Euler-Fokker genus

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An Euler-Fokker genus is a musical scale in just intonation generated by a set of prime factors. Every possible product of the set of prime factors (including the empty product, 1) is a pitch in the scale (powers of two are usually ignored, because of the way the human ear perceives octaves). For example, the Euler-Fokker genus [3,3,7] contains the pitches 3⁰7⁰=1, 3⁰7¹=7, 3¹7⁰=3, 3¹7¹=21, 3²7⁰=9, and 3²7¹=63. Normalized to fall within an octave, this is 1/1, 9/8, 21/16, 3/2, 7/4, 63/32.

An Euler genus is usually restricted to the prime factors 3 and 5 (5-limit), whereas an Euler-Fokker genus can have factors of 7 or any higher prime number.

Adriaan Fokker wrote most of his music in Euler-Fokker genera expressed in 31-tone equal temperament.