MOS scale: Difference between revisions
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<span style="display: block; text-align: right;">[[de:MOS-Skalen]]</span> | <span style="display: block; text-align: right;">[[de:MOS-Skalen]]</span> | ||
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=Definition= | =Definition= | ||
An '''MOS''' or '''Moment Of Symmetry''' is a scale in which every interval except for the period comes in two sizes. The term "MOS," and the method of scale construction it entails, were invented by [[Erv Wilson]] in 1975. His original paper can be found at | An '''MOS''' or '''Moment Of Symmetry''' is a scale in which every interval except for the period comes in two sizes. The term "MOS," and the method of scale construction it entails, were invented by [[Erv Wilson]] in 1975. His original paper can be found at http://anaphoria.com/mos.PDF. There is also an introduction at http://anaphoria.com/wilsonintroMOS.html. | ||
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-MOS''''s. MOS's in which the equivalence interval is equal to the period are sometimes called '''Strict MOS''''s. 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-MOS'<nowiki/>'''s. MOS's in which the equivalence interval is equal to the period are sometimes called '''Strict MOS''''s. 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 Wilsons' concept. They are in a sense the MOS of MOS patterns. This is used to explain the pentatonics used in traditional Japanese music, where the 5 tone cycles are derieved from a 7 tone MOS, which are not found in the concept of DE. | 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 Wilsons' concept. They are in a sense the MOS of MOS patterns. This is used to explain the pentatonics used in traditional Japanese music, where the 5 tone cycles are derieved from a 7 tone MOS, which are not found in the concept of DE. | ||
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=MOS As Applied To Rhythms= | =MOS As Applied To Rhythms= | ||
David Canright was the first to suggest Fibonacci Rhythms in 1/1. This led to Kraig Grady to be the first to apply MOS patterns to rhythms. Two papers on the subject can be found here | David Canright was the first to suggest Fibonacci Rhythms in 1/1. This led to Kraig Grady to be the first to apply MOS patterns to rhythms. Two papers on the subject can be found here http://anaphoria.com/hora.pdf and [http://%20http://anaphoria.com/horo2.pdf http://anaphoria.com/horo2.pdf] | ||
MOS structures and thinking can be applied to the design of rhythms as well. See [[MOS Rhythm Tutorial]] [[Category:Math]] | MOS structures and thinking can be applied to the design of rhythms as well. See [[MOS Rhythm Tutorial]] | ||
[[Category:Math]] | |||
[[Category:Mos]] | [[Category:Mos]] | ||
[[Category:Overview]] | [[Category:Overview]] | ||