MOS scale: Difference between revisions
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{{Beginner|Mathematics of MOS}} | {{Beginner|Mathematics of MOS}} | ||
An '''MOS''' (sometimes '''mos'''; originally pronounced "em-oh-ess," but sometimes also pronounced "moss"; plural '''MOSes''' or '''mosses''') or '''moment of symmetry''' is a [[periodic scale]] in which every interval except for the [[period]] comes in two sizes. | An '''MOS''' (sometimes '''mos'''; originally pronounced "em-oh-ess," but sometimes also pronounced "moss"; plural '''MOSes''' or '''mosses''') or '''moment of symmetry''' is a [[periodic scale]] in which every [[interval]] except for the [[period]] comes in two sizes. | ||
See the [[catalog of MOS]]. | See the [[catalog of MOS]]. | ||
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== History and terminology == | == History and terminology == | ||
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'']. | 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, 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'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 Wilson's concept. They are in a sense the MOS of MOS patterns. This is used to explain the | 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. | ||
As for using MOS scales in practice for making music, the period and equivalence interval are often taken to be the octave, but an additional parameter is required for defining a scale: the ''step ratio'', which is the ratio of the small step (usually denoted ''s'') to the large step (usually denoted ''L''). This is usually written as ''L''/''s'', however, using ''s''/''L'' has the advantage of avoiding division by zero in the trivial case where {{nowrap|''s'' {{=}} 0}}. Different step ratios can produce very varied sounding scales (and very varied corresponding potential temperament interpretations) for a given MOS pattern and period, so it's useful to consider a spectrum of simple step ratios for tunings. The [[TAMNAMS#Step ratio spectrum|TAMNAMS]] system has names for both specific ratios and ranges of ratios. | As for using MOS scales in practice for making music, the period and equivalence interval are often taken to be the octave, but an additional parameter is required for defining a scale: the ''step ratio'', which is the ratio of the small step (usually denoted ''s'') to the large step (usually denoted ''L''). This is usually written as ''L''/''s'', however, using ''s''/''L'' has the advantage of avoiding division by zero in the trivial case where {{nowrap|''s'' {{=}} 0}}. Different step ratios can produce very varied sounding scales (and very varied corresponding potential temperament interpretations) for a given MOS pattern and period, so it's useful to consider a spectrum of simple step ratios for tunings. The [[TAMNAMS#Step ratio spectrum|TAMNAMS]] system has names for both specific ratios and ranges of ratios. | ||
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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 A Rhythmic Application of the Horagrams] from Xenharmonikon 16 | * [http://anaphoria.com/hora.pdf A Rhythmic Application of the Horagrams] from ''[[Xenharmonikon]] 16'' | ||
* [http://anaphoria.com/horo2.pdf More on Horogram Rhythms] | * [http://anaphoria.com/horo2.pdf More on Horogram Rhythms] | ||
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== See also == | == See also == | ||
* [[Diamond-mos notation]], a microtonal notation system | * [[Diamond-mos notation]], a microtonal [[notation]] system focused on MOS scales | ||
* [[Metallic MOS]], an article focusing on MOS scales based on metallic means, such as [[phi]] | * [[Metallic MOS]], an article focusing on MOS scales based on metallic means, such as [[phi]] | ||
* [[:Category:MOS scales|Category:MOS scales]], the category including all MOS-related articles on this wiki | * [[:Category:MOS scales|Category:MOS scales]], the category including all MOS-related articles on this wiki | ||