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 tile of scale pitches that can tessellate the entire temperament pitch-class lattice it lives in ("Pitch class lattice" means that the interval of equivalence is ignored). A Fokker block can be shaped like a parallelogram or other shapes. In a sense, 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 (rank-r) Fokker block is a(n (r-1)-dimensional) tile of scale pitches that can tessellate the entire temperament pitch-class lattice it lives in ("Pitch class lattice" means that the interval of equivalence is ignored). A Fokker block can be shaped like a parallelogram or other shapes. In a sense, 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 tile of scale pitches that can tessellate the entire temperament pitch-class lattice it lives in ("Pitch class lattice" means that the interval of equivalence is ignored). A Fokker block can be shaped like a parallelogram or other shapes. In a sense, 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 (rank-r) Fokker block is a(n (r-1)-dimensional) tile of scale pitches that can tessellate the entire temperament pitch-class lattice it lives in ("Pitch class lattice" means that the interval of equivalence is ignored). A Fokker block can be shaped like a parallelogram or other shapes. In a sense, 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.