About: Euler–Fokker genus

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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 as equivalent. 1 3 =3 7=7 3×3 =9 3×7=21 3×3×7=63 Normalized to fall within an octave, these become: 1/1, 9/8, 21/16, 3/2, 7/4, 63/32.

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rdf:type	yago:WikicatMusicalScales yago:Abstraction100002137 yago:Communication100033020 yago:MusicalNotation106814870 yago:Notation106808493 yago:Writing106359877 yago:WrittenCommunication106349220 aircraft yago:Scale106856568
rdfs:label	Euler–Fokker genus (en)
rdfs: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 as equivalent. 1 3 =3 7=7 3×3 =9 3×7=21 3×3×7=63 Normalized to fall within an octave, these become: 1/1, 9/8, 21/16, 3/2, 7/4, 63/32. (en)
foaf:depiction
dcterms:subject	Musical scales Musical tuning
Wikipage page ID	3213692 (xsd:integer)
Wikipage revision ID	1070819374 (xsd:integer)
Link from a Wikipage to another Wikipage	Greatest common divisor Multiplication Multiset Music theory Leonhard Euler Harmonic seventh Major second Just major seventh Adriaan Fokker 31 equal temperament Musical scales Perfect fifth Prime number Musical tuning Alan Ridout Just intonation Hexany Musical tuning Octave Scale (music) Septimal comma Unison Otonality and utonality Twenty-first harmonic Lowest common multiple Just augmented fifth
sameAs	Euler–Fokker genus Euler–Fokker genus Euler–Fokker genus
dbp:wikiPageUsesTemplate	dbt:Audio dbt:ISBN dbt:Multiple_image dbt:Musical_tuning dbt:Reflist
thumbnail	wiki-commons:Special:FilePath/Euler_genus_337.png?width=300
align	right (en)
caption	Euler genus {3, 3, 5} as parallelepiped (en) Euler genus {3, 5, 5} as parallelepiped (en) Euler genus {3, 5} as rectangle (en)
direction	vertical (en)
image	Euler genus 335.png (en) Euler genus 35.png (en) Euler genus 355.png (en)
width	100 (xsd:integer)
has 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 as equivalent. 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=63 Normalized to fall within an octave, these become: 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. 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. (en)
gold:hypernym	Scale
prov:wasDerivedFrom	wikipedia-en:Euler–Fokker_genus?oldid=1070819374&ns=0
page length (characters) of wiki page	5640 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Euler–Fokker_genus
is Link from a Wikipage to another Wikipage of	Euler-Fokker genera Euler genera Euler genus List of things named after Leonhard Euler Joel Mandelbaum List of musical scales and modes Multiplication (music) Euler-Fokker genus Adriaan Fokker Fokker (disambiguation) Hexany Octony Genus musicum Complete contracted chord Exponens consonantiae
is Wikipage redirect of	Euler-Fokker genera Euler genera Euler genus Euler-Fokker genus Octony Genus musicum Complete contracted chord Exponens consonantiae
is Wikipage disambiguates of	Fokker (disambiguation)
is foaf:primaryTopic of	wikipedia-en:Euler–Fokker_genus

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