Fokker block: Difference between revisions

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The '''Fokker block''' is one of the most notable inventions of the physicist and music theorist [http://en.wikipedia.org/wiki/Adriaan_Fokker Adriaan Fokker]. Informally, a Fokker block is a parallelogram-shaped tile of scale pitches (in a [[JI subgroup]] or a [[regular temperament]]) that can tessellate the entire lattice of pitch classes that it lives in ("Pitch class" means that the interval of equivalence is ignored). Fokker blocks in rank-r temperaments ~~are~~ (r-1)-dimensional. Fokker blocks are one way to generalize [[MOS]]es; MOSes are 1-dimensional Fokker blocks.

The '''Fokker block''' is one of the most notable inventions of the physicist and music theorist [http://en.wikipedia.org/wiki/Adriaan_Fokker Adriaan Fokker]. Informally, a Fokker block is a parallelogram-shaped tile of scale pitches (in a [[JI subgroup]] or a [[regular temperament]]) that can tessellate the entire lattice of pitch classes that it lives in ("Pitch class" means that the interval of equivalence is ignored). Fokker blocks in rank-r temperaments live in (r-1)-dimensional pitch-class lattices. Fokker blocks are one way to generalize [[MOS]]es; MOSes are 1-dimensional Fokker blocks.

A Fokker block of rank r has [[maximum variety]] less than or equal to 2^(r-1). For example, a rank-1 Fokker block has max variety <= 2 (hence is a MOS); a rank-2 Fokker block has max variety <= 4.

While the idea generalizes easily to [[Just_intonation_subgroups|just intonation subgroups]] and tempered groups, for ease of exposition we will suppose that we are in a [[Harmonic_Limit|p-limit]] situation with n=pi(p) primes up to an including p.

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-The '''Fokker block''' is one of the most notable inventions of the physicist and music theorist [http://en.wikipedia.org/wiki/Adriaan_Fokker Adriaan Fokker]. Informally, a Fokker block is a parallelogram-shaped tile of scale pitches (in a [[JI subgroup]] or a [[regular temperament]]) that can tessellate the entire lattice of pitch classes that it lives in ("Pitch class" means that the interval of equivalence is ignored). Fokker blocks in rank-r temperaments are (r-1)-dimensional. Fokker blocks are one way to generalize [[MOS]]es; MOSes are 1-dimensional Fokker blocks.
+The '''Fokker block''' is one of the most notable inventions of the physicist and music theorist [http://en.wikipedia.org/wiki/Adriaan_Fokker Adriaan Fokker]. Informally, a Fokker block is a parallelogram-shaped tile of scale pitches (in a [[JI subgroup]] or a [[regular temperament]]) that can tessellate the entire lattice of pitch classes that it lives in ("Pitch class" means that the interval of equivalence is ignored). Fokker blocks in rank-r temperaments live in (r-1)-dimensional pitch-class lattices. Fokker blocks are one way to generalize [[MOS]]es; MOSes are 1-dimensional Fokker blocks.
+A Fokker block of rank r has [[maximum variety]] less than or equal to 2^(r-1). For example, a rank-1 Fokker block has max variety <= 2 (hence is a MOS); a rank-2 Fokker block has max variety <= 4.
 While the idea generalizes easily to [[Just_intonation_subgroups|just intonation subgroups]] and tempered groups, for ease of exposition we will suppose that we are in a [[Harmonic_Limit|p-limit]] situation with n=pi(p) primes up to an including p.