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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Infobox ET}} |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | {{ED intro}} |
| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-07-13 17:17:35 UTC</tt>.<br>
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| : The original revision id was <tt>241229109</tt>.<br>
| | In the 5-limit the equal temperament [[tempering out|tempers out]] the [[parakleisma]], {{monzo| 8 14 -13 }}; in the 7-limit [[65625/65536]] and 420175/419904; in the 11-limit [[441/440]] and [[8019/8000]]; in the 13-limit [[729/728]] and [[4225/4224]], and provides the [[optimal patent val]] for 11-limit [[history (temperament)|history]], tempering out 441/440 and 4000/3993. |
| : The revision comment was: <tt></tt><br>
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| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| | === Odd harmonics === |
| <h4>Original Wikitext content:</h4>
| | {{Harmonics in equal|491}} |
| <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">The //491 equal division// divides the octave into 491 equal parts of 2.444 cents each. In the 5-limit it tempers out the parakleima, |8 14 -13>; in the 7-limit 65625/65536 and 420175/419904; in the 11-limit 441/440 and 8019/8000; in the 13-limit 729/728 and 4225/4224, and provides the [[optimal patent val]] for 11-limit [[Werckismic temperaments#History|history temperament]], tempering out 441/440 and 4000/3993.</pre></div>
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| <h4>Original HTML content:</h4>
| | === Subsets and supersets === |
| <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>491edo</title></head><body>The <em>491 equal division</em> divides the octave into 491 equal parts of 2.444 cents each. In the 5-limit it tempers out the parakleima, |8 14 -13&gt;; in the 7-limit 65625/65536 and 420175/419904; in the 11-limit 441/440 and 8019/8000; in the 13-limit 729/728 and 4225/4224, and provides the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for 11-limit <a class="wiki_link" href="/Werckismic%20temperaments#History">history temperament</a>, tempering out 441/440 and 4000/3993.</body></html></pre></div>
| | 491edo is the 94th [[prime edo]]. |
Latest revision as of 06:59, 20 February 2025
| Prime factorization
|
491 (prime)
|
| Step size
|
2.44399 ¢
|
| Fifth
|
287\491 (701.426 ¢)
|
| Semitones (A1:m2)
|
45:38 (110 ¢ : 92.87 ¢)
|
| Consistency limit
|
9
|
| Distinct consistency limit
|
9
|
491 equal divisions of the octave (abbreviated 491edo or 491ed2), also called 491-tone equal temperament (491tet) or 491 equal temperament (491et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 491 equal parts of about 2.44 ¢ each. Each step represents a frequency ratio of 21/491, or the 491st root of 2.
In the 5-limit the equal temperament tempers out the parakleisma, [8 14 -13⟩; in the 7-limit 65625/65536 and 420175/419904; in the 11-limit 441/440 and 8019/8000; in the 13-limit 729/728 and 4225/4224, and provides the optimal patent val for 11-limit history, tempering out 441/440 and 4000/3993.
Odd harmonics
Approximation of odd harmonics in 491edo
| Harmonic
|
3
|
5
|
7
|
9
|
11
|
13
|
15
|
17
|
19
|
21
|
23
|
| Error
|
Absolute (¢)
|
-0.53
|
-0.16
|
-1.01
|
-1.06
|
+1.02
|
+0.21
|
-0.69
|
+0.14
|
+0.65
|
+0.91
|
-0.17
|
| Relative (%)
|
-21.7
|
-6.7
|
-41.1
|
-43.3
|
+41.9
|
+8.4
|
-28.3
|
+5.6
|
+26.8
|
+37.2
|
-6.9
|
Steps
(reduced)
|
778
(287)
|
1140
(158)
|
1378
(396)
|
1556
(83)
|
1699
(226)
|
1817
(344)
|
1918
(445)
|
2007
(43)
|
2086
(122)
|
2157
(193)
|
2221
(257)
|
Subsets and supersets
491edo is the 94th prime edo.