Step variety: Difference between revisions

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The '''step variety''' (or '''arity''') of a [[scale]] is the number of distinct [[step]] sizes it has. '''Unary''', '''binary''', '''ternary''', and '''quaternary''' scales are scales with exactly 1, 2, 3, and 4 step sizes, respectively. An ''n'''''-ary scale''' is a scale with exactly ''n'' distinct step sizes.

Unary scales are [[equal tuning]]s. The class of binary scales consists of all [[MOS scale]]s and every alteration-by-permutation of an MOS scale, but do not include [[altered MOS scale]]s such as the harmonic minor scale (abstract [[step pattern]]: MsMMsLs), which gain additional step sizes from the alteration. Ternary scales are much less well-understood 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]] ~~(which is mostly about specifically~~ ternary ~~scales)~~.

Unary scales are [[equal tuning]]s. The class of binary scales consists of all [[MOS scale]]s and every alteration-by-permutation of an MOS scale, but do not include [[altered MOS scale]]s such as the harmonic minor scale (abstract [[step pattern]]: MsMMsLs), which gain additional step sizes from the alteration. Ternary scales are much less well-understood 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 pages [[rank-3 scale]] and [[ternary scale theorems]].

== Etymology ==

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 The '''step variety''' (or '''arity''') of a [[scale]] is the number of distinct [[step]] sizes it has. '''Unary''', '''binary''', '''ternary''', and '''quaternary''' scales are scales with exactly 1, 2, 3, and 4 step sizes, respectively. An ''n'''''-ary scale''' is a scale with exactly ''n'' distinct step sizes.
-Unary scales are [[equal tuning]]s. The class of binary scales consists of all [[MOS scale]]s and every alteration-by-permutation of an MOS scale, but do not include [[altered MOS scale]]s such as the harmonic minor scale (abstract [[step pattern]]: MsMMsLs), which gain additional step sizes from the alteration. Ternary scales are much less well-understood 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]] (which is mostly about specifically ternary scales).
+Unary scales are [[equal tuning]]s. The class of binary scales consists of all [[MOS scale]]s and every alteration-by-permutation of an MOS scale, but do not include [[altered MOS scale]]s such as the harmonic minor scale (abstract [[step pattern]]: MsMMsLs), which gain additional step sizes from the alteration. Ternary scales are much less well-understood 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 pages [[rank-3 scale]] and [[ternary scale theorems]].
 == Etymology ==