Archytas–chromatic equivalence continuum - Revision history

Overthink: + another 7-limit temperament of 29&36, with 36edo patent val

2025-11-19T08:24:44Z

+ another 7-limit temperament of 29&36, with 36edo patent val

← Older revision		Revision as of 08:24, 19 November 2025
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	\|-		\|-
	\| 3		\| 3
	\| [[Coendou]] restriction		\| [[Coendou]]/[[Squirrel]] restriction
	\| [[546852789/536870912]]		\| [[546852789/536870912]]
	\| {{Monzo\| -29 13 0 3 }}		\| {{Monzo\| -29 13 0 3 }}

Overthink: 29&36c has a name, 7-limit restriction of which is 29&36

2025-10-26T17:36:24Z

29&36c has a name, 7-limit restriction of which is 29&36

← Older revision		Revision as of 17:36, 26 October 2025
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	\|-		\|-
	\| 3		\| 3
	\| ~~(29 & 36)~~		\| [[Coendou]] restriction
	\| [[546852789/536870912]]		\| [[546852789/536870912]]
	\| {{Monzo\| -29 13 0 3 }}		\| {{Monzo\| -29 13 0 3 }}

FloraC: Cleanup

2025-09-06T14:17:56Z

Cleanup

← Older revision		Revision as of 14:17, 6 September 2025
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	All temperaments in the continuum satisfy {{nowrap\|(64/63)<sup>''n''</sup> ~ 2187/2048}}. Varying ''n'' results in different temperaments listed in the table below. It converges to [[archy]] as ''n'' approaches infinity. The just value of ''n'' is 4.169771, and temperaments near this tend to be the most accurate ones.		All temperaments in the continuum satisfy {{nowrap\|(64/63)<sup>''n''</sup> ~ 2187/2048}}. Varying ''n'' results in different temperaments listed in the table below. It converges to [[archy]] as ''n'' approaches infinity. The just value of ''n'' is 4.169771, and temperaments near this tend to be the most accurate ones.

	{\| class="wikitable center-1 ~~center-2~~"		{\| class="wikitable center-1"
	\|+ style="font-size: 105%;" \| Temperaments in the continuum		\|+ style="font-size: 105%;" \| Temperaments in the continuum
	\|-		\|-
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	\|-		\|-
	\| −2		\| −2
	\| [[Dicot]]		\| [[Dicot]] restriction
	\| [[54/49]]		\| [[54/49]]
	\| {{~~monzo~~\| 1 3 0 -2 }}		\| {{Monzo\| 1 3 0 -2 }}
	\|-		\|-
	\| −1		\| −1
	\| [[Armodue]]		\| [[Armodue (temperament)\|Armodue]] restriction
	\| [[243/224]]		\| [[243/224]]
	\| {{~~monzo~~\| -5 5 0 -1 }}		\| {{Monzo\| -5 5 0 -1 }}
	\|-		\|-
	\| 0		\| 0
	\| [[Whitewood]]		\| [[Whitewood]] restriction
	\| [[2187/2048]]		\| [[2187/2048]]
	\| {{~~monzo~~\| -11 7 }}		\| {{Monzo\| -11 7 }}
	\|-		\|-
	\| 1		\| 1
	\| [[Flattone]]		\| [[Flattone]] restriction
	\| [[137781/131072]]		\| [[137781/131072]]
	\| {{~~monzo~~\| -17 9 0 1 }}		\| {{Monzo\| -17 9 0 1 }}
	\|-		\|-
	\| 2		\| 2
	\| [[Mohajira]]		\| [[Mohajira]] restriction
	\| [[8680203/8388608]]		\| [[8680203/8388608]]
	\| {{~~monzo~~\| -23 11 0 2 }}		\| {{Monzo\| -23 11 0 2 }}
	\|-		\|-
	\| 3		\| 3
	\| (29 &~~amp;~~ 36)		\| (29 & 36)
	\| [[546852789/536870912]]		\| [[546852789/536870912]]
	\| {{~~monzo~~\| -29 13 0 3 }}		\| {{Monzo\| -29 13 0 3 }}
	\|-		\|-
	\| 4		\| 4
	\| [[Sesquiquartififths]]		\| [[Sesquiquartififths]] restriction
	\| [[34451725707/34359738368]]		\| [[34451725707/34359738368]]
	\| {{~~monzo~~\| -35 15 0 4 }}		\| {{Monzo\| -35 15 0 4 }}
	\|-		\|-
	\| 4{{frac\|1\|6}}		\| 4{{frac\|1\|6}}
	\| ({{nowrap\|1848 &~~amp;~~ 3431}})		\| ({{nowrap\|1848 & 3431}})
	\| <abbr title="105343182492594861947326056299830127783078740498060829800981944087/105312291668557186697918027683670432318895095400549111254310977536">[very long]</abbr>		\| <abbr title="105343182492594861947326056299830127783078740498060829800981944087/105312291668557186697918027683670432318895095400549111254310977536">[very long]</abbr>
	\| {{~~monzo~~\| -216 92 0 25 }}		\| {{Monzo\| -216 92 0 25 }}
	\|-		\|-
	\| …		\| …
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	\|-		\|-
	\| ∞		\| ∞
	\| [[~~Archytas clan#Archy\|~~Archy]]		\| [[Archy]]
	\| [[64/63]]		\| [[64/63]]
	\| {{~~monzo~~\| 6 -2 0 -1 }}		\| {{Monzo\| 6 -2 0 -1 }}
	\|}		\|}

	[[Category:Equivalence continua]]		[[Category:Equivalence continua]]

ArrowHead294 at 21:53, 25 May 2025

2025-05-25T21:53:39Z

← Older revision		Revision as of 21:53, 25 May 2025
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	\|-		\|-
	\| 4{{frac\|1\|6}}		\| 4{{frac\|1\|6}}
	\| (1848 & 3431)		\| ({{nowrap\|1848 & 3431}})
	\| <abbr title="105343182492594861947326056299830127783078740498060829800981944087/105312291668557186697918027683670432318895095400549111254310977536">[very long]</abbr>		\| <abbr title="105343182492594861947326056299830127783078740498060829800981944087/105312291668557186697918027683670432318895095400549111254310977536">[very long]</abbr>
	\| {{monzo\| -216 92 0 25 }}		\| {{monzo\| -216 92 0 25 }}

ArrowHead294: Recategorise

2025-04-13T15:40:06Z

Recategorise

← Older revision		Revision as of 15:40, 13 April 2025
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	{{~~niche~~}}		{{Mathematical interest}}
	The '''Archytas–chromatic equivalence continuum''', or '''septimal–chromatic equivalence continuum''', is a [[equivalence continuum\|continuum]] of [[7-limit]] temperaments which equate a number of [[64/63\|Archytas commas (64/63)]] with the [[2187/2048\|Pythagorean apotome (2187/2048)]].		The '''Archytas–chromatic equivalence continuum''', or '''septimal–chromatic equivalence continuum''', is a [[equivalence continuum\|continuum]] of [[7-limit]] temperaments which equate a number of [[64/63\|Archytas commas (64/63)]] with the [[2187/2048\|Pythagorean apotome (2187/2048)]].

ArrowHead294 at 15:07, 12 April 2025

2025-04-12T15:07:17Z

← Older revision		Revision as of 15:07, 12 April 2025
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	! Monzo		! Monzo
	\|-		\|-
	\| -2		\| −2
	\| [[Dicot]]		\| [[Dicot]]
	\| [[54/49]]		\| [[54/49]]
	\| {{monzo\| 1 3 0 -2 }}		\| {{monzo\| 1 3 0 -2 }}
	\|-		\|-
	\| -1		\| −1
	\| [[Armodue]]		\| [[Armodue]]
	\| [[243/224]]		\| [[243/224]]

Xenllium at 10:55, 12 April 2025

2025-04-12T10:55:08Z

← Older revision		Revision as of 10:55, 12 April 2025
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	! Ratio		! Ratio
	! Monzo		! Monzo
			\|-
			\| -2
			\| [[Dicot]]
			\| [[54/49]]
			\| {{monzo\| 1 3 0 -2 }}
			\|-
			\| -1
			\| [[Armodue]]
			\| [[243/224]]
			\| {{monzo\| -5 5 0 -1 }}
	\|-		\|-
	\| 0		\| 0
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	\|-		\|-
	\| 2		\| 2
	\|		\| [[Mohajira]]
	\| [[8680203/8388608]]		\| [[8680203/8388608]]
	\| {{monzo\| -23 11 0 2 }}		\| {{monzo\| -23 11 0 2 }}
	\|-		\|-
	\| 3		\| 3
	\|		\| (29 & 36)
	\| [[546852789/536870912]]		\| [[546852789/536870912]]
	\| {{monzo\| -29 13 0 3 }}		\| {{monzo\| -29 13 0 3 }}
	\|-		\|-
	\| 4		\| 4
	\| ~~Schismatic<br />(~~[[Sesquiquartififths]])		\| [[Sesquiquartififths]]
	\| [[34451725707/34359738368]]		\| [[34451725707/34359738368]]
	\| {{monzo\| -35 15 0 4 }}		\| {{monzo\| -35 15 0 4 }}
	\|-		\|-
	\| 4{{frac\|1\|6}}		\| 4{{frac\|1\|6}}
	\|		\| (1848 & 3431)
	\| <abbr title="105343182492594861947326056299830127783078740498060829800981944087/105312291668557186697918027683670432318895095400549111254310977536">[very long]</abbr>		\| <abbr title="105343182492594861947326056299830127783078740498060829800981944087/105312291668557186697918027683670432318895095400549111254310977536">[very long]</abbr>
	\| {{monzo\| -216 92 0 25 }}		\| {{monzo\| -216 92 0 25 }}
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	\| [[Archytas clan#Archy\|Archy]]		\| [[Archytas clan#Archy\|Archy]]
	\| [[64/63]]		\| [[64/63]]
	\| {{monzo\| 6 -2 -1 }}		\| {{monzo\| 6 -2 0 -1 }}
	\|}		\|}

	[[Category:Equivalence continua]]		[[Category:Equivalence continua]]

BudjarnLambeth: Niche

2025-03-18T02:57:59Z

Niche

← Older revision		Revision as of 02:57, 18 March 2025
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	{{~~Novelty~~}}		{{niche}}
	The '''Archytas–chromatic equivalence continuum''', or '''septimal–chromatic equivalence continuum''', is a [[equivalence continuum\|continuum]] of [[7-limit]] temperaments which equate a number of [[64/63\|Archytas commas (64/63)]] with the [[2187/2048\|Pythagorean apotome (2187/2048)]].		The '''Archytas–chromatic equivalence continuum''', or '''septimal–chromatic equivalence continuum''', is a [[equivalence continuum\|continuum]] of [[7-limit]] temperaments which equate a number of [[64/63\|Archytas commas (64/63)]] with the [[2187/2048\|Pythagorean apotome (2187/2048)]].

ArrowHead294 at 14:34, 1 January 2025

2025-01-01T14:34:02Z

← Older revision		Revision as of 14:34, 1 January 2025
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	\|-		\|-
	\| 4		\| 4
	\|		\| Schismatic<br />([[Sesquiquartififths]])
	\| [[34451725707/34359738368]]		\| [[34451725707/34359738368]]
	\| {{monzo\| -35 15 0 4 }}		\| {{monzo\| -35 15 0 4 }}

ArrowHead294 at 14:30, 1 January 2025

2025-01-01T14:30:27Z

← Older revision		Revision as of 14:30, 1 January 2025
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	\|-		\|-
	\| 1		\| 1
	\| [[Flattone~~]], [[Flattertone~~]]		\| [[Flattone]]
	\| [[137781/131072]]		\| [[137781/131072]]
	\| {{monzo\| -17 9 0 1 }}		\| {{monzo\| -17 9 0 1 }}