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 [[~~Wikipedia: Adriaan Fokker|~~Adriaan Fokker]]~~. A Fokker block can be thought of as 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 can be visualized as subsets of~~ (''r'' ~~− 1~~)~~-dimensional pitch-class lattices~~. ~~Fokker blocks are one way to generalize~~ [[~~mos~~]]~~ses; mosses are "1-dimensional Fokker blocks" in~~ the ~~sense~~ of ~~having~~ a ~~1-dimensional~~ pitch~~-class~~ lattice.

A '''Fokker block''' (an invention of physicist and music theorist [[Adriaan Fokker]]) is a [[Constant structure|constant-structure]] scale comprising elements of the [[lattice]] of pitch classes which fall inside or on the boundary of a parellelotope, the edges of which correspond to small intervals called '''chromata''' (singular '''chroma'''). The scale repeats at the [[interval of equivalence]], and the interval of equivalence does not lie on the lattice (as it is a lattice of pitch classes). The rank of a Fokker block is the rank of the underlying lattice of pitches including the interval of equivalence.

A Fokker block of rank ''r'' has [[maximum variety]] at most 2~~<sup style="white-space: nowrap;">~~(''r'' − 1)~~</sup>~~. For example, a rank-2 Fokker block has max variety at most 2 (hence is a mos); a rank-3 Fokker block has max variety at most 4.

A Fokker block of rank r has [[maximum variety]] at most 2(r − 1). For example, a rank-2 Fokker block has max variety at most 2 (hence is a [[MOS scale|mos]]), and a rank-3 Fokker block has max variety at most 4. In this way, Fokker blocks generalize mosses.

== Mathematical description ==

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 {{Inaccessible}} <!-- add beginner section that explains how to build Fokker blocks either by hand or using common software, along with visualizations? -->
 {{Wikipedia| Fokker periodicity block }}
-The '''Fokker block''' is one of the most notable inventions of the physicist and music theorist [[Wikipedia: Adriaan Fokker|Adriaan Fokker]]. A Fokker block can be thought of as 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 can be visualized as subsets of (''r'' − 1)-dimensional pitch-class lattices. Fokker blocks are one way to generalize [[mos]]ses; mosses are "1-dimensional Fokker blocks" in the sense of having a 1-dimensional pitch-class lattice.
+A '''Fokker block''' (an invention of physicist and music theorist [[Adriaan Fokker]]) is a [[Constant structure|constant-structure]] scale comprising elements of the [[lattice]] of pitch classes which fall inside or on the boundary of a parellelotope, the edges of which correspond to small intervals called '''chromata''' (singular '''chroma'''). The scale repeats at the [[interval of equivalence]], and the interval of equivalence does not lie on the lattice (as it is a lattice of pitch classes). The rank of a Fokker block is the rank of the underlying lattice of pitches including the interval of equivalence.
-A Fokker block of rank ''r'' has [[maximum variety]] at most 2<sup style="white-space: nowrap;">(''r'' − 1)</sup>. For example, a rank-2 Fokker block has max variety at most 2 (hence is a mos); a rank-3 Fokker block has max variety at most 4.
+A Fokker block of rank r has [[maximum variety]] at most 2(r − 1). For example, a rank-2 Fokker block has max variety at most 2 (hence is a [[MOS scale|mos]]), and a rank-3 Fokker block has max variety at most 4. In this way, Fokker blocks generalize mosses.
 == Mathematical description ==