Relative cent: 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:~~xenwolf~~|~~xenwolf~~]] and made on <tt>~~2010~~-10-~~05 15~~:22:43 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-05-26 19:45:42 UTC</tt>.<br>

: The original revision id was <tt>~~168042559~~</tt>.<br>

: The original revision id was <tt>232248110</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>

<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">Given any [[EDO]] N, the size of an interval in //relative cents// is N/12 times its size in [[Cent|cents]]; or equivalently, 100 N times its logarithm base 2. Hence in [[7edo]], the octave is 700 relative cents, in [[53edo]], 53000 relative cents and so forth.

Measuring the error of an approximation of an interval in an edo in terms of relative cents gives the relative error, which so long as the corresponding val is used is additive. For instance, the fifth of 12edo is 1.995 cents flat, or -1.955 cents sharp, which is therefore also its error in relative cents. The fifth of [[41edo]] is 1.654 relative cents sharp. Thus for 53=41+12, the fifth is -1.955 + 1.654 = -0.301 relative cents sharp, and hence (-0.301)*(12/53) = -0.068 cents sharp, which is to say 0.068 cents flat.</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>Relative cent</title></head><body>~~see~~ <a class="wiki_link" href="/Cent">~~Cent~~</a></body></html></pre></div>

<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>Relative cent</title></head><body>Given any <a class="wiki_link" href="/EDO">EDO</a> N, the size of an interval in <em>relative cents</em> is N/12 times its size in <a class="wiki_link" href="/Cent">cents</a>; or equivalently, 100 N times its logarithm base 2. Hence in <a class="wiki_link" href="/7edo">7edo</a>, the octave is 700 relative cents, in <a class="wiki_link" href="/53edo">53edo</a>, 53000 relative cents and so forth.<br />

<br />

Measuring the error of an approximation of an interval in an edo in terms of relative cents gives the relative error, which so long as the corresponding val is used is additive. For instance, the fifth of 12edo is 1.995 cents flat, or -1.955 cents sharp, which is therefore also its error in relative cents. The fifth of <a class="wiki_link" href="/41edo">41edo</a> is 1.654 relative cents sharp. Thus for 53=41+12, the fifth is -1.955 + 1.654 = -0.301 relative cents sharp, and hence (-0.301)*(12/53) = -0.068 cents sharp, which is to say 0.068 cents flat.</body></html></pre></div>

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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:xenwolf|xenwolf]] and made on <tt>2010-10-05 15:22:43 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-05-26 19:45:42 UTC</tt>.<br>
-: The original revision id was <tt>168042559</tt>.<br>
+: The original revision id was <tt>232248110</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>
 <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">see [[Cent]]</pre></div>
+<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">Given any [[EDO]] N, the size of an interval in //relative cents// is N/12 times its size in [[Cent|cents]]; or equivalently, 100 N times its logarithm base 2. Hence in [[7edo]], the octave is 700 relative cents, in [[53edo]], 53000 relative cents and so forth.
+Measuring the error of an approximation of an interval in an edo in terms of relative cents gives the relative error, which so long as the corresponding val is used is additive. For instance, the fifth of 12edo is 1.995 cents flat, or -1.955 cents sharp, which is therefore also its error in relative cents. The fifth of [[41edo]] is 1.654 relative cents sharp. Thus for 53=41+12, the fifth is -1.955 + 1.654 = -0.301 relative cents sharp, and hence (-0.301)*(12/53) = -0.068 cents sharp, which is to say 0.068 cents flat.</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;Relative cent&lt;/title&gt;&lt;/head&gt;&lt;body&gt;see &lt;a class="wiki_link" href="/Cent"&gt;Cent&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
+<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;Relative cent&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Given any &lt;a class="wiki_link" href="/EDO"&gt;EDO&lt;/a&gt; N, the size of an interval in &lt;em&gt;relative cents&lt;/em&gt; is N/12 times its size in &lt;a class="wiki_link" href="/Cent"&gt;cents&lt;/a&gt;; or equivalently, 100 N times its logarithm base 2. Hence in &lt;a class="wiki_link" href="/7edo"&gt;7edo&lt;/a&gt;, the octave is 700 relative cents, in &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt;, 53000 relative cents and so forth.&lt;br /&gt;
+&lt;br /&gt;
+Measuring the error of an approximation of an interval in an edo in terms of relative cents gives the relative error, which so long as the corresponding val is used is additive. For instance, the fifth of 12edo is 1.995 cents flat, or -1.955 cents sharp, which is therefore also its error in relative cents. The fifth of &lt;a class="wiki_link" href="/41edo"&gt;41edo&lt;/a&gt; is 1.654 relative cents sharp. Thus for 53=41+12, the fifth is -1.955 + 1.654 = -0.301 relative cents sharp, and hence (-0.301)*(12/53) = -0.068 cents sharp, which is to say 0.068 cents flat.&lt;/body&gt;&lt;/html&gt;</pre></div>