Cent
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- This revision was by author mbattaglia1 and made on 2012-03-22 11:30:09 UTC.
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Original Wikitext content:
=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. 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 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;">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;">=</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.
Original HTML content:
<html><head><title>cent</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h1> --><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 "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.<br /> <br /> 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 /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><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 /> <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;">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;">=</span> after the division.</em><br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h1> --><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 /> 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 /> 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>