Rank-3 scale: Difference between revisions
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A rank-''n'' scale 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''' 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. | ||
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. | ||
Rank-2 scales include [[MOS scales]] and other generated scales, [[MODMOS scale]]s, and other more complex scales that we are not as interested in. | Rank-2, or binary, scales include [[MOS scales]] and other generated scales, [[MODMOS scale]]s, and other more complex scales that we are not as interested in. | ||
Rank-3 scales described on this page are generalizations of MOS scales, and similar rank-2 scales, which will first be introduced. | Rank-3, or ternary, scales described on this page are generalizations of MOS scales, and similar rank-2 scales, which will first be introduced. | ||
== Rank-2 scales == | == Rank-2 scales == | ||