Fokker block: Difference between revisions

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{{~~Inaccessible~~}}

{{Inacc}}

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 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{{nowrap|(''r'' − 1)}}. 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.

== 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? -->
+{{Inacc}} <!-- 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 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{{nowrap|(''r'' − 1)}}. 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.
 == Mathematical description ==