Fokker block: Difference between revisions

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A '''Fokker block''' (or periodicity block) is a [[periodic scale|periodic]] [[scale]] that can be thought of as a tile on a lattice of [[pitch class]]es (of a [[JI subgroup]] or a [[regular temperament]]) shaped as a parallelogram, parallelepiped or higher-dimensional analog. It comprises those intervals in the lattice which fall inside the tile after moving the tile on the lattice to a place where no lattice point is on its boundary. (Different positions of the tile can create scales which are not rotations of each other.) The scale repeats at the [[interval of equivalence]], which lies on the [[1/1|unison]] in the lattice of pitch classes.

A '''Fokker block''' (or '''periodicity block''') is a [[periodic scale|periodic]] [[scale]] that can be thought of as a tile on a [[lattice]] of [[pitch class]]es (of a [[JI subgroup]] or a [[regular temperament]]) shaped as a parallelogram, parallelepiped or higher-dimensional analog. It comprises those intervals in the lattice which fall inside the tile after moving the tile on the lattice to a place where no lattice point is on its boundary. (Different positions of the tile can create scales which are not rotations of each other.) The scale repeats at the [[interval of equivalence]], which lies on the [[1/1|unison]] in the lattice of pitch classes.

All Fokker blocks are [[~~Periodic scale#Epimorphism|weakly~~ epimorphic]]; if a Fokker block is (~~strongly~~) ~~epimorphic~~, it is ~~called~~ '''~~strong~~'''.

All Fokker blocks are weakly [[epimorphic]]; if a Fokker block is epimorphic (i.e. it has no negative steps), it is a ''strong'' Fokker block, otherwise it is a ''weak'' Fokker block. An unqualified Fokker block is generally assumed to be strong.

The concept of the Fokker block was developed by the physicist and music theorist [[Adriaan Fokker]].

== Theory ==

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 {{Beginner| Mathematical theory of Fokker blocks }}
 {{Wikipedia| Fokker periodicity block }}
-A '''Fokker block''' (or periodicity block) is a [[periodic scale|periodic]] [[scale]] that can be thought of as a tile on a lattice of [[pitch class]]es (of a [[JI subgroup]] or a [[regular temperament]]) shaped as a parallelogram, parallelepiped or higher-dimensional analog. It comprises those intervals in the lattice which fall inside the tile after moving the tile on the lattice to a place where no lattice point is on its boundary. (Different positions of the tile can create scales which are not rotations of each other.) The scale repeats at the [[interval of equivalence]], which lies on the [[1/1|unison]] in the lattice of pitch classes.
+A '''Fokker block''' (or '''periodicity block''') is a [[periodic scale|periodic]] [[scale]] that can be thought of as a tile on a [[lattice]] of [[pitch class]]es (of a [[JI subgroup]] or a [[regular temperament]]) shaped as a parallelogram, parallelepiped or higher-dimensional analog. It comprises those intervals in the lattice which fall inside the tile after moving the tile on the lattice to a place where no lattice point is on its boundary. (Different positions of the tile can create scales which are not rotations of each other.) The scale repeats at the [[interval of equivalence]], which lies on the [[1/1|unison]] in the lattice of pitch classes.
-All Fokker blocks are [[Periodic scale#Epimorphism|weakly epimorphic]]; if a Fokker block is (strongly) epimorphic, it is called '''strong'''.
+All Fokker blocks are weakly [[epimorphic]]; if a Fokker block is epimorphic (i.e. it has no negative steps), it is a ''strong'' Fokker block, otherwise it is a ''weak'' Fokker block. An unqualified Fokker block is generally assumed to be strong.
 The concept of the Fokker block was developed by the physicist and music theorist [[Adriaan Fokker]].
 == Theory ==