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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>2015-08-20 13:58:02 UTC</tt>.<br>
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| : The original revision id was <tt>557051617</tt>.<br>
| | == Theory == |
| : The revision comment was: <tt></tt><br>
| | 6079edo is a very strong [[11-limit|11-]] and [[13-limit]] system, with a lower 11- and 13-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] than any smaller division. It is also a [[zeta peak edo]] and distinctly [[consistent]] through the [[29-odd-limit]]. |
| 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>
| | We may note it is a [[pirate]], [[euzenius]], [[starscape]], and [[nanismic]] system. A basis for the 11-limit [[comma]]s is {3294225/3294172, 14348907/14348180, 35156250/35153041, 100663296/100656875}, and for the 13-limit commas, {[[123201/123200]], 1574640/1574573, 1664000/1663893, 1990656/1990625, 3294225/3294172}. |
| <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 6079 division divides the octave into 6079 equal parts of 0.1974 cents each. It is a very strong 11 and 13 limit system, with a lower 11 and 13 limit [[Tenney-Euclidean temperament measures#TE simple badness|relative error]] than any smaller division. It is also a [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta peak edo]] and distinctly consistent through the 29 limit. A basis for the 11-limit commas is {3294225/3294172, 14348907/14348180, 35156250/35153041, 100663296/100656875}, and for the 13-limit commas, {123201/123200, 1574640/1574573, 1664000/1663893, 1990656/1990625, 3294225/3294172}.</pre></div>
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| <h4>Original HTML content:</h4>
| | The approximation to [[harmonic]]s [[17/1|17]] and [[23/1|23]] is weaker, though still quite impressive. It [[tempering out|tempers out]] [[14400/14399]], [[28561/28560]], [[31213/31212]], [[37180/37179]], [[194481/194480]], [[336141/336140]] in the 17-limit; 10830/10829, 43681/43680, 89376/89375, 104976/104975, 165376/165375, 228096/228095 in the 19-limit; 12168/12167, 16929/16928, 19551/19550, 21736/21735, 25025/25024, 43264/43263 among others in the 23-limit. Its 2.3.5.7.11.13.19-subgroup is particularly strong, holding the record of lowest relative error until [[8269edo|8269]]. |
| <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>6079edo</title></head><body>The 6079 division divides the octave into 6079 equal parts of 0.1974 cents each. It is a very strong 11 and 13 limit system, with a lower 11 and 13 limit <a class="wiki_link" href="/Tenney-Euclidean%20temperament%20measures#TE simple badness">relative error</a> than any smaller division. It is also a <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta EDO lists">zeta peak edo</a> and distinctly consistent through the 29 limit. A basis for the 11-limit commas is {3294225/3294172, 14348907/14348180, 35156250/35153041, 100663296/100656875}, and for the 13-limit commas, {123201/123200, 1574640/1574573, 1664000/1663893, 1990656/1990625, 3294225/3294172}.</body></html></pre></div>
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| | Since it tempers out 12168/12167, it allows [[vicetertismic chords]] in the [[23-odd-limit]]. |
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| | === Prime harmonics === |
| | {{Harmonics in equal|6079|columns=11}} |
| | {{Harmonics in equal|6079|columns=11|start=12|collapsed=true|title=Approximation of prime harmonics in 6079edo (continued)}} |
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| | === Subsets and supersets === |
| | 6079edo is the 793rd [[prime edo]]. |
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| | == Music == |
| | ; [[Francium]] |
| | * "Make It Darker" from ''Void'' (2025) – [https://open.spotify.com/track/1rxglDtAvOEHHDx4HSjtSh Spotify] | [https://francium223.bandcamp.com/track/make-it-darker Bandcamp] | [https://www.youtube.com/watch?v=-L_KsVEK6kU YouTube] |
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| | ; [[Gene Ward Smith]] |
| | * [https://archive.org/details/ThrenodyForTheVictimsOfWolfgangAmadeusMozart ''Threnody for the Victims of Wolfgang Amadeus Mozart''] (archived 2010) – 13-limit JI in 6079edo tuning |