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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>2013-09-09 13:12:40 UTC</tt>.<br>
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| : The original revision id was <tt>449703270</tt>.<br>
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| : 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>
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| <h4>Original Wikitext content:</h4>
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| <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">**271 EDO** divides the [[octave]] into 271 [[equal]] intervals, each 4.428 [[cent]]s in size. It tempers out 4000/3969 and 65625/65536 in the 7-limit, 896/891 and 1375/1372 in the 11-limit, and 352/351, 364/363, 676/675, 1575/1573 and 2200/2197 in the 13-limit. It is an optimal patent val by some measures for the 13-limit pentacircle temperament, tempering out 352/351 and 364/363 on the 2.11/7.13/7 subgroup of the 13-limit.
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| =Scales= | | == Theory == |
| [[pepperoni7]] | | 271edo is the highest edo where the [[3/2|perfect fifth]] has greater absolute error than [[12edo]]. It is in[[consistent]] in the [[5-odd-limit]]. Using the [[patent val]] nonetheless, the equal temperament [[tempering out|tempers out]] [[4000/3969]] and [[65625/65536]] in the 7-limit, [[896/891]] and 1375/1372 in the 11-limit, and [[352/351]], [[364/363]], [[676/675]], [[1575/1573]] and [[2200/2197]] in the 13-limit. It is the [[optimal patent val]] for the [[pepperoni]] temperament, tempering out 352/351 and 364/363 on the 2.3.11/7.13/7 [[subgroup]] of the 13-limit. |
| [[pepperoni12]] | | |
| [[cantonpenta]]</pre></div> | | === Odd harmonics === |
| <h4>Original HTML content:</h4>
| | {{Harmonics in equal|271}} |
| <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>271edo</title></head><body><strong>271 EDO</strong> divides the <a class="wiki_link" href="/octave">octave</a> into 271 <a class="wiki_link" href="/equal">equal</a> intervals, each 4.428 <a class="wiki_link" href="/cent">cent</a>s in size. It tempers out 4000/3969 and 65625/65536 in the 7-limit, 896/891 and 1375/1372 in the 11-limit, and 352/351, 364/363, 676/675, 1575/1573 and 2200/2197 in the 13-limit. It is an optimal patent val by some measures for the 13-limit pentacircle temperament, tempering out 352/351 and 364/363 on the 2.11/7.13/7 subgroup of the 13-limit.<br />
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| <br />
| | === Subsets and supersets === |
| <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Scales"></a><!-- ws:end:WikiTextHeadingRule:0 -->Scales</h1>
| | 271edo is the 58th [[prime edo]]. |
| <a class="wiki_link" href="/pepperoni7">pepperoni7</a><br />
| | |
| <a class="wiki_link" href="/pepperoni12">pepperoni12</a><br />
| | == Scales == |
| <a class="wiki_link" href="/cantonpenta">cantonpenta</a></body></html></pre></div>
| | * [[Pepperoni7]] |
| | * [[Pepperoni12]] |
| | * [[Cantonpenta]] |
| | |
| | [[Category:Pepperoni]] |
| Prime factorization
|
271 (prime)
|
| Step size
|
4.42804 ¢
|
| Fifth
|
159\271 (704.059 ¢)
|
| Semitones (A1:m2)
|
29:18 (128.4 ¢ : 79.7 ¢)
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| Dual sharp fifth
|
159\271 (704.059 ¢)
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| Dual flat fifth
|
158\271 (699.631 ¢)
|
| Dual major 2nd
|
46\271 (203.69 ¢)
|
| Consistency limit
|
3
|
| Distinct consistency limit
|
3
|
271 equal divisions of the octave (abbreviated 271edo or 271ed2), also called 271-tone equal temperament (271tet) or 271 equal temperament (271et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 271 equal parts of about 4.43 ¢ each. Each step represents a frequency ratio of 21/271, or the 271st root of 2.
Theory
271edo is the highest edo where the perfect fifth has greater absolute error than 12edo. It is inconsistent in the 5-odd-limit. Using the patent val nonetheless, the equal temperament tempers out 4000/3969 and 65625/65536 in the 7-limit, 896/891 and 1375/1372 in the 11-limit, and 352/351, 364/363, 676/675, 1575/1573 and 2200/2197 in the 13-limit. It is the optimal patent val for the pepperoni temperament, tempering out 352/351 and 364/363 on the 2.3.11/7.13/7 subgroup of the 13-limit.
Odd harmonics
Approximation of odd harmonics in 271edo
| Harmonic
|
3
|
5
|
7
|
9
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11
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13
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15
|
17
|
19
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21
|
23
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| Error
|
Absolute (¢)
|
+2.10
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-1.07
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+0.92
|
-0.22
|
+2.19
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+0.80
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+1.03
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+1.32
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-0.83
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-1.41
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+0.51
|
| Relative (%)
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+47.5
|
-24.3
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+20.7
|
-5.0
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+49.4
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+18.1
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+23.3
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+29.8
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-18.8
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-31.8
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+11.5
|
Steps
(reduced)
|
430
(159)
|
629
(87)
|
761
(219)
|
859
(46)
|
938
(125)
|
1003
(190)
|
1059
(246)
|
1108
(24)
|
1151
(67)
|
1190
(106)
|
1226
(142)
|
Subsets and supersets
271edo is the 58th prime edo.
Scales