2024edo - Revision history

Eliora: /* Theory */ duplicate text removed

2025-12-18T17:58:42Z

Theory: duplicate text removed

← Older revision		Revision as of 17:58, 18 December 2025
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	{{ED intro}}		{{ED intro}}
	== Theory ==		== Theory ==
	2024edo is [[Enfactoring\|enfactored]] in the 13-limit, with the same tuning as [[1012edo]], which is also a [[zeta]] edo. It corrects 1012edo's mapping for 17, being a strong 2.3.7.11.17.19 subgroup temperament. A comma basis for the said subgroup is {23409/23408, 117649/117612, 323456/323433, 131072/131043, 26042368/26040609}.		2024edo is [[Enfactoring\|enfactored]] in the 13-limit, with the same tuning as [[1012edo]], which is also a [[zeta]] edo. It corrects 1012edo's mapping for 17, being a strong 2.3.7.11.17.19 subgroup temperament. A comma basis for the said subgroup is {23409/23408, 117649/117612, 323456/323433, 131072/131043, 26042368/26040609}. In the said subgroup, it tunes the {{nowrap\|629 & 2024}} temperament, which has [[19/17]] as a generator and reaches [[17/16]] in 13 steps.

	In the ~~2.3.7.11.17.19~~, it tunes the {{nowrap\|629 & 2024}} temperament, which has [[19/17]] as a generator and reaches [[17/16]] in 13 steps~~. The comma basis in the 2.3.7.11.17.19 subgroup is {23409/23408, 131072/131043, 323456/323433, 818107136/817887699}~~.

	It has two suitable mappings for [[5/1\|5th harmonic]], one which derives from 1012edo, and other in the 2024c val. In the 2024c val, it [[tempering out\|tempers out]] the [[wizma]], 420175/419904 in the 7-limit, as well as [[3025/3024]], [[4225/4224]] and [[10648/10647]] in the 13-limit. If the sharp and flat mappings of 5/4 are combined, then 2024edo is a good 2.3.25 [[subgroup]] tuning. In the 2.3.25.7.11 subgroup, it tempers out [[4375/4374]] and tunes a messed-up version of the [[heimdall]] temperament, which reaches 7th harmonic in 2 second generators instead of 4, and 11th harmonic in 6 second generators instead of 12, taking half as much.		It has two suitable mappings for [[5/1\|5th harmonic]], one which derives from 1012edo, and other in the 2024c val. In the 2024c val, it [[tempering out\|tempers out]] the [[wizma]], 420175/419904 in the 7-limit, as well as [[3025/3024]], [[4225/4224]] and [[10648/10647]] in the 13-limit. If the sharp and flat mappings of 5/4 are combined, then 2024edo is a good 2.3.25 [[subgroup]] tuning. In the 2.3.25.7.11 subgroup, it tempers out [[4375/4374]] and tunes a messed-up version of the [[heimdall]] temperament, which reaches 7th harmonic in 2 second generators instead of 4, and 11th harmonic in 6 second generators instead of 12, taking half as much.

ArrowHead294 at 23:18, 20 February 2025

2025-02-20T23:18:37Z

← Older revision		Revision as of 23:18, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}
	== Theory ==		== Theory ==
	2024edo is [[Enfactoring\|enfactored]] in the 13-limit, with the same tuning as [[1012edo]], which is also a [[zeta]] edo. It corrects 1012edo's mapping for 17, being a strong 2.3.7.11.17.19 subgroup temperament. A comma basis for the said subgroup is {23409/23408, 117649/117612, 323456/323433, 131072/131043, 26042368/26040609}.		2024edo is [[Enfactoring\|enfactored]] in the 13-limit, with the same tuning as [[1012edo]], which is also a [[zeta]] edo. It corrects 1012edo's mapping for 17, being a strong 2.3.7.11.17.19 subgroup temperament. A comma basis for the said subgroup is {23409/23408, 117649/117612, 323456/323433, 131072/131043, 26042368/26040609}.

ArrowHead294 at 23:17, 20 February 2025

2025-02-20T23:17:28Z

← Older revision		Revision as of 23:17, 20 February 2025
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	== Music ==		== Music ==
	; [[Eliora]]		; [[Eliora]]
	* ''[https://youtu.be/6wO9uONbJhY Piano Juice]'' (2024) - palladium[92] (from [[506edo]]), ruthenium[88] (from [[1012edo]]), {{nowrap\|629 & 2024~~{{!(}}~~25~~{{)!}}~~}}, major-arcana[88] (from [[506edo]])		* ''[https://youtu.be/6wO9uONbJhY Piano Juice]'' (2024) - palladium[92] (from [[506edo]]), ruthenium[88] (from [[1012edo]]), {{nowrap\|629 & 2024[25]}}, major-arcana[88] (from [[506edo]])

	[[Category:Listen]]		[[Category:Listen]]

ArrowHead294 at 23:17, 20 February 2025

2025-02-20T23:17:08Z

← Older revision		Revision as of 23:17, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro~~\|2024~~}}		{{EDO intro}}
	== Theory ==		== Theory ==
	2024edo is [[Enfactoring\|enfactored]] in the 13-limit, with the same tuning as [[1012edo]], which is also a [[zeta]] edo. It corrects 1012edo's mapping for 17, being a strong 2.3.7.11.17.19 subgroup temperament. A comma basis for the said subgroup is {23409/23408, 117649/117612, 323456/323433, 131072/131043, 26042368/26040609}.		2024edo is [[Enfactoring\|enfactored]] in the 13-limit, with the same tuning as [[1012edo]], which is also a [[zeta]] edo. It corrects 1012edo's mapping for 17, being a strong 2.3.7.11.17.19 subgroup temperament. A comma basis for the said subgroup is {23409/23408, 117649/117612, 323456/323433, 131072/131043, 26042368/26040609}.

	In the 2.3.7.11.17.19, it tunes the 629 & 2024 temperament, which has [[19/17]] as a generator and reaches [[17/16]] in 13 steps. The comma basis in the 2.3.7.11.17.19 subgroup is {23409/23408, 131072/131043, 323456/323433, 818107136/817887699}.		In the 2.3.7.11.17.19, it tunes the {{nowrap\|629 & 2024}} temperament, which has [[19/17]] as a generator and reaches [[17/16]] in 13 steps. The comma basis in the 2.3.7.11.17.19 subgroup is {23409/23408, 131072/131043, 323456/323433, 818107136/817887699}.

	It has two suitable mappings for [[5/1\|5th harmonic]], one which derives from 1012edo, and other in the 2024c val. In the 2024c val, it [[tempering out\|tempers out]] the [[wizma]], 420175/419904 in the 7-limit, as well as [[3025/3024]], [[4225/4224]] and [[10648/10647]] in the 13-limit. If the sharp and flat mappings of 5/4 are combined, then 2024edo is a good 2.3.25 [[subgroup]] tuning. In the 2.3.25.7.11 subgroup, it tempers out [[4375/4374]] and tunes a messed-up version of the [[heimdall]] temperament, which reaches 7th harmonic in 2 second generators instead of 4, and 11th harmonic in 6 second generators instead of 12, taking half as much.		It has two suitable mappings for [[5/1\|5th harmonic]], one which derives from 1012edo, and other in the 2024c val. In the 2024c val, it [[tempering out\|tempers out]] the [[wizma]], 420175/419904 in the 7-limit, as well as [[3025/3024]], [[4225/4224]] and [[10648/10647]] in the 13-limit. If the sharp and flat mappings of 5/4 are combined, then 2024edo is a good 2.3.25 [[subgroup]] tuning. In the 2.3.25.7.11 subgroup, it tempers out [[4375/4374]] and tunes a messed-up version of the [[heimdall]] temperament, which reaches 7th harmonic in 2 second generators instead of 4, and 11th harmonic in 6 second generators instead of 12, taking half as much.
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	== Music ==		== Music ==
	; [[Eliora]]		; [[Eliora]]
	* ''[https://youtu.be/6wO9uONbJhY Piano Juice]'' (2024) - palladium[92] (from [[506edo]]), ruthenium[88] (from [[1012edo]]), 629 & 2024[25], major-arcana[88] (from [[506edo]])		* ''[https://youtu.be/6wO9uONbJhY Piano Juice]'' (2024) - palladium[92] (from [[506edo]]), ruthenium[88] (from [[1012edo]]), {{nowrap\|629 & 2024{{!(}}25{{)!}}}}, major-arcana[88] (from [[506edo]])

	[[Category:Listen]]		[[Category:Listen]]

Eliora: /* Music */ category listen

2024-01-09T00:33:14Z

Music: category listen

← Older revision		Revision as of 00:33, 9 January 2024
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	; [[Eliora]]		; [[Eliora]]
	* ''[https://youtu.be/6wO9uONbJhY Piano Juice]'' (2024) - palladium[92] (from [[506edo]]), ruthenium[88] (from [[1012edo]]), 629 & 2024[25], major-arcana[88] (from [[506edo]])		* ''[https://youtu.be/6wO9uONbJhY Piano Juice]'' (2024) - palladium[92] (from [[506edo]]), ruthenium[88] (from [[1012edo]]), 629 & 2024[25], major-arcana[88] (from [[506edo]])

			[[Category:Listen]]

Eliora: add music

2024-01-09T00:32:24Z

add music

← Older revision		Revision as of 00:32, 9 January 2024
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	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|2024}}		{{EDO intro\|2024}}
			== Theory ==
			2024edo is [[Enfactoring\|enfactored]] in the 13-limit, with the same tuning as [[1012edo]], which is also a [[zeta]] edo. It corrects 1012edo's mapping for 17, being a strong 2.3.7.11.17.19 subgroup temperament. A comma basis for the said subgroup is {23409/23408, 117649/117612, 323456/323433, 131072/131043, 26042368/26040609}.

	~~2024edo is [[Enfactoring\|enfactored]] in~~ the ~~13-limit~~, ~~with~~ the ~~same tuning as~~ [[~~1012edo~~]]~~, which is also~~ a [[~~zeta~~]] ~~edo~~. ~~It corrects 1012edo's mapping for 17, being a strong~~ 2.3.7.11.17.19 ~~subgroup temperament. A comma basis for the said~~ subgroup is {23409/23408, ~~117649~~/~~117612~~, 323456/323433, ~~131072/131043, 26042368~~/~~26040609~~}.		In the 2.3.7.11.17.19, it tunes the 629 & 2024 temperament, which has [[19/17]] as a generator and reaches [[17/16]] in 13 steps. The comma basis in the 2.3.7.11.17.19 subgroup is {23409/23408, 131072/131043, 323456/323433, 818107136/817887699}.

	It has two suitable mappings for [[5/1\|5th harmonic]], one which derives from 1012edo, and other in the 2024c val. In the 2024c val, it [[tempering out\|tempers out]] the [[wizma]], 420175/419904 in the 7-limit, as well as [[3025/3024]], [[4225/4224]] and [[10648/10647]] in the 13-limit. If the sharp and flat mappings of 5/4 are combined, then 2024edo is a good 2.3.25 [[subgroup]] tuning. In the 2.3.25.7.11 subgroup, it tempers out [[4375/4374]] and tunes a messed-up version of the [[heimdall]] temperament, which reaches 7th harmonic in 2 second generators instead of 4, and 11th harmonic in 6 second generators instead of 12, taking half as much.		It has two suitable mappings for [[5/1\|5th harmonic]], one which derives from 1012edo, and other in the 2024c val. In the 2024c val, it [[tempering out\|tempers out]] the [[wizma]], 420175/419904 in the 7-limit, as well as [[3025/3024]], [[4225/4224]] and [[10648/10647]] in the 13-limit. If the sharp and flat mappings of 5/4 are combined, then 2024edo is a good 2.3.25 [[subgroup]] tuning. In the 2.3.25.7.11 subgroup, it tempers out [[4375/4374]] and tunes a messed-up version of the [[heimdall]] temperament, which reaches 7th harmonic in 2 second generators instead of 4, and 11th harmonic in 6 second generators instead of 12, taking half as much.
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 2024 factors into {{factorization\|2024}}, 2024edo has subset edos {{EDOs\| 2, 4, 8, 11, 22, 23, 44, 46, 88, 92, 184, 253, 506, and 1012 }}.		Since 2024 factors into {{factorization\|2024}}, 2024edo has subset edos {{EDOs\| 2, 4, 8, 11, 22, 23, 44, 46, 88, 92, 184, 253, 506, and 1012 }}.

			== Music ==
			; [[Eliora]]
			* ''[https://youtu.be/6wO9uONbJhY Piano Juice]'' (2024) - palladium[92] (from [[506edo]]), ruthenium[88] (from [[1012edo]]), 629 & 2024[25], major-arcana[88] (from [[506edo]])

Eliora: rework

2024-01-03T16:50:37Z

rework

← Older revision		Revision as of 16:50, 3 January 2024
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	{{EDO intro\|2024}}		{{EDO intro\|2024}}

	2024edo is [[Enfactoring\|enfactored]] in the 13-limit, with the same tuning as [[1012edo]], which is also a [[zeta]] edo. ~~Beyond that~~, ~~it does make for~~ a ~~reasonable~~ 17~~- an~~ 19~~-limit system~~.		2024edo is [[Enfactoring\|enfactored]] in the 13-limit, with the same tuning as [[1012edo]], which is also a [[zeta]] edo. It corrects 1012edo's mapping for 17, being a strong 2.3.7.11.17.19 subgroup temperament. A comma basis for the said subgroup is {23409/23408, 117649/117612, 323456/323433, 131072/131043, 26042368/26040609}.

	It has two suitable mappings for [[5/1\|5th harmonic]], one which derives from 1012edo, and other in the 2024c val. In the 2024c val, it [[tempering out\|tempers out]] the [[wizma]], 420175/419904 in the 7-limit, as well as [[3025/3024]], [[4225/4224]] and [[10648/10647]] in the 13-limit.		It has two suitable mappings for [[5/1\|5th harmonic]], one which derives from 1012edo, and other in the 2024c val. In the 2024c val, it [[tempering out\|tempers out]] the [[wizma]], 420175/419904 in the 7-limit, as well as [[3025/3024]], [[4225/4224]] and [[10648/10647]] in the 13-limit. If the sharp and flat mappings of 5/4 are combined, then 2024edo is a good 2.3.25 [[subgroup]] tuning. In the 2.3.25.7.11 subgroup, it tempers out [[4375/4374]] and tunes a messed-up version of the [[heimdall]] temperament, which reaches 7th harmonic in 2 second generators instead of 4, and 11th harmonic in 6 second generators instead of 12, taking half as much.

	If the sharp and flat mappings of 5/4 are combined, then 2024edo is a good 2.3.25 [[subgroup]] tuning. In the 2.3.25.7.11 subgroup, it tempers out [[4375/4374~~]] and [[117649/117612~~]] and tunes a messed-up version of the [[heimdall]] temperament, which reaches 7th harmonic in 2 second generators instead of 4, and 11th harmonic in 6 second generators instead of 12, taking half as much.

	=== Prime harmonics ===		=== Prime harmonics ===

FloraC: Adopt template: Factorization

2023-10-30T11:35:59Z

Adopt template: Factorization

← Older revision		Revision as of 11:35, 30 October 2023
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	2024edo is [[Enfactoring\|enfactored]] in the 13-limit, with the same tuning as [[1012edo]], which is also a [[zeta]] edo. Beyond that, it does make for a reasonable 17- an 19-limit system.		2024edo is [[Enfactoring\|enfactored]] in the 13-limit, with the same tuning as [[1012edo]], which is also a [[zeta]] edo. Beyond that, it does make for a reasonable 17- an 19-limit system.

	It has two suitable mappings for [[5/1\|5th harmonic]], one which derives from 1012edo, and other in the 2024c val. In the 2024c val, it tempers out the [[wizma]], 420175/419904 in the 7-limit, as well as [[3025/3024]], [[4225/4224]] and [[10648/10647]] in the 13-limit.		It has two suitable mappings for [[5/1\|5th harmonic]], one which derives from 1012edo, and other in the 2024c val. In the 2024c val, it [[tempering out\|tempers out]] the [[wizma]], 420175/419904 in the 7-limit, as well as [[3025/3024]], [[4225/4224]] and [[10648/10647]] in the 13-limit.

	If the sharp and flat mappings of 5/4 are combined, then 2024edo is a good 2.3.25 [[subgroup]] tuning. In the 2.3.25.7.11 subgroup, it tempers out [[4375/4374]] and [[117649/117612]] and tunes a messed-up version of the [[heimdall]] temperament, which reaches 7th harmonic in 2 second generators instead of 4, and 11th harmonic in 6 second generators instead of 12, taking half as much.		If the sharp and flat mappings of 5/4 are combined, then 2024edo is a good 2.3.25 [[subgroup]] tuning. In the 2.3.25.7.11 subgroup, it tempers out [[4375/4374]] and [[117649/117612]] and tunes a messed-up version of the [[heimdall]] temperament, which reaches 7th harmonic in 2 second generators instead of 4, and 11th harmonic in 6 second generators instead of 12, taking half as much.
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 2024 factors into ~~2<sup>3</sup> × 11 × 23~~, 2024edo has subset edos {{EDOs\| 2, 4, 8, 11, 22, 23, 44, 46, 88, 92, 184, 253, 506, and 1012 }}.		Since 2024 factors into {{factorization\|2024}}, 2024edo has subset edos {{EDOs\| 2, 4, 8, 11, 22, 23, 44, 46, 88, 92, 184, 253, 506, and 1012 }}.

FloraC: Cleanup; +subsets and supersets

2023-10-15T13:35:30Z

Cleanup; +subsets and supersets

← Older revision		Revision as of 13:35, 15 October 2023
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	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|2024}}		{{EDO intro\|2024}}
	~~==Theory==~~
	~~2024edo is [[enfactored]] in the 13-limit, with the same tuning as [[1012edo]], which is also a [[zeta]] EDO. Beyond that, it does make for a reasonable 17- an 19-limit system.~~

	~~It has two suitable mappings for 5th harmonic, one which derives from 1012edo, and other in the 2024c val. In the 2024c val, it tempers out the~~ [[~~wizma~~]]~~, 420175/419904~~ in the 7-limit, ~~as well~~ as [[~~3025/3024~~]], [[~~4225/4224~~]] ~~and [[10648/10647]] in the 13~~-limit.		2024edo is [[Enfactoring\|enfactored]] in the 13-limit, with the same tuning as [[1012edo]], which is also a [[zeta]] edo. Beyond that, it does make for a reasonable 17- an 19-limit system.

	If the sharp and flat mappings of 5/4 are combined, then 2024edo is a good 2.3.25 subgroup tuning. In the 2.3.25.7.11 subgroup, it tempers out [[4375/4374]] and [[117649/117612]] and tunes a messed-up version of the [[heimdall]] temperament, which reaches 7th harmonic in 2 second generators instead of 4, and 11th harmonic in 6 second generators instead of 12, taking half as much.		It has two suitable mappings for [[5/1\|5th harmonic]], one which derives from 1012edo, and other in the 2024c val. In the 2024c val, it tempers out the [[wizma]], 420175/419904 in the 7-limit, as well as [[3025/3024]], [[4225/4224]] and [[10648/10647]] in the 13-limit.
	===~~Harmonics~~===
	{{~~harmonics~~ in equal\|2024}}		If the sharp and flat mappings of 5/4 are combined, then 2024edo is a good 2.3.25 [[subgroup]] tuning. In the 2.3.25.7.11 subgroup, it tempers out [[4375/4374]] and [[117649/117612]] and tunes a messed-up version of the [[heimdall]] temperament, which reaches 7th harmonic in 2 second generators instead of 4, and 11th harmonic in 6 second generators instead of 12, taking half as much.

			=== Prime harmonics ===
			{{Harmonics in equal\|2024}}

			=== Subsets and supersets ===
			Since 2024 factors into 2<sup>3</sup> × 11 × 23, 2024edo has subset edos {{EDOs\| 2, 4, 8, 11, 22, 23, 44, 46, 88, 92, 184, 253, 506, and 1012 }}.

BudjarnLambeth at 07:00, 9 July 2023

2023-07-09T07:00:24Z

← Older revision		Revision as of 07:00, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|2024}}		{{EDO intro\|2024}}
	==Theory==		==Theory==