Euler-Fokker genus
From Wikipedia, the free encyclopedia
 |
All or part of this article may be confusing or unclear. Please help clarify the article. Suggestions may be on the talk page. (October 2007) |
 |
This article does not cite any references or sources. (April 2008) Please help improve this article by adding citations to reliable sources. Unverifiable material may be challenged and removed. |
An Euler-Fokker genus is a musical scale in just intonation whose pitches can be expressed as products over the elements of a power set of some multiset of generating prime factors. Powers of 2 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.
Euler genera are generated from the prime factors 3 and 5, whereas an Euler-Fokker genus can have factors of 7 or any higher prime number.
Adriaan Fokker wrote much of his music in Euler-Fokker genera expressed in 31-tone equal temperament.
