Rank-3 scale: Difference between revisions

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== Terminology ==

The related 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. To respect the subtlety of the notion of scale rank, certain abstract scale theorists in the xen community have taken to using the ''n-ary'' terminology. Examples of this subtlety are:

The related term ''n'''-ary scale''''' is used in certain academic scale theory literature for a scale with exactly ''n'' distinct step sizes, with '''''unary''''', '''''binary''''' and '''''ternary''''' being used for ''n'' = 1, 2 and 3. To respect the subtlety of the notion of scale rank, certain abstract scale theorists in the xen community have taken to using the ''n-ary'' terminology. Examples of this subtlety are:

* 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.

* 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 in any non-edo diatonic tuning, a chroma-alteration of the diatonic MOS with step pattern msmmsLs.

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 == Terminology ==
-The related 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. To respect the subtlety of the notion of scale rank, certain abstract scale theorists in the xen community have taken to using the ''n-ary'' terminology. Examples of this subtlety are:
+The related term ''n'''-ary scale''''' is used in certain academic scale theory literature for a scale with exactly ''n'' distinct step sizes, with '''''unary''''', '''''binary''''' and '''''ternary''''' being used for ''n'' = 1, 2 and 3. To respect the subtlety of the notion of scale rank, certain abstract scale theorists in the xen community have taken to using the ''n-ary'' terminology. Examples of this subtlety are:
 * 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.
 * 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 in any non-edo diatonic tuning, a chroma-alteration of the diatonic MOS with step pattern msmmsLs.