MOS scale: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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: This revision was by author [[User:~~genewardsmith~~|~~genewardsmith~~]] and made on <tt>2010-05-~~25 17~~:21:13 UTC</tt>.<br>

: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2010-05-30 16:21:07 UTC</tt>.<br>

: The original revision id was <tt>~~144672913~~</tt>.<br>

: The original revision id was <tt>145906329</tt>.<br>

: The revision comment was: <tt>~~Reverted to May 23, 2010 5:31 pm: The changes to the comment line of the Maple code will cause it not to work~~</tt><br>

: The revision comment was: <tt>typo</tt><br>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>

<h4>Original Wikitext content:</h4>

<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">=MOS scales=

An important class of scales are MOS scales (the acronym MOS coming from "Moment Of Symmetry"). These are derived by iterating an interval g, called the generator, inside a larger interval, called the period, and reducing to the period when the iterates become larger than the period. Usually the period is an octave or an nth root of 2, but it can in theory be any positive number. The resulting scale is called a MOS when it has exactly two sizes of steps when sorted into ascending order of size.

An important class of scales are MOS scales (the acronym **MOS** coming from **"Moment Of Symmetry"**). These are derived by iterating an interval g, called the generator, inside a larger interval, called the period, and reducing to the period when the iterates become larger than the period. Usually the period is an octave or an nth root of 2, but it can in theory be any positive number. The resulting scale is called a MOS when it has exactly two sizes of steps when sorted into ascending order of size.

The term and scale construction method were invented by Erv Wilson. His original paper can be found here [[http://anaphoria.com/mos.PDF]]. There is also an introduction [[http://anaphoria.com/wilsonintroMOS.html]]. It generalizes the classical diatonic and pentatonic scales. In academic music theory, MOS are known as //well-formed scales// and the introduction of the concept is attributed to a 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.

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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;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>MOSScales</title></head><body><h1 id="toc0"><a name="MOS scales"></a>MOS scales</h1>

<br />

An important class of scales are MOS scales (the acronym MOS coming from &quot;Moment Of Symmetry&quot;). These are derived by iterating an interval g, called the generator, inside a larger interval, called the period, and reducing to the period when the iterates become larger than the period. Usually the period is an octave or an nth root of 2, but it can in theory be any positive number. The resulting scale is called a MOS when it has exactly two sizes of steps when sorted into ascending order of size.<br />

An important class of scales are MOS scales (the acronym <strong>MOS</strong> coming from <strong>&quot;Moment Of Symmetry&quot;</strong>). These are derived by iterating an interval g, called the generator, inside a larger interval, called the period, and reducing to the period when the iterates become larger than the period. Usually the period is an octave or an nth root of 2, but it can in theory be any positive number. The resulting scale is called a MOS when it has exactly two sizes of steps when sorted into ascending order of size.<br />

<br />

The term and scale construction method were invented by Erv Wilson. His original paper can be found here <a class="wiki_link_ext" href="http://anaphoria.com/mos.PDF" rel="nofollow">http://anaphoria.com/mos.PDF</a>. There is also an introduction <a class="wiki_link_ext" href="http://anaphoria.com/wilsonintroMOS.html" rel="nofollow">http://anaphoria.com/wilsonintroMOS.html</a>. It generalizes the classical diatonic and pentatonic scales. In academic music theory, MOS are known as <em>well-formed scales</em> and the introduction of the concept is attributed to a 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.<br />

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 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-05-25 17:21:13 UTC</tt>.<br>
+: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2010-05-30 16:21:07 UTC</tt>.<br>
-: The original revision id was <tt>144672913</tt>.<br>
+: The original revision id was <tt>145906329</tt>.<br>
-: The revision comment was: <tt>Reverted to May 23, 2010 5:31 pm: The changes to the comment line of the Maple code will cause it not to work</tt><br>
+: The revision comment was: <tt>typo</tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
 <h4>Original Wikitext content:</h4>
 <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">=MOS scales=
-An important class of scales are MOS scales (the acronym MOS coming from "Moment Of Symmetry"). These are derived by iterating an interval g, called the generator, inside a larger interval, called the period, and reducing to the period when the iterates become larger than the period. Usually the period is an octave or an nth root of 2, but it can in theory be any positive number. The resulting scale is called a MOS when it has exactly two sizes of steps when sorted into ascending order of size.
+An important class of scales are MOS scales (the acronym **MOS** coming from **"Moment Of Symmetry"**). These are derived by iterating an interval g, called the generator, inside a larger interval, called the period, and reducing to the period when the iterates become larger than the period. Usually the period is an octave or an nth root of 2, but it can in theory be any positive number. The resulting scale is called a MOS when it has exactly two sizes of steps when sorted into ascending order of size.
 The term and scale construction method were invented by Erv Wilson. His original paper can be found here [[http://anaphoria.com/mos.PDF]]. There is also an introduction [[http://anaphoria.com/wilsonintroMOS.html]]. It generalizes the classical diatonic and pentatonic scales. In academic music theory, MOS are known as //well-formed scales// and the introduction of the concept is attributed to a 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.
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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;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;MOSScales&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="MOS scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;MOS scales&lt;/h1&gt;
   &lt;br /&gt;
-An important class of scales are MOS scales (the acronym MOS coming from &amp;quot;Moment Of Symmetry&amp;quot;). These are derived by iterating an interval g, called the generator, inside a larger interval, called the period, and reducing to the period when the iterates become larger than the period. Usually the period is an octave or an nth root of 2, but it can in theory be any positive number. The resulting scale is called a MOS when it has exactly two sizes of steps when sorted into ascending order of size.&lt;br /&gt;
+An important class of scales are MOS scales (the acronym &lt;strong&gt;MOS&lt;/strong&gt; coming from &lt;strong&gt;&amp;quot;Moment Of Symmetry&amp;quot;&lt;/strong&gt;). These are derived by iterating an interval g, called the generator, inside a larger interval, called the period, and reducing to the period when the iterates become larger than the period. Usually the period is an octave or an nth root of 2, but it can in theory be any positive number. The resulting scale is called a MOS when it has exactly two sizes of steps when sorted into ascending order of size.&lt;br /&gt;
 &lt;br /&gt;
 The term and scale construction method were invented by Erv Wilson. His original paper can be found here &lt;a class="wiki_link_ext" href="http://anaphoria.com/mos.PDF" rel="nofollow"&gt;http://anaphoria.com/mos.PDF&lt;/a&gt;. There is also an introduction &lt;a class="wiki_link_ext" href="http://anaphoria.com/wilsonintroMOS.html" rel="nofollow"&gt;http://anaphoria.com/wilsonintroMOS.html&lt;/a&gt;. It generalizes the classical diatonic and pentatonic scales. In academic music theory, MOS are known as &lt;em&gt;well-formed scales&lt;/em&gt; and the introduction of the concept is attributed to a 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.&lt;br /&gt;