Glossary of scale properties: Difference between revisions
→Properties: DE should be generalized to arbitrary arity; DE isn't a commonly used synonym of MOS, anyway. |
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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. | : 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 | ; MOS/Myhill's | ||
* '''[[ | * '''[[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). | * '''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. | * '''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. | ||