Step variety: Difference between revisions

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The terms ''binary'' and ''ternary'' are already used in some academic literature in reference to scale words; see e.g. Bulgakova, Buzhinsky and Goncharov (2023), "[https://www.sciencedirect.com/science/article/pii/S0304397522006417 On balanced and abelian properties of circular words over a ternary alphabet]".

== Difference from scale rank ==

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

Certain abstract scale theorists in the xen community have taken to using the ''n-ary'' terminology, to respect the subtlety of the notion of a scale's [[rank]]. 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.

@@ Line 5: / Line 5: @@
 The terms ''binary'' and ''ternary'' are already used in some academic literature in reference to scale words; see e.g. Bulgakova, Buzhinsky and Goncharov (2023), "[https://www.sciencedirect.com/science/article/pii/S0304397522006417 On balanced and abelian properties of circular words over a ternary alphabet]".
 == Difference from scale rank ==
-To respect the subtlety of the notion of a scale's [[rank]], certain abstract scale theorists in the xen community have taken to using this ''n-ary'' terminology. Examples of this subtlety are:
+Certain abstract scale theorists in the xen community have taken to using the ''n-ary'' terminology, to respect the subtlety of the notion of a scale's [[rank]]. 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.