MOS scale: Difference between revisions

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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>2010-05-18 03:22:22 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-05-18 03:26:47 UTC</tt>.<br>

: The original revision id was <tt>~~142751603~~</tt>.<br>

: The original revision id was <tt>142752091</tt>.<br>

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

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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|| [[DecatonicMOS|Decatonic MOS]] || [[1L 9s]] || || [[2L 8s]] || || [[3L 7s]] || || [[4L 6s]] || || [[5L 5s]] || || [[6L 4s]] || || [[7L 3s]] || || [[8L 2s]] || || [[9L 1s]] ||

=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://anaphoria.com/horo2.PDF]]

MOS structures and thinking can be applied to the design of rhythms as well. See [[MOS Rhythm Tutorial]]

=Algorithms=

==Algorithms==

Below is some Maple code for various mathematical routines having to do with MOS. If you have access to Maple, you can of course copy and run these programs. Even if you do not, since Maple code makes better pseudocode than most languages or computer ~~algebr~~ packages afford, it can be used as pseudocode. For that purpose, it will be helpful to know that "modp(x, n)" means reducing x mod the integer n to 0, 1, ..., n-1 not only when x is an integer, but also when it is a rational number with denominator prime to n. In that case, p/q mod n = r means p = qr mod n.

Below is some Maple code for various mathematical routines having to do with MOS. If you have access to Maple, you can of course copy and run these programs. Even if you do not, since Maple code makes better pseudocode than most languages or computer algebra packages afford, it can be used as pseudocode. For that purpose, it will be helpful to know that "modp(x, n)" means reducing x mod the integer n to 0, 1, ..., n-1 not only when x is an integer, but also when it is a rational number with denominator prime to n. In that case, p/q mod n = r means p = qr mod n.

nextfarey := proc(q, n)

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=[[MOSDiagrams]]= </pre></div>

==[[MOSDiagrams]]== </pre></div>

<h4>Original HTML 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;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>

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<h1 id="toc5"><a name="MOS As Applied To Rhythms"></a>MOS As Applied To Rhythms</h1>

<br />

<h2 id="toc5"><a name="MOS scales-MOS As Applied To Rhythms"></a>MOS As Applied To Rhythms</h2>

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://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><br />

<br />

<h1 id="toc6"><a name="Algorithms"></a>Algorithms</h1>

<h2 id="toc6"><a name="MOS scales-Algorithms"></a>Algorithms</h2>

Below is some Maple code for various mathematical routines having to do with MOS. If you have access to Maple, you can of course copy and run these programs. Even if you do not, since Maple code makes better pseudocode than most languages or computer ~~algebr~~ packages afford, it can be used as pseudocode. For that purpose, it will be helpful to know that &quot;modp(x, n)&quot; means reducing x mod the integer n to 0, 1, ..., n-1 not only when x is an integer, but also when it is a rational number with denominator prime to n. In that case, p/q mod n = r means p = qr mod n.<br />

Below is some Maple code for various mathematical routines having to do with MOS. If you have access to Maple, you can of course copy and run these programs. Even if you do not, since Maple code makes better pseudocode than most languages or computer algebra packages afford, it can be used as pseudocode. For that purpose, it will be helpful to know that &quot;modp(x, n)&quot; means reducing x mod the integer n to 0, 1, ..., n-1 not only when x is an integer, but also when it is a rational number with denominator prime to n. In that case, p/q mod n = r means p = qr mod n.<br />

<br />

nextfarey := proc(q, n)<br />

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<br />

<h1 id="toc7"><a name="MOSDiagrams"></a><a class="wiki_link" href="/MOSDiagrams">MOSDiagrams</a></h1>

<h2 id="toc7"><a name="MOS scales-MOSDiagrams"></a><a class="wiki_link" href="/MOSDiagrams">MOSDiagrams</a></h2>

</body></html></pre></div>

@@ Line 1: / Line 1: @@
 <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>2010-05-18 03:22:22 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-05-18 03:26:47 UTC</tt>.<br>
-: The original revision id was <tt>142751603</tt>.<br>
+: The original revision id was <tt>142752091</tt>.<br>
 : The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
@@ Line 49: / Line 49: @@
 || [[DecatonicMOS|Decatonic MOS]] || [[1L 9s]] ||   || [[2L 8s]] ||   || [[3L 7s]] ||   || [[4L 6s]] ||   || [[5L 5s]] ||   || [[6L 4s]] ||   || [[7L 3s]] ||   || [[8L 2s]] ||   || [[9L 1s]] ||
 &lt;span style="color: #0000ee;"&gt; &lt;/span&gt;
-=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://anaphoria.com/horo2.PDF]]
 MOS structures and thinking can be applied to the design of rhythms as well. See [[MOS Rhythm Tutorial]]
-=Algorithms=
+==Algorithms==
-Below is some Maple code for various mathematical routines having to do with MOS. If you have access to Maple, you can of course copy and run these programs. Even if you do not, since Maple code makes better pseudocode than most languages or computer algebr packages afford, it can be used as pseudocode. For that purpose, it will be helpful to know that "modp(x, n)" means reducing x mod the integer n to 0, 1, ..., n-1 not only when x is an integer, but also when it is a rational number with denominator prime to n. In that case, p/q mod n = r means p = qr mod n.
+Below is some Maple code for various mathematical routines having to do with MOS. If you have access to Maple, you can of course copy and run these programs. Even if you do not, since Maple code makes better pseudocode than most languages or computer algebra packages afford, it can be used as pseudocode. For that purpose, it will be helpful to know that "modp(x, n)" means reducing x mod the integer n to 0, 1, ..., n-1 not only when x is an integer, but also when it is a rational number with denominator prime to n. In that case, p/q mod n = r means p = qr mod n.
 nextfarey := proc(q, n)
@@ Line 136: / Line 137: @@
-=[[MOSDiagrams]]= </pre></div>
+==[[MOSDiagrams]]== </pre></div>
 <h4>Original HTML 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;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;
@@ Line 408: / Line 409: @@
 &lt;span style="color: #0000ee;"&gt; &lt;/span&gt;&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="MOS As Applied To Rhythms"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;MOS As Applied To Rhythms&lt;/h1&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="MOS scales-MOS As Applied To Rhythms"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;MOS As Applied To Rhythms&lt;/h2&gt;
   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 &lt;a class="wiki_link_ext" href="http://anaphoria.com/hora.PDF" rel="nofollow"&gt;http://anaphoria.com/hora.PDF&lt;/a&gt; and &lt;a class="wiki_link_ext" href="http://anaphoria.com/horo2.PDF" rel="nofollow"&gt;http://anaphoria.com/horo2.PDF&lt;/a&gt;&lt;br /&gt;
 MOS structures and thinking can be applied to the design of rhythms as well. See &lt;a class="wiki_link" href="/MOS%20Rhythm%20Tutorial"&gt;MOS Rhythm Tutorial&lt;/a&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Algorithms"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Algorithms&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="MOS scales-Algorithms"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Algorithms&lt;/h2&gt;
-Below is some Maple code for various mathematical routines having to do with MOS. If you have access to Maple, you can of course copy and run these programs. Even if you do not, since Maple code makes better pseudocode than most languages or computer algebr packages afford, it can be used as pseudocode. For that purpose, it will be helpful to know that &amp;quot;modp(x, n)&amp;quot; means reducing x mod the integer n to 0, 1, ..., n-1 not only when x is an integer, but also when it is a rational number with denominator prime to n. In that case, p/q mod n = r means p = qr mod n.&lt;br /&gt;
+Below is some Maple code for various mathematical routines having to do with MOS. If you have access to Maple, you can of course copy and run these programs. Even if you do not, since Maple code makes better pseudocode than most languages or computer algebra packages afford, it can be used as pseudocode. For that purpose, it will be helpful to know that &amp;quot;modp(x, n)&amp;quot; means reducing x mod the integer n to 0, 1, ..., n-1 not only when x is an integer, but also when it is a rational number with denominator prime to n. In that case, p/q mod n = r means p = qr mod n.&lt;br /&gt;
 &lt;br /&gt;
 nextfarey := proc(q, n)&lt;br /&gt;
@@ Line 495: / Line 497: @@
 &lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="MOSDiagrams"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;&lt;a class="wiki_link" href="/MOSDiagrams"&gt;MOSDiagrams&lt;/a&gt;&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="MOS scales-MOSDiagrams"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;&lt;a class="wiki_link" href="/MOSDiagrams"&gt;MOSDiagrams&lt;/a&gt;&lt;/h2&gt;
 &lt;/body&gt;&lt;/html&gt;</pre></div>