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 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]]. 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]]es; when viewed as temperaments, MOSes 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.

Revision as of 09:15, 16 January 2021 view source Inthar (talk \| contribs) autopatrolled, emailconfirmed 15,668 edits m using <math> for non-inline math ← Older edit		Revision as of 19:21, 26 March 2021 view source Inthar (talk \| contribs) autopatrolled, emailconfirmed 15,668 edits m mos as one dim fokker block comes from a temperament interpretation of a mos Newer edit →
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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 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]]. 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]]es; when viewed as temperaments, MOSes 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.		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.