Fokker block: Difference between revisions

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{{Inaccessible}}

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 [[wikipedia:Parallelepiped#Parallelotope|parellelotope]]~~, the edges of which correspond to ~~small~~ intervals ~~called '''chromas''' (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''' is a [[periodic scale|periodic]] [[scale]] that can be thought of as a {{w|parallelepiped #Parallelotope|parallelogram-shaped}} tile of [[pitch class]]es (in a [[JI subgroup]] or a [[regular temperament]]) that can tessellate the entire [[lattice]]. It comprises elements of the lattice which fall inside or on the boundary of the tile, the edges of which correspond to intervals that separate the same scale degree but different qualities, i.e. [[chroma]]s. The scale repeats at the [[interval of equivalence]] (which lies on the [[1/1|unison]] in the lattice due to [[equivalence]]). 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(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~~.

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 scale|mos]]), and a rank-3 Fokker block has max variety at most 4. In this way, Fokker blocks generalize mos scales.

~~If the chromas of a~~ Fokker block ~~are too large~~, ~~the result will~~ not be ~~CS;~~ it is ~~then~~ called a weak Fokker block.

A Fokker block is usually a [[constant structure]]. However, in certain tunings, it may not be, in which case it is called a ''weak Fokker block''.

The Fokker block is one of the most notable inventions of the physicist and music theorist [[Adriaan Fokker]].

== 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 }}
-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 [[wikipedia:Parallelepiped#Parallelotope|parellelotope]], the edges of which correspond to small intervals called '''chromas''' (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''' is a [[periodic scale|periodic]] [[scale]] that can be thought of as a {{w|parallelepiped #Parallelotope|parallelogram-shaped}} tile of [[pitch class]]es (in a [[JI subgroup]] or a [[regular temperament]]) that can tessellate the entire [[lattice]]. It comprises elements of the lattice which fall inside or on the boundary of the tile, the edges of which correspond to intervals that separate the same scale degree but different qualities, i.e. [[chroma]]s. The scale repeats at the [[interval of equivalence]] (which lies on the [[1/1|unison]] in the lattice due to [[equivalence]]). 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(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.
+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 scale|mos]]), and a rank-3 Fokker block has max variety at most 4. In this way, Fokker blocks generalize mos scales.
-If the chromas of a Fokker block are too large, the result will not be CS; it is then called a weak Fokker block.
+A Fokker block is usually a [[constant structure]]. However, in certain tunings, it may not be, in which case it is called a ''weak Fokker block''.
+The Fokker block is one of the most notable inventions of the physicist and music theorist [[Adriaan Fokker]].
 == Mathematical description ==