Rank-3 scale: Difference between revisions

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Rank-3 scales described on this page are generalizations of MOS scales, and similar rank-2 scales, which will first be introduced.

The term ''n'''-ary scale''''' is used in certain academic scale theory literature for a scale with exactly ''n'' distinct step sizes, with '''''binary''''' and '''''ternary''''' being used for ''n'' = 2 and 3. This is more concrete terminology than the above, as it simply counts step sizes rather than impose an analysis in terms of rank. Equal tunings contain ~~mos~~ scales and ternary scales, but the group generated by the step sizes in these tunings of the scales must be rank 1.

The term ''n'''-ary scale''''' is used in certain academic scale theory literature for a scale with exactly ''n'' distinct step sizes, with '''''binary''''' and '''''ternary''''' being used for ''n'' = 2 and 3. This is more concrete terminology than the above, as it simply counts step sizes rather than impose an analysis in terms of rank. Equal tunings contain MOS scales and ternary scales, but the group generated by the step sizes in these tunings of the scales must be rank 1. This subtle difference also manifests in the fact that certain chroma-altered MOS scales, which are contained in the group generated by the period and the generator of the unaltered mos, are ternary. An example is harmonic minor which has the step pattern msmmsLs.

== Rank-2 scales ==

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 Rank-3 scales described on this page are generalizations of MOS scales, and similar rank-2 scales, which will first be introduced.
-The term ''n'''-ary scale''''' is used in certain academic scale theory literature for a scale with exactly ''n'' distinct step sizes, with '''''binary''''' and '''''ternary''''' being used for ''n'' = 2 and 3. This is more concrete terminology than the above, as it simply counts step sizes rather than impose an analysis in terms of rank. Equal tunings contain mos scales and ternary scales, but the group generated by the step sizes in these tunings of the scales must be rank 1.
+The term ''n'''-ary scale''''' is used in certain academic scale theory literature for a scale with exactly ''n'' distinct step sizes, with '''''binary''''' and '''''ternary''''' being used for ''n'' = 2 and 3. This is more concrete terminology than the above, as it simply counts step sizes rather than impose an analysis in terms of rank. Equal tunings contain MOS scales and ternary scales, but the group generated by the step sizes in these tunings of the scales must be rank 1. This subtle difference also manifests in the fact that certain chroma-altered MOS scales, which are contained in the group generated by the period and the generator of the unaltered mos, are ternary. An example is harmonic minor which has the step pattern msmmsLs.
 == Rank-2 scales ==