MODMOS scale: Difference between revisions

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== Introduction ==

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. The familiar melodic and harmonic minor scales are examples of MODMOS's: although these scales are not MOS (the fourths come in three sizes), they can be obtained by applying one chromatic alteration each to one of the modes of the diatonic MOS.

~~In theory~~, although ~~numerous options exist for~~ the ~~choice~~ of chromatic alteration, the ~~standard is alteration~~ by the MOS's ''chroma'', where the chroma is the difference between any pair of intervals sharing the same interval class. ~~This choice~~ of ~~chromatic alteration~~ interval is ~~so fundamental to~~ the ~~structure~~ of ~~these~~ scales ~~that the term MODMOS~~, ~~in its main sense~~, ~~is generally interpreted as referring~~ to ~~only those~~ scales ~~being altered by this interval in particular~~. In the exposition below, we give a formal treatment of MODMOS~~'s that looks only at chroma-altered~~ scales~~. These scales are distinguished by the sense that they are [[Periodic scale|epimorphic]], and hence of special musical interest. However, alterations by other intervals may also be useful~~.

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.

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.

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.

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

== Definitions ==

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 __FORCETOC__
 == Introduction ==
-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. The familiar melodic and harmonic minor scales are examples of MODMOS's: although these scales are not MOS (the fourths come in three sizes), they can be obtained by applying one chromatic alteration each to one of the modes of the diatonic MOS.
-In theory, although numerous options exist for the choice of chromatic alteration, the standard is alteration by the MOS's ''chroma'', where the chroma is the difference between any pair of intervals sharing the same interval class. This choice of chromatic alteration interval is so fundamental to the structure of these scales that the term MODMOS, in its main sense, is generally interpreted as referring to only those scales being altered by this interval in particular. In the exposition below, we give a formal treatment of MODMOS's that looks only at chroma-altered scales. These scales are distinguished by the sense that they are [[Periodic scale|epimorphic]], and hence of special musical interest. However, alterations by other intervals may also be useful.
+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.
+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.
+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.
+In the exposition below, we give a formal treatment of MODMOS scales.
 == Definitions ==