Combination product set: Difference between revisions
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Created page with "{{Expert}} A '''combination product set''' (CPS) is a scale generated by the following means: # A set S of n intervals is the starting point. # All the combinations of k elements of the set are obtained, and their products taken. # 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). # The resulting elements are octave-reduced an..." |
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# A set S of n intervals is the starting point. | # A set S of n intervals is the starting point. | ||
# All the combinations of k elements of the set are obtained, and | # All the combinations of k elements of the set are obtained, and each combination is stacked together. | ||
# 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). | # 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). | ||
# 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). | ||
[[Category:Scale constructions]] | [[Category:Scale constructions]] | ||
Revision as of 05:49, 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 is the starting point.
- All the combinations of k elements of the set are obtained, and each combination is stacked together.
- 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).
- 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).
