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- Q5409001 subject Q7034249.
- Q5409001 subject Q8933665.
- Q5409001 abstract "In music theory and tuning, an Euler–Fokker genus (plural: genera), named after Leonhard Euler and Adriaan Fokker, is a musical scale in just intonation whose pitches can be expressed as products of some of the members of some multiset of generating prime factors. Powers of two are usually ignored, because of the way the human ear perceives octaves.An x-dimensional tone-dimension contains x factors. "An Euler-Fokker genus with two dimensions may be represented in a two-dimensional (rectangular) tone-grid, one with three dimensions in a three-dimensional (block-shaped) tone-lattice. Euler-Fokker genera are characterized by a listing of the number of steps in each dimension. The number of steps is represented by a repeated mention of the dimension, so that there arise descriptions such as [3 3 5 5], [3 5 7], [3 3 5 5 7 7 11 11], etc." For example, the multiset {3, 3, 7} yields the Euler–Fokker genus [3, 3, 7], which contains these pitches: 1 3 =3 7=7 3×3 =9 3×7=21 3×3×7=63Normalized to fall within an octave, these become: 1/1, 9/8, 21/16, 3/2, 7/4, 63/32. About this sound Play 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. The degree is the number of intervals which generate a genus. However, not all genera of the same degree have the same number of tones since [XXXYYY] may also be notated [XxYy], "the degree is thus the sum of the exponents," and the number of pitches is obtained adding one to each exponent and then multiplying those ((X+1)×(Y+1)=Z).Adriaan Fokker wrote much of his music in Euler–Fokker genera expressed in 31-tone equal temperament. Alan Ridout also used Euler-Fokker genera.".
- Q5409001 thumbnail Cuboid.png?width=300.
- Q5409001 wikiPageWikiLink Q102761.
- Q5409001 wikiPageWikiLink Q12372854.
- Q5409001 wikiPageWikiLink Q131752.
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- Q5409001 wikiPageWikiLink Q263961.
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- Q5409001 wikiPageWikiLink Q386025.
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- Q5409001 wikiPageWikiLink Q49008.
- Q5409001 wikiPageWikiLink Q4920951.
- Q5409001 wikiPageWikiLink Q5748840.
- Q5409001 wikiPageWikiLink Q7034249.
- Q5409001 wikiPageWikiLink Q7452277.
- Q5409001 wikiPageWikiLink Q752518.
- Q5409001 wikiPageWikiLink Q7604.
- Q5409001 wikiPageWikiLink Q858576.
- Q5409001 wikiPageWikiLink Q864377.
- Q5409001 wikiPageWikiLink Q8933665.
- Q5409001 comment "In music theory and tuning, an Euler–Fokker genus (plural: genera), named after Leonhard Euler and Adriaan Fokker, is a musical scale in just intonation whose pitches can be expressed as products of some of the members of some multiset of generating prime factors. Powers of two are usually ignored, because of the way the human ear perceives octaves.An x-dimensional tone-dimension contains x factors.".
- Q5409001 label "Euler–Fokker genus".
- Q5409001 depiction Cuboid.png.