Cent: Difference between revisions
Wikispaces>guest **Imported revision 313590874 - Original comment: merge** |
Wikispaces>mbattaglia1 **Imported revision 313602954 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User: | : This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2012-03-22 11:30:09 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>313602954</tt>.<br> | ||
: The revision comment was: <tt> | : 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> | 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> | <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"> | <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">=Cents= | ||
A //cent// is an interval equal to exactly 1/100th of a 12-EDO semitone. In other words, cents equally divide the 12-EDO half step into 100 equal parts. Cents are often used to express the size of intervals in different tuning systems. | |||
For example, a 12-EDO perfect fifth is 700.000 cents, and the major third is 400.0 cents. In contrast, the "just" perfect fifth, which corresponds to two notes in a frequency ratio of 3/2 is 701.955 cents, and the just major third of 5/4 is 386.314 cents. The 24-EDO neutral third is 350.000 cents. The 22-EDO approximation to 3/2 is 709.091 cents. | |||
=How to calculate= | The cent, which was 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 the size of an interval in cents= | |||
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 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: | 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 | After input your number, press <span style="background-color: #d4c2c2;">ln ÷ 2 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 | //Note: If you try to calculate the size of a ratio in cents, don't forget the <span style="background-color: #d4c2c2;">=</span> after the division.// | ||
=Other Units of Interval Measure= | |||
The cent is commonly used because of its ease in communicating information about intervals to a 12-EDO-savvy audience. However, some have suggested that the cent be deprecated, as other than societal convention there's no reason to give 12-EDO inherent importance over any other decent tuning. In contrast, others have suggested that cents are a useful unit of interval measure for purely mathematical reasons, even despite of 12-EDO's current status as the dominant tuning in Western society. | |||
Whatever your stance, alternative measures of interval size can be found at [[Interval size measure]]. | |||
One prominent alternative interval measure is the [[millioctave]] ([[mO]]). | |||
Additionally, a useful generalization for the cent measure is the **[[relative cent]],** which is one 100th of two neighboring [[pitch|pitches]] in any [[equal]] tuning.</pre></div> | |||
<h4>Original HTML content:</h4> | <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>cent</title></head><body>< | <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>cent</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Cents"></a><!-- ws:end:WikiTextHeadingRule:0 -->Cents</h1> | ||
A <em>cent</em> is an interval equal to exactly 1/100th of a 12-EDO semitone. In other words, cents equally divide the 12-EDO half step into 100 equal parts. Cents are often used to express the size of intervals in different tuning systems.<br /> | |||
<br /> | |||
For example, a 12-EDO perfect fifth is 700.000 cents, and the major third is 400.0 cents. In contrast, the &quot;just&quot; perfect fifth, which corresponds to two notes in a frequency ratio of 3/2 is 701.955 cents, and the just major third of 5/4 is 386.314 cents. The 24-EDO neutral third is 350.000 cents. The 22-EDO approximation to 3/2 is 709.091 cents.<br /> | |||
<br /> | <br /> | ||
The | The cent, which was 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 /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="How to calculate the size of an interval in cents"></a><!-- ws:end:WikiTextHeadingRule:2 -->How to calculate the size of an interval in cents</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 /> | 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 /> | <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 /> | 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 | After input your number, press <span style="background-color: #d4c2c2;">ln ÷ 2 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 | <em>Note: If you try to calculate the size of a ratio in cents, don't forget the <span style="background-color: #d4c2c2;">=</span> after the division.</em><br /> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Other Units of Interval Measure"></a><!-- ws:end:WikiTextHeadingRule:4 -->Other Units of Interval Measure</h1> | |||
The cent is commonly used because of its ease in communicating information about intervals to a 12-EDO-savvy audience. However, some have suggested that the cent be deprecated, as other than societal convention there's no reason to give 12-EDO inherent importance over any other decent tuning. In contrast, others have suggested that cents are a useful unit of interval measure for purely mathematical reasons, even despite of 12-EDO's current status as the dominant tuning in Western society.<br /> | |||
<br /> | |||
Whatever your stance, alternative measures of interval size can be found at <a class="wiki_link" href="/Interval%20size%20measure">Interval size measure</a>. <br /> | |||
<br /> | <br /> | ||
One prominent alternative interval measure is the <a class="wiki_link" href="/millioctave">millioctave</a> (<a class="wiki_link" href="/mO">mO</a>).<br /> | |||
<br /> | <br /> | ||
Additionally, a useful 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 neighboring <a class="wiki_link" href="/pitch">pitches</a> in any <a class="wiki_link" href="/equal">equal</a> tuning.</body></html></pre></div> | |||