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| <h2>IMPORTED REVISION FROM WIKISPACES</h2> | | <span style="display: block; text-align: right;">Other languages: [[:de:MOS-Skalen Deutsch]]</span> |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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| : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2018-03-25 06:07:30 UTC</tt>.<br>
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| : The original revision id was <tt>627987291</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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| <h4>Original Wikitext content:</h4>
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| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html"><span style="display: block; text-align: right;">Other languages: [[xenharmonie/MOS-Skalen|Deutsch]]
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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 [[http://anaphoria.com/mos.PDF]]. There is also an introduction at [[http://anaphoria.com/wilsonintroMOS.html]]. | | 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|Erv Wilson]] in 1975. His original paper can be found at [http://anaphoria.com/mos.PDF http://anaphoria.com/mos.PDF]. There is also an introduction at [http://anaphoria.com/wilsonintroMOS.html http://anaphoria.com/wilsonintroMOS.html]. |
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| 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. |
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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 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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| See [[Mathematics of MOS]] for a more formal definition and a discussion of their mathematical properties. | | See [[Mathematics_of_MOS|Mathematics of MOS]] for a more formal definition and a discussion of their mathematical properties. |
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| =Names for MOS= | | =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. | | Since numbers tend to be dry, Graham Breed has proposed a [[MOSNamingScheme|naming scheme for MOS scales]]. See the [[Catalog_of_MOS|Catalog of MOS]] for a listing of MOS in the more usual Ls scheme. See also the [[pergen|pergens]] page. |
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| ==[[MOSDiagrams]]== | | ==[[MOSDiagrams|MOSDiagrams]]== |
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| =Variations on MOS Scales= | | =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".
| | <ol><li>[[MODMOS_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".</li><li>[[Muddle|Muddles]] are subsets of MOS parent scales with the general shape of a smaller (and possibly unrelated) MOS scale.</li><li>[[MOS_Cradle|MOS Cradle]] is a technique of embedding MOS-like structures inside MOS scales and may or may not produce subsets of MOS scales.</li></ol> |
| # [[Muddle|Muddles]] are subsets of MOS parent scales with the general shape of a smaller (and possibly unrelated) MOS scale.
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| # [[MOS Cradle]] is a technique of embedding MOS-like structures inside MOS scales and may or may not produce subsets of MOS scales.
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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 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]] | | 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 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]]</pre></div> | | |
| <h4>Original HTML content:</h4>
| | MOS structures and thinking can be applied to the design of rhythms as well. See [[MOS_Rhythm_Tutorial|MOS Rhythm Tutorial]] [[Category:math]] |
| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><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 />
| | [[Category:mos]] |
| </span><br />
| | [[Category:overview]] |
| <!-- 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: -->
| | [[Category:scale]] |
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| | [[Category:scales]] |
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| | [[Category:theory]] |
| <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Definition"></a><!-- ws:end:WikiTextHeadingRule:0 -->Definition</h1>
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| 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 />
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| 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 />
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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 <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 />
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| 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 />
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| <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Names for MOS"></a><!-- ws:end:WikiTextHeadingRule:2 -->Names for MOS</h1>
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| 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 />
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| <!-- 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>
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| <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 />
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| <!-- 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>
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| 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 />
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| 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></pre></div>
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Other languages: de:MOS-Skalen Deutsch
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 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 naming scheme for MOS scales. See the Catalog of MOS for a listing of MOS in the more usual Ls scheme. See also the pergens page.
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".
- 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 andhttp://anaphoria.com/horo2.pdf
MOS structures and thinking can be applied to the design of rhythms as well. See MOS Rhythm Tutorial