MOS scale

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<span style="display: block; text-align: right;">Other languages: [[xenharmonie/MOS-Skalen|Deutsch]]
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[[toc|flat]]
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=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 [[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.

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.

See [[Mathematics of MOS]] for a more formal definition and a discussion of their mathematical properties.

=Names for MOS= 
Since numbers tend to be dry, Graham Breed has proposed a [[MOSNamingScheme|naming scheme for MOS scales]]. See the [[Catalog of MOS]] for a listing of MOS in the more usual Ls scheme. See also the [[pergen|pergens]] page.

==[[MOSDiagrams]]== 

=Variations on MOS Scales= 
# [[MODMOS Scales]] are derived from chromatic alterations of one or more tones of an MOS scale, typically by the interval of L-s, the "chroma".
# [[Muddle|Muddles]] are subsets of MOS parent scales with the general shape of a smaller (and possibly unrelated) MOS scale.
# [[MOS Cradle]] is a technique of embedding MOS-like structures inside MOS scales and may or may not produce subsets of MOS scales.

=MOS As Applied To Rhythms= 
David Canright was the first to suggest Fibonacci Rhythms in 1/1. This lead 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]]

Original HTML content:

<html><head><title>MOSScales</title></head><body><span style="display: block; text-align: right;">Other languages: <a class="wiki_link" href="http://xenharmonie.wikispaces.com/MOS-Skalen">Deutsch</a><br />
</span><br />
<!-- ws:start:WikiTextTocRule:10:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:10 --><!-- ws:start:WikiTextTocRule:11: --><a href="#Definition">Definition</a><!-- ws:end:WikiTextTocRule:11 --><!-- ws:start:WikiTextTocRule:12: --> | <a href="#Names for MOS">Names for MOS</a><!-- ws:end:WikiTextTocRule:12 --><!-- ws:start:WikiTextTocRule:13: --><!-- ws:end:WikiTextTocRule:13 --><!-- ws:start:WikiTextTocRule:14: --> | <a href="#Variations on MOS Scales">Variations on MOS Scales</a><!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --> | <a href="#MOS As Applied To Rhythms">MOS As Applied To Rhythms</a><!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: -->
<!-- ws:end:WikiTextTocRule:16 --><hr />
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<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Definition"></a><!-- ws:end:WikiTextHeadingRule:0 -->Definition</h1>
 An <strong>MOS</strong> or <strong>Moment Of Symmetry</strong> is a scale in which every interval except for the period comes in two sizes. The term &quot;MOS,&quot; and the method of scale construction it entails, were invented by <a class="wiki_link" href="/Erv%20Wilson">Erv Wilson</a> in 1975. His original paper can be found at <a class="wiki_link_ext" href="http://anaphoria.com/mos.PDF" rel="nofollow">http://anaphoria.com/mos.PDF</a>. There is also an introduction at <a class="wiki_link_ext" href="http://anaphoria.com/wilsonintroMOS.html" rel="nofollow">http://anaphoria.com/wilsonintroMOS.html</a>.<br />
<br />
Sometimes, scales are defined with respect to a period and an additional &quot;equivalence interval,&quot; 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 <strong>Multi-MOS</strong>'s. MOS's in which the equivalence interval is equal to the period are sometimes called <strong>Strict MOS</strong>'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.<br />
<br />
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 <a class="wiki_link" href="/Distributional%20Evenness">distributionally even scale</a>, 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 <em>well-formed scales</em>, 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.<br />
<br />
See <a class="wiki_link" href="/Mathematics%20of%20MOS">Mathematics of MOS</a> for a more formal definition and a discussion of their mathematical properties.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Names for MOS"></a><!-- ws:end:WikiTextHeadingRule:2 -->Names for MOS</h1>
 Since numbers tend to be dry, Graham Breed has proposed a <a class="wiki_link" href="/MOSNamingScheme">naming scheme for MOS scales</a>. See the <a class="wiki_link" href="/Catalog%20of%20MOS">Catalog of MOS</a> for a listing of MOS in the more usual Ls scheme. See also the <a class="wiki_link" href="/pergen">pergens</a> page.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Names for MOS-MOSDiagrams"></a><!-- ws:end:WikiTextHeadingRule:4 --><a class="wiki_link" href="/MOSDiagrams">MOSDiagrams</a></h2>
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<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Variations on MOS Scales"></a><!-- ws:end:WikiTextHeadingRule:6 -->Variations on MOS Scales</h1>
 <ol><li><a class="wiki_link" href="/MODMOS%20Scales">MODMOS Scales</a> are derived from chromatic alterations of one or more tones of an MOS scale, typically by the interval of L-s, the &quot;chroma&quot;.</li><li><a class="wiki_link" href="/Muddle">Muddles</a> are subsets of MOS parent scales with the general shape of a smaller (and possibly unrelated) MOS scale.</li><li><a class="wiki_link" href="/MOS%20Cradle">MOS Cradle</a> is a technique of embedding MOS-like structures inside MOS scales and may or may not produce subsets of MOS scales.</li></ol><br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="MOS As Applied To Rhythms"></a><!-- ws:end:WikiTextHeadingRule:8 -->MOS As Applied To Rhythms</h1>
 David Canright was the first to suggest Fibonacci Rhythms in 1/1. This lead to Kraig Grady to be the first to apply MOS patterns to rhythms. Two papers on the subject can be found here <a class="wiki_link_ext" href="http://anaphoria.com/hora.PDF" rel="nofollow">http://anaphoria.com/hora.PDF</a> and<a class="wiki_link_ext" href="http://%20http://anaphoria.com/horo2.pdf" rel="nofollow"> http://anaphoria.com/horo2.pdf</a><br />
MOS structures and thinking can be applied to the design of rhythms as well. See <a class="wiki_link" href="/MOS%20Rhythm%20Tutorial">MOS Rhythm Tutorial</a></body></html>