Combination Product Sets (CPS)

Harmonically symmetrical musical structures invented by Ervin M. Wilson in the late 1960's. CPS's are generated by taking the products of n harmonic factors m at a time and reducing the derived tones to a common octave.

The best studied sets are the six tone Hexany (n=4, m=2) and the 20 element Eikosany (n=6, m=3).

CPS may be partitioned into sets of inversionally related chords, triads in the case of the Hexany and tetrads in the Eikosany. CPS are also characterized by intervallically symmetrical melodic properties and may be defined in equal temperaments as well as Just Intonation.

[from John Chalmers, Divisions of the Tetrachord]

see further comments by Paul Erlich and Carl Lumma

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