2022edo - Revision history

Tristanbay: /* Theory */ added that it's the optimal patent val for tristanismic

2025-11-07T08:12:04Z

Theory: added that it's the optimal patent val for tristanismic

← Older revision		Revision as of 08:12, 7 November 2025
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	In the 2.5.11.17.29.41.43.53.61 subgroup, 2022edo tempers out 17630/17629, 18491/18490, 21200/21199, and 22528/22525.		In the 2.5.11.17.29.41.43.53.61 subgroup, 2022edo tempers out 17630/17629, 18491/18490, 21200/21199, and 22528/22525.

			In the full 13-limit, it is the [[optimal patent val]] for tristanismic, the rank-5 [[4459/4455]] temperament.

	If the 29-limit is taken as a whole even including the 7-limit inconsistency, 2022edo tempers out 2002/2001, 3451/3450, 5104/5103, and 16445/16443.		If the 29-limit is taken as a whole even including the 7-limit inconsistency, 2022edo tempers out 2002/2001, 3451/3450, 5104/5103, and 16445/16443.

ArrowHead294 at 22:56, 20 February 2025

2025-02-20T22:56:45Z

← Older revision		Revision as of 22:56, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|2022~~}}		{{ED intro}}

	== Theory ==		== Theory ==
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	== Regular temperament properties ==		== Regular temperament properties ==
	{\| class="wikitable center-4 center-5 center-6"		{\| class="wikitable center-4 center-5 center-6"
			\|-
	! rowspan="2" \| [[Subgroup]]		! rowspan="2" \| [[Subgroup]]
	! rowspan="2" \| [[Comma list\|Comma List]]		! rowspan="2" \| [[Comma list\|Comma List]]
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	\| {{monzo\| 3205 -2022 }}		\| {{monzo\| 3205 -2022 }}
	\| {{mapping\| 2022 3205 }}		\| {{mapping\| 2022 3205 }}
	\| -0.038534		\| −0.038534
	\| 0.038533		\| 0.038533
	\| 6.493		\| 6.493
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	\| {{monzo\| 25 -48 22 }}, {{monzo\| -90 -15 49 }}		\| {{monzo\| 25 -48 22 }}, {{monzo\| -90 -15 49 }}
	\| {{mapping\| 2022 3205 4695 }}		\| {{mapping\| 2022 3205 4695 }}
	\| -0.030920		\| −0.030920
	\| 0.033254		\| 0.033254
	\| 5.603		\| 5.603
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	\| 2431/2430, 2755/2754, 3520/3519, 142025/141984, 2582624/2581875, 9096256/9092061, 11293425/11290976, 51054848/51046875		\| 2431/2430, 2755/2754, 3520/3519, 142025/141984, 2582624/2581875, 9096256/9092061, 11293425/11290976, 51054848/51046875
	\| {{mapping\| 2022 3205 4695 6955 7482 8265 8589 9147 9283 }}		\| {{mapping\| 2022 3205 4695 6955 7482 8265 8589 9147 9283 }}
	\| -0.010752		\| −0.010752
	\| 0.036910		\| 0.036910
	\| 6.219		\| 6.219

Francium: +categories

2024-02-13T18:31:20Z

+categories

← Older revision		Revision as of 18:31, 13 February 2024
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	; [[Eliora]]		; [[Eliora]]
	* [https://www.youtube.com/watch?v=IulKlMjxAM8 ''Noble Gas''] (2021)		* [https://www.youtube.com/watch?v=IulKlMjxAM8 ''Noble Gas''] (2021)

			[[Category:Listen]]

FloraC: Rework theory; +subsets and supersets

2023-10-30T11:41:17Z

Rework theory; +subsets and supersets

← Older revision		Revision as of 11:41, 30 October 2023
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	== Theory ==		== Theory ==
	2022edo offers good appoximations of the 2.5.11.17.29.41.43.53.61 [[subgroup]]. When using smaller numbers, 2.3.5.11 is a good choice, and if rougher errors are allowed, no-sevens 29-limit is a satisfactory choice.		2022edo is only [[consistent]] to the [[5-odd-limit]] since [[harmonic]] [[7/1\|7]] is about halfway between its steps. Nonetheless, it offers good appoximations of the 2.3.5.11.17.29.41.43.53.61 [[subgroup]]. When using smaller numbers, 2.3.5.11 is a good choice, and if rougher errors are allowed, no-sevens 29-limit is a satisfactory choice.

	In the 5-limit, 2022edo supports the [[pirate]] temperament, 323 & 407, and tempers out the {{monzo\| -90 -15 49 }} comma.		In the 5-limit, 2022edo supports the [[pirate]] temperament, 323 & 407, and tempers out the {{monzo\| -90 -15 49 }} comma.
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	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|2022\|columns=11}}		{{Harmonics in equal\|2022\|columns=11}}

			=== Subsets and supersets ===
			Since 2022 factors into {{factorization\|2022}}, 2022edo has subset edos 2, 3, 6, 337, 674, and 1011.

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

FloraC: Cleanup

2023-10-15T13:44:33Z

Cleanup

← Older revision		Revision as of 13:44, 15 October 2023
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	== Theory ==		== Theory ==
	2022edo offers good appoximations of the 2.5.11.17.29.41.43.53.61 subgroup. When using smaller numbers, 2.3.5.11 is a good choice, and if rougher errors are allowed, no-sevens 29-limit is a satisfactory choice.		2022edo offers good appoximations of the 2.5.11.17.29.41.43.53.61 [[subgroup]]. When using smaller numbers, 2.3.5.11 is a good choice, and if rougher errors are allowed, no-sevens 29-limit is a satisfactory choice.

	In the 5-limit, 2022edo supports the pirate temperament, 323 & 407, and tempers out the {{monzo\| -90 -15 49 }} comma.		In the 5-limit, 2022edo supports the [[pirate]] temperament, 323 & 407, and tempers out the {{monzo\| -90 -15 49 }} comma.

	In the 2.3.5.11 subgroup, 2022edo [[support]]s the rank-3 temperament that eliminates the {{monzo\| 25 -17 -23 16 }} comma. If the 11-limit is taken as a whole, 2022edo tempers out [[3025/3024]] and [[4375/4374]] when it is [[7/4]] is put on the 1633rd step (2022d val), and [[41503/41472]] with [[250047/250000]] when using the 1632nd step of the patent val.		In the 2.3.5.11 subgroup, 2022edo [[support]]s the rank-3 temperament that eliminates the {{monzo\| 25 -17 -23 16 }} comma. If the 11-limit is taken as a whole, 2022edo tempers out [[3025/3024]] and [[4375/4374]] when it is [[7/4]] is put on the 1633rd step (2022d val), and [[41503/41472]] with [[250047/250000]] when using the 1632nd step of the patent val.
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	If the 29-limit is taken as a whole even including the 7-limit inconsistency, 2022edo tempers out 2002/2001, 3451/3450, 5104/5103, and 16445/16443.		If the 29-limit is taken as a whole even including the 7-limit inconsistency, 2022edo tempers out 2002/2001, 3451/3450, 5104/5103, and 16445/16443.

			=== Prime harmonics ===
	{{Harmonics in equal\|2022\|columns=11}}		{{Harmonics in equal\|2022\|columns=11}}

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	{\| class="wikitable center-4 center-5 center-6"		{\| class="wikitable center-4 center-5 center-6"
	! rowspan="2" \| [[Subgroup]]		! rowspan="2" \| [[Subgroup]]
	! rowspan="2" \| [[Comma list]]		! rowspan="2" \| [[Comma list\|Comma List]]
	! rowspan="2" \| [[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \| Optimal<br>8ve Stretch (¢)		! rowspan="2" \| Optimal<br>8ve Stretch (¢)
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	\|-		\|-
	\| 2.3		\| 2.3
	\| {{~~Monzo~~\| 3205 -2022 }}		\| {{monzo\| 3205 -2022 }}
	\| [{{~~Val~~\| 2022 3205 }}]		\| {{mapping\| 2022 3205 }}
	\| -0.038534		\| -0.038534
	\| 0.038533		\| 0.038533
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	\|-		\|-
	\| 2.3.5		\| 2.3.5
	\| {{~~Monzo~~\| 25 -48 22 }}, {{monzo\| -90 -15 49 }}		\| {{monzo\| 25 -48 22 }}, {{monzo\| -90 -15 49 }}
	\| [{{~~Val~~\| 2022 3205 4695 }}]		\| {{mapping\| 2022 3205 4695 }}
	\| -0.030920		\| -0.030920
	\| 0.033254		\| 0.033254
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	\| 2.3.5.11.13.17.19.23.29		\| 2.3.5.11.13.17.19.23.29
	\| 2431/2430, 2755/2754, 3520/3519, 142025/141984, 2582624/2581875, 9096256/9092061, 11293425/11290976, 51054848/51046875		\| 2431/2430, 2755/2754, 3520/3519, 142025/141984, 2582624/2581875, 9096256/9092061, 11293425/11290976, 51054848/51046875
	\| ~~[⟨2022~~ 3205 4695 6955 7482 8265 8589 9147 9283]]		\| {{mapping\| 2022 3205 4695 6955 7482 8265 8589 9147 9283 }}
	\| -0.010752		\| -0.010752
	\| 0.036910		\| 0.036910
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	== Music ==		== Music ==
	* [https://www.youtube.com/watch?v=IulKlMjxAM8 Noble Gas] ~~by [[Cinnamon Mavka]]~~		; [[Eliora]]
			* [https://www.youtube.com/watch?v=IulKlMjxAM8 ''Noble Gas''] (2021)
	~~[[Category:Equal divisions of the octave\|####]] <!-- 4-digit number -->~~

BudjarnLambeth at 07:00, 9 July 2023

2023-07-09T07:00:03Z

← Older revision		Revision as of 07:00, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|2022}}		{{EDO intro\|2022}}

BudjarnLambeth at 04:40, 9 July 2023

2023-07-09T04:40:21Z

← Older revision		Revision as of 04:40, 9 July 2023
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	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	{{EDO intro\|2022}}		{{EDO intro\|2022}}

FloraC: -"current year". Note to editors: don't add stuff like that

2022-12-31T16:05:31Z

-"current year". Note to editors: don't add stuff like that

← Older revision		Revision as of 16:05, 31 December 2022
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	== Theory ==		== Theory ==
	~~{{Harmonics in equal\|2022}}~~
	2022edo offers good appoximations of the 2.5.11.17.29.41.43.53.61 subgroup. When using smaller numbers, 2.3.5.11 is a good choice, and if rougher errors are allowed, no-sevens 29-limit is a satisfactory choice.		2022edo offers good appoximations of the 2.5.11.17.29.41.43.53.61 subgroup. When using smaller numbers, 2.3.5.11 is a good choice, and if rougher errors are allowed, no-sevens 29-limit is a satisfactory choice.

	In the 5-limit, 2022edo supports the pirate temperament, 323 & 407, and tempers out the [-90, -15~~, 49⟩~~ comma.		In the 5-limit, 2022edo supports the pirate temperament, 323 & 407, and tempers out the {{monzo\| -90 -15 49 }} comma.

	In the 2.3.5.11 subgroup, 2022edo [[support]]s the rank 3 temperament that eliminates the [25,-17,-23~~,16⟩~~ comma. If the 11-limit is taken as a whole, 2022edo tempers out [[3025/3024]] and [[4375/4374]] when it's [[7/4]] is put on the 1633rd step (2022d val), and [[41503/41472]] with [[250047/250000]] when using the 1632nd step of the patent val.		In the 2.3.5.11 subgroup, 2022edo [[support]]s the rank-3 temperament that eliminates the {{monzo\| 25 -17 -23 16 }} comma. If the 11-limit is taken as a whole, 2022edo tempers out [[3025/3024]] and [[4375/4374]] when it is [[7/4]] is put on the 1633rd step (2022d val), and [[41503/41472]] with [[250047/250000]] when using the 1632nd step of the patent val.

	In the 2.5.11.17.29.41.43.53.61 subgroup, 2022edo tempers out 17630/17629, 18491/18490, 21200/21199, and 22528/22525.		In the 2.5.11.17.29.41.43.53.61 subgroup, 2022edo tempers out 17630/17629, 18491/18490, 21200/21199, and 22528/22525.

	If the 29-limit is taken as a whole even including the 7-limit inconsistency, 2022edo tempers out 2002/2001, 3451/3450, 5104/5103, and 16445/16443.		If the 29-limit is taken as a whole even including the 7-limit inconsistency, 2022edo tempers out 2002/2001, 3451/3450, 5104/5103, and 16445/16443.

			{{Harmonics in equal\|2022\|columns=11}}

	== Regular temperament properties ==		== Regular temperament properties ==
	~~Assuming a no-seven 29 limit subgroup, 2.3.5.11.13.17.19.23.29~~
	{\| class="wikitable center-4 center-5 center-6"		{\| class="wikitable center-4 center-5 center-6"
	! rowspan="2" \|[[Subgroup]]		! rowspan="2" \| [[Subgroup]]
	! rowspan="2" \|[[Comma list]]		! rowspan="2" \| [[Comma list]]
	! rowspan="2" \|[[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \|Optimal		! rowspan="2" \| Optimal<br>8ve Stretch (¢)
	8ve ~~stretch~~ (¢)		! colspan="2" \| Tuning Error
	! colspan="2" \|Tuning ~~error~~
	\|-		\|-
	![[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
	![[TE simple badness\|Relative]] (%)		! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\|2.3		\| 2.3
	\|{{Monzo\|3205, -2022}}		\| {{Monzo\| 3205 -2022 }}
	\|[{{Val\|2022 3205}}]		\| [{{Val\| 2022 3205 }}]
	\|~~<nowiki>~~-0.038534~~</nowiki>~~		\| -0.038534
	\|0.038533		\| 0.038533
	\|6.493		\| 6.493
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|{{Monzo\|25, -48, 22}}, {{~~Monzo~~\|-90, -15, 49}}		\| {{Monzo\| 25 -48 22 }}, {{monzo\| -90 -15 49 }}
	\|[{{Val\|2022 3205 4695}}]		\| [{{Val\| 2022 3205 4695 }}]
	\| -0.030920		\| -0.030920
	\|0.033254		\| 0.033254
	\|5.603		\| 5.603
	\|-		\|-
	\|2.3.5.11.13.17.19.23.29		\| 2.3.5.11.13.17.19.23.29
	\|2431/2430, 2755/2754, 3520/3519, 142025/141984,		\| 2431/2430, 2755/2754, 3520/3519, 142025/141984, 2582624/2581875, 9096256/9092061, 11293425/11290976, 51054848/51046875
			\| [⟨2022 3205 4695 6955 7482 8265 8589 9147 9283]]
	2582624/2581875, 9096256/9092061, 11293425/11290976, 51054848/51046875
	\|[⟨2022 3205 4695
	6955 7482 8265

	8589 9147 9283]]
	\| -0.010752		\| -0.010752
	\|0.036910		\| 0.036910
	\|6.219		\| 6.219
	\|}		\|}

	== Music ==		== Music ==
			* [https://www.youtube.com/watch?v=IulKlMjxAM8 Noble Gas] by [[Cinnamon Mavka]]
	* [https://www.youtube.com/watch?v=IulKlMjxAM8 Noble Gas] by Cinnamon Mavka

	~~== Trivia ==~~
	~~It is notable that it is the equal division corresponding to the current year, and also that music was composed in it before the wiki page about it was written.~~

	[[Category:Equal divisions of the octave\|####]] <!-- 4-digit number -->		[[Category:Equal divisions of the octave\|####]] <!-- 4-digit number -->

Plumtree: Infobox ET added

2022-10-04T22:14:08Z

Infobox ET added

← Older revision		Revision as of 22:14, 4 October 2022
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			{{Infobox ET}}
	{{EDO intro\|2022}}		{{EDO intro\|2022}}

Fredg999 category edits: Categories

2022-07-04T01:25:10Z

← Older revision		Revision as of 01:25, 4 July 2022
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	== Trivia ==		== Trivia ==
	It is notable that it is the equal division corresponding to the current year, and also that music was composed in it before the wiki page about it was written.		It is notable that it is the equal division corresponding to the current year, and also that music was composed in it before the wiki page about it was written.

			[[Category:Equal divisions of the octave\|####]] <!-- 4-digit number -->