
- All the combinations of k intervals from the set are obtained, and each combination of intervals is stacked together.
- The results are combined into a set, and then one element of that set is chosen as the tonic.
- 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).
CPSes were developed by Erv Wilson.
