Fokker block: Difference between revisions

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==== Third definition of a Fokker block ====

The ''n'' - 1 vals u1, u2, …, u''n'' - 1 defined in the previous section gave us ''n'' - 1 inequalities ''a''''k'' - P < u''k'' (''q'') ≤ ''a''''k'', which apply to any ''q'' in the Fokker block. If we restrict ''q'' to 1 ≤ ''q'' < 2, and regard it as representing a pitch class, then it is associated to a lattice point in an ''n'' - 1 dimensional vector space, and in that space the ''n'' - 1 inequalities define the boundaries of a parallelepiped. The Fokker blocks can be defined as the pitch classes lying within such a parallelepiped. By moving the ~~parallelepipeds~~ around in all ways which retain the same orientation and have the unison inside them, we obtain an arena.

The ''n'' - 1 vals u1, u2, …, u''n'' - 1 defined in the previous section gave us ''n'' - 1 inequalities ''a''''k'' - P < u''k'' (''q'') ≤ ''a''''k'', which apply to any ''q'' in the Fokker block. If we restrict ''q'' to 1 ≤ ''q'' < 2, and regard it as representing a pitch class, then it is associated to a lattice point in an ''n'' - 1 dimensional vector space, and in that space the ''n'' - 1 inequalities define the boundaries of a parallelepiped. The Fokker blocks can be defined as the pitch classes lying within such a parallelepiped. By moving the parallelepiped around (in '''R'''2) in all ways which retain the same orientation and have the unison inside them, we obtain an arena.

==== Fourth definition of a Fokker block ====

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 ==== Third definition of a Fokker block ====
-The ''n'' - 1 vals u<sub>1</sub>, u<sub>2</sub>, …, u<sub>''n'' - 1</sub> defined in the previous section gave us ''n'' - 1 inequalities ''a''<sub>''k''</sub> - P &lt; u<sub>''k''</sub> (''q'') ≤ ''a''<sub>''k''</sub>, which apply to any ''q'' in the Fokker block. If we restrict ''q'' to 1 ≤ ''q'' &lt; 2, and regard it as representing a pitch class, then it is associated to a lattice point in an ''n'' - 1 dimensional vector space, and in that space the ''n'' - 1 inequalities define the boundaries of a parallelepiped. The Fokker blocks can be defined as the pitch classes lying within such a parallelepiped. By moving the parallelepipeds around in all ways which retain the same orientation and have the unison inside them, we obtain an arena.
+The ''n'' - 1 vals u<sub>1</sub>, u<sub>2</sub>, …, u<sub>''n'' - 1</sub> defined in the previous section gave us ''n'' - 1 inequalities ''a''<sub>''k''</sub> - P &lt; u<sub>''k''</sub> (''q'') ≤ ''a''<sub>''k''</sub>, which apply to any ''q'' in the Fokker block. If we restrict ''q'' to 1 ≤ ''q'' &lt; 2, and regard it as representing a pitch class, then it is associated to a lattice point in an ''n'' - 1 dimensional vector space, and in that space the ''n'' - 1 inequalities define the boundaries of a parallelepiped. The Fokker blocks can be defined as the pitch classes lying within such a parallelepiped. By moving the parallelepiped around (in '''R'''<sup>2</sup>) in all ways which retain the same orientation and have the unison inside them, we obtain an arena.
 ==== Fourth definition of a Fokker block ====