MODMOS scale: Difference between revisions

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A scale is considered to be a [[MOS scale]] if every generic [[interval class]] comes in two specific [[interval]] sizes. For example, the familiar [[diatonic scale]] is an MOS.

MODMOS scales generalize the class of scales which are not MOS, but which have been obtained by applying a finite number of "chromatic alterations" to an MOS.

'''MODMOS scales''', also known as '''altered MOS scales''', generalize the class of scales which are not MOS, but which have been obtained by applying a finite number of "chromatic alterations" to an MOS.

The familiar melodic and harmonic minor scales are examples of MODMOS's: although these scales are not MOS, they can be obtained by applying one chromatic alteration each to one of the [[mode]]s of the diatonic MOS.

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A chromatic alteration means changing the size of an interval by increments of the MOS's [[chroma]], where the chroma is the difference between any pair of intervals sharing the same interval class.

Alteration by increments of some other interval is possible, but they lack the useful properties of MODMOS scales, most importantly [[epimorphism]], so they are ~~considered to be~~ [[inflected MOS]] scales, rather than true MODMOS scales.

Alteration by increments of some other interval is possible, but they lack the useful properties of MODMOS scales, most importantly [[epimorphism]], so they are [[inflected MOS]] scales, rather than true MODMOS scales.

In the exposition below, we give a formal treatment of MODMOS scales.

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 A scale is considered to be a [[MOS scale]] if every generic [[interval class]] comes in two specific [[interval]] sizes. For example, the familiar [[diatonic scale]] is an MOS.
-MODMOS scales generalize the class of scales which are not MOS, but which have been obtained by applying a finite number of "chromatic alterations" to an MOS.
+'''MODMOS scales''', also known as '''altered MOS scales''', generalize the class of scales which are not MOS, but which have been obtained by applying a finite number of "chromatic alterations" to an MOS.
 The familiar melodic and harmonic minor scales are examples of MODMOS's: although these scales are not MOS, they can be obtained by applying one chromatic alteration each to one of the [[mode]]s of the diatonic MOS.
@@ Line 10: / Line 10: @@
 A chromatic alteration means changing the size of an interval by increments of the MOS's [[chroma]], where the chroma is the difference between any pair of intervals sharing the same interval class.
-Alteration by increments of some other interval is possible, but they lack the useful properties of MODMOS scales, most importantly [[epimorphism]], so they are considered to be [[inflected MOS]] scales, rather than true MODMOS scales.
+Alteration by increments of some other interval is possible, but they lack the useful properties of MODMOS scales, most importantly [[epimorphism]], so they are [[inflected MOS]] scales, rather than true MODMOS scales.
 In the exposition below, we give a formal treatment of MODMOS scales.