Step variety: Difference between revisions

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An ''n'''-ary scale''''' is a scale with exactly ''n'' distinct step sizes. The terms '''''unary''''', '''''binary''''' and '''''ternary''''' are used for ''n'' = 1, 2 and 3.

A unary scale is an [[equal tuning]]. The class of binary scales consists of all [[MOS]] scales and every alteration-by-permutation of a MOS scale. Ternary scales are much more subtle, but one well-studied type of ternary scales is the class of [[generator-offset]] scales.

== History of the term ==

The terms ''binary'' and ''ternary'' are already used in some academic literature in reference to scale words; see e.g. Bulgakova, Buzhinsky and Goncharov (2023), "[https://www.sciencedirect.com/science/article/pii/S0304397522006417 On balanced and abelian properties of circular words over a ternary alphabet]".

== Difference from scale rank ==

To respect the subtlety of the notion of a scale's [[rank]], certain abstract scale theorists in the xen community have taken to using this ''n-ary'' terminology. Examples of this subtlety are:

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 An ''n'''-ary scale''''' is a scale with exactly ''n'' distinct step sizes. The terms '''''unary''''', '''''binary''''' and '''''ternary''''' are used for ''n'' = 1, 2 and 3.
 A unary scale is an [[equal tuning]]. The class of binary scales consists of all [[MOS]] scales and every alteration-by-permutation of a MOS scale. Ternary scales are much more subtle, but one well-studied type of ternary scales is the class of [[generator-offset]] scales.
+== History of the term ==
+The terms ''binary'' and ''ternary'' are already used in some academic literature in reference to scale words; see e.g. Bulgakova, Buzhinsky and Goncharov (2023), "[https://www.sciencedirect.com/science/article/pii/S0304397522006417 On balanced and abelian properties of circular words over a ternary alphabet]".
 == Difference from scale rank ==
 To respect the subtlety of the notion of a scale's [[rank]], certain abstract scale theorists in the xen community have taken to using this ''n-ary'' terminology. Examples of this subtlety are: