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 that can tessellate the entire lattice of pitch classes that it lives in ("Pitch class" means that the interval of equivalence is ignored). ~~Rank~~-r ~~Fokker blocks~~ 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 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.

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 that can tessellate the entire lattice of pitch classes that it lives in ("Pitch class" means that the interval of equivalence is ignored). ~~Rank~~-r ~~Fokker blocks~~ 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 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.

	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.		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.