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 can be made~~ [[~~constant structure~~]] (with negative steps allowed) by moving the generator sizes by an arbitrarily small amount. If the logarithmic sizes of the generators are linearly independent (as happens in JI, for example), the generator sizes need not be moved. If the constant structure does not have negative steps, the Fokker block is ~~called '''strong'''; otherwise~~, it is called '''~~weak~~'''.

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

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

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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 can be made [[constant structure]] (with negative steps allowed) by moving the generator sizes by an arbitrarily small amount. If the logarithmic sizes of the generators are linearly independent (as happens in JI, for example), the generator sizes need not be moved. If the constant structure does not have negative steps, the Fokker block is called '''strong'''; otherwise, it is called '''weak'''.
+All Fokker blocks are [[Periodic scale#Epimorphism|weakly epimorphic]]; if a Fokker block is (strongly) epimorphic, it is called '''strong'''.
 The concept of the Fokker block was developed by the physicist and music theorist [[Adriaan Fokker]].