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]]. Informally, a Fokker block is 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]]es; MOSes 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]]. Informally, a Fokker block is 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]]es; MOSes are "1-dimensional Fokker blocks".

A Fokker block of rank ''r'' has [[maximum variety]] less than or equal to 2<sup>(''r'' - 1)</sup>. For example, a rank-1 Fokker block has max variety ≤ 2 (hence is a MOS); a rank-2 Fokker block has max variety ≤ 4.

A Fokker block of rank ''r'' has [[maximum variety]] less than or equal to 2<sup>(''r'' - 1)</sup>. For example, a rank-2 Fokker block has max variety ≤ 2 (hence is a MOS); a rank-3 Fokker block has max variety ≤ 4.

== Preliminaries ==

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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]]. Informally, a Fokker block is 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]]es; MOSes 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]]. Informally, a Fokker block is 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]]es; MOSes are "1-dimensional Fokker blocks".
-A Fokker block of rank ''r'' has [[maximum variety]] less than or equal to 2<sup>(''r'' - 1)</sup>. For example, a rank-1 Fokker block has max variety ≤ 2 (hence is a MOS); a rank-2 Fokker block has max variety ≤ 4.
+A Fokker block of rank ''r'' has [[maximum variety]] less than or equal to 2<sup>(''r'' - 1)</sup>. For example, a rank-2 Fokker block has max variety ≤ 2 (hence is a MOS); a rank-3 Fokker block has max variety ≤ 4.
 == Preliminaries ==