22nd-octave temperaments - Revision history

Eliora: /* Major arcana */

2026-10-07T18:38:03Z

Major arcana

← Older revision		Revision as of 18:38, 7 October 2026
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	''Major arcana'' is named after a [[wikipedia:Major Arcana\|subset of Tarot cards of which there is 22]] and it tempers out the {{monzo\|-193 154 -22}} comma in the 5-limit.		''Major arcana'' is named after a [[wikipedia:Major Arcana\|subset of Tarot cards of which there is 22]] and it tempers out the {{monzo\|-193 154 -22}} comma in the 5-limit.

	It is similar to the icosidillic temperament, having the same [[pergen]] (P8/22, P5), however while icosidillic is merely an extension of [[Miscellaneous 5-limit temperaments#Hendecatonic\|5-limit hendecatonic]], major arcana stands as a an independent and properly not [[enfactoring\|enfactored]] 22nd-octave comma.		It is similar to the icosidillic temperament, having the same [[pergen]] (P8/22, P5), however while icosidillic is merely an extension of [[Miscellaneous 5-limit temperaments#Hendecatonic\|5-limit hendecatonic]], major arcana stands as an independent and properly not [[enfactoring\|enfactored]] 22nd-octave comma.

	An extension is possible to the 7-limit as the 506 & 682 temperament, however due to inconsistency the temperament branches at the 11-limit. Although notably, a 2.3.5.11/7 extension of remarkably low badness, described as 1848 & 1342, is prescribed. [[1848edo]] as a whole is also a strong tuning despite being only in the optimal ET sequence for 2.3.5.11/7 subgroup version.		An extension is possible to the 7-limit as the 506 & 682 temperament, however due to inconsistency the temperament branches at the 11-limit. Although notably, a 2.3.5.11/7 extension of remarkably low badness, described as 1848 & 1342, is prescribed. [[1848edo]] as a whole is also a strong tuning despite being only in the optimal ET sequence for 2.3.5.11/7 subgroup version.

Eliora: expand, cleanup, supporting ETs > optimal ET sequence, elaborate where relevant

2026-10-07T18:35:40Z

expand, cleanup, supporting ETs > optimal ET sequence, elaborate where relevant

Show changes

Eliora: /* Vigintiduo */ oops

2026-10-07T17:32:07Z

Vigintiduo: oops

← Older revision		Revision as of 17:32, 7 October 2026
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	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[WE]]: ~25/24 = 54.462{{c}}, ~11/8 = 556.713		* [[WE]]: ~25/24 = 54.462{{c}}, ~11/8 = 556.713{{c}}
	: [[error map]]: {{val\| -1.830, 4.225, -8.737, 7.836, -0.093 }}		: [[error map]]: {{val\| -1.830, 4.225, -8.737, 7.836, -0.093 }}
	* [[CWE]]: ~25/24 = 1\22, ~11/8 = 556.295		* [[CWE]]: ~25/24 = 1\22, ~11/8 = 556.295{{c}}
	: error map: {{val\| 0.000 -0.068 -0.088 -0.106 -0.375 }}		: error map: {{val\| 0.000 -0.068 -0.088 -0.106 -0.375 }}

Eliora: /* Vigintiduo */ to new CWE stuff, switch to Sintel badness, etc. (+also in constrained WE I would literally write 1\period as it is that by definition)

2026-10-07T17:31:44Z

Vigintiduo: to new CWE stuff, switch to Sintel badness, etc. (+also in constrained WE I would literally write 1\period as it is that by definition)

← Older revision		Revision as of 17:31, 7 October 2026
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	== Vigintiduo ==		== Vigintiduo ==
	''Vigintiduo'' ~~has~~ the ~~same~~ 7-limit ~~mapping as 22et with~~ harmonic 11 ~~mapped to an~~ independent ~~generator~~.		''Vigintiduo'' sets the [[7-limit]] to that of 22edo and harmonic 11 and the rest are independent generators.

	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11
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	{{Mapping\|legend=1\| 22 35 51 62 0 \| 0 0 0 0 1 }}		{{Mapping\|legend=1\| 22 35 51 62 0 \| 0 0 0 0 1 }}
			: mapping generators: ~25/24, ~11/8

	[[Optimal tuning]] ([[~~POTE~~]]): ~36/35 = 1\22, ~11/8 = ~~557~~.~~563~~		[[Optimal tuning]]s:
			* [[WE]]: ~25/24 = 54.462{{c}}, ~11/8 = 556.713
			: [[error map]]: {{val\| -1.830, 4.225, -8.737, 7.836, -0.093 }}
			* [[CWE]]: ~25/24 = 1\22, ~11/8 = 556.295
			: error map: {{val\| 0.000 -0.068 -0.088 -0.106 -0.375 }}

	{{Optimal ET sequence\|legend=1\| 22, 66de, 88bde, 110bd, 198bcdde }}		{{Optimal ET sequence\|legend=1\| 22, 66de, 88bde, 110bd, 198bcdde }}

	[[Badness]]: 0.~~048372~~		[[Badness]]: 1.599

	== Vigin ==		== Vigin ==

Eliora: /* Major arcana */ link to what it is

2026-10-07T17:17:42Z

Major arcana: link to what it is

← Older revision		Revision as of 17:17, 7 October 2026
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	== Major arcana ==		== Major arcana ==
	''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.		''Major arcana'' is named after a [[wikipedia:Major Arcana\|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

Eliora: /* 13-limit */ oops

2026-09-02T22:43:45Z

13-limit: oops

← Older revision		Revision as of 22:43, 2 September 2026
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	Comma list: 2401/2400, 9801/9800, 67392/67375, 142884/142805		Comma list: 2401/2400, 9801/9800, 67392/67375, 142884/142805

	Mapping: [{{val\|22 2 10 33 72 28}}, {{val\|0 8 10 7 1 3}}]		Mapping: [{{val\|22 2 10 33 72 28}}, {{val\|0 8 10 7 1 13}}]

	Mapping generators: ~65/63 = 1\22, 338/297 = 224.100		Mapping generators: ~65/63 = 1\22, 338/297 = 224.100

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 }}