Glossary of scale properties: Difference between revisions

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: A scale is symmetrical if at least one mode of the scale is symmetrical. Therefore, every interval of that mode must have an inverse. These scales will always have an odd number of notes ''per period''. They may not always have an odd number of notes ''per octave'', however. The diatonic scale is symmetrical, but so is 12edo.

; ~~MOS/~~Myhill's

; Myhill's property and MOS

* '''[[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).~~

* '''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).

* '''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".

* '''[[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".

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

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[[Category:Scale]]

[[Category:Todo:add examples]]

[[Category:Todo:add illustration]]s

[[Category:Todo:add illustration]]

@@ Line 32: / Line 32: @@
 : A scale is symmetrical if at least one mode of the scale is symmetrical. Therefore, every interval of that mode must have an inverse. These scales will always have an odd number of notes ''per period''. They may not always have an odd number of notes ''per octave'', however. The diatonic scale is symmetrical, but so is 12edo.
-; MOS/Myhill's
+; Myhill's property and MOS
-* '''[[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).
 * '''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).
 * '''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".
+* '''[[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".
 The 12-tone diatonic scale has Myhill's property, and is also distributionally even.
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 [[Category:Scale]]
 [[Category:Todo:add examples]]
-[[Category:Todo:add illustration]]s
+[[Category:Todo:add illustration]]