Interval variety: Difference between revisions
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Note: A standard academic counterpart to the xen term ''variety'' is the ''abelian complexity function of a [[word]]'': a function ρ<sup>ab</sup> : '''N''' -> '''N''' where ρ<sup>ab</sup>(''n'') is the number of distinct sizes (abelianizations, living in a free abelian group over the step sizes) that length-''n'' subwords can have in a word. | Note: A standard academic counterpart to the xen term ''variety'' is the ''abelian complexity function of a [[word]]'': a function ρ<sup>ab</sup> : '''N''' -> '''N''' where ρ<sup>ab</sup>(''n'') is the number of distinct sizes (abelianizations, living in a free abelian group over the step sizes) that length-''n'' subwords can have in a word. | ||
There is a critical distinction between '''abstract interval variety''' and '''conditional interval variety'''. ''Abstract'' means that the interval variety property holds for any tuning of the scale steps, and ''conditional'' means that the interval variety property only holds for a particular tuning of the steps. | |||
== Facts == | == Facts == | ||
In the following, two letters are to be considered the same if their numerical values are congruent modulo ''n''. | In the following, two letters are to be considered the same if their numerical values are congruent modulo ''n''. | ||