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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>2011-07-08 00:46:06 UTC</tt>.<br>
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| : The original revision id was <tt>240471879</tt>.<br>
| | The equal temperament [[tempering out|tempers out]] [[225/224]] in the 7-limit, and [[243/242]] and [[4000/3993]] in the 11-limit, so that it [[support]]s [[marvo]] and provides the [[optimal patent val]]; it also gives the optimal patent val for the rank-3 [[spectacle]] temperament. |
| : 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|281}} |
| <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 //281 equal division// divides the octave into 281 equal parts of 4.270 cents each. It tempers out 225/224 in the 7-limit, and 243/242 and 4000/3993 in the 11-limit limit, so that it supports [[Marvel temperaments#Marvo|marvo temperament]] and provides the [[optimal patent val]]; it also gives the optimal patent val for the rank three [[Marvel family#Spectacle|spectacle temperament]].</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>281edo</title></head><body>The <em>281 equal division</em> divides the octave into 281 equal parts of 4.270 cents each. It tempers out 225/224 in the 7-limit, and 243/242 and 4000/3993 in the 11-limit limit, so that it supports <a class="wiki_link" href="/Marvel%20temperaments#Marvo">marvo temperament</a> and provides the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a>; it also gives the optimal patent val for the rank three <a class="wiki_link" href="/Marvel%20family#Spectacle">spectacle temperament</a>.</body></html></pre></div>
| | 281edo is the 60th [[prime edo]]. |
| | |
| | [[Category:Spectacle]] |
| | [[Category:Marvo]] |
Latest revision as of 06:55, 20 February 2025
| Prime factorization
|
281 (prime)
|
| Step size
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4.27046 ¢
|
| Fifth
|
164\281 (700.356 ¢)
|
| Semitones (A1:m2)
|
24:23 (102.5 ¢ : 98.22 ¢)
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| Dual sharp fifth
|
165\281 (704.626 ¢)
|
| Dual flat fifth
|
164\281 (700.356 ¢)
|
| Dual major 2nd
|
48\281 (204.982 ¢)
|
| Consistency limit
|
5
|
| Distinct consistency limit
|
5
|
281 equal divisions of the octave (abbreviated 281edo or 281ed2), also called 281-tone equal temperament (281tet) or 281 equal temperament (281et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 281 equal parts of about 4.27 ¢ each. Each step represents a frequency ratio of 21/281, or the 281st root of 2.
The equal temperament tempers out 225/224 in the 7-limit, and 243/242 and 4000/3993 in the 11-limit, so that it supports marvo and provides the optimal patent val; it also gives the optimal patent val for the rank-3 spectacle temperament.
Odd harmonics
Approximation of odd harmonics in 281edo
| Harmonic
|
3
|
5
|
7
|
9
|
11
|
13
|
15
|
17
|
19
|
21
|
23
|
| Error
|
Absolute (¢)
|
-1.60
|
-1.97
|
+0.57
|
+1.07
|
-0.43
|
+0.75
|
+0.70
|
+1.81
|
+1.42
|
-1.03
|
-0.52
|
| Relative (%)
|
-37.4
|
-46.2
|
+13.3
|
+25.1
|
-10.0
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+17.6
|
+16.4
|
+42.3
|
+33.2
|
-24.1
|
-12.1
|
Steps
(reduced)
|
445
(164)
|
652
(90)
|
789
(227)
|
891
(48)
|
972
(129)
|
1040
(197)
|
1098
(255)
|
1149
(25)
|
1194
(70)
|
1234
(110)
|
1271
(147)
|
Subsets and supersets
281edo is the 60th prime edo.