22nd-octave temperaments - Revision history

FloraC: Text replacement - "{{Technical data page}}

" to "{{Technical data page}}"

2025-04-13T13:46:53Z

Text replacement - "{{Technical data page}}<br><br>" to "{{Technical data page}}"

← Older revision		Revision as of 13:46, 13 April 2025
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	{{Technical data page}}~~<br><br>~~		{{Technical data page}}
	{{Infobox fractional-octave\|22}}		{{Infobox fractional-octave\|22}}
	[[22edo]] is a notable tuning system, and as such it gives rise to some fractional-octave temperaments. This page accommodates a number of temperaments that are otherwise difficult to catalog because they belong to multiple families.		[[22edo]] is a notable tuning system, and as such it gives rise to some fractional-octave temperaments. This page accommodates a number of temperaments that are otherwise difficult to catalog because they belong to multiple families.

BudjarnLambeth: {{Technical data page}}

2025-04-13T07:02:41Z

{{Technical data page}}<br><br>

← Older revision		Revision as of 07:02, 13 April 2025
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			{{Technical data page}}<br><br>
	{{Infobox fractional-octave\|22}}		{{Infobox fractional-octave\|22}}
	[[22edo]] is a notable tuning system, and as such it gives rise to some fractional-octave temperaments. This page accommodates a number of temperaments that are otherwise difficult to catalog because they belong to multiple families.		[[22edo]] is a notable tuning system, and as such it gives rise to some fractional-octave temperaments. This page accommodates a number of temperaments that are otherwise difficult to catalog because they belong to multiple families.

ArrowHead294 at 03:40, 14 February 2025

2025-02-14T03:40:48Z

← Older revision		Revision as of 03:40, 14 February 2025
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	{{~~Fractional~~-octave ~~navigation~~\|22}}		{{Infobox fractional-octave\|22}}
	[[22edo]] is a notable tuning system, and as such it gives rise to some fractional-octave temperaments. This page accommodates a number of temperaments that are otherwise difficult to catalog because they belong to multiple families.		[[22edo]] is a notable tuning system, and as such it gives rise to some fractional-octave temperaments. This page accommodates a number of temperaments that are otherwise difficult to catalog because they belong to multiple families.

BudjarnLambeth: navbox

2024-12-05T07:20:12Z

navbox

← Older revision		Revision as of 07:20, 5 December 2024
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	[[Support]]ing [[ET]]s: {{EDOs\|198, 616, 814, 1012, 1210}}		[[Support]]ing [[ET]]s: {{EDOs\|198, 616, 814, 1012, 1210}}

			{{Navbox fractional-octave}}


	{{Todo\| cleanup }}		{{Todo\| cleanup }}

Eliora: rename to a common name per discussion in #wiki discord and given that old titanium is just beep

2024-02-24T14:40:10Z

rename to a common name per discussion in #wiki discord and given that old titanium is just beep

← Older revision		Revision as of 14:40, 24 February 2024
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	{{Fractional-octave navigation\|22}}		{{Fractional-octave navigation\|22}}
	[[22edo]] is a notable tuning system, and as such it gives rise to some fractional-octave temperaments. This page accommodates a number of temperaments that are otherwise difficult to catalog because they belong to multiple families. ~~Vigintiduo has the same 7-limit mapping as 22et with harmonic 11 mapped to an independent generator. Vigin has the same 11-limit mapping as 22et with harmonic 13 mapped to an independent generator.~~		[[22edo]] is a notable tuning system, and as such it gives rise to some fractional-octave temperaments. This page accommodates a number of temperaments that are otherwise difficult to catalog because they belong to multiple families.

	See also:		See also:
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	== Vigintiduo ==		== Vigintiduo ==
			''Vigintiduo'' has the same 7-limit mapping as 22et with harmonic 11 mapped to an independent generator.

	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

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	== Vigin ==		== Vigin ==
			''Vigin'' has the same 11-limit mapping as 22et with harmonic 13 mapped to an independent generator.

	[[Subgroup]]: 2.3.5.7.11.13		[[Subgroup]]: 2.3.5.7.11.13

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	== Major arcana ==		== Major arcana ==
	~~Named~~ after a subset of Tarot cards of which there is 22. Tempers out the {{monzo\|-193 154 -22}} comma in the 5-limit. Can be conceptualized as a more precise version of icosidillic in the 5-limit and the 7-limit bearing the same [[pergen]] (P8/22, P5), however there's no single way to extend it to the 11-limit due to inconsistency.		''Major arcana'' is named after a subset of Tarot cards of which there is 22. Tempers out the {{monzo\|-193 154 -22}} comma in the 5-limit. Can be conceptualized as a more precise version of icosidillic in the 5-limit and the 7-limit bearing the same [[pergen]] (P8/22, P5), however there's no single way to extend it to the 11-limit due to inconsistency.

	Subgroup: 2.3.5		Subgroup: 2.3.5
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	[[Support]]ing [[ET]]s: {{EDOs\|176, 506, 682}}		[[Support]]ing [[ET]]s: {{EDOs\|176, 506, 682}}

	== ~~Bibium~~ ==		== Titanium ==
	~~Bibium~~ is named after ~~an "extended provisional name" for~~ the 22nd element ~~[[wikipedia:~~titanium~~\|titanium]], which is needed~~ to ~~resolve a name conflict~~ as [[~~Titanium~~]] ~~is already a temperament~~. It reaches [[11/8]] and [[7/6]] in one generator, and as a corollary tempers [[96/77]] to 7 steps of 22edo.		''Titanium'' is named after the 22nd element after the previous temperament called "titanium" was found to be the same thing as [[beep]]. It reaches [[11/8]] and [[7/6]] in one generator, and as a corollary tempers [[96/77]] to 7 steps of 22edo.

	Subgroup: 2.3.5.7.11		Subgroup: 2.3.5.7.11

Eliora: /* Major arcana */ rework: apply simpler mapping in the 7-limit (6 gensteps vs. 40)

2023-11-08T19:57:03Z

Major arcana: rework: apply simpler mapping in the 7-limit (6 gensteps vs. 40)

← Older revision		Revision as of 19:57, 8 November 2023
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	Mapping: [{{val\|22 22 -39}}, {{val\|0 1 7}}]		Mapping: [{{val\|22 22 -39}}, {{val\|0 1 7}}]

	~~Mapping~~ generators: ~{{monzo\|79 -63 9}}, ~3/2		: mapping generators: ~{{monzo\|79 -63 9}}, ~3/2

	Optimal tuning (CTE): ~3/2 = 701.942		Optimal tuning (CTE): ~3/2 = 701.942

	{{~~Optimal ET sequence\|legend=1~~\|176, 330, 506, 836, 1342, 1848}}, ...		[[Support]]ing [[ET]]s: {{EDOs\|176, 330, 506, 836, 1342, 1848}}, ...

	=== 7-limit ===		=== 7-limit ===
	Subgroup: 2.3.5.7		Subgroup: 2.3.5.7

	Comma list: ~~{{monzo\|51 -24 -8 2}}~~, {{monzo\|-~~20 41~~ -~~23 3~~}}		Comma list: 14348907/14336000, {{monzo\|39 11 -11 -11}}

	Mapping: [{{val\|22 22 -~~39 -453~~}}, {{val\|0 1 7 40}}]		Mapping: [{{val\|22 0 -193 271}}, {{val\|0 1 7 -6}}]

	~~Mapping~~ generators: ~~~16128~~/~~15625~~, ~3/2		: mapping generators: ~8388608/8103375, ~3/2

	Optimal tuning (CTE): ~3/2 = ~~701~~.~~948~~		Optimal tuning (CTE): ~3/2 = 702.014

	{{~~Optimal ET sequence\|legend=1~~\|506}}		[[Support]]ing [[ET]]s: {{EDOs\|176, 506, 682}}

	== Bibium ==		== Bibium ==

Eliora: /* Major arcana */ 330, not 336 - there

2023-10-23T20:39:25Z

Major arcana: 330, not 336 - there

← Older revision		Revision as of 20:39, 23 October 2023
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	Optimal tuning (CTE): ~3/2 = 701.942		Optimal tuning (CTE): ~3/2 = 701.942

	{{Optimal ET sequence\|legend=1\|176, 506, 836, 1342, 1848}}, ...		{{Optimal ET sequence\|legend=1\|176, 330, 506, 836, 1342, 1848}}, ...

	=== 7-limit ===		=== 7-limit ===

Eliora: /* Major arcana */ how'd this wind up here, 336 is not divisible by 22

2023-10-23T20:35:33Z

Major arcana: how'd this wind up here, 336 is not divisible by 22

← Older revision		Revision as of 20:35, 23 October 2023
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	Optimal tuning (CTE): ~3/2 = 701.942		Optimal tuning (CTE): ~3/2 = 701.942

	{{Optimal ET sequence\|legend=1\|176~~, 336~~, 506, 836, 1342, 1848}}, ...		{{Optimal ET sequence\|legend=1\|176, 506, 836, 1342, 1848}}, ...

	=== 7-limit ===		=== 7-limit ===

Eliora: remove rank 2 category, as this isn't a family page

2023-09-21T12:12:22Z

remove rank 2 category, as this isn't a family page

← Older revision		Revision as of 12:12, 21 September 2023
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	[[Support]]ing [[ET]]s: {{EDOs\|198, 616, 814, 1012, 1210}}		[[Support]]ing [[ET]]s: {{EDOs\|198, 616, 814, 1012, 1210}}

	~~[[Category:Rank 2]]~~

	{{Todo\| cleanup }}		{{Todo\| cleanup }}

FloraC: Looks like many of these categories are redundant

2023-09-21T11:17:57Z

Looks like many of these categories are redundant

← Older revision		Revision as of 11:17, 21 September 2023
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	[[Support]]ing [[ET]]s: {{EDOs\|198, 616, 814, 1012, 1210}}		[[Support]]ing [[ET]]s: {{EDOs\|198, 616, 814, 1012, 1210}}

	~~[[Category:Temperament collections]]~~
	~~[[Category:Fractional-octave temperaments]]~~
	~~[[Category:22edo]]~~
	[[Category:Rank 2]]		[[Category:Rank 2]]

	{{Todo\| cleanup }}		{{Todo\| cleanup }}