Glossary of scale properties: Difference between revisions

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* '''Trivalence property''': Same as Myhill's property, but replace "two interval sizes" with "three interval sizes." The scale formed from the notes of a dominant 7th chord (e.g. C-E-G-Bb-C) is an example of a trivalent scale.

* '''[[Moment of symmetry]]''': Both DE and Myhill's are essentially synonymous with MOS; Myhill's property is sometimes called "strict MOS".

~~; Arity, ''n''-ary~~

: The number of distinct step sizes occurring in a given scale. Arity ''disregards other properties'', such as [[rank]] or [[maximum variety]]. For example, 12edo melodic minor is a binary scale which is not rank-2 or MV2 (MOS).

The 12-tone diatonic scale has Myhill's property, and is also distributionally even.

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An EDO is a kind of degenerate MOS, in that it is distributionally even. It does not have Myhill's property. In other words, it has no more than two interval sizes for each generic interval class, but does not have exactly two interval sizes.

; Arity, ''n''-ary

: The number of distinct step sizes occurring in a given scale. Arity ''disregards other properties'', such as [[rank]] or [[maximum variety]]. For example, 12edo melodic minor is a binary scale which is not rank-2 or MV2 (MOS).

; Convexity

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 * '''Trivalence property''': Same as Myhill's property, but replace "two interval sizes" with "three interval sizes." The scale formed from the notes of a dominant 7th chord (e.g. C-E-G-Bb-C) is an example of a trivalent scale.
 * '''[[Moment of symmetry]]''': Both DE and Myhill's are essentially synonymous with MOS; Myhill's property is sometimes called "strict MOS".
-; Arity, ''n''-ary
-: The number of distinct step sizes occurring in a given scale. Arity ''disregards other properties'', such as [[rank]] or [[maximum variety]]. For example, 12edo melodic minor is a binary scale which is not rank-2 or MV2 (MOS).
 The 12-tone diatonic scale has Myhill's property, and is also distributionally even.
@@ Line 45: / Line 42: @@
 An EDO is a kind of degenerate MOS, in that it is distributionally even. It does not have Myhill's property. In other words, it has no more than two interval sizes for each generic interval class, but does not have exactly two interval sizes.
+; Arity, ''n''-ary
+: The number of distinct step sizes occurring in a given scale. Arity ''disregards other properties'', such as [[rank]] or [[maximum variety]]. For example, 12edo melodic minor is a binary scale which is not rank-2 or MV2 (MOS).
 ; Convexity