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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>2015-08-17 12:55:32 UTC</tt>.<br>
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| : The original revision id was <tt>556814183</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 1920 division divides the octave into 1920 equal parts of exactly 0.625 cents each. It is distinctly consistent through the 25 limit, and in terms of 23-limit [[Tenney-Euclidean temperament measures#TE simple badness|relative error]], only [[1578edo|1578]] and [[1889edo|1889]] are both smaller and with a lower relative error. In the 29-limit, only 1578 beats it, and in the 31, 37, 41, 43 and 47 limits, nothing beats it. Because of this and because it is a highly composite number divisible by 12, it is another candidate for [[interval size measure]].
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| 1920 = 2^7 * 3 * 5; some of its divisors are [[10edo|10]], [[12edo|12]], [[15edo|15]], [[16edo|16]], [[24edo|24]], [[60edo|60]], [[80edo|80]], [[96edo|96]], [[128edo|128]], [[240edo|240]], [[320edo|320]] and [[640edo|640]].</pre></div>
| | == Theory == |
| <h4>Original HTML content:</h4>
| | 1920edo is [[consistency|distinctly consistent]] through the [[25-odd-limit]], and in terms of [[23-limit]] [[Tenney-Euclidean temperament measures #TE simple badness|relative error]], only [[1578edo|1578]] and [[1889edo|1889]] are both smaller and with a lower relative error. In the [[29-limit]], only 1578 beats it, and in the [[31-limit|31-]], [[37-limit|37-]], [[41-limit|41-]], [[43-limit|43-]] and [[47-limit]], nothing beats it. Because of this and because it is a very composite number divisible by 12, it is another candidate for [[interval size measure]]. |
| <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>1920edo</title></head><body>The 1920 division divides the octave into 1920 equal parts of exactly 0.625 cents each. It is distinctly consistent through the 25 limit, and in terms of 23-limit <a class="wiki_link" href="/Tenney-Euclidean%20temperament%20measures#TE simple badness">relative error</a>, only <a class="wiki_link" href="/1578edo">1578</a> and <a class="wiki_link" href="/1889edo">1889</a> are both smaller and with a lower relative error. In the 29-limit, only 1578 beats it, and in the 31, 37, 41, 43 and 47 limits, nothing beats it. Because of this and because it is a highly composite number divisible by 12, it is another candidate for <a class="wiki_link" href="/interval%20size%20measure">interval size measure</a>.<br />
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| | As a micro- (or nano-) temperament, it is a [[landscape]] system in the [[7-limit]], [[tempering out]] [[250047/250000]], and in the [[11-limit]] it tempers out [[9801/9800]]. Beyond that, it tempers out [[10648/10647]] in the [[13-limit]]; [[5832/5831]] and [[14400/14399]] in the [[17-limit]]; [[4200/4199]], [[5985/5984]], and 6860/6859 in the [[19-limit]]; and [[3381/3380]] in the 23-limit. |
| 1920 = 2^7 * 3 * 5; some of its divisors are <a class="wiki_link" href="/10edo">10</a>, <a class="wiki_link" href="/12edo">12</a>, <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/16edo">16</a>, <a class="wiki_link" href="/24edo">24</a>, <a class="wiki_link" href="/60edo">60</a>, <a class="wiki_link" href="/80edo">80</a>, <a class="wiki_link" href="/96edo">96</a>, <a class="wiki_link" href="/128edo">128</a>, <a class="wiki_link" href="/240edo">240</a>, <a class="wiki_link" href="/320edo">320</a> and <a class="wiki_link" href="/640edo">640</a>.</body></html></pre></div> | | |
| | === Prime harmonics === |
| | {{Harmonics in equal|1920|columns=11}} |
| | {{Harmonics in equal|1920|columns=11|start=12|collapsed=true|title=Approximation of prime harmonics in 1920edo (continued)}} |
| | |
| | === Subsets and supersets === |
| | Since 1920 factors into {{nowrap| 2<sup>7</sup> × 3 × 5 }}, 1920edo has subset edos {{EDOs| 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 128, 160, 192, 240, 320, 384, 480, 640, 960 }}. |
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| | == Regular temperament properties == |
| | 1920edo has the lowest relative error in the 31-, 37-, 41-, and 47-limit. |
| | |
| | === Rank-2 temperaments === |
| | {| class="wikitable center-all left-5" |
| | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator |
| | |- |
| | ! Periods<br>per 8ve |
| | ! Generator* |
| | ! Cents* |
| | ! Associated<br>ratio* |
| | ! Temperaments |
| | |- |
| | | 1 |
| | | 179\1920 |
| | | 111.875 |
| | | 16/15 |
| | | [[Vavoom]] |
| | |- |
| | | 30 |
| | | 583\1920<br>(7\1920) |
| | | 364.375<br>(4.375) |
| | | 216/175<br>(385/384) |
| | | [[Zinc]] |
| | |- |
| | | 60 |
| | | 583\1920<br>(7\1920) |
| | | 364.375<br>(4.375) |
| | | 216/175<br>(385/384) |
| | | [[Neodymium]] / [[neodymium magnet]] |
| | |} |
| | <nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct |
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| | == Music == |
| | ; [[Eliora]] |
| | * [https://www.youtube.com/watch?v=ShbfCHv8Lj0 ''Jazz Improvisation''] (2023) |
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| | [[Category:Listen]] |