6079edo: Difference between revisions

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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]]. 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}.

== Theory ==

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]].

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}.

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]].

Since it tempers out 12168/12167, it allows [[vicetertismic chords]] in the [[23-odd-limit]].

=== Prime harmonics ===

{{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

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|6079}}
+{{ED intro}}
-edo 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]]. 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}.
+== Theory ==
+edo 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]].
+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}.
+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]].
+Since it tempers out 12168/12167, it allows [[vicetertismic chords]] in the [[23-odd-limit]].
 === Prime harmonics ===
-{{Harmonics in equal|6079}}
+{{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 ===
 edo 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