Rank-3 scale: Difference between revisions

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	A '''rank-'''''n'' '''scale''' or an ''n'''''-ary scale''' is a scale whose intervals (in cents, or any other logarithmic [[interval size measure]]) generate a rank-''n'' group. Alternatively, a rank-''n'' scale is a finite set of notes of a rank-''n'' tuning, which is an infinite set of notes that can be generated by ''n'' generators, one of which is taken to be the period, at which any scale of the tuning repeats.		A '''rank-'''''n'' '''scale''', known as an ''n'''''-ary scale''' in certain academic scale theory literature, is a scale whose intervals (in cents, or any other logarithmic [[interval size measure]]) generate a rank-''n'' group. Alternatively, a rank-''n'' scale is a finite set of notes of a rank-''n'' tuning, which is an infinite set of notes that can be generated by ''n'' generators, one of which is taken to be the period, at which any scale of the tuning repeats.

	Rank-1 tunings and scales are [[equal temperament]]s (ET). ETs are rank-1 because the generator achieves the octave by default. Thus, the octave is not counted as a generator.		Rank-1 tunings and scales are [[equal temperament]]s (ET). ETs are rank-1 because the generator achieves the octave by default. Thus, the octave is not counted as a generator.