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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>2015-08-21 13:09:10 UTC</tt>.<br>
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| : The original revision id was <tt>557121779</tt>.<br>
| | 7033edo is a [[Riemann zeta function #Zeta EDO lists|zeta peak and integral edo]], though not a gap edo. This excellence is partly explained by the fact that it is very strong in the [[17-limit]], with a lower [[Tenney–Euclidean temperament measures #TE simple badness|relative error]] than any smaller division, and a lower [[Tenney–Euclidean temperament measures #TE simple badness|TE logflat badness]] than any lower edo excepting [[72edo|72]]. It has a flat tendency, with all the lower [[harmonic]]s until [[19/1|19]] tuned flat. A [[comma basis|basis]] for its 17-limit [[comma]]s is {[[28561/28560]], [[31213/31212]], [[37180/37179]], 918750/918731, 1257795/1257728, 3070625/3070548}. It also [[tempering out|tempers out]] [[123201/123200]], [[194481/194480]], and [[336141/336140]], the three smallest 17-limit [[superparticular]]s. |
| : 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>
| | Since the approximation to harmonic 19 is weak, it can be used as a no-19 system, in which it continues to be strong up to the [[37-limit]], and is [[consistent]] to the no-19 39-odd-limit. |
| <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 7033 equal division divides the octave into 7033 equal parts of 0.17062 cents each. It is a [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta peak and integral edo]]; it is not known at this time (2015) if it is a gap edo, but it seems unlikely. This excellence is explained by the fact that it is very strong in the 17-limit, with a lower [[Tenney-Euclidean temperament measures#TE simple badness|relative error]] than any smaller division, and a lower [[Tenney-Euclidean metrics#Logflat TE badness| TE loglfat badness]] than any lower edo excepting [[72edo|72]]. A basis for its 17-limit commas is {28561/28560, 31213/31212, 37180/37179, 918750/918731, 1257795/1257728, 3070625/3070548}.</pre></div>
| | === Prime harmonics === |
| <h4>Original HTML content:</h4>
| | {{Harmonics in equal|7033|columns=11}} |
| <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>7033edo</title></head><body>The 7033 equal division divides the octave into 7033 equal parts of 0.17062 cents each. It is a <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta EDO lists">zeta peak and integral edo</a>; it is not known at this time (2015) if it is a gap edo, but it seems unlikely. This excellence is explained by the fact that it is very strong in the 17-limit, with a lower <a class="wiki_link" href="/Tenney-Euclidean%20temperament%20measures#TE simple badness">relative error</a> than any smaller division, and a lower <a class="wiki_link" href="/Tenney-Euclidean%20metrics#Logflat TE badness"> TE loglfat badness</a> than any lower edo excepting <a class="wiki_link" href="/72edo">72</a>. A basis for its 17-limit commas is {28561/28560, 31213/31212, 37180/37179, 918750/918731, 1257795/1257728, 3070625/3070548}.</body></html></pre></div>
| | {{Harmonics in equal|7033|columns=11|start=12|collapsed=true|title=Approximation of prime harmonics in 7033edo (continued)}} |
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| | === Subsets and supersets === |
| | Since 7033 factors into primes as {{nowrap| 13 × 541 }}, 7033edo contains [[13edo]] and [[541edo]] as subsets. |