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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 00:16:41 UTC</tt>.<br>
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| : The original revision id was <tt>241113311</tt>.<br>
| | Uinsg the [[patent val]], the equal temperament [[tempering out|tempers out]] [[2401/2400]] and [[78732/78125]] in the 7-limit; [[243/242]], [[441/440]] and [[540/539]] in the 11-limit; [[351/350]], [[1716/1715]] and [[1575/1573]] in the 13-limit; and provides the [[optimal patent val]] for [[Breed family #Jovis|jovis 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|363}} |
| <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 //363 equal temperament// divides the octave into 363 equal parts of 3.306 cents each. It tempers out 2401/2400 and 78732/78125 in the 7-limit; 243/242, 441/440 and 540/539 in the 11-limit; 351/350, 1716/1715 and 1575/1573 in the 13-limit; and provides the [[optimal patent val]] for [[Breed family|jovis 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>363edo</title></head><body>The <em>363 equal temperament</em> divides the octave into 363 equal parts of 3.306 cents each. It tempers out 2401/2400 and 78732/78125 in the 7-limit; 243/242, 441/440 and 540/539 in the 11-limit; 351/350, 1716/1715 and 1575/1573 in the 13-limit; and provides the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for <a class="wiki_link" href="/Breed%20family">jovis temperament</a>.</body></html></pre></div>
| | Since 363 factors into {{factorization|363}}, 363edo has subset edos {{EDOs| 3, 11, 33, and 121 }}. |
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| | [[Category:Jovis]] |
Latest revision as of 14:47, 20 February 2025
| Prime factorization
|
3 × 112
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| Step size
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3.30579 ¢
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| Fifth
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212\363 (700.826 ¢)
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| Semitones (A1:m2)
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32:29 (105.8 ¢ : 95.87 ¢)
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| Dual sharp fifth
|
213\363 (704.132 ¢) (→ 71\121)
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| Dual flat fifth
|
212\363 (700.826 ¢)
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| Dual major 2nd
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62\363 (204.959 ¢)
|
| Consistency limit
|
7
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| Distinct consistency limit
|
7
|
363 equal divisions of the octave (abbreviated 363edo or 363ed2), also called 363-tone equal temperament (363tet) or 363 equal temperament (363et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 363 equal parts of about 3.31 ¢ each. Each step represents a frequency ratio of 21/363, or the 363rd root of 2.
Uinsg the patent val, the equal temperament tempers out 2401/2400 and 78732/78125 in the 7-limit; 243/242, 441/440 and 540/539 in the 11-limit; 351/350, 1716/1715 and 1575/1573 in the 13-limit; and provides the optimal patent val for jovis temperament.
Odd harmonics
Approximation of odd harmonics in 363edo
| Harmonic
|
3
|
5
|
7
|
9
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11
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13
|
15
|
17
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19
|
21
|
23
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| Error
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Absolute (¢)
|
-1.13
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+0.46
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-0.23
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+1.05
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+0.75
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-0.86
|
-0.67
|
+0.83
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+0.01
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-1.36
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-0.18
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| Relative (%)
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-34.1
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+14.0
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-7.0
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+31.7
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+22.6
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-26.0
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-20.1
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+25.1
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+0.2
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-41.1
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-5.3
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Steps
(reduced)
|
575
(212)
|
843
(117)
|
1019
(293)
|
1151
(62)
|
1256
(167)
|
1343
(254)
|
1418
(329)
|
1484
(32)
|
1542
(90)
|
1594
(142)
|
1642
(190)
|
Subsets and supersets
Since 363 factors into 3 × 112, 363edo has subset edos 3, 11, 33, and 121.