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 '''~~chromata~~''' (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''' (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 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.

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

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

== 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 '''chromata''' (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''' (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 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.
-If the chromata of a Fokker block are too large, the result will not be CS; it is then called a weak Fokker block.
+If the chromas of a Fokker block are too large, the result will not be CS; it is then called a weak Fokker block.
 == Mathematical description ==