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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>2015-08-15 13:23:45 UTC</tt>.<br>
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| : The original revision id was <tt>556732897</tt>.<br>
| | == Theory == |
| : The revision comment was: <tt></tt><br>
| | 1012edo is a strong 13-limit system, [[consistency|distinctly consistent]] through the [[15-odd-limit]]. It is a [[zeta peak edo]], though not [[zeta integral edo|zeta integral]] nor [[zeta gap edo|zeta gap]]. A basis for the 13-limit [[comma]]s consists of [[2401/2400]], [[4096/4095]], [[6656/6655]], [[9801/9800]] and {{monzo| 2 6 -1 2 0 4 }}. |
| 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>
| | In the 5-limit, 1012edo is [[enfactoring|enfactored]], with the same tuning as [[506edo]], [[support]]ing [[vishnu]], [[monzismic]], and [[lafa]]. In the 7-limit, it [[tempering out|tempers out]] the [[breedsma]], 2401/2400, and tunes the [[osiris]] temperament. Furthermore, noting its exceptional strength in the 2.3.7 [[subgroup]], it is a [[septiruthenia]]n system, tempering 64/63 comma to 1/44th of the octave, that is 23 steps. It provides the [[optimal patent val]] for [[quarvish]] temperament in the 7-limit and also in the 11-limit. |
| <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 1012 equal division divides the octave into 1012 equal parts of 1.1858 cents each. It is a strong 13-limit system, distinctly consistent through the 15 limit. It is a [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta peak edo]], though not zeta integral nor zeta gap. A basis for the 13-limit commas is 2401/2400, 4096/4095, 6656/6655, 9801/9800 and 142884/142805. 1012 is divisible by [[22edo|22]], [[46edo|46]] and [[253edo|253]].</pre></div>
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| <h4>Original HTML content:</h4>
| | === Prime harmonics === |
| <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>1012edo</title></head><body>The 1012 equal division divides the octave into 1012 equal parts of 1.1858 cents each. It is a strong 13-limit system, distinctly consistent through the 15 limit. It is a <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta EDO lists">zeta peak edo</a>, though not zeta integral nor zeta gap. A basis for the 13-limit commas is 2401/2400, 4096/4095, 6656/6655, 9801/9800 and 142884/142805. 1012 is divisible by <a class="wiki_link" href="/22edo">22</a>, <a class="wiki_link" href="/46edo">46</a> and <a class="wiki_link" href="/253edo">253</a>.</body></html></pre></div>
| | {{Harmonics in equal|1012}} |
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| | === Subsets and supersets === |
| | Since 1012 factors into {{nowrap| 2<sup>2</sup> × 11 × 23 }}, 1012edo has subset edos {{EDOs| 2, 4, 11, 22, 23, 44, 46, 92, 253, 506 }}. [[2024edo]], which divides the edostep in two, provides a good correction for the 17th harmonic. |
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| | == Regular temperament properties == |
| | === 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 |
| | | 361\1012 |
| | | 428.06 |
| | | 2800/2187 |
| | | [[Osiris]] |
| | |- |
| | | 2 |
| | | 145\1012 |
| | | 171.94 |
| | | 243/220 |
| | | [[Semiosiris]] |
| | |- |
| | | 2 |
| | | 420\1012 |
| | | 498.02 |
| | | 7/5 |
| | | [[Quarvish]] |
| | |- |
| | | 44 |
| | | 420\1012<br>(6\1012) |
| | | 498.02<br>(7.11) |
| | | 4/3<br>(18375/18304) |
| | | [[Ruthenium]] |
| | |} |
| | <nowiki/>* In [[normal forms #Minimal-generator form|minimal-generator form]] |