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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>2011-10-24 01:02:51 UTC</tt>.<br>
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| : The original revision id was <tt>267790746</tt>.<br>
| | The equal temperament [[tempering out|tempers out]] the kleisma, [[15625/15552]], and the breedsma, [[2401/2400]], and is a good tuning for [[quadritikleismic]] temperament which tempers out both. This is particularly true for the 11-limit version of quadritikleismic, which also tempers out [[385/384]], for which it provides the [[optimal patent val]]. In fact, if 385/384 is tempered out essentially the same tuning accuracy can be obtained using quadritikleismic, since 284 provides the optimal patent val for quadritikleismic, the rank-3 temperaments [[agni]] and [[enlil]] and keenanismic, the 385/384 rank-4 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>
| | === Prime harmonics === |
| <h4>Original Wikitext content:</h4>
| | {{Harmonics in equal|284}} |
| <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 //284 equal division// divides the octave into 284 equal parts of size 4.225 cents each. It tempers out the kleisma, 15625/15552, and the breedsma, 2401/2400, and is a good tuning for [[Kleismic family|quadritikleismic temperament]] which tempers out both. This is particularly true for the 11-limit version of quadritikleismic, which also tempers out 385/384, for which it provides the [[optimal patent val]]. In fact, if 385/384 is tempered out essentially the same tuning accuracy can be obtained using quadritikleismic, since 284 provides the optimal patent val for quadritikleismic, the rank three temperament [[Kleismic rank three family#Enlil|enlil]] and keenanismic, the 385/384 rank four 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>284edo</title></head><body>The <em>284 equal division</em> divides the octave into 284 equal parts of size 4.225 cents each. It tempers out the kleisma, 15625/15552, and the breedsma, 2401/2400, and is a good tuning for <a class="wiki_link" href="/Kleismic%20family">quadritikleismic temperament</a> which tempers out both. This is particularly true for the 11-limit version of quadritikleismic, which also tempers out 385/384, for which it provides the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a>. In fact, if 385/384 is tempered out essentially the same tuning accuracy can be obtained using quadritikleismic, since 284 provides the optimal patent val for quadritikleismic, the rank three temperament <a class="wiki_link" href="/Kleismic%20rank%20three%20family#Enlil">enlil</a> and keenanismic, the 385/384 rank four temperament.</body></html></pre></div>
| | Since 284 factors into {{factorization|284}}, 284edo has subset edos {{EDOs| 2, 4, 71, and 142 }}. |
| | |
| | [[Category:Keenanismic]] |
| | [[Category:Agni]] |
| | [[Category:Enlil]] |
| | [[Category:Quadritikleismic]] |
| Prime factorization
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22 × 71
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| Step size
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4.22535 ¢
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| Fifth
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166\284 (701.408 ¢) (→ 83\142)
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| Semitones (A1:m2)
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26:22 (109.9 ¢ : 92.96 ¢)
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| Consistency limit
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11
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| Distinct consistency limit
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11
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284 equal divisions of the octave (abbreviated 284edo or 284ed2), also called 284-tone equal temperament (284tet) or 284 equal temperament (284et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 284 equal parts of about 4.23 ¢ each. Each step represents a frequency ratio of 21/284, or the 284th root of 2.
The equal temperament tempers out the kleisma, 15625/15552, and the breedsma, 2401/2400, and is a good tuning for quadritikleismic temperament which tempers out both. This is particularly true for the 11-limit version of quadritikleismic, which also tempers out 385/384, for which it provides the optimal patent val. In fact, if 385/384 is tempered out essentially the same tuning accuracy can be obtained using quadritikleismic, since 284 provides the optimal patent val for quadritikleismic, the rank-3 temperaments agni and enlil and keenanismic, the 385/384 rank-4 temperament.
Prime harmonics
Approximation of odd harmonics in 284edo
| Harmonic
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3
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5
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7
|
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
|
23
|
| Error
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Absolute (¢)
|
-0.55
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-1.81
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-1.22
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-1.09
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-2.02
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+0.32
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+1.87
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+0.68
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-1.74
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-1.77
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+1.30
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| Relative (%)
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-12.9
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-42.8
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-28.9
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-25.9
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-47.9
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+7.5
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+44.3
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+16.1
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-41.1
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-41.8
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+30.8
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Steps
(reduced)
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450
(166)
|
659
(91)
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797
(229)
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900
(48)
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982
(130)
|
1051
(199)
|
1110
(258)
|
1161
(25)
|
1206
(70)
|
1247
(111)
|
1285
(149)
|
Subsets and supersets
Since 284 factors into 22 × 71, 284edo has subset edos 2, 4, 71, and 142.