130edo - Revision history

FloraC: /* Theory */ - OPSL (XW:NG). Misc. cleanup

2026-07-06T08:47:16Z

Theory: - OPSL (XW:NG). Misc. cleanup

← Older revision		Revision as of 08:47, 6 July 2026
Line 3:		Line 3:

	== Theory ==		== Theory ==
	130edo ~~is a [[zeta peak edo]], a [[zeta peak integer edo]], and a [[zeta integral edo]] but not a gap edo. It~~ is [[distinctly consistent]] to the [[15-odd~~-limit]] and is the first [[trivial temperament\|nontrivial edo]] to be consistent in the 14-[[odd prime sum limit\|odd-prime-sum~~-limit]]. It is also almost consistent in the no-29 [[31-odd-limit]], missing [[19/11]] (50.5%), [[25/19]] (52.9%), [[17/11]] (64,4%), [[25/17]] (66.8%), and [[octave complement]]~~<nowiki/>~~s.		130edo is [[distinctly consistent]] to the [[15-odd-limit]]. It is also almost consistent in the no-29 [[31-odd-limit]], missing [[19/11]] (50.5%), [[25/19]] (52.9%), [[17/11]] (64,4%), [[25/17]] (66.8%), and [[octave complement]]s. It is a [[zeta peak edo]], a [[zeta peak integer edo]], and a [[zeta integral edo]] but not a [[zeta gap edo]].

	As an equal temperament, it [[tempering out\|tempers out]] [[2401/2400]], [[3136/3125]], [[6144/6125]], and [[19683/19600]] in the 7-limit; [[243/242]], [[441/440]], [[540/539]], and [[4000/3993]] in the 11-limit; and [[351/350]], [[364/363]], [[676/675]], [[729/728]], [[1001/1000]], [[1575/1573]], [[1716/1715]], [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit. It can be used to tune a variety of temperaments, including [[hemiwürschmidt]], [[sesquiquartififths]], [[harry]] and [[hemischis]]. It also can be used to tune the [[rank-3 temperament]] [[jove]], tempering out 243/242 and 441/440, plus 364/363 for the 13-limit and [[595/594]] for the 17-limit. It gives the [[optimal patent val]] for 11-limit [[hemiwürschmidt]] and [[~~Schismatic family #Sesquiquartififths\|~~sesquart]] and 13-limit [[harry]].		As an equal temperament, it [[tempering out\|tempers out]] [[2401/2400]], [[3136/3125]], [[6144/6125]], and [[19683/19600]] in the [[7-limit]]; [[243/242]], [[441/440]], [[540/539]], and [[4000/3993]] in the [[11-limit]]; and [[351/350]], [[364/363]], [[676/675]], [[729/728]], [[1001/1000]], [[1575/1573]], [[1716/1715]], [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the [[13-limit]]. It can be used to tune a variety of temperaments, including [[hemiwürschmidt]], [[sesquiquartififths]], [[harry]] and [[hemischis]]. It also can be used to tune the [[rank-3 temperament]] [[jove]], tempering out 243/242 and 441/440, plus 364/363 for the 13-limit and [[595/594]] for the 17-limit. It gives the [[optimal patent val]] for 11-limit [[hemiwürschmidt]] and [[sesquart]] and 13-limit [[harry]].

	=== Prime harmonics ===		=== Prime harmonics ===
Line 12:		Line 12:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 130 factors into 2 × 5 × 13, 130edo has subset edos {{EDOs\| 2, 5, 10, 13, 26, and 65 }}.		Since 130 factors into primes as {{nowrap\| 2 × 5 × 13 }}, 130edo has subset edos {{EDOs\| 2, 5, 10, 13, 26, and 65 }}.

	[[260edo]], which divides the edostep in two, provides a strong correction for the 29th harmonic.		[[260edo]], which divides the edostep in two, provides a strong correction for the 29th harmonic.

FloraC: - zeta table. + 23-odd-limit interval table. Restore prime harmonics table to 11 columns.

2026-07-06T08:43:56Z

- zeta table. + 23-odd-limit interval table. Restore prime harmonics table to 11 columns.

← Older revision		Revision as of 08:43, 6 July 2026
Line 8:		Line 8:

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|130\|columns=9}}		{{Harmonics in equal\|130\|columns=11}}
	{{Harmonics in equal\|130\|columns=9\|start=10\|collapsed=true\|title=Approximation of prime harmonics in 130edo (continued)}}		{{Harmonics in equal\|130\|columns=11\|start=12\|collapsed=true\|title=Approximation of prime harmonics in 130edo (continued)}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
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	== Approximation to JI ==		== Approximation to JI ==
	~~=== Zeta peak index ===~~		{{Q-odd-limit intervals\|130\|23}}
	{{~~ZPI~~
	\| ~~zpi = 796~~
	~~\| steps =~~ 130~~.003910460506~~
	~~\| step size = 9.23049157328654~~
	~~\| tempered height = 10.355108~~
	~~\| pure height = 10.339572~~
	~~\| integral = 1.634018~~
	~~\| gap = 19.594551~~
	~~\| octave = 1199.96390452725~~
	~~\| consistent = 16~~
	\| ~~distinct = 16~~
	}}

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

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"

2026-03-13T13:32:08Z

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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	\| [[Bosonic]]		\| [[Bosonic]]
	\|}		\|}
	<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

	== Scales ==		== Scales ==

Eufalesio: Standardize format Sagittal

2026-03-07T12:02:56Z

Standardize format Sagittal

← Older revision		Revision as of 12:02, 7 March 2026
Line 299:		Line 299:
	130edo can be notated in [[Sagittal notation\|Sagittal]] using the [[Sagittal notation#Spartan single-shaft\|Spartan extension]], with the apotome equal to 12 edosteps and the limma to 10 edosteps. Since the the [[243/242\|rastma]] is tempered out, a SZ half-sharp and a half-flat may be used instead of pakai/pakao. Here is a simplified table:		130edo can be notated in [[Sagittal notation\|Sagittal]] using the [[Sagittal notation#Spartan single-shaft\|Spartan extension]], with the apotome equal to 12 edosteps and the limma to 10 edosteps. Since the the [[243/242\|rastma]] is tempered out, a SZ half-sharp and a half-flat may be used instead of pakai/pakao. Here is a simplified table:
	{\| class="wikitable" data-darkreader-inline-color="" style="text-align: center;"		{\| class="wikitable" data-darkreader-inline-color="" style="text-align: center;"
	!~~Degree~~		! colspan="2" \|Steps
	\|0		!0
	~~\| +~~1		! 1
	~~\| +~~2		! 2
	~~\| +~~3		! 3
	~~\| +~~4		! 4
	~~\| +~~5		! 5
	~~\| +~~6		! 6
	~~\| +~~7		! 7
	~~\| +~~8		! 8
	~~\| +~~9		! 9
	~~\| +~~10		! 10
	~~\| +~~11		! 11
	~~\| +~~12		! 12
	\|-		\|-
			! rowspan="3" \|Symbol
	!Evo+SZ		!Evo+SZ
	\| rowspan="3" \|<big>{{sagittal\|\|//\|}}</big>		\| rowspan="3" \|<big>{{sagittal\|\|//\|}}</big>

Eufalesio: Little thning

2026-03-07T11:57:29Z

Little thning

← Older revision		Revision as of 11:57, 7 March 2026
Line 346:		Line 346:
	\|}		\|}

	*		Because it uses the entire Spartan extension, it allows no accidental enharmonic respellings.

	~~See [[Sagittal notation#Revo\|apotome complements]] for equivalent~~ accidental ~~pairs~~.

	== Approximation to JI ==		== Approximation to JI ==

Eufalesio: Wrong downwards sagittal

2026-03-07T11:33:16Z

Wrong downwards sagittal

← Older revision		Revision as of 11:33, 7 March 2026
Line 3:		Line 3:

	== Theory ==		== Theory ==
	130edo is a [[zeta peak edo]], a [[zeta peak integer edo]], and a [[zeta integral edo]] but not a gap edo. It is [[distinctly consistent]] to the [[15-odd-limit]] and is the first [[trivial temperament\|nontrivial edo]] to be consistent in the 14-[[odd prime sum limit\|odd-prime-sum-limit]]. It is also almost consistent in the no-29 [[31-odd-limit]], missing [[19/11]] (50.5%), [[25/19]] (52.9%), [[17/11]] (64,4%), [[25/17]] (66.8%), and [[octave complement]]<nowiki/>s.		130edo is a [[zeta peak edo]], a [[zeta peak integer edo]], and a [[zeta integral edo]] but not a gap edo. It is [[distinctly consistent]] to the [[15-odd-limit]] and is the first [[trivial temperament\|nontrivial edo]] to be consistent in the 14-[[odd prime sum limit\|odd-prime-sum-limit]]. It is also almost consistent in the no-29 [[31-odd-limit]], missing [[19/11]] (50.5%), [[25/19]] (52.9%), [[17/11]] (64,4%), [[25/17]] (66.8%), and [[octave complement]]<nowiki/>s.

	As an equal temperament, it [[tempering out\|tempers out]] [[2401/2400]], [[3136/3125]], [[6144/6125]], and [[19683/19600]] in the 7-limit; [[243/242]], [[441/440]], [[540/539]], and [[4000/3993]] in the 11-limit; and [[351/350]], [[364/363]], [[676/675]], [[729/728]], [[1001/1000]], [[1575/1573]], [[1716/1715]], [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit. It can be used to tune a variety of temperaments, including [[hemiwürschmidt]], [[sesquiquartififths]], [[harry]] and [[hemischis]]. It also can be used to tune the [[rank-3 temperament]] [[jove]], tempering out 243/242 and 441/440, plus 364/363 for the 13-limit and [[595/594]] for the 17-limit. It gives the [[optimal patent val]] for 11-limit [[hemiwürschmidt]] and [[Schismatic family #Sesquiquartififths\|sesquart]] and 13-limit [[harry]].		As an equal temperament, it [[tempering out\|tempers out]] [[2401/2400]], [[3136/3125]], [[6144/6125]], and [[19683/19600]] in the 7-limit; [[243/242]], [[441/440]], [[540/539]], and [[4000/3993]] in the 11-limit; and [[351/350]], [[364/363]], [[676/675]], [[729/728]], [[1001/1000]], [[1575/1573]], [[1716/1715]], [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit. It can be used to tune a variety of temperaments, including [[hemiwürschmidt]], [[sesquiquartififths]], [[harry]] and [[hemischis]]. It also can be used to tune the [[rank-3 temperament]] [[jove]], tempering out 243/242 and 441/440, plus 364/363 for the 13-limit and [[595/594]] for the 17-limit. It gives the [[optimal patent val]] for 11-limit [[hemiwürschmidt]] and [[Schismatic family #Sesquiquartififths\|sesquart]] and 13-limit [[harry]].
Line 331:		Line 331:
	!Evo		!Evo
	\| rowspan="2" \|<big>{{sagittal\|/\|\}}</big>		\| rowspan="2" \|<big>{{sagittal\|/\|\}}</big>
			\|<small>{{sagittal\|#}}<big>{{sagittal\|\!)}}</big></small>
			\|<small>{{sagittal\|#}}</small><small><big>{{sagittal\|\\!}}</big></small>
			\|<small>{{sagittal\|#}}<big>{{sagittal\|!)}}</big></small>
			\|<small>{{sagittal\|#}}<big>{{sagittal\|\!}}</big></small>
	\|<small>{{sagittal\|#}}<big>{{sagittal\|!(}}</big></small>		\|<small>{{sagittal\|#}}<big>{{sagittal\|!(}}</big></small>
	~~\|<small>{{sagittal\|#}}<big>{{sagittal\|\!}}</big></small>~~
	~~\|<small>{{sagittal\|#}}<big>{{sagittal\|!)}}</big></small>~~
	~~\|<small>{{sagittal\|#}}<big>{{sagittal\|\\!}}</big></small>~~
	~~\|<small>{{sagittal\|#}}<big>{{sagittal\|\!)}}</big></small>~~
	\|-		\|-
	!Revo		!Revo

Eufalesio: no-29 31-limit goodness

2026-03-01T16:55:36Z

no-29 31-limit goodness

← Older revision		Revision as of 16:55, 1 March 2026
Line 3:		Line 3:

	== Theory ==		== Theory ==
	130edo is a [[zeta peak edo]], a [[zeta peak integer edo]], and a [[zeta integral edo]] but not a gap edo. It is [[distinctly consistent]] to the [[15-odd-limit]] and is the first [[trivial temperament\|nontrivial edo]] to be consistent in the 14-[[odd prime sum limit\|odd-prime-sum-limit]]. As an equal temperament, it [[tempering out\|tempers out]] [[2401/2400]], [[3136/3125]], [[6144/6125]], and [[19683/19600]] in the 7-limit; [[243/242]], [[441/440]], [[540/539]], and [[4000/3993]] in the 11-limit; and [[351/350]], [[364/363]], [[676/675]], [[729/728]], [[1001/1000]], [[1575/1573]], [[1716/1715]], [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit. It can be used to tune a variety of temperaments, including [[hemiwürschmidt]], [[sesquiquartififths]], [[harry]] and [[hemischis]]. It also can be used to tune the [[rank-3 temperament]] [[jove]], tempering out 243/242 and 441/440, plus 364/363 for the 13-limit and [[595/594]] for the 17-limit. It gives the [[optimal patent val]] for 11-limit [[hemiwürschmidt]] and [[Schismatic family #Sesquiquartififths\|sesquart]] and 13-limit [[harry]].		130edo is a [[zeta peak edo]], a [[zeta peak integer edo]], and a [[zeta integral edo]] but not a gap edo. It is [[distinctly consistent]] to the [[15-odd-limit]] and is the first [[trivial temperament\|nontrivial edo]] to be consistent in the 14-[[odd prime sum limit\|odd-prime-sum-limit]]. It is also almost consistent in the no-29 [[31-odd-limit]], missing [[19/11]] (50.5%), [[25/19]] (52.9%), [[17/11]] (64,4%), [[25/17]] (66.8%), and [[octave complement]]<nowiki/>s.

			As an equal temperament, it [[tempering out\|tempers out]] [[2401/2400]], [[3136/3125]], [[6144/6125]], and [[19683/19600]] in the 7-limit; [[243/242]], [[441/440]], [[540/539]], and [[4000/3993]] in the 11-limit; and [[351/350]], [[364/363]], [[676/675]], [[729/728]], [[1001/1000]], [[1575/1573]], [[1716/1715]], [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit. It can be used to tune a variety of temperaments, including [[hemiwürschmidt]], [[sesquiquartififths]], [[harry]] and [[hemischis]]. It also can be used to tune the [[rank-3 temperament]] [[jove]], tempering out 243/242 and 441/440, plus 364/363 for the 13-limit and [[595/594]] for the 17-limit. It gives the [[optimal patent val]] for 11-limit [[hemiwürschmidt]] and [[Schismatic family #Sesquiquartififths\|sesquart]] and 13-limit [[harry]].

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

Eufalesio: Whoops sharp pao not sharp kao

2026-02-25T15:20:05Z

Whoops sharp pao not sharp kao

← Older revision		Revision as of 15:20, 25 February 2026
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	\| rowspan="2" \|<big>{{sagittal\|/\|\}}</big>		\| rowspan="2" \|<big>{{sagittal\|/\|\}}</big>
	\|<small>{{sagittal\|#}}<big>{{sagittal\|!(}}</big></small>		\|<small>{{sagittal\|#}}<big>{{sagittal\|!(}}</big></small>
	\|<small>{{sagittal\|#}}<big>{{sagittal\|!/}}</big></small>		\|<small>{{sagittal\|#}}<big>{{sagittal\|\!}}</big></small>
	\|<small>{{sagittal\|#}}<big>{{sagittal\|!)}}</big></small>		\|<small>{{sagittal\|#}}<big>{{sagittal\|!)}}</big></small>
	\|<small>{{sagittal\|#}}<big>{{sagittal\|\\!}}</big></small>		\|<small>{{sagittal\|#}}<big>{{sagittal\|\\!}}</big></small>

Eufalesio: /* Sagittal notation */

2026-02-25T12:14:08Z

Sagittal notation

← Older revision		Revision as of 12:14, 25 February 2026
Line 295:		Line 295:
	{{Ups and downs sharpness\|130\|true}}		{{Ups and downs sharpness\|130\|true}}
	=== Sagittal notation ===		=== Sagittal notation ===
	{\| class="wikitable center~~-all~~"		130edo can be notated in [[Sagittal notation\|Sagittal]] using the [[Sagittal notation#Spartan single-shaft\|Spartan extension]], with the apotome equal to 12 edosteps and the limma to 10 edosteps. Since the the [[243/242\|rastma]] is tempered out, a SZ half-sharp and a half-flat may be used instead of pakai/pakao. Here is a simplified table:
	! ~~Steps~~		{\| class="wikitable" data-darkreader-inline-color="" style="text-align: center;"
	\| 0		!Degree
	\| 1		\|0
	\| 2		\| +1
	\| 3		\| +2
	\| 4		\| +3
	\| 5		\| +4
	\| 6		\| +5
	\| 7		\| +6
	\| 8		\| +7
	\| 9		\| +8
	\| 10		\| +9
	\| 11		\| +10
	\| 12		\| +11
			\| +12
	\|-		\|-
	! ~~Symbol~~		!Evo+SZ
	\| ~~[[File:~~Sagittal ~~natural.png]]~~		\| rowspan="3" \|<big>{{sagittal\|\|//\|}}</big>
	\| ~~[[File:~~Sagittal ~~nai.png]]~~		\| rowspan="3" \|<big>{{sagittal\|\|(}}</big>
	\| ~~[[File:~~Sagittal ~~pai.png]]~~		\| rowspan="3" \|<big>{{sagittal\|/\|}}</big>
	\| ~~[[File:~~Sagittal ~~tai.png]]~~		\| rowspan="3" \|<big>{{sagittal\|\|)}}</big>
	\| ~~[[File:~~Sagittal ~~phai.png]]~~		\| rowspan="3" \|<big>{{sagittal\|//\|}}</big>
	\| ~~[[File:~~Sagittal ~~patai.png]]~~		\| rowspan="3" \|<big>{{sagittal\|/\|)}}</big>
	\| ~~[[File:Sagittal pakai.png]]~~		\|<big>{{Sagittal\|t}}</big>
	\| ~~[[File:Sagittal jakai.png]]~~		\|<small>{{Sagittal\|t}}<big>{{sagittal\|\|(}}</big></small>
	\| ~~[[File:Sagittal sharp phao.png]]~~		\|<small>{{Sagittal\|t}}<big>{{sagittal\|/\|}}</big></small>
	\| ~~[[File:Sagittal sharp tao.png]]~~		\|<small>{{Sagittal\|t}}<big>{{sagittal\|\|)}}</big></small>
	\| ~~[[File:Sagittal sharp pao.png]]~~		\|<small>{{Sagittal\|t}}<big>{{sagittal\|//\|}}</big></small>
	\| ~~[[File:Sagittal sharp nao.png]]~~		\|<small>{{Sagittal\|t}}<big>{{sagittal\|/\|)}}</big></small>
	\| ~~[[File:Sagittal sharp.png]]~~		\| rowspan="2" \|<big>{{sagittal\|#}}</big>
			\|-
			!Evo
			\| rowspan="2" \|<big>{{sagittal\|/\|\}}</big>
			\|<small>{{sagittal\|#}}<big>{{sagittal\|!(}}</big></small>
			\|<small>{{sagittal\|#}}<big>{{sagittal\|!/}}</big></small>
			\|<small>{{sagittal\|#}}<big>{{sagittal\|!)}}</big></small>
			\|<small>{{sagittal\|#}}<big>{{sagittal\|\\!}}</big></small>
			\|<small>{{sagittal\|#}}<big>{{sagittal\|\!)}}</big></small>
			\|-
			!Revo
			\|<big>{{sagittal\|(\|3=\}}</big>
			\|<big>{{sagittal\|)\|\|(}}</big>
			\|<big>{{sagittal\|\|\|)}}</big>
			\|<big>{{sagittal\|\|\|\}}</big>
			\|<big>{{sagittal\|/\|\|)}}</big>
			\|<big>{{sagittal\|/\|\|\}}</big>
	\|}		\|}

			*

			See [[Sagittal notation#Revo\|apotome complements]] for equivalent accidental pairs.

	== Approximation to JI ==		== Approximation to JI ==

Tristanbay: /* Notation */ Added ups and downs notation

2025-10-14T06:22:38Z

Notation: Added ups and downs notation

← Older revision		Revision as of 06:22, 14 October 2025
Line 291:		Line 291:

	== Notation ==		== Notation ==
			=== Ups and downs notation ===
			130edo can be notated using [[Kite's ups and downs notation\|ups and downs]] and quarter-tone accidentals:
			{{Ups and downs sharpness\|130\|true}}
	=== Sagittal notation ===		=== Sagittal notation ===
	{\| class="wikitable center-all"		{\| class="wikitable center-all"

← Older revision		Revision as of 11:33, 7 March 2026
Line 3:		Line 3:

	== Theory ==		== Theory ==
	130edo is a [[zeta peak edo]], a [[zeta peak integer edo]], and a [[zeta integral edo]] but not a gap edo. It is [[distinctly consistent]] to the [[15-odd-limit]] and is the first [[trivial temperament\|nontrivial edo]] to be consistent in the 14-[[odd prime sum limit\|odd-prime-sum-limit]]. It is also almost consistent in the no-29 [[31-odd-limit]], missing [[19/11]] (50.5%), [[25/19]] (52.9%), [[17/11]] (64,4%), [[25/17]] (66.8%), and [[octave complement]]<nowiki/>s.		130edo is a [[zeta peak edo]], a [[zeta peak integer edo]], and a [[zeta integral edo]] but not a gap edo. It is [[distinctly consistent]] to the [[15-odd-limit]] and is the first [[trivial temperament\|nontrivial edo]] to be consistent in the 14-[[odd prime sum limit\|odd-prime-sum-limit]]. It is also almost consistent in the no-29 [[31-odd-limit]], missing [[19/11]] (50.5%), [[25/19]] (52.9%), [[17/11]] (64,4%), [[25/17]] (66.8%), and [[octave complement]]<nowiki/>s.

	As an equal temperament, it [[tempering out\|tempers out]] [[2401/2400]], [[3136/3125]], [[6144/6125]], and [[19683/19600]] in the 7-limit; [[243/242]], [[441/440]], [[540/539]], and [[4000/3993]] in the 11-limit; and [[351/350]], [[364/363]], [[676/675]], [[729/728]], [[1001/1000]], [[1575/1573]], [[1716/1715]], [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit. It can be used to tune a variety of temperaments, including [[hemiwürschmidt]], [[sesquiquartififths]], [[harry]] and [[hemischis]]. It also can be used to tune the [[rank-3 temperament]] [[jove]], tempering out 243/242 and 441/440, plus 364/363 for the 13-limit and [[595/594]] for the 17-limit. It gives the [[optimal patent val]] for 11-limit [[hemiwürschmidt]] and [[Schismatic family #Sesquiquartififths\|sesquart]] and 13-limit [[harry]].		As an equal temperament, it [[tempering out\|tempers out]] [[2401/2400]], [[3136/3125]], [[6144/6125]], and [[19683/19600]] in the 7-limit; [[243/242]], [[441/440]], [[540/539]], and [[4000/3993]] in the 11-limit; and [[351/350]], [[364/363]], [[676/675]], [[729/728]], [[1001/1000]], [[1575/1573]], [[1716/1715]], [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit. It can be used to tune a variety of temperaments, including [[hemiwürschmidt]], [[sesquiquartififths]], [[harry]] and [[hemischis]]. It also can be used to tune the [[rank-3 temperament]] [[jove]], tempering out 243/242 and 441/440, plus 364/363 for the 13-limit and [[595/594]] for the 17-limit. It gives the [[optimal patent val]] for 11-limit [[hemiwürschmidt]] and [[Schismatic family #Sesquiquartififths\|sesquart]] and 13-limit [[harry]].
Line 331:		Line 331:
	!Evo		!Evo
	\| rowspan="2" \|<big>{{sagittal\|/\|\}}</big>		\| rowspan="2" \|<big>{{sagittal\|/\|\}}</big>
			\|<small>{{sagittal\|#}}<big>{{sagittal\|\!)}}</big></small>
			\|<small>{{sagittal\|#}}</small><small><big>{{sagittal\|\\!}}</big></small>
			\|<small>{{sagittal\|#}}<big>{{sagittal\|!)}}</big></small>
			\|<small>{{sagittal\|#}}<big>{{sagittal\|\!}}</big></small>
	\|<small>{{sagittal\|#}}<big>{{sagittal\|!(}}</big></small>		\|<small>{{sagittal\|#}}<big>{{sagittal\|!(}}</big></small>
	~~\|<small>{{sagittal\|#}}<big>{{sagittal\|\!}}</big></small>~~
	~~\|<small>{{sagittal\|#}}<big>{{sagittal\|!)}}</big></small>~~
	~~\|<small>{{sagittal\|#}}<big>{{sagittal\|\\!}}</big></small>~~
	~~\|<small>{{sagittal\|#}}<big>{{sagittal\|\!)}}</big></small>~~
	\|-		\|-
	!Revo		!Revo

← Older revision		Revision as of 15:20, 25 February 2026
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	\| rowspan="2" \|<big>{{sagittal\|/\|\}}</big>		\| rowspan="2" \|<big>{{sagittal\|/\|\}}</big>
	\|<small>{{sagittal\|#}}<big>{{sagittal\|!(}}</big></small>		\|<small>{{sagittal\|#}}<big>{{sagittal\|!(}}</big></small>
	\|<small>{{sagittal\|#}}<big>{{sagittal\|!/}}</big></small>		\|<small>{{sagittal\|#}}<big>{{sagittal\|\!}}</big></small>
	\|<small>{{sagittal\|#}}<big>{{sagittal\|!)}}</big></small>		\|<small>{{sagittal\|#}}<big>{{sagittal\|!)}}</big></small>
	\|<small>{{sagittal\|#}}<big>{{sagittal\|\\!}}</big></small>		\|<small>{{sagittal\|#}}<big>{{sagittal\|\\!}}</big></small>