Parallelogram substring scale: Difference between revisions
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A '''parallelogram substring scale''' is a scale whose pitch class lattice forms either a parallelogram or an incomplete traversal of one. Such scales are currently being investigated in ternary generator-offset theory. | A '''parallelogram substring scale''' is a scale whose pitch class lattice forms either a parallelogram or an incomplete traversal of one. Such scales are currently being investigated in ternary generator-offset theory. | ||
== Mathematical definition == | == Mathematical definition == | ||
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* '''v''' and '''w''' are the generator and offset | * '''v''' and '''w''' are the generator and offset | ||
This concept generalizes in the obvious way to arbitrary ranks (where each (n - 1)-dimensional "hyperrow" is traversed lexicographically, and the first and last hyperrows must be a suffix resp. prefix of such a traversal). In this case the property is called the '''parallelotope substring property'''. | |||
== Ternary scales with this property == | == Ternary scales with this property == | ||
=== Examples === | === Examples === | ||