Glossary of scale properties: Difference between revisions

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; Myhill's property and MOS

* '''Myhill's property''': A scale has Myhill's property if there are exactly two interval sizes for each generic interval class (except octaves or other equivalence intervals such as tritaves).

* '''Myhill's/MOS property''': A scale has Myhill's property if there are ''exactly'' two interval sizes for each non-equave-equivalent generic interval class (except octaves or other equivalence intervals such as tritaves). A scale is a MOS scale if there are ''no more than'' two interval sizes for each non-equave-equivalent generic interval class. This is equivalent to a scale being Myhill with a smaller equave. Both [[distributional evenness|distributionally even]] and Myhill's are essentially synonymous with MOS; Myhill's property is sometimes called "strict MOS".

* '''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.

* '''[[MOS|Moment of symmetry (MOS)]]''': A scale is a MOS scale if there are no more than two interval sizes for each generic interval class (e.g. major/minor thirds, perfect/augmented fourths, etc). Both [[distributional evenness|distributionally even]] and Myhill's are essentially synonymous with MOS; Myhill's property is sometimes called "strict MOS".

;'''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.

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

@@ Line 33: / Line 33: @@
 ; Myhill's property and MOS
-* '''Myhill's property''': A scale has Myhill's property if there are exactly two interval sizes for each generic interval class (except octaves or other equivalence intervals such as tritaves).
+* '''Myhill's/MOS property''': A scale has Myhill's property if there are ''exactly'' two interval sizes for each non-equave-equivalent generic interval class (except octaves or other equivalence intervals such as tritaves). A scale is a MOS scale if there are ''no more than'' two interval sizes for each non-equave-equivalent generic interval class. This is equivalent to a scale being Myhill with a smaller equave. Both [[distributional evenness|distributionally even]] and Myhill's are essentially synonymous with MOS; Myhill's property is sometimes called "strict MOS".
-* '''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.
-* '''[[MOS|Moment of symmetry (MOS)]]''': A scale is a MOS scale if there are no more than two interval sizes for each generic interval class (e.g. major/minor thirds, perfect/augmented fourths, etc). Both [[distributional evenness|distributionally even]] and Myhill's are essentially synonymous with MOS; Myhill's property is sometimes called "strict MOS".
+;'''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.
 The 12-tone diatonic scale has Myhill's property, and is also distributionally even.