56th-octave temperaments - Revision history

Lucius Chiaraviglio: /* Barium */ Link to barium comma

2025-11-23T23:31:17Z

Barium: Link to barium comma

← Older revision		Revision as of 23:31, 23 November 2025
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	== Barium ==		== Barium ==
	One step of 56edo is close to a syntonic comma. Named after the 56th element, barium tempers out the {{monzo\| -225 224 -56 }} ~~comma~~, which sets 56 syntonic commas equal to the octave. It can be expressed as the 224 & 2072 temperament.		One step of 56edo is close to a syntonic comma. Named after the 56th element, barium tempers out the [[barium comma]] ({{monzo\| -225 224 -56 }}), which sets 56 syntonic commas equal to the octave. It can be expressed as the 224 & 2072 temperament.

	[[Subgroup]]: 2.3.5		[[Subgroup]]: 2.3.5

ArrowHead294 at 03:44, 14 February 2025

2025-02-14T03:44:10Z

← Older revision		Revision as of 03:44, 14 February 2025
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	{{~~Fractional~~-octave ~~navigation~~\|56}}{{todo\|intro}}		{{Infobox fractional-octave\|56}}{{todo\|intro}}
	==Barium==
			== Barium ==
	One step of 56edo is close to a syntonic comma. Named after the 56th element, barium tempers out the {{monzo\| -225 224 -56 }} comma, which sets 56 syntonic commas equal to the octave. It can be expressed as the 224 & 2072 temperament.		One step of 56edo is close to a syntonic comma. Named after the 56th element, barium tempers out the {{monzo\| -225 224 -56 }} comma, which sets 56 syntonic commas equal to the octave. It can be expressed as the 224 & 2072 temperament.

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	[[Badness]]: 4.70		[[Badness]]: 4.70
	====7-limit====
			==== 7-limit ====
	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

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	[[Badness]]: 0.227		[[Badness]]: 0.227
	====11-limit====
			==== 11-limit ====
	Subgroup: 2.3.5.7.11		Subgroup: 2.3.5.7.11

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	Badness: 0.0345		Badness: 0.0345
	====13-limit====
			==== 13-limit ====
	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

BudjarnLambeth: navbox, todo

2024-12-05T07:37:02Z

navbox, todo

← Older revision		Revision as of 07:37, 5 December 2024
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	{{Fractional-octave navigation\|56}}		{{Fractional-octave navigation\|56}}{{todo\|intro}}
	==Barium==		==Barium==
	One step of 56edo is close to a syntonic comma. Named after the 56th element, barium tempers out the {{monzo\| -225 224 -56 }} comma, which sets 56 syntonic commas equal to the octave. It can be expressed as the 224 & 2072 temperament.		One step of 56edo is close to a syntonic comma. Named after the 56th element, barium tempers out the {{monzo\| -225 224 -56 }} comma, which sets 56 syntonic commas equal to the octave. It can be expressed as the 224 & 2072 temperament.
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	{{Optimal ET sequence\|legend=1\| 224, 1848, 2072}}		{{Optimal ET sequence\|legend=1\| 224, 1848, 2072}}

			{{Navbox fractional-octave}}

	[[Category:56edo]]		[[Category:56edo]]

Eliora at 13:08, 3 September 2023

2023-09-03T13:08:09Z

← Older revision		Revision as of 13:08, 3 September 2023
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			{{Fractional-octave navigation\|56}}
	==Barium==		==Barium==
	One step of 56edo is close to a syntonic comma. Named after the 56th element, barium tempers out the {{monzo\| -225 224 -56 }} comma, which sets 56 syntonic commas equal to the octave. It can be expressed as the 224 & 2072 temperament.		One step of 56edo is close to a syntonic comma. Named after the 56th element, barium tempers out the {{monzo\| -225 224 -56 }} comma, which sets 56 syntonic commas equal to the octave. It can be expressed as the 224 & 2072 temperament.

Eliora: /* 13-limit */ only members of this sequence in the 13-limit per sintel's method

2023-09-02T19:00:32Z

13-limit: only members of this sequence in the 13-limit per sintel's method

← Older revision		Revision as of 19:00, 2 September 2023
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	Optimal tuning (CTE): ~3/2 = 701.9431		Optimal tuning (CTE): ~3/2 = 701.9431

	{{Optimal ET sequence\|legend=1\| 224, 1848, 2072}}~~, ...~~		{{Optimal ET sequence\|legend=1\| 224, 1848, 2072}}

	[[Category:56edo]]		[[Category:56edo]]

Eliora at 15:10, 15 June 2023

2023-06-15T15:10:15Z

← Older revision		Revision as of 15:10, 15 June 2023
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	{{Optimal ET sequence\|legend=1\| 224, 1848, 2072}}, ...		{{Optimal ET sequence\|legend=1\| 224, 1848, 2072}}, ...

			[[Category:56edo]]

Eliora: Created page with "==Barium== One step of 56edo is close to a syntonic comma. Named after the 56th element, barium tempers out the {{monzo| -225 224 -56 }} comma, which sets 56 syntonic commas e..."

2023-06-15T13:52:01Z

Created page with "==Barium== One step of 56edo is close to a syntonic comma. Named after the 56th element, barium tempers out the {{monzo| -225 224 -56 }} comma, which sets 56 syntonic commas e..."

New page

==Barium==
One step of 56edo is close to a syntonic comma. Named after the 56th element, barium tempers out the {{monzo| -225 224 -56 }} comma, which sets 56 syntonic commas equal to the octave. It can be expressed as the 224 & 2072 temperament.

[[Subgroup]]: 2.3.5

[[Comma list]]: {{monzo| -225 224 -56 }}

[[Mapping]]: [{{val| 56 0 -225 }}, {{val| 0 1 4 }}]

Mapping generators: ~81/80, ~3

[[Optimal tuning]] ([[CTE]]): ~3/2 = 701.9379

{{Optimal ET sequence|legend=1| 224, 1176, 1400, 1624, 1848, 2072, 5992, 8064, 26264, 34328b, 42392b }}

[[Badness]]: 4.70
====7-limit====
[[Subgroup]]: 2.3.5.7

[[Comma list]]: {{monzo| -12 29 -11 -3 }}, {{monzo| 47 -7 -7 -7 }}

[[Mapping]]: [{{val| 56 0 -225 601 }}, {{val| 0 1 4 -5 }}]

[[Optimal tuning]] ([[CTE]]): ~3/2 = 701.9433

{{Optimal ET sequence|legend=1| 224, 1176, 1400, 1624, 1848, 2072, 5768, 7616, 17080, 24696cd }}

[[Badness]]: 0.227
====11-limit====
Subgroup: 2.3.5.7.11

Comma list: 9801/9800, 1019215872/1019046875, 14765025303/14763950080

Mapping: [{{val| 56 0 -225 601 460 }}, {{val| 0 1 4 -5 -3 }}]

Optimal tuning (CTE): ~3/2 = 701.9431

{{Optimal ET sequence|legend=1| 224, 1176, 1400, 1624, 1848, 3920, 5768, 7616, 21000cd, 28616cd }}

Badness: 0.0345
====13-limit====
Subgroup: 2.3.5.7.11.13

Comma list: 4225/4224, 9801/9800, 67392/67375, 26802913280/26795786661

Mapping: [{{val| 56 0 -225 601 460 651}}, {{val| 0 1 4 -5 -3 -5}}]

Optimal tuning (CTE): ~3/2 = 701.9431

{{Optimal ET sequence|legend=1| 224, 1848, 2072}}, ...