Step variety: Difference between revisions

Line 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. 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]".

The terms ''binary'' and ''ternary'' are already used in some academic literature in reference to scales; 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 ==

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

@@ Line 3: / Line 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. 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]".
+The terms ''binary'' and ''ternary'' are already used in some academic literature in reference to scales; 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 ==
 Certain abstract scale theorists in the xen community have taken to using the ''n-ary'' terminology, to respect the subtlety of the notion of a scale's [[rank]]. Examples of this subtlety are: