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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>2011-07-10 21:39:50 UTC</tt>.<br>
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| : The original revision id was <tt>240755753</tt>.<br>
| | The equal temperament [[tempering out|tempers out]] {{monzo| 23 6 -14 }} ([[vishnu comma]]) in the [[5-limit]], and [[2401/2400]], [[5120/5103]] and [[10976/10935]] in the [[7-limit]]. It provides the [[optimal patent val]] for 7-limit [[hemififths]], the {{nowrap| 99 & 239 }} 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|338}} |
| <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 //338 equal division// divides the octave into 338 equal parts of 3.550 cents each. In the 5-limit it tempers out the vishnuzma, 6115295232/6103515625, and in the 7-limit 2401/2400, 5120/5103 and 10976/10935. It provides the [[optimal patent val]] for [[Breedsmic temperaments#Hemififths|hemififths 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>338edo</title></head><body>The <em>338 equal division</em> divides the octave into 338 equal parts of 3.550 cents each. In the 5-limit it tempers out the vishnuzma, 6115295232/6103515625, and in the 7-limit 2401/2400, 5120/5103 and 10976/10935. It provides the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for <a class="wiki_link" href="/Breedsmic%20temperaments#Hemififths">hemififths temperament</a>.</body></html></pre></div>
| | Since 338 factors into {{nowrap| 2 × 13<sup>2</sup> }}, 338edo has subset edos {{EDOs| 2, 13, 26, and 169 }}. |
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| | [[Category:Hemififths]] |
Latest revision as of 06:44, 18 June 2026
| Prime factorization
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2 × 132
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| Step size
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3.5503 ¢
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| Fifth
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198\338 (702.959 ¢) (→ 99\169)
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| Semitones (A1:m2)
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34:24 (120.7 ¢ : 85.21 ¢)
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| Consistency limit
|
7
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| Distinct consistency limit
|
7
|
338 equal divisions of the octave (abbreviated 338edo or 338ed2), also called 338-tone equal temperament (338tet) or 338 equal temperament (338et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 338 equal parts of about 3.55 ¢ each. Each step represents a frequency ratio of 21/338, or the 338th root of 2.
The equal temperament tempers out [23 6 -14⟩ (vishnu comma) in the 5-limit, and 2401/2400, 5120/5103 and 10976/10935 in the 7-limit. It provides the optimal patent val for 7-limit hemififths, the 99 & 239 temperament.
Odd harmonics
Approximation of odd harmonics in 338edo
| Harmonic
|
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
|
19
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21
|
23
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| Error
|
Absolute (¢)
|
+1.00
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+0.67
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+0.40
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-1.54
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-1.02
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+0.89
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+1.67
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+1.55
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+0.71
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+1.41
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+0.13
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| Relative (%)
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+28.3
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+18.8
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+11.4
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-43.5
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-28.8
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+25.1
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+47.1
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+43.8
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+20.1
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+39.7
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+3.6
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Steps
(reduced)
|
536
(198)
|
785
(109)
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949
(273)
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1071
(57)
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1169
(155)
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1251
(237)
|
1321
(307)
|
1382
(30)
|
1436
(84)
|
1485
(133)
|
1529
(177)
|
Subsets and supersets
Since 338 factors into 2 × 132, 338edo has subset edos 2, 13, 26, and 169.