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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>2011-07-01 00:47:08 UTC</tt>.<br>
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| : The original revision id was <tt>239611519</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 //**154edo**// divides the octave into 154 equal parts of 7.79221 cents each. It is a [[contorted]] 77et in the 7-limit; in the 11-limit, it tempers out 126/125, 1029/1024 and 243/242, which define the 11-limit 31&123 temperament, for which 154 provides a good tuning, though [[185edo]] gives the patent val. In the 13-limit, it tempers out 196/195, 364/363 and 676/675.
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| 154 = 2 * 7 * 11, with divisors 2, 7, 11, 14, 22 and 77.</pre></div>
| | 154edo is a [[contorted]] 77et in the 7-limit; in the 11-limit, it tempers out [[126/125]], [[1029/1024]] and [[243/242]], which define the 11-limit 31 & 123 temperament, for which 154 provides a good tuning, though [[185edo]] gives the [[optimal patent val]]. In the 13-limit, it tempers out [[196/195]], [[364/363]] and [[676/675]]. |
| <h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>154edo</title></head><body>The <em><strong>154edo</strong></em> divides the octave into 154 equal parts of 7.79221 cents each. It is a <a class="wiki_link" href="/contorted">contorted</a> 77et in the 7-limit; in the 11-limit, it tempers out 126/125, 1029/1024 and 243/242, which define the 11-limit 31&amp;123 temperament, for which 154 provides a good tuning, though <a class="wiki_link" href="/185edo">185edo</a> gives the patent val. In the 13-limit, it tempers out 196/195, 364/363 and 676/675.<br />
| | === Prime harmonics === |
| <br />
| | {{Harmonics in equal|154}} |
| 154 = 2 * 7 * 11, with divisors 2, 7, 11, 14, 22 and 77.</body></html></pre></div> | | |
| | === Subsets and supersets === |
| | 154 = {{factorization|154}}, 154edo has subset edos {{EDOs| 2, 7, 11, 14, 22, and 77 }}. |
| Prime factorization
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2 × 7 × 11
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| Step size
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7.79221 ¢
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| Fifth
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90\154 (701.299 ¢) (→ 45\77)
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| Semitones (A1:m2)
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14:12 (109.1 ¢ : 93.51 ¢)
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| Consistency limit
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3
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| Distinct consistency limit
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3
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154 equal divisions of the octave (abbreviated 154edo or 154ed2), also called 154-tone equal temperament (154tet) or 154 equal temperament (154et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 154 equal parts of about 7.79 ¢ each. Each step represents a frequency ratio of 21/154, or the 154th root of 2.
154edo is a contorted 77et in the 7-limit; in the 11-limit, it tempers out 126/125, 1029/1024 and 243/242, which define the 11-limit 31 & 123 temperament, for which 154 provides a good tuning, though 185edo gives the optimal patent val. In the 13-limit, it tempers out 196/195, 364/363 and 676/675.
Prime harmonics
Approximation of prime harmonics in 154edo
| Harmonic
|
2
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3
|
5
|
7
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11
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13
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17
|
19
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23
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29
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31
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| Error
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Absolute (¢)
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+0.00
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-0.66
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+3.30
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-2.59
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+1.93
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+1.03
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-3.66
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-1.41
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+2.89
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-1.01
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+0.42
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| Relative (%)
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+0.0
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-8.4
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+42.3
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-33.3
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+24.8
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+13.2
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-46.9
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-18.1
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+37.1
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-12.9
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+5.4
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Steps
(reduced)
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154
(0)
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244
(90)
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358
(50)
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432
(124)
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533
(71)
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570
(108)
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629
(13)
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654
(38)
|
697
(81)
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748
(132)
|
763
(147)
|
Subsets and supersets
154 = 2 × 7 × 11, 154edo has subset edos 2, 7, 11, 14, 22, and 77.