3395edo - Revision history

FloraC: Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

2026-03-13T13:31:31Z

Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

← Older revision		Revision as of 13:31, 13 March 2026
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	\| [[Berkelium]]		\| [[Berkelium]]
	\|}		\|}
	<nowiki />* [[Normal ~~lists~~\|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal lists~~\|minimal form]] in parentheses if distinct		<nowiki />* [[Normal forms #Equave-reduced-generator form\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form\|minimal form]] in parentheses if distinct

	[[Category:Jacobin]]		[[Category:Jacobin]]
	[[Category:Quartismic]]		[[Category:Quartismic]]

ArrowHead294 at 13:00, 10 April 2025

2025-04-10T13:00:19Z

← Older revision		Revision as of 13:00, 10 April 2025
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	== Theory ==		== Theory ==
	3395edo is an extremely strong 17- and 19-limit system, and a [[The Riemann ~~Zeta~~ function and tuning #Zeta EDO lists\|zeta peak, integral, and gap edo]]. It has a lower 17-limit [[TE relative error]] than any edo until [[7033edo\|7033]], and a lower 19-limit relative error than any edo until [[8269edo\|8269]]. Besides, it provides the [[optimal patent val]] for the 13-limit rank-5 temperament tempering out [[6656/6655]], the jacobin comma, and for [[quartismic]], which also tempers out [[123201/123200]]. A basis for the 17-limit commas is {6656/6655, 12376/12375, 28561/28560, 31213/31212, 37180/37179, 937125/937024}, and for the 19-limit, {6656/6655, 12376/12375, 12636/12635, 13377/13376, 14365/14364, 23409/23408, 28561/28560}.		3395edo is an extremely strong 17- and 19-limit system, and a [[The Riemann zeta function and tuning #Zeta EDO lists\|zeta peak, integral, and gap edo]]. It has a lower 17-limit [[TE relative error]] than any edo until [[7033edo\|7033]], and a lower 19-limit relative error than any edo until [[8269edo\|8269]]. Besides, it provides the [[optimal patent val]] for the 13-limit rank-5 temperament tempering out [[6656/6655]], the jacobin comma, and for [[quartismic]], which also tempers out [[123201/123200]]. A basis for the 17-limit commas is {6656/6655, 12376/12375, 28561/28560, 31213/31212, 37180/37179, 937125/937024}, and for the 19-limit, {6656/6655, 12376/12375, 12636/12635, 13377/13376, 14365/14364, 23409/23408, 28561/28560}.

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

ArrowHead294 at 14:42, 20 February 2025

2025-02-20T14:42:52Z

← Older revision		Revision as of 14:42, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|3395~~}}		{{ED intro}}

	== Theory ==		== Theory ==
	3395edo is an extremely strong 17- and 19-limit system, and a [[The Riemann Zeta function and tuning #Zeta EDO lists\|zeta peak, integral and gap edo]]. It has a lower 17-limit [[TE relative error]] than any edo until [[7033edo\|7033]], and a lower 19-limit relative error than any edo until [[8269edo\|8269]]. Besides, it provides the [[optimal patent val]] for the 13-limit rank-5 temperament tempering out [[6656/6655]], the jacobin comma, and for [[quartismic]], which also tempers out [[123201/123200]]. A basis for the 17-limit commas is {6656/6655, 12376/12375, 28561/28560, 31213/31212, 37180/37179, 937125/937024}, and for the 19-limit, {6656/6655, 12376/12375, 12636/12635, 13377/13376, 14365/14364, 23409/23408, 28561/28560}.		3395edo is an extremely strong 17- and 19-limit system, and a [[The Riemann Zeta function and tuning #Zeta EDO lists\|zeta peak, integral, and gap edo]]. It has a lower 17-limit [[TE relative error]] than any edo until [[7033edo\|7033]], and a lower 19-limit relative error than any edo until [[8269edo\|8269]]. Besides, it provides the [[optimal patent val]] for the 13-limit rank-5 temperament tempering out [[6656/6655]], the jacobin comma, and for [[quartismic]], which also tempers out [[123201/123200]]. A basis for the 17-limit commas is {6656/6655, 12376/12375, 28561/28560, 31213/31212, 37180/37179, 937125/937024}, and for the 19-limit, {6656/6655, 12376/12375, 12636/12635, 13377/13376, 14365/14364, 23409/23408, 28561/28560}.

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

ArrowHead294 at 16:58, 15 January 2025

2025-01-15T16:58:03Z

← Older revision		Revision as of 16:58, 15 January 2025
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	\| [[Berkelium]]		\| [[Berkelium]]
	\|}		\|}
	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if ~~it is~~ distinct		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

	[[Category:Jacobin]]		[[Category:Jacobin]]
	[[Category:Quartismic]]		[[Category:Quartismic]]

ArrowHead294: Partial undo

2024-11-16T13:15:10Z

Partial undo

← Older revision		Revision as of 13:15, 16 November 2024
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	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{{rank-2 ~~begin}}~~		{\| class="wikitable center-all left-5"
			\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
			\|-
			! Periods<br />per 8ve
			! Generator*
			! Cents*
			! Associated<br />ratio*
			! Temperaments
	\|-		\|-
	\| 1		\| 1
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	\| 4/3<br />(?)		\| 4/3<br />(?)
	\| [[Berkelium]]		\| [[Berkelium]]
	~~{{rank-2 end}~~}		\|}
	~~{{orf}}~~		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

	[[Category:Jacobin]]		[[Category:Jacobin]]
	[[Category:Quartismic]]		[[Category:Quartismic]]

ArrowHead294 at 01:48, 16 November 2024

2024-11-16T01:48:36Z

← Older revision		Revision as of 01:48, 16 November 2024
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	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{~~\| class="wikitable center-all left-5"~~		{{rank-2 begin}}
	~~\|+ style="font-size: 105%;" \| Table of~~ rank-2 ~~temperaments by generator~~
	\|-
	~~! Periods<br />per 8ve~~
	! Generator*
	! Cents*
	~~! Associated<br />Ratio~~
	~~! Temperament~~
	\|-		\|-
	\| 1		\| 1
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	\| 4/3<br />(?)		\| 4/3<br />(?)
	\| [[Berkelium]]		\| [[Berkelium]]
	\|}		{{rank-2 end}}
	{{orf}}		{{orf}}

	[[Category:Jacobin]]		[[Category:Jacobin]]
	[[Category:Quartismic]]		[[Category:Quartismic]]

ArrowHead294 at 01:10, 16 November 2024

2024-11-16T01:10:15Z

← Older revision		Revision as of 01:10, 16 November 2024
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	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
	! Periods<br>per 8ve		\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
			\|-
			! Periods<br />per 8ve
	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br>Ratio		! Associated<br />Ratio
	! Temperament		! Temperament
	\|-		\|-
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	\|-		\|-
	\| 35		\| 35
	\| 1409\3395<br>(51\3395)		\| 1409\3395<br />(51\3395)
	\| 498.027<br>(18.026)		\| 498.027<br />(18.026)
	\| 4/3<br>(?)		\| 4/3<br />(?)
	\| [[Bromine]]		\| [[Bromine]]
	\|-		\|-
	\| 97		\| 97
	\| 1409\3395<br>(9\3395)		\| 1409\3395<br />(9\3395)
	\| 498.027<br>(3.181)		\| 498.027<br />(3.181)
	\| 4/3<br>(?)		\| 4/3<br />(?)
	\| [[Berkelium]]		\| [[Berkelium]]
	\|}		\|}
	~~<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct~~		{{orf}}

	[[Category:Jacobin]]		[[Category:Jacobin]]
	[[Category:Quartismic]]		[[Category:Quartismic]]

Eliora: /* Regular temperament properties */ update name

2023-12-16T23:58:04Z

Regular temperament properties: update name

← Older revision		Revision as of 23:58, 16 December 2023
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	\| 819.676		\| 819.676
	\| 55115776/34328125		\| 55115776/34328125
	\| [[~~Gene's jacobin~~]]		\| [[Genojacobin]]
	\|-		\|-
	\| 35		\| 35

FloraC: Adopt template: Factorization

2023-10-30T09:51:03Z

Adopt template: Factorization

← Older revision		Revision as of 09:51, 30 October 2023
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	3395 ~~= 5 × 7 × 97~~, ~~with~~ subset edos 5, 7, 35, 97, 485, and 679.		Since 3395 factors into {{factorization\|3395}}, 3395edo has subset edos 5, 7, 35, 97, 485, and 679.

	== Regular temperament properties ==		== Regular temperament properties ==

FloraC: Section title; clarify the title row of the rank-2 temp table

2023-10-15T11:29:36Z

Section title; clarify the title row of the rank-2 temp table

← Older revision		Revision as of 11:29, 15 October 2023
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	{{Harmonics in equal\|3395\|columns=11}}		{{Harmonics in equal\|3395\|columns=11}}

	=== ~~Divisors~~ ===		=== Subsets and supersets ===
	3395 = 5 × 7 × 97, with subset edos 5, 7, 35, 97, 485, and 679.		3395 = 5 × 7 × 97, with subset edos 5, 7, 35, 97, 485, and 679.

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	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
	! Periods<br>per 8ve		! Periods<br>per 8ve
	! Generator~~<br>(Reduced)~~		! Generator*
	! Cents~~<br>(Reduced)~~		! Cents*
	! Associated<br>Ratio		! Associated<br>Ratio
	! Temperament		! Temperament
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	\| [[Berkelium]]		\| [[Berkelium]]
	\|}		\|}
			<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

	[[Category:Jacobin]]		[[Category:Jacobin]]
	[[Category:Quartismic]]		[[Category:Quartismic]]