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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>2012-02-09 16:33:55 UTC</tt>.<br>
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| : The original revision id was <tt>300283196</tt>.<br>
| | The equal temperament tempers out [[15625/15552]] in the 5-limit and [[5120/5103]] in the 7-limit, so it [[support]]s [[countercata]]. In the 11-limit it tempers out 1375/1372 and [[4000/3993]], and in the 13-limit [[325/324]], [[364/363]], [[625/624]] and [[676/675]], and provides the [[optimal patent val]] for the rank-2 temperament [[novemkleismic]], for the rank-3 temperament tempering out 325/324, 625/624 and 676/675, the rank-4 temperament tempering out 325/324 and 1375/1372, and the rank-5 temperament tempering out 325/324. |
| : 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>
| | === Prime harmonics === |
| <h4>Original Wikitext content:</h4>
| | {{Harmonics in equal|333}} |
| <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 //333 equal temperament// divides the octave into 333 equal parts of 3.604 cents each. It tempers out 15625/15552 in the 5-limit and 5120/5013 in the 7-limit, so it supports [[Kleismic family#Countercata|countercata temperament]]. In the 11-limit it tempers out 1375/1372 and 4000/3993, and in the 13-limit 325/324, 364/363, 625/624 and 676/675, and provides the [[optimal patent val]] for the rank two temperament [[Kleismic family#Novemkleismic|novemkleismic]], for the rank three temperament tempering out 325/324, 625/624 and 676/675, the rank four temperament tempering out 325/324 and 1375/1372, and the rank five temperament tempering out 325/324.</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>333edo</title></head><body>The <em>333 equal temperament</em> divides the octave into 333 equal parts of 3.604 cents each. It tempers out 15625/15552 in the 5-limit and 5120/5013 in the 7-limit, so it supports <a class="wiki_link" href="/Kleismic%20family#Countercata">countercata temperament</a>. In the 11-limit it tempers out 1375/1372 and 4000/3993, and in the 13-limit 325/324, 364/363, 625/624 and 676/675, and provides the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for the rank two temperament <a class="wiki_link" href="/Kleismic%20family#Novemkleismic">novemkleismic</a>, for the rank three temperament tempering out 325/324, 625/624 and 676/675, the rank four temperament tempering out 325/324 and 1375/1372, and the rank five temperament tempering out 325/324.</body></html></pre></div>
| | Since 333 factors into 3<sup>2</sup> × 37, 333edo has subset edos {{EDOs| 3, 9, 37, and 111 }}. |
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| | [[Category:Countercata]] |
| | [[Category:Marveltwin]] |
| Prime factorization
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32 × 37
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| Step size
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3.6036 ¢
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| Fifth
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195\333 (702.703 ¢) (→ 65\111)
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| Semitones (A1:m2)
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33:24 (118.9 ¢ : 86.49 ¢)
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| Consistency limit
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7
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| Distinct consistency limit
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7
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333 equal divisions of the octave (abbreviated 333edo or 333ed2), also called 333-tone equal temperament (333tet) or 333 equal temperament (333et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 333 equal parts of about 3.6 ¢ each. Each step represents a frequency ratio of 21/333, or the 333rd root of 2.
The equal temperament tempers out 15625/15552 in the 5-limit and 5120/5103 in the 7-limit, so it supports countercata. In the 11-limit it tempers out 1375/1372 and 4000/3993, and in the 13-limit 325/324, 364/363, 625/624 and 676/675, and provides the optimal patent val for the rank-2 temperament novemkleismic, for the rank-3 temperament tempering out 325/324, 625/624 and 676/675, the rank-4 temperament tempering out 325/324 and 1375/1372, and the rank-5 temperament tempering out 325/324.
Prime harmonics
Approximation of prime harmonics in 333edo
| Harmonic
|
2
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3
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5
|
7
|
11
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13
|
17
|
19
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23
|
29
|
31
|
| Error
|
Absolute (¢)
|
+0.00
|
+0.75
|
-0.73
|
+0.54
|
+0.03
|
-0.89
|
-0.45
|
+1.59
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-1.25
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+1.05
|
+0.91
|
| Relative (%)
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+0.0
|
+20.7
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-20.2
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+15.1
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+0.9
|
-24.6
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-12.5
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+44.0
|
-34.6
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+29.2
|
+25.3
|
Steps
(reduced)
|
333
(0)
|
528
(195)
|
773
(107)
|
935
(269)
|
1152
(153)
|
1232
(233)
|
1361
(29)
|
1415
(83)
|
1506
(174)
|
1618
(286)
|
1650
(318)
|
Subsets and supersets
Since 333 factors into 32 × 37, 333edo has subset edos 3, 9, 37, and 111.