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.

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.

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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.
+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.