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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>2013-02-19 13:46:50 UTC</tt>.<br>
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| : The original revision id was <tt>408213556</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 294 equal division divides the octave into 294 parts of 4.082 cents each. It has a very accurate fifth, only 0.086 cents sharp, but it has a 5/4 which is 1.441 cents sharp and a 7/4 which is 1.479 cents flat, so that 7/5 is 2.920 cents flat. In the 5-limit it tempers out 393216/390625, the wuerschmidt comma, and |54 -37 2>, the monzisma. The patent val tempers out 10976/10935, the hemimage comma, and 50421/50000, the trimyna comma, and supplies the [[optimal patent val]] for [[Trimyna family|trymyna temperament]] tempering out the trymyna, as well as its 11-limit extension, anmd also supplies the optimal patent val for the rank four temperament tempering out 3773/3750. The 294d val tempers out 16875/16807 and 19683/19600 instead, supporting [[Mirkwai clan#Mirkat|mirkat temperament]], whereas 294c tempers out 126/125 and 1029/1024, supporting [[Starling temperaments#Valentine temperament|valentine temperament]].
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| 294 = 2*3*49, and has divisors 2, 3, 6, 7, 14, 21, 42, 49, 98 and 147.</pre></div>
| | 294edo has a very accurate fifth inherited from [[147edo]], only 0.086{{c}} sharp, but it has a [[5/4]] which is 1.441{{c}} sharp and a [[7/4]] which is 1.479{{c}} flat, so that 7/5 is 2.920{{c}} flat, rendering it in[[consistent]] in the [[7-odd-limit]]. |
| <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>294edo</title></head><body>The 294 equal division divides the octave into 294 parts of 4.082 cents each. It has a very accurate fifth, only 0.086 cents sharp, but it has a 5/4 which is 1.441 cents sharp and a 7/4 which is 1.479 cents flat, so that 7/5 is 2.920 cents flat. In the 5-limit it tempers out 393216/390625, the wuerschmidt comma, and |54 -37 2&gt;, the monzisma. The patent val tempers out 10976/10935, the hemimage comma, and 50421/50000, the trimyna comma, and supplies the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for <a class="wiki_link" href="/Trimyna%20family">trymyna temperament</a> tempering out the trymyna, as well as its 11-limit extension, anmd also supplies the optimal patent val for the rank four temperament tempering out 3773/3750. The 294d val tempers out 16875/16807 and 19683/19600 instead, supporting <a class="wiki_link" href="/Mirkwai%20clan#Mirkat">mirkat temperament</a>, whereas 294c tempers out 126/125 and 1029/1024, supporting <a class="wiki_link" href="/Starling%20temperaments#Valentine temperament">valentine temperament</a>.<br />
| | In the 5-limit 294edo [[tempering out|tempers out]] 393216/390625, the [[würschmidt comma]], and {{monzo| 54 -37 2 }}, the [[monzisma]]. The [[patent val]] tempers out 10976/10935, the [[hemimage comma]], and 50421/50000, the [[trimyna comma]], and supplies the [[optimal patent val]] for [[trimyna]] temperament, as well as its 11-limit [[extension]], and also supplies the optimal patent val for the rank-4 temperament tempering out [[3773/3750]]. The 294d val tempers out [[16875/16807]] and [[19683/19600]] instead, supporting [[mirkat]], whereas 294c tempers out [[126/125]] and [[1029/1024]], supporting [[valentine]]. |
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| 294 = 2*3*49, and has divisors 2, 3, 6, 7, 14, 21, 42, 49, 98 and 147.</body></html></pre></div> | | === Prime harmonics === |
| | {{Harmonics in equal|294}} |
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| | === Subsets and supersets === |
| | Since 294 factors into 2 × 3 × 49, 294edo has {{EDOs| 2, 3, 6, 7, 14, 21, 42, 49, 98, and 147 }} as its subsets. |
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| | [[Category:Trimyna]] |
| Prime factorization
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2 × 3 × 72
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| Step size
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4.08163 ¢
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| Fifth
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172\294 (702.041 ¢) (→ 86\147)
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| Semitones (A1:m2)
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28:22 (114.3 ¢ : 89.8 ¢)
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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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294 equal divisions of the octave (abbreviated 294edo or 294ed2), also called 294-tone equal temperament (294tet) or 294 equal temperament (294et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 294 equal parts of about 4.08 ¢ each. Each step represents a frequency ratio of 21/294, or the 294th root of 2.
294edo has a very accurate fifth inherited from 147edo, only 0.086 ¢ sharp, but it has a 5/4 which is 1.441 ¢ sharp and a 7/4 which is 1.479 ¢ flat, so that 7/5 is 2.920 ¢ flat, rendering it inconsistent in the 7-odd-limit.
In the 5-limit 294edo tempers out 393216/390625, the würschmidt comma, and [54 -37 2⟩, the monzisma. The patent val tempers out 10976/10935, the hemimage comma, and 50421/50000, the trimyna comma, and supplies the optimal patent val for trimyna temperament, as well as its 11-limit extension, and also supplies the optimal patent val for the rank-4 temperament tempering out 3773/3750. The 294d val tempers out 16875/16807 and 19683/19600 instead, supporting mirkat, whereas 294c tempers out 126/125 and 1029/1024, supporting valentine.
Prime harmonics
Approximation of prime harmonics in 294edo
| Harmonic
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2
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3
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5
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7
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11
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13
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17
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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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+0.09
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+1.44
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-1.48
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-0.30
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+0.29
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+1.17
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+0.45
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+0.30
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-1.01
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+1.90
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| Relative (%)
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+0.0
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+2.1
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+35.3
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-36.2
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-7.3
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+7.1
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+28.6
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+10.9
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+7.3
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-24.6
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+46.6
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Steps
(reduced)
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294
(0)
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466
(172)
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683
(95)
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825
(237)
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1017
(135)
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1088
(206)
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1202
(26)
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1249
(73)
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1330
(154)
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1428
(252)
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1457
(281)
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Subsets and supersets
Since 294 factors into 2 × 3 × 49, 294edo has 2, 3, 6, 7, 14, 21, 42, 49, 98, and 147 as its subsets.