Xenharmonic Wiki

6079edo: Difference between revisions

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**Imported revision 557051075 - Original comment: **
 
m Expand the harmonics table a little
 
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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 13:50:51 UTC</tt>.<br>
 
: The original revision id was <tt>557051075</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>
 
<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.</pre></div>
 
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;6079edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;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 &lt;a class="wiki_link" href="/Tenney-Euclidean%20temperament%20measures#TE simple badness"&gt;relative error&lt;/a&gt; than any smaller division. It is also a &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta EDO lists"&gt;zeta peak edo&lt;/a&gt; and distinctly consistent through the 29 limit.&lt;/body&gt;&lt;/html&gt;</pre></div>
 
Since it tempers out 12168/12167, it allows [[vicetertismic chords]] in the [[23-odd-limit]].
 
=== 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)}}
 
=== Subsets and supersets ===
6079edo is the 793rd [[prime edo]].
 
== 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]
 
; [[Gene Ward Smith]]
* [https://archive.org/details/ThrenodyForTheVictimsOfWolfgangAmadeusMozart ''Threnody for the Victims of Wolfgang Amadeus Mozart''] (archived 2010) – 13-limit JI in 6079edo tuning
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