Cent: Difference between revisions

Revision as of 03:11, 23 August 2011

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This revision was by author xenwolf and made on 2011-08-23 03:11:13 UTC.

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**Cent** (**¢**) is an [[interval size measure]]. It's a 100th--or one percent--of the interval between two neighboring pitches in [[12edo]]. A generalization for the cent measure is the **[[relative cent]]** which is one 100th of two neigbhboring [[pitch|pitches]] in any [[equal]] tuning.

The [[http://en.wikipedia.org/wiki/Cent_(music)|cent]], first proposed by [[http://en.wikipedia.org/wiki/Alexander_J._Ellis|Alexander Ellis]], is a logarithmic measure which may also be defined as the [[http://en.wikipedia.org/wiki/Logarithm|logarithm]] to the base 1200th root of 2.

=How to calculate=
If you want to get the size of an interval in cents, you have to calculate the [[log2|binary logarithm]] of its [[frequency ratio]], and multiply it by 1200.

If you use a pocket calculator, you don't have a //log2// key on it, but you can get it this way:
After input your number, press <span style="background-color: #d4c2c2;padding:2px 4px; margin: 0px 6px">ln</span> <span style="background-color: #d4c2c2;padding:2px 4px; margin: 0px 6px">÷</span> <span style="background-color: #d4c2c2;padding:2px 4px; margin: 0px 6px">2</span> <span style="background-color: #d4c2c2;padding:2px 4px; margin: 0px 6px">ln</span> (the //ln// key can also be replaced by the //log// key)
//Note: If you try to calculate the size of a ratio in cents, don't forget the <span style="background-color: #d4c2c2;padding:2px 4px; margin: 0px 6px">=</span> after the division.//

=See also=
An alternative interval measure is the [[millioctave]] ([[mO]]).

Original HTML content:

<html><head><title>cent</title></head><body><strong>Cent</strong> (<strong>¢</strong>) is an <a class="wiki_link" href="/interval%20size%20measure">interval size measure</a>. It's a 100th--or one percent--of the interval between two neighboring pitches in <a class="wiki_link" href="/12edo">12edo</a>. A generalization for the cent measure is the <strong><a class="wiki_link" href="/relative%20cent">relative cent</a></strong> which is one 100th of two neigbhboring <a class="wiki_link" href="/pitch">pitches</a> in any <a class="wiki_link" href="/equal">equal</a> tuning.<br />
<br />
The <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Cent_(music)" rel="nofollow">cent</a>, first proposed by <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Alexander_J._Ellis" rel="nofollow">Alexander Ellis</a>, is a logarithmic measure which may also be defined as the <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Logarithm" rel="nofollow">logarithm</a> to the base 1200th root of 2.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="How to calculate"></a><!-- ws:end:WikiTextHeadingRule:0 -->How to calculate</h1>
If you want to get the size of an interval in cents, you have to calculate the <a class="wiki_link" href="/log2">binary logarithm</a> of its <a class="wiki_link" href="/frequency%20ratio">frequency ratio</a>, and multiply it by 1200.<br />
<br />
If you use a pocket calculator, you don't have a <em>log2</em> key on it, but you can get it this way:<br />
After input your number, press <span style="background-color: #d4c2c2;padding:2px 4px; margin: 0px 6px">ln</span> <span style="background-color: #d4c2c2;padding:2px 4px; margin: 0px 6px">÷</span> <span style="background-color: #d4c2c2;padding:2px 4px; margin: 0px 6px">2</span> <span style="background-color: #d4c2c2;padding:2px 4px; margin: 0px 6px">ln</span> (the <em>ln</em> key can also be replaced by the <em>log</em> key)<br />
<em>Note: If you try to calculate the size of a ratio in cents, don't forget the <span style="background-color: #d4c2c2;padding:2px 4px; margin: 0px 6px">=</span> after the division.</em><br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="See also"></a><!-- ws:end:WikiTextHeadingRule:2 -->See also</h1>
An alternative interval measure is the <a class="wiki_link" href="/millioctave">millioctave</a> (<a class="wiki_link" href="/mO">mO</a>).</body></html>

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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>2011-08-23 03:10:03 UTC</tt>.<br>
+: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-08-23 03:11:13 UTC</tt>.<br>
-: The original revision id was <tt>247861815</tt>.<br>
+: The original revision id was <tt>247861933</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 8: / Line 8: @@
 <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">**Cent** (**¢**) is an [[interval size measure]]. It's a 100th--or one percent--of the interval between two neighboring pitches in [[12edo]]. A generalization for the cent measure is the **[[relative cent]]** which is one 100th of two neigbhboring [[pitch|pitches]] in any [[equal]] tuning.
-The [[http://en.wikipedia.org/wiki/Cent_(music)|cent]], first proposed by [[http://en.wikipedia.org/wiki/Alexander_J._Ellis|Alexander Ellis]], is a logarithmic measure which may also be defined as the [[http://en.wikipedia.org/wiki/Logarithm|logarithm]] base the 1200th root of 2 of a ratio, which is by definition one cent.
+The [[http://en.wikipedia.org/wiki/Cent_(music)|cent]], first proposed by [[http://en.wikipedia.org/wiki/Alexander_J._Ellis|Alexander Ellis]], is a logarithmic measure which may also be defined as the [[http://en.wikipedia.org/wiki/Logarithm|logarithm]] to the base 1200th root of 2.
 =How to calculate=
@@ Line 22: / Line 22: @@
 <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;cent&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;Cent&lt;/strong&gt; (&lt;strong&gt;¢&lt;/strong&gt;) is an &lt;a class="wiki_link" href="/interval%20size%20measure"&gt;interval size measure&lt;/a&gt;. It's a 100th--or one percent--of the interval between two neighboring pitches in &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;. A generalization for the cent measure is the &lt;strong&gt;&lt;a class="wiki_link" href="/relative%20cent"&gt;relative cent&lt;/a&gt;&lt;/strong&gt; which is one 100th of two neigbhboring &lt;a class="wiki_link" href="/pitch"&gt;pitches&lt;/a&gt; in any &lt;a class="wiki_link" href="/equal"&gt;equal&lt;/a&gt; tuning.&lt;br /&gt;
 &lt;br /&gt;
-The &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Cent_(music)" rel="nofollow"&gt;cent&lt;/a&gt;, first proposed by &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Alexander_J._Ellis" rel="nofollow"&gt;Alexander Ellis&lt;/a&gt;, is a logarithmic measure which may also be defined as the &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Logarithm" rel="nofollow"&gt;logarithm&lt;/a&gt; base the 1200th root of 2 of a ratio, which is by definition one cent.&lt;br /&gt;
+The &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Cent_(music)" rel="nofollow"&gt;cent&lt;/a&gt;, first proposed by &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Alexander_J._Ellis" rel="nofollow"&gt;Alexander Ellis&lt;/a&gt;, is a logarithmic measure which may also be defined as the &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Logarithm" rel="nofollow"&gt;logarithm&lt;/a&gt; to the base 1200th root of 2.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="How to calculate"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;How to calculate&lt;/h1&gt;

Cent: Difference between revisions

Revision as of 03:11, 23 August 2011

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