Step variety: Difference between revisions

Line 1:

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 less well-known than binary ones, but one well-studied type of ternary scales is the class of [[generator-offset]] scales.

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 less well-known than binary ones, but one well-studied type of ternary scales is the class of [[generator-offset]] scales. Most known facts about ternary scales on the wiki can be found on the page [[rank-3 scale]].

== 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]".

@@ Line 1: / Line 1: @@
 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 less well-known than binary ones, but one well-studied type of ternary scales is the class of [[generator-offset]] scales.
+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 less well-known than binary ones, but one well-studied type of ternary scales is the class of [[generator-offset]] scales. Most known facts about ternary scales on the wiki can be found on the page [[rank-3 scale]].
 == 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]".