7033edo - Revision history

FloraC: Fix overwidth tables. Cleanup

2026-01-15T11:29:02Z

Fix overwidth tables. Cleanup

← Older revision		Revision as of 11:29, 15 January 2026
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	{{ED intro}}		{{ED intro}}

	7033edo is a [[~~The~~ Riemann zeta function and tuning #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 basis for its 17-limit ~~commas~~ is {[[28561/28560]], [[31213/31212]], [[37180/37179]], 918750/918731, 1257795/1257728, 3070625/3070548}. It also tempers out [[123201/123200]], [[194481/194480]], and [[336141/336140]], the three smallest 17-limit [[superparticular]]s.		7033edo is a [[the Riemann zeta function and tuning #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.

	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.		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.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|7033\|columns=12}}		{{Harmonics in equal\|7033\|columns=11}}
			{{Harmonics in equal\|7033\|columns=11\|start=12\|collapsed=true\|title=Approximation of prime harmonics in 7033edo (continued)}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 7033 factors into {{~~factorization~~\|~~7033~~}}, 7033edo contains [[13edo]] and [[541edo]] as subsets.		Since 7033 factors into primes as {{nowrap\| 13 × 541 }}, 7033edo contains [[13edo]] and [[541edo]] as subsets.

Francium: changed EDO intro to ED intro

2025-02-20T07:00:40Z

changed EDO intro to ED intro

← Older revision		Revision as of 07:00, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|7033~~}}		{{ED intro}}

	7033edo is a [[The Riemann zeta function and tuning #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 basis for its 17-limit commas is {[[28561/28560]], [[31213/31212]], [[37180/37179]], 918750/918731, 1257795/1257728, 3070625/3070548}. It also tempers out [[123201/123200]], [[194481/194480]], and [[336141/336140]], the three smallest 17-limit [[superparticular]]s.		7033edo is a [[The Riemann zeta function and tuning #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 basis for its 17-limit commas is {[[28561/28560]], [[31213/31212]], [[37180/37179]], 918750/918731, 1257795/1257728, 3070625/3070548}. It also tempers out [[123201/123200]], [[194481/194480]], and [[336141/336140]], the three smallest 17-limit [[superparticular]]s.

FloraC: Expand

2024-08-21T13:49:28Z

Expand

← Older revision		Revision as of 13:49, 21 August 2024
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	{{EDO intro\|7033}}		{{EDO intro\|7033}}

	7033edo is a [[The Riemann zeta function and tuning #Zeta EDO lists\|zeta peak and integral edo]], though not a gap edo. 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 temperament measures #TE simple badness\|TE logflat 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}.		7033edo is a [[The Riemann zeta function and tuning #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 basis for its 17-limit commas is {[[28561/28560]], [[31213/31212]], [[37180/37179]], 918750/918731, 1257795/1257728, 3070625/3070548}. It also tempers out [[123201/123200]], [[194481/194480]], and [[336141/336140]], the three smallest 17-limit [[superparticular]]s.

			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.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|7033}}		{{Harmonics in equal\|7033\|columns=12}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 7033 factors into {{factorization\|7033}}, 7033edo contains [[13edo]] and [[541edo]] as subsets.		Since 7033 factors into {{factorization\|7033}}, 7033edo contains [[13edo]] and [[541edo]] as subsets.

FloraC: +subsets and supersets

2024-08-20T16:52:05Z

+subsets and supersets

← Older revision		Revision as of 16:52, 20 August 2024
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	{{EDO intro\|7033}}		{{EDO intro\|7033}}

	It is a [[The Riemann zeta function and tuning #Zeta EDO lists\|zeta peak and integral edo]], though not a gap edo. 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 temperament measures #TE simple badness\|TE logflat 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}.		7033edo is a [[The Riemann zeta function and tuning #Zeta EDO lists\|zeta peak and integral edo]], though not a gap edo. 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 temperament measures #TE simple badness\|TE logflat 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}.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|7033}}		{{Harmonics in equal\|7033}}

			=== Subsets and supersets ===
			Since 7033 factors into {{factorization\|7033}}, 7033edo contains [[13edo]] and [[541edo]] as subsets.

BudjarnLambeth: Broke long paragraph into 2 smaller ones

2024-01-26T11:38:25Z

Broke long paragraph into 2 smaller ones

← Older revision		Revision as of 11:38, 26 January 2024
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	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|7033}} It is a [[The Riemann zeta function and tuning #Zeta EDO lists\|zeta peak and integral edo]], though not a gap edo. 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 temperament measures #TE simple badness\|TE logflat 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}.		{{EDO intro\|7033}}

			It is a [[The Riemann zeta function and tuning #Zeta EDO lists\|zeta peak and integral edo]], though not a gap edo. 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 temperament measures #TE simple badness\|TE logflat 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}.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|7033}}		{{Harmonics in equal\|7033}}

BudjarnLambeth at 07:09, 9 July 2023

2023-07-09T07:09:48Z

← Older revision		Revision as of 07:09, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|7033}} It is a [[The Riemann zeta function and tuning #Zeta EDO lists\|zeta peak and integral edo]], though not a gap edo. 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 temperament measures #TE simple badness\|TE logflat 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}.		{{EDO intro\|7033}} It is a [[The Riemann zeta function and tuning #Zeta EDO lists\|zeta peak and integral edo]], though not a gap edo. 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 temperament measures #TE simple badness\|TE logflat 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}.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|7033}}		{{Harmonics in equal\|7033}}

BudjarnLambeth at 04:20, 9 July 2023

2023-07-09T04:20:13Z

← Older revision		Revision as of 04:20, 9 July 2023
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	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	{{EDO intro\|7033}} It is a [[The Riemann zeta function and tuning #Zeta EDO lists\|zeta peak and integral edo]], though not a gap edo. 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 temperament measures #TE simple badness\|TE logflat 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}.		{{EDO intro\|7033}} It is a [[The Riemann zeta function and tuning #Zeta EDO lists\|zeta peak and integral edo]], though not a gap edo. 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 temperament measures #TE simple badness\|TE logflat 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}.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|7033}}		{{Harmonics in equal\|7033}}

FloraC: Template and findings of not being a gap edo

2023-02-10T11:24:24Z

Template and findings of not being a gap edo

← Older revision		Revision as of 11:24, 10 February 2023
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	{{Infobox ET}}		{{Infobox ET}}
	~~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}.		{{EDO intro\|7033}} It is a [[The Riemann zeta function and tuning #Zeta EDO lists\|zeta peak and integral edo]], though not a gap edo. 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 temperament measures #TE simple badness\|TE logflat 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}.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|7033}}		{{Harmonics in equal\|7033}}

FloraC: +prime error table

2023-02-10T11:20:56Z

+prime error table

← Older revision		Revision as of 11:20, 10 February 2023
Line 2:		Line 2:
	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}.		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}.

	~~[[Category:Equal divisions of the octave~~\|~~####]] <!-- 4-digit number -->~~		=== Prime harmonics ===
			{{Harmonics in equal\|7033}}

Plumtree: Infobox ET added

2022-10-04T22:20:16Z

Infobox ET added

← Older revision		Revision as of 22:20, 4 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	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}.		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}.

	[[Category:Equal divisions of the octave\|####]] <!-- 4-digit number -->		[[Category:Equal divisions of the octave\|####]] <!-- 4-digit number -->