289edo - 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"

2026-03-13T13:32:16Z

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 13:32, 13 March 2026
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	\| [[Chlorine]]		\| [[Chlorine]]
	\|}		\|}
	<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:History (temperament)]]		[[Category:History (temperament)]]

Lériendil: renamed sextilififths to sextilifourths

2025-04-01T20:49:06Z

renamed sextilififths to sextilifourths

← Older revision		Revision as of 20:49, 1 April 2025
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	[[Category:Quincy]]		[[Category:Quincy]]
	[[Category:Quintaschis]]		[[Category:Quintaschis]]
	[[Category:~~Sextilififths~~]]		[[Category:Sextilifourths]]

Lériendil at 20:46, 1 April 2025

2025-04-01T20:46:53Z

← Older revision		Revision as of 20:46, 1 April 2025
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	289edo is a strong 5-limit system with decent [[11-limit\|11-]] and [[13-limit]] interpretations despite in[[consistency]] in the [[13-odd-limit]]. As an equal temperament, it [[tempering out\|tempers out]] the [[schisma]], 32805/32768 in the [[5-limit]]; [[4375/4374]] and [[65625/65536]] in the [[7-limit]]; [[441/440]] and [[4000/3993]] in the 11-limit; and [[364/363]], [[676/675]], [[1001/1000]], [[1575/1573]] and [[2080/2079]] in the 13-limit.		289edo is a strong 5-limit system with decent [[11-limit\|11-]] and [[13-limit]] interpretations despite in[[consistency]] in the [[13-odd-limit]]. As an equal temperament, it [[tempering out\|tempers out]] the [[schisma]], 32805/32768 in the [[5-limit]]; [[4375/4374]] and [[65625/65536]] in the [[7-limit]]; [[441/440]] and [[4000/3993]] in the 11-limit; and [[364/363]], [[676/675]], [[1001/1000]], [[1575/1573]] and [[2080/2079]] in the 13-limit.

	It is the [[optimal patent val]] for the [[13-limit]] rank-5 temperament tempering out 364/363, and the 13-limit [[history (temperament)\|history]] temperament, which tempers out 364/363, 441/440 and 676/675. It provides a good tuning for the 11-limit version also. It is also the optimal patent val for [[~~sextilififths~~]], [[quintaschis]], and [[quincy]] in both the 11- and 13-limit.		It is the [[optimal patent val]] for the [[13-limit]] rank-5 temperament tempering out 364/363, and the 13-limit [[history (temperament)\|history]] temperament, which tempers out 364/363, 441/440 and 676/675. It provides a good tuning for the 11-limit version also. It is also the optimal patent val for [[sextilifourths]], [[quintaschis]], and [[quincy]] in both the 11- and 13-limit.

	=== Prime harmonics ===		=== Prime harmonics ===
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	\| 83.04		\| 83.04
	\| 21/20		\| 21/20
	\| [[~~Sextilififths~~]]		\| [[Sextilifourths]]
	\|-		\|-
	\| 1		\| 1

ArrowHead294 at 14:29, 20 February 2025

2025-02-20T14:29:08Z

← Older revision		Revision as of 14:29, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|289~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: /* Theory */ cleanup

2025-01-17T15:46:55Z

Theory: cleanup

← Older revision		Revision as of 15:46, 17 January 2025
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	== Theory ==		== Theory ==
	289edo is a strong 5-limit system with decent 11- and 13-limit interpretations despite in[[consistency]] in the [[13-odd-limit]]. It [[tempers out]] the [[schisma]], 32805/32768 in the 5-limit; [[4375/4374]] and [[65625/65536]] in the 7-limit; [[441/440]] and [[4000/3993]] in the 11-limit; and [[364/363]], [[676/675]], [[1001/1000]], [[1575/1573]] and [[2080/2079]] in the 13-limit.		289edo is a strong 5-limit system with decent [[11-limit\|11-]] and [[13-limit]] interpretations despite in[[consistency]] in the [[13-odd-limit]]. As an equal temperament, it [[tempering out\|tempers out]] the [[schisma]], 32805/32768 in the [[5-limit]]; [[4375/4374]] and [[65625/65536]] in the [[7-limit]]; [[441/440]] and [[4000/3993]] in the 11-limit; and [[364/363]], [[676/675]], [[1001/1000]], [[1575/1573]] and [[2080/2079]] in the 13-limit.

	It is the [[optimal patent val]] for the [[13-limit]] rank-5 temperament tempering out 364/363, and the 13-limit [[~~History~~ (temperament)\|history]] temperament, which tempers out 364/363, 441/440 and 676/675. It provides a good tuning for the 11-limit version also. It is also the optimal patent val for [[sextilififths]], [[quintaschis]], and [[quincy]] in both the 11- and 13-limit.		It is the [[optimal patent val]] for the [[13-limit]] rank-5 temperament tempering out 364/363, and the 13-limit [[history (temperament)\|history]] temperament, which tempers out 364/363, 441/440 and 676/675. It provides a good tuning for the 11-limit version also. It is also the optimal patent val for [[sextilififths]], [[quintaschis]], and [[quincy]] in both the 11- and 13-limit.

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

ArrowHead294 at 19:28, 15 January 2025

2025-01-15T19:28:51Z

← Older revision		Revision as of 19:28, 15 January 2025
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	== Theory ==		== Theory ==
	289edo is a strong 5-limit system with decent 11- and 13-limit interpretations despite in[[consistency]] in the [[13-odd-limit]]. ~~The equal temperament~~ [[~~tempering out\|~~tempers out]] the [[schisma]], 32805/32768 in the 5-limit; [[4375/4374]] and [[65625/65536]] in the 7-limit; [[441/440]] and [[4000/3993]] in the 11-limit; and [[364/363]], [[676/675]], [[1001/1000]], [[1575/1573]] and [[2080/2079]] in the 13-limit.		289edo is a strong 5-limit system with decent 11- and 13-limit interpretations despite in[[consistency]] in the [[13-odd-limit]]. It [[tempers out]] the [[schisma]], 32805/32768 in the 5-limit; [[4375/4374]] and [[65625/65536]] in the 7-limit; [[441/440]] and [[4000/3993]] in the 11-limit; and [[364/363]], [[676/675]], [[1001/1000]], [[1575/1573]] and [[2080/2079]] in the 13-limit.

	It is the [[optimal patent val]] for the [[13-limit]] rank-5 temperament tempering out 364/363, and the 13-limit [[History (temperament)\|history]] temperament, which tempers out 364/363, 441/440 and 676/675. It provides a good tuning for the 11-limit version also. It is also the optimal patent val for [[sextilififths]], [[quintaschis]], and [[quincy]] in both the 11- and 13-limit.		It is the [[optimal patent val]] for the [[13-limit]] rank-5 temperament tempering out 364/363, and the 13-limit [[History (temperament)\|history]] temperament, which tempers out 364/363, 441/440 and 676/675. It provides a good tuning for the 11-limit version also. It is also the optimal patent val for [[sextilififths]], [[quintaschis]], and [[quincy]] in both the 11- and 13-limit.
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	\| [[Chlorine]]		\| [[Chlorine]]
	\|}		\|}
	<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:History (temperament)]]		[[Category:History (temperament)]]

ArrowHead294: Partial undo

2024-11-16T12:28:10Z

Partial undo

← Older revision		Revision as of 12:28, 16 November 2024
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	== Regular temperament properties ==		== Regular temperament properties ==
	{~~{comma basis begin}}~~		{\| class="wikitable center-4 center-5 center-6"
			\|-
			! rowspan="2" \| [[Subgroup]]
			! rowspan="2" \| [[Comma list]]
			! rowspan="2" \| [[Mapping]]
			! rowspan="2" \| Optimal<br />8ve stretch (¢)
			! colspan="2" \| Tuning error
			\|-
			! [[TE error\|Absolute]] (¢)
			! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\| 2.3		\| 2.3
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	\| 0.2657		\| 0.2657
	\| 6.40		\| 6.40
	~~{{comma basis end}~~}		\|}
	* 289et has a lower absolute error in the 5-limit than any previous equal temperaments, past [[171edo\|171]] and followed by [[323edo\|323]].		* 289et has a lower absolute error in the 5-limit than any previous equal temperaments, past [[171edo\|171]] and followed by [[323edo\|323]].

	=== 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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	\| {{monzo\| -23 5 9 -2 }}<br />(100352/98415)		\| {{monzo\| -23 5 9 -2 }}<br />(100352/98415)
	\| [[Chlorine]]		\| [[Chlorine]]
	~~{{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:History (temperament)]]		[[Category:History (temperament)]]

ArrowHead294 at 04:37, 16 November 2024

2024-11-16T04:37:37Z

← Older revision		Revision as of 04:37, 16 November 2024
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	== Regular temperament properties ==		== Regular temperament properties ==
	{~~\| class="wikitable center-4 center-5 center-6"~~		{{comma basis begin}}
	~~! rowspan="2" \| [[Subgroup]]~~
	~~! rowspan="2" \| [[Comma list\|Comma List]]~~
	~~! rowspan="2" \| [[Mapping]]~~
	~~! rowspan="2" \| Optimal<br>8ve Stretch (¢)~~
	~~! colspan="2" \| Tuning Error~~
	\|-
	~~! [[TE error\|Absolute]] (¢)~~
	~~! [[TE simple badness\|Relative]] (%)~~
	\|-		\|-
	\| 2.3		\| 2.3
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	\| 0.2657		\| 0.2657
	\| 6.40		\| 6.40
	\|}		{{comma basis end}}
	* 289et has a lower absolute error in the 5-limit than any previous equal temperaments, past [[171edo\|171]] and followed by [[323edo\|323]].		* 289et has a lower absolute error in the 5-limit than any previous equal temperaments, past [[171edo\|171]] and followed by [[323edo\|323]].

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{~~\| class="wikitable center~~-~~all left-5"~~		{{rank-2 begin}}
	~~! Periods<br>per 8ve~~
	! Generator*
	! Cents*
	! Associated<br>Ratio*
	~~! Temperaments~~
	\|-		\|-
	\| 1		\| 1
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	\|-		\|-
	\| 17		\| 17
	\| 93\289<br>(8\289)		\| 93\289<br />(8\289)
	\| 386.16<br>(33.22)		\| 386.16<br />(33.22)
	\| {{monzo\| -23 5 9 -2 }}<br>(100352/98415)		\| {{monzo\| -23 5 9 -2 }}<br />(100352/98415)
	\| [[Chlorine]]		\| [[Chlorine]]
	\|}		{{rank-2 end}}
	~~<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:History (temperament)]]
	[[Category:Minor minthmic]]		[[Category:Minor minthmic]]
	[[Category:~~History (temperament)~~]]		[[Category:Quincy]]
			[[Category:Quintaschis]]
	[[Category:Sextilififths]]		[[Category:Sextilififths]]
	~~[[Category:Quintaschis]]~~
	~~[[Category:Quincy]]~~

FloraC: 5-limit

2024-04-23T08:36:36Z

5-limit

← Older revision		Revision as of 08:36, 23 April 2024
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	== Theory ==		== Theory ==
	289edo ~~has~~ decent 11- and 13-limit interpretations despite ~~not being~~ [[~~consistent~~]]. The equal temperament [[tempering out\|tempers out]] the [[schisma]], 32805/32768 in the 5-limit; [[4375/4374]] and [[65625/65536]] in the 7-limit; [[441/440]] and [[4000/3993]] in the 11-limit; and [[364/363]], [[676/675]], [[1001/1000]], [[1575/1573]] and [[2080/2079]] in the 13-limit.		289edo is a strong 5-limit system with decent 11- and 13-limit interpretations despite in[[consistency]] in the [[13-odd-limit]]. The equal temperament [[tempering out\|tempers out]] the [[schisma]], 32805/32768 in the 5-limit; [[4375/4374]] and [[65625/65536]] in the 7-limit; [[441/440]] and [[4000/3993]] in the 11-limit; and [[364/363]], [[676/675]], [[1001/1000]], [[1575/1573]] and [[2080/2079]] in the 13-limit.

	It is the [[optimal patent val]] for the [[13-limit]] rank-5 temperament tempering out 364/363, and the 13-limit [[History (temperament)\|history]] temperament, which tempers out 364/363, 441/440 and 676/675. It provides a good tuning for the 11-limit version also. It is also the optimal patent val for [[sextilififths]], [[quintaschis]], and [[quincy]] in both the 11- and 13-limit.		It is the [[optimal patent val]] for the [[13-limit]] rank-5 temperament tempering out 364/363, and the 13-limit [[History (temperament)\|history]] temperament, which tempers out 364/363, 441/440 and 676/675. It provides a good tuning for the 11-limit version also. It is also the optimal patent val for [[sextilififths]], [[quintaschis]], and [[quincy]] in both the 11- and 13-limit.
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	\| 6.40		\| 6.40
	\|}		\|}
			* 289et has a lower absolute error in the 5-limit than any previous equal temperaments, past [[171edo\|171]] and followed by [[323edo\|323]].

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===

FloraC: OPV for quincy

2024-04-10T04:02:16Z

OPV for quincy

← Older revision		Revision as of 04:02, 10 April 2024
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	289edo has decent 11- and 13-limit interpretations despite not being [[consistent]]. The equal temperament [[tempering out\|tempers out]] the [[schisma]], 32805/32768 in the 5-limit; [[4375/4374]] and [[65625/65536]] in the 7-limit; [[441/440]] and [[4000/3993]] in the 11-limit; and [[364/363]], [[676/675]], [[1001/1000]], [[1575/1573]] and [[2080/2079]] in the 13-limit.		289edo has decent 11- and 13-limit interpretations despite not being [[consistent]]. The equal temperament [[tempering out\|tempers out]] the [[schisma]], 32805/32768 in the 5-limit; [[4375/4374]] and [[65625/65536]] in the 7-limit; [[441/440]] and [[4000/3993]] in the 11-limit; and [[364/363]], [[676/675]], [[1001/1000]], [[1575/1573]] and [[2080/2079]] in the 13-limit.

	It is the [[optimal patent val]] for the [[13-limit]] rank-5 temperament tempering out 364/363, and the 13-limit [[History (temperament)\|history]] temperament, which tempers out 364/363, 441/440 and 676/675. It provides a good tuning for the 11-limit version also. It is also the optimal patent val for [[sextilififths]] ~~in both the 11- and 13-limit~~, and ~~for~~ [[~~quintaschis~~]] in both the 11- and 13-limit.		It is the [[optimal patent val]] for the [[13-limit]] rank-5 temperament tempering out 364/363, and the 13-limit [[History (temperament)\|history]] temperament, which tempers out 364/363, 441/440 and 676/675. It provides a good tuning for the 11-limit version also. It is also the optimal patent val for [[sextilififths]], [[quintaschis]], and [[quincy]] in both the 11- and 13-limit.

	=== Prime harmonics ===		=== Prime harmonics ===
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	[[Category:Sextilififths]]		[[Category:Sextilififths]]
	[[Category:Quintaschis]]		[[Category:Quintaschis]]
			[[Category:Quincy]]