MOS scale: Difference between revisions

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The term ''MOS'', and the method of scale construction it entails, were invented by [[Erv Wilson]] in 1975. His original paper is archived on Anaphoria.com here: [http://anaphoria.com/mos.PDF ''Moments of Symmetry'']. There is also an introduction by [[Kraig Grady]] here: [http://anaphoria.com/wilsonintroMOS.html ''Introduction to Erv Wilson's Moments of Symmetry''].

Sometimes, scales are defined with respect to a period and an additional "[[equivalence interval]]," considered to be the interval at which pitch classes repeat. MOS's in which the equivalence interval is a multiple of the period ~~(including 1)~~, and in which there is more than one period per equivalence interval, are sometimes called '''Multi-MOSs'''. MOS's in which the equivalence interval is equal to the period are sometimes called '''Strict MOSs'''. MOS's in which the equivalence interval and period are simply disjunct, with no rational relationship between them, are simply MOS and have no additional distinguishing label.

Sometimes, scales are defined with respect to a period and an additional "[[equivalence interval]]," considered to be the interval at which pitch classes repeat. MOS's in which the equivalence interval is a multiple of the period, and in which there is more than one period per equivalence interval, are sometimes called '''Multi-MOSs'''. MOS's in which the equivalence interval is equal to the period are sometimes called '''Strict MOSs'''. MOS's in which the equivalence interval and period are simply disjunct, with no rational relationship between them, are simply MOS and have no additional distinguishing label.

With a few notable exceptions, Wilson generally focused his attention on MOS with period equal to the equivalence interval. Hence, some people prefer to use the term [[distributional evenness|distributionally even scale]], with acronym DE, for the more general class of scales which are MOS with respect to other intervals. MOS/DE scales are also sometimes known as ''well-formed scales'', the term used in the 1989 paper by Norman Carey and David Clampitt. A great deal of interesting work has been done on scales in academic circles extending these ideas. The idea of MOS also includes secondary or bi-level MOS scales which are actually the inspiration of Wilson's concept. They are in a sense the MOS of MOS patterns. This is used to explain the [[pentatonic]]s used in traditional [[Japanese]] music, where the 5 tone cycles are derived from a 7 tone MOS, which are not found in the concept of DE.

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 The term ''MOS'', and the method of scale construction it entails, were invented by [[Erv Wilson]] in 1975. His original paper is archived on Anaphoria.com here: [http://anaphoria.com/mos.PDF ''Moments of Symmetry'']. There is also an introduction by [[Kraig Grady]] here: [http://anaphoria.com/wilsonintroMOS.html ''Introduction to Erv Wilson's Moments of Symmetry''].
-Sometimes, scales are defined with respect to a period and an additional "[[equivalence interval]]," considered to be the interval at which pitch classes repeat. MOS's in which the equivalence interval is a multiple of the period (including 1), and in which there is more than one period per equivalence interval, are sometimes called '''Multi-MOSs'''. MOS's in which the equivalence interval is equal to the period are sometimes called '''Strict MOSs'''. MOS's in which the equivalence interval and period are simply disjunct, with no rational relationship between them, are simply MOS and have no additional distinguishing label.
+Sometimes, scales are defined with respect to a period and an additional "[[equivalence interval]]," considered to be the interval at which pitch classes repeat. MOS's in which the equivalence interval is a multiple of the period, and in which there is more than one period per equivalence interval, are sometimes called '''Multi-MOSs'''. MOS's in which the equivalence interval is equal to the period are sometimes called '''Strict MOSs'''. MOS's in which the equivalence interval and period are simply disjunct, with no rational relationship between them, are simply MOS and have no additional distinguishing label.
 With a few notable exceptions, Wilson generally focused his attention on MOS with period equal to the equivalence interval. Hence, some people prefer to use the term [[distributional evenness|distributionally even scale]], with acronym DE, for the more general class of scales which are MOS with respect to other intervals. MOS/DE scales are also sometimes known as ''well-formed scales'', the term used in the 1989 paper by Norman Carey and David Clampitt. A great deal of interesting work has been done on scales in academic circles extending these ideas. The idea of MOS also includes secondary or bi-level MOS scales which are actually the inspiration of Wilson's concept. They are in a sense the MOS of MOS patterns. This is used to explain the [[pentatonic]]s used in traditional [[Japanese]] music, where the 5 tone cycles are derived from a 7 tone MOS, which are not found in the concept of DE.