Interval variety: Difference between revisions
mNo edit summary |
mNo edit summary |
||
| Line 9: | Line 9: | ||
In addition, '''strict variety''' scales, such as single-period [[MOS scale]]s and [[trivalent scale]]s, have the same interval variety for all interval classes (except the unison, which always trivially has interval variety 1). | In addition, '''strict variety''' scales, such as single-period [[MOS scale]]s and [[trivalent scale]]s, have the same interval variety for all interval classes (except the unison, which always trivially has interval variety 1). | ||
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 | 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. | ||
== Facts == | == Facts == | ||
Theorem: for all ''n'' ≥ 1, the word '''0123'''...('''''n''-1''') is SV''n''. | Theorem: for all ''n'' ≥ 1, the word '''0123'''...('''''n''-1''') is SV''n''. | ||