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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:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2012-05-20 15:37:36 UTC</tt>.<br>
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| : The original revision id was <tt>337607418</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">The //446 equal division// divides the octave into 446 equal parts of 2.691 cents each. It tempers out 3136/3125 and 420175/419904 in the 7-limit, and provides the [[optimal patent val]] for the hemimean temperament tempering out 3136/3125 and [[Hemimean clan#Sengagen|sengagen]], the 49&50 temperament. In the 11-limit it tempers out 9801/9800 and gives the optimal patent val for the 50&198 temperament.
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| **PRIME FACTORIZATION:**
| | 446edo is only [[consistent]] to the [[5-odd-limit]] and the error of [[harmonic]] [[5/1|5]] is quite large. The equal temperament [[tempering out|tempers out]] [[3136/3125]] and 420175/419904 in the 7-limit, and provides the [[optimal patent val]] for the [[hemimean]] temperament tempering out 3136/3125, and [[sengagen]], the {{nowrap|99 & 347}} temperament. In the 11-limit it tempers out [[9801/9800]] and gives the optimal patent val for the 198 & 248 temperament. |
| [[2edo|2]] * [[223edo|223]]</pre></div> | | |
| <h4>Original HTML content:</h4>
| | === Odd harmonics === |
| <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>446edo</title></head><body>The <em>446 equal division</em> divides the octave into 446 equal parts of 2.691 cents each. It tempers out 3136/3125 and 420175/419904 in the 7-limit, and provides the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for the hemimean temperament tempering out 3136/3125 and <a class="wiki_link" href="/Hemimean%20clan#Sengagen">sengagen</a>, the 49&amp;50 temperament. In the 11-limit it tempers out 9801/9800 and gives the optimal patent val for the 50&amp;198 temperament.<br />
| | {{Harmonics in equal|446}} |
| <br />
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| <strong>PRIME FACTORIZATION:</strong><br />
| | === Subsets and supersets === |
| <a class="wiki_link" href="/2edo">2</a> * <a class="wiki_link" href="/223edo">223</a></body></html></pre></div>
| | Since 446 factors into {{factorization|446}}, 446edo contains [[2edo]] and [[223edo]] as subsets. |
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| | [[Category:Hemimean]] |
| | [[Category:Sengagen]] |
Latest revision as of 14:57, 20 February 2025
| Prime factorization
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2 × 223
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| Step size
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2.69058 ¢
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| Fifth
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261\446 (702.242 ¢)
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| Semitones (A1:m2)
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43:33 (115.7 ¢ : 88.79 ¢)
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| Consistency limit
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5
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| Distinct consistency limit
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5
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446 equal divisions of the octave (abbreviated 446edo or 446ed2), also called 446-tone equal temperament (446tet) or 446 equal temperament (446et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 446 equal parts of about 2.69 ¢ each. Each step represents a frequency ratio of 21/446, or the 446th root of 2.
446edo is only consistent to the 5-odd-limit and the error of harmonic 5 is quite large. The equal temperament tempers out 3136/3125 and 420175/419904 in the 7-limit, and provides the optimal patent val for the hemimean temperament tempering out 3136/3125, and sengagen, the 99 & 347 temperament. In the 11-limit it tempers out 9801/9800 and gives the optimal patent val for the 198 & 248 temperament.
Odd harmonics
Approximation of odd harmonics in 446edo
| Harmonic
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3
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5
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7
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9
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11
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13
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15
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17
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19
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21
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23
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| Error
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Absolute (¢)
|
+0.29
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+1.13
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-0.22
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+0.57
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+0.25
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-1.07
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-1.27
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-0.02
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+1.14
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+0.07
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+1.32
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| Relative (%)
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+10.7
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+42.0
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-8.0
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+21.3
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+9.3
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-39.6
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-47.3
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-0.8
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+42.4
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+2.6
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+49.1
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Steps
(reduced)
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707
(261)
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1036
(144)
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1252
(360)
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1414
(76)
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1543
(205)
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1650
(312)
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1742
(404)
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1823
(39)
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1895
(111)
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1959
(175)
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2018
(234)
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Subsets and supersets
Since 446 factors into 2 × 223, 446edo contains 2edo and 223edo as subsets.