Fokker block: Difference between revisions

Line 1:

{{Inaccessible}}

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 ~~live in~~ (''r'' - 1)-dimensional pitch-class lattices. Fokker blocks are one way to generalize [[mos]]ses; mosses are "1-dimensional Fokker blocks".

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".

A Fokker block of rank ''r'' has [[maximum variety]] at most 2<sup>(''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.

@@ Line 1: / Line 1: @@
 {{Inaccessible}} <!-- add beginner section that explains how to build Fokker blocks either by hand or using common software, along with visualizations? -->
-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 live in (''r'' - 1)-dimensional pitch-class lattices. Fokker blocks are one way to generalize [[mos]]ses; mosses are "1-dimensional Fokker blocks".
+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".
 A Fokker block of rank ''r'' has [[maximum variety]] at most 2<sup>(''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.