Combination product set: Difference between revisions
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# A set S of n intervals (usually odd harmonics) is the starting point. | # 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. | # All the combinations of k intervals from the set are obtained, and each combination of intervals is stacked together. | ||
# | # This results in a bunch of notes. One note 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). | # 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. | CPSes were developed by Erv Wilson. | ||
== Example (hexany) == | == Example (hexany) == | ||
[[Category:Scale construction]] | [[Category:Scale construction]] | ||
Revision as of 06:01, 23 December 2025
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.
- This results in a bunch of notes. One note 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.
