Relative cent: Difference between revisions
Jump to navigation
Jump to search
Wikispaces>xenwolf **Imported revision 232324134 - Original comment: Sorry, it's my German English that made the confusion happen.** |
Wikispaces>xenwolf **Imported revision 232379056 - Original comment: typo corr.** |
||
| Line 1: | Line 1: | ||
<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:xenwolf|xenwolf]] and made on <tt>2011-05-27 | : This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-05-27 09:55:45 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>232379056</tt>.<br> | ||
: The revision comment was: <tt> | : The revision comment was: <tt>typo corr.</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> | ||
| Line 11: | Line 11: | ||
----- | ----- | ||
//...also the term [[centidegree]] was suggested, but this | //...also the term [[centidegree]] was suggested, but this seems to be used already as a unit for temperature.//</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>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 /> | <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 /> | ||
| Line 18: | Line 18: | ||
<br /> | <br /> | ||
<hr /> | <hr /> | ||
<em>...also the term <a class="wiki_link" href="/centidegree">centidegree</a> was suggested, but this | <em>...also the term <a class="wiki_link" href="/centidegree">centidegree</a> was suggested, but this seems to be used already as a unit for temperature.</em></body></html></pre></div> | ||
Revision as of 09:55, 27 May 2011
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author xenwolf and made on 2011-05-27 09:55:45 UTC.
- The original revision id was 232379056.
- The revision comment was: typo corr.
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
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. ----- //...also the term [[centidegree]] was suggested, but this seems to be used already as a unit for temperature.//
Original HTML content:
<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.<br /> <br /> <hr /> <em>...also the term <a class="wiki_link" href="/centidegree">centidegree</a> was suggested, but this seems to be used already as a unit for temperature.</em></body></html>