Step variety: Difference between revisions

Line 1:

An ''n'''''-ary scale''' is a scale with exactly ''n'' distinct step sizes; a scale's '''arity''' is the number of distinct step sizes it has. '''Unary''', '''binary''' and '''ternary''' scales are scales with exactly 1, 2 and 3 step sizes, respectively.

An ''n'''''-ary scale''' is a scale with exactly ''n'' distinct step sizes; a scale's '''arity''' is the number of distinct step sizes it has. '''Unary''', '''binary''' and '''ternary''' scales are scales with exactly 1, 2 and 3 step sizes, respectively. This use of term ''arity'', while generalized from the use of ''binary'', ''ternary'', and ''n-ary'' to refer to the number of letters in an alphabet in combinatorics on words, is an extrapolation from it and is not standard usage.

Unary scales are [[equal tuning]]s. The class of binary scales consists of all [[MOS]] scales and every alteration-by-permutation of a MOS scale, but do not include altered MOS scales such as the harmonic minor scale, 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).

Revision as of 00:38, 11 November 2023 view source CompactStar (talk \| contribs) 5,020 edits Ganaram has stated a different definition of temperament-agnostic so my previous edit can be reverted. ← Older edit		Revision as of 23:57, 23 December 2023 view source Inthar (talk \| contribs) autopatrolled, emailconfirmed 15,004 edits No edit summary Newer edit →
Line 1:		Line 1:
	An ''n'''''-ary scale''' is a scale with exactly ''n'' distinct step sizes; a scale's '''arity''' is the number of distinct step sizes it has. '''Unary''', '''binary''' and '''ternary''' scales are scales with exactly 1, 2 and 3 step sizes, respectively.		An ''n'''''-ary scale''' is a scale with exactly ''n'' distinct step sizes; a scale's '''arity''' is the number of distinct step sizes it has. '''Unary''', '''binary''' and '''ternary''' scales are scales with exactly 1, 2 and 3 step sizes, respectively. This use of term ''arity'', while generalized from the use of ''binary'', ''ternary'', and ''n-ary'' to refer to the number of letters in an alphabet in combinatorics on words, is an extrapolation from it and is not standard usage.

	Unary scales are [[equal tuning]]s. The class of binary scales consists of all [[MOS]] scales and every alteration-by-permutation of a MOS scale, but do not include altered MOS scales such as the harmonic minor scale, 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]] scales and every alteration-by-permutation of a MOS scale, but do not include altered MOS scales such as the harmonic minor scale, 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).