6079edo - Revision history

FloraC: Expand the harmonics table a little

2025-10-02T16:06:16Z

Expand the harmonics table a little

← Older revision		Revision as of 16:06, 2 October 2025
Line 12:		Line 12:

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|6079\|columns=9}}		{{Harmonics in equal\|6079\|columns=11}}
	{{Harmonics in equal\|6079\|columns=9\|start=10\|collapsed=true\|title=Approximation of prime harmonics in 6079edo (continued)}}		{{Harmonics in equal\|6079\|columns=11\|start=12\|collapsed=true\|title=Approximation of prime harmonics in 6079edo (continued)}}

	=== Subsets and supersets ===		=== Subsets and supersets ===

Francium: /* Music */ +music

2025-05-19T11:15:06Z

Music: +music

← Older revision		Revision as of 11:15, 19 May 2025
Line 19:		Line 19:

	== Music ==		== 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]]		; [[Gene Ward Smith]]
	* [https://archive.org/details/ThrenodyForTheVictimsOfWolfgangAmadeusMozart ''Threnody for the Victims of Wolfgang Amadeus Mozart''] (archived 2010) – 13-limit JI in 6079edo tuning		* [https://archive.org/details/ThrenodyForTheVictimsOfWolfgangAmadeusMozart ''Threnody for the Victims of Wolfgang Amadeus Mozart''] (archived 2010) – 13-limit JI in 6079edo tuning

FloraC: Note nanisma

2025-03-16T15:48:41Z

Note nanisma

← Older revision		Revision as of 15:48, 16 March 2025
Line 5:		Line 5:
	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]].		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]] and [[~~starscape~~]] 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}.		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]].		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]].

FloraC: Extend the harmonics table to the 61-limit

2025-03-07T08:32:49Z

Extend the harmonics table to the 61-limit

← Older revision		Revision as of 08:32, 7 March 2025
Line 5:		Line 5:
	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]].		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]] and [[starscape]] system. 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}.		We may note it is a [[pirate]], [[euzenius]] and [[starscape]] 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]].		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]].
Line 12:		Line 12:

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|6079}}		{{Harmonics in equal\|6079\|columns=9}}
			{{Harmonics in equal\|6079\|columns=9\|start=10\|collapsed=true\|title=Approximation of prime harmonics in 6079edo (continued)}}

	=== Subsets and supersets ===		=== Subsets and supersets ===

ArrowHead294 at 15:40, 20 February 2025

2025-02-20T15:40:30Z

← Older revision		Revision as of 15:40, 20 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|6079~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: Expand

2025-01-12T10:12:14Z

Expand

← Older revision		Revision as of 10:12, 12 January 2025
Line 2:		Line 2:
	{{EDO intro\|6079}}		{{EDO intro\|6079}}

			== 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]].		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]] and [[starscape]] system. 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}.		We may note it is a [[pirate]], [[euzenius]] and [[starscape]] system. 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}.

	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 relative error until [[8269edo\|8269]].		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 ===		=== Prime harmonics ===

FloraC: +music

2024-12-01T14:52:41Z

+music

← Older revision		Revision as of 14:52, 1 December 2024
Line 13:		Line 13:
	=== Subsets and supersets ===		=== Subsets and supersets ===
	6079edo is the 793rd [[prime edo]].		6079edo is the 793rd [[prime edo]].

			== Music ==
			; [[Gene Ward Smith]]
			* [https://archive.org/details/ThrenodyForTheVictimsOfWolfgangAmadeusMozart ''Threnody for the Victims of Wolfgang Amadeus Mozart''] (archived 2010) – 13-limit JI in 6079edo tuning

FloraC: Expand

2024-08-21T12:19:24Z

Expand

← Older revision		Revision as of 12:19, 21 August 2024
Line 2:		Line 2:
	{{EDO intro\|6079}}		{{EDO intro\|6079}}

	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}.		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]] and [[starscape]] system. 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}.

			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 relative error until [[8269edo\|8269]].

	=== Prime harmonics ===		=== Prime harmonics ===

FloraC: Cleanup; +substs and supersets

2024-08-20T16:47:31Z

Cleanup; +substs and supersets

← Older revision		Revision as of 16:47, 20 August 2024
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|6079}} 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-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}.		{{EDO intro\|6079}}

			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}.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|6079}}		{{Harmonics in equal\|6079}}

			=== Subsets and supersets ===
			6079edo is the 793rd [[prime edo]].

BudjarnLambeth at 07:09, 9 July 2023

2023-07-09T07:09:16Z

← Older revision		Revision as of 07:09, 9 July 2023
Line 1:		Line 1:
	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|6079}} 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-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}.		{{EDO intro\|6079}} 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-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}.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|6079}}		{{Harmonics in equal\|6079}}