MOS scale: Difference between revisions

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An '''MOS''' (sometimes '''mos'''; originally pronounced "em-oh-ess," but sometimes also pronounced "moss"; plural '''MOSes''' or '''mosses''') or '''~~Moment Of Symmetry~~''' is a scale in which every interval except for the period comes in two sizes. See the [[catalog 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 scale in which every interval except for the period comes in two sizes. See the [[catalog of MOS]].

== History and terminology ==

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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 pentatonics 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 ''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 ''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.

== Naming ==

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The melodic sound of a MOS is not just affected by the tuning of its intervals, but by the sizes of its steps. MOSes with L more similar to s sound smoother and more mellow. MOSes with L much larger than s sound jagged and dramatic. The ''step ratio'', the ratio between the sizes of L and s, is thus important to the sound of the scale.

An in-depth analysis of this can be found at [[~~MOS~~ Step ~~Ratio Spectrum~~]].

An in-depth analysis of this can be found at [[Step ratio]].

== Mathematics ==

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-An '''MOS''' (sometimes '''mos'''; originally pronounced "em-oh-ess," but sometimes also pronounced "moss"; plural '''MOSes''' or '''mosses''') or '''Moment Of Symmetry''' is a scale in which every interval except for the period comes in two sizes. See the [[catalog 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 scale in which every interval except for the period comes in two sizes. See the [[catalog of MOS]].
 == History and terminology ==
@@ Line 14: / Line 14: @@
 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 pentatonics 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 ''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 ''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.
 == Naming ==
@@ Line 26: / Line 26: @@
 The melodic sound of a MOS is not just affected by the tuning of its intervals, but by the sizes of its steps. MOSes with L more similar to s sound smoother and more mellow. MOSes with L much larger than s sound jagged and dramatic. The ''step ratio'', the ratio between the sizes of L and s, is thus important to the sound of the scale.
-An in-depth analysis of this can be found at [[MOS Step Ratio Spectrum]].
+An in-depth analysis of this can be found at [[Step ratio]].
 == Mathematics ==