126edo - Revision history

VectorGraphics at 20:08, 17 April 2025

2025-04-17T20:08:03Z

← Older revision		Revision as of 20:08, 17 April 2025
Line 2:		Line 2:
	{{ED intro}}		{{ED intro}}

	126edo has a distinctly sharp tendency, with the [[3/1\|3]], [[5/1\|5]], [[7/1\|7]] and [[11/1\|11]] all sharp. The equal temperament [[tempering out\|tempers out]] [[2048/2025]] in the 5-limit, [[2401/2400]] and [[4375/4374]] in the 7-limit, and [[176/175]], [[896/891]], and 1331/1323 in the 11-limit. It provides the [[optimal patent val]] for 7- and 11-limit [[srutal]] temperament. It also creates an excellent [[Porcupine]][8] scale, mapping the ~~large [[quill]]s~~ to 17 steps, and the ~~small~~ to 7, which is the precise amount of tempering needed to make the thirds and fourths equally consonant within a few fractions of a cent.		126edo has a distinctly sharp tendency, with the [[3/1\|3]], [[5/1\|5]], [[7/1\|7]] and [[11/1\|11]] all sharp. The equal temperament [[tempering out\|tempers out]] [[2048/2025]] in the 5-limit, [[2401/2400]] and [[4375/4374]] in the 7-limit, and [[176/175]], [[896/891]], and 1331/1323 in the 11-limit. It provides the [[optimal patent val]] for 7- and 11-limit [[srutal]] temperament. It also creates an excellent [[Porcupine]][8] scale, mapping the generators to 17 steps, and the smaller interval to 7, which is the precise amount of tempering needed to make the thirds and fourths equally consonant within a few fractions of a cent.

	=== Odd harmonics ===		=== Odd harmonics ===

ArrowHead294 at 17:00, 18 February 2025

2025-02-18T17:00:00Z

← Older revision		Revision as of 17:00, 18 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|126~~}}		{{ED intro}}

	126edo has a distinctly sharp tendency, with the [[3/1\|3]], [[5/1\|5]], [[7/1\|7]] and [[11/1\|11]] all sharp. The equal temperament [[tempering out\|tempers out]] [[2048/2025]] in the 5-limit, [[2401/2400]] and [[4375/4374]] in the 7-limit, and [[176/175]], [[896/891]], and 1331/1323 in the 11-limit. It provides the [[optimal patent val]] for 7- and 11-limit [[srutal]] temperament. It also creates an excellent [[Porcupine]][8] scale, mapping the large [[quill]]s to 17 steps, and the small to 7, which is the precise amount of tempering needed to make the thirds and fourths equally consonant within a few fractions of a cent.		126edo has a distinctly sharp tendency, with the [[3/1\|3]], [[5/1\|5]], [[7/1\|7]] and [[11/1\|11]] all sharp. The equal temperament [[tempering out\|tempers out]] [[2048/2025]] in the 5-limit, [[2401/2400]] and [[4375/4374]] in the 7-limit, and [[176/175]], [[896/891]], and 1331/1323 in the 11-limit. It provides the [[optimal patent val]] for 7- and 11-limit [[srutal]] temperament. It also creates an excellent [[Porcupine]][8] scale, mapping the large [[quill]]s to 17 steps, and the small to 7, which is the precise amount of tempering needed to make the thirds and fourths equally consonant within a few fractions of a cent.

FloraC: Rework the subsets and supersets section

2024-05-29T05:38:20Z

Rework the subsets and supersets section

← Older revision		Revision as of 05:38, 29 May 2024
Line 8:		Line 8:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	It has ~~divisors~~ 2, 3, 6, 7, 9, 14, 18, 21, 42, and 63.		Since 126 factors into {{factorization\|126}}, 126edo has subset edos {{EDOs\| 2, 3, 6, 7, 9, 14, 18, 21, 42, and 63 }}.

	[[Category:Srutal]]		[[Category:Srutal]]

FloraC: Cleanup

2024-05-29T05:36:36Z

Cleanup

← Older revision		Revision as of 05:36, 29 May 2024
Line 2:		Line 2:
	{{EDO intro\|126}}		{{EDO intro\|126}}

	126edo has a distinctly sharp tendency, with the 3, 5, 7 and 11 all sharp. It tempers out 2048/2025 in the 5-limit, 2401/2400 and 4375/4374 in the 7-limit, and 176/175, 1331/1323 ~~and 896/891~~ in the 11-limit. It provides the optimal patent val for 7- and 11-limit [[~~Diaschismic_family#Srutal-11-limit\|~~srutal ~~temperament~~]]. It also creates an excellent [[Porcupine]][8] scale, mapping the large ~~quills~~ to 17 steps, and the small to 7, which is the precise amount of tempering needed to make the ~~3rds~~ and ~~4ths~~ equally consonant within a few fractions of a cent. ~~It has divisors 2, 3, 6, 7, 9, 14, 18, 21, 42, and 63.~~		126edo has a distinctly sharp tendency, with the [[3/1\|3]], [[5/1\|5]], [[7/1\|7]] and [[11/1\|11]] all sharp. The equal temperament [[tempering out\|tempers out]] [[2048/2025]] in the 5-limit, [[2401/2400]] and [[4375/4374]] in the 7-limit, and [[176/175]], [[896/891]], and 1331/1323 in the 11-limit. It provides the [[optimal patent val]] for 7- and 11-limit [[srutal]] temperament. It also creates an excellent [[Porcupine]][8] scale, mapping the large [[quill]]s to 17 steps, and the small to 7, which is the precise amount of tempering needed to make the thirds and fourths equally consonant within a few fractions of a cent.

			=== Odd harmonics ===
	{{Harmonics in equal\|126}}		{{Harmonics in equal\|126}}
	[[Category:~~Equal divisions of the octave\|###~~]] ~~<!-- 3-digit number -->~~
			=== Subsets and supersets ===
			It has divisors 2, 3, 6, 7, 9, 14, 18, 21, 42, and 63.

			[[Category:Srutal]]

BudjarnLambeth: Edo intro

2024-01-25T09:51:46Z

Edo intro

← Older revision		Revision as of 09:51, 25 January 2024
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	~~The~~ 126 ~~equal temperament divides the [[octave]] into 126 equal parts of 9.524 cents each. It~~ has a distinctly sharp tendency, with the 3, 5, 7 and 11 all sharp. It tempers out 2048/2025 in the 5-limit, 2401/2400 and 4375/4374 in the 7-limit, and 176/175, 1331/1323 and 896/891 in the 11-limit. It provides the optimal patent val for 7- and 11-limit [[Diaschismic_family#Srutal-11-limit\|srutal temperament]]. It also creates an excellent [[Porcupine]][8] scale, mapping the large quills to 17 steps, and the small to 7, which is the precise amount of tempering needed to make the 3rds and 4ths equally consonant within a few fractions of a cent. It has divisors 2, 3, 6, 7, 9, 14, 18, 21, 42, and 63.		{{EDO intro\|126}}

			126edo has a distinctly sharp tendency, with the 3, 5, 7 and 11 all sharp. It tempers out 2048/2025 in the 5-limit, 2401/2400 and 4375/4374 in the 7-limit, and 176/175, 1331/1323 and 896/891 in the 11-limit. It provides the optimal patent val for 7- and 11-limit [[Diaschismic_family#Srutal-11-limit\|srutal temperament]]. It also creates an excellent [[Porcupine]][8] scale, mapping the large quills to 17 steps, and the small to 7, which is the precise amount of tempering needed to make the 3rds and 4ths equally consonant within a few fractions of a cent. It has divisors 2, 3, 6, 7, 9, 14, 18, 21, 42, and 63.
	{{Harmonics in equal\|126}}		{{Harmonics in equal\|126}}
	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

BudjarnLambeth: Add link to octave

2024-01-04T01:45:22Z

Add link to octave

← Older revision		Revision as of 01:45, 4 January 2024
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	The 126 equal temperament divides the octave into 126 equal parts of 9.524 cents each. It has a distinctly sharp tendency, with the 3, 5, 7 and 11 all sharp. It tempers out 2048/2025 in the 5-limit, 2401/2400 and 4375/4374 in the 7-limit, and 176/175, 1331/1323 and 896/891 in the 11-limit. It provides the optimal patent val for 7- and 11-limit [[Diaschismic_family#Srutal-11-limit\|srutal temperament]]. It also creates an excellent [[Porcupine]][8] scale, mapping the large quills to 17 steps, and the small to 7, which is the precise amount of tempering needed to make the 3rds and 4ths equally consonant within a few fractions of a cent. It has divisors 2, 3, 6, 7, 9, 14, 18, 21, 42, and 63.		The 126 equal temperament divides the [[octave]] into 126 equal parts of 9.524 cents each. It has a distinctly sharp tendency, with the 3, 5, 7 and 11 all sharp. It tempers out 2048/2025 in the 5-limit, 2401/2400 and 4375/4374 in the 7-limit, and 176/175, 1331/1323 and 896/891 in the 11-limit. It provides the optimal patent val for 7- and 11-limit [[Diaschismic_family#Srutal-11-limit\|srutal temperament]]. It also creates an excellent [[Porcupine]][8] scale, mapping the large quills to 17 steps, and the small to 7, which is the precise amount of tempering needed to make the 3rds and 4ths equally consonant within a few fractions of a cent. It has divisors 2, 3, 6, 7, 9, 14, 18, 21, 42, and 63.
	{{Harmonics in equal\|126}}		{{Harmonics in equal\|126}}
	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

BudjarnLambeth: Add link to porcupine

2024-01-04T01:45:07Z

Add link to porcupine

← Older revision		Revision as of 01:45, 4 January 2024
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	The 126 equal temperament divides the octave into 126 equal parts of 9.524 cents each. It has a distinctly sharp tendency, with the 3, 5, 7 and 11 all sharp. It tempers out 2048/2025 in the 5-limit, 2401/2400 and 4375/4374 in the 7-limit, and 176/175, 1331/1323 and 896/891 in the 11-limit. It provides the optimal patent val for 7- and 11-limit [[Diaschismic_family#Srutal-11-limit\|srutal temperament]]. It also creates an excellent Porcupine [8] scale, mapping the large quills to 17 steps, and the small to 7, which is the precise amount of tempering needed to make the 3rds and 4ths equally consonant within a few fractions of a cent. It has divisors 2, 3, 6, 7, 9, 14, 18, 21, 42, and 63.		The 126 equal temperament divides the octave into 126 equal parts of 9.524 cents each. It has a distinctly sharp tendency, with the 3, 5, 7 and 11 all sharp. It tempers out 2048/2025 in the 5-limit, 2401/2400 and 4375/4374 in the 7-limit, and 176/175, 1331/1323 and 896/891 in the 11-limit. It provides the optimal patent val for 7- and 11-limit [[Diaschismic_family#Srutal-11-limit\|srutal temperament]]. It also creates an excellent [[Porcupine]][8] scale, mapping the large quills to 17 steps, and the small to 7, which is the precise amount of tempering needed to make the 3rds and 4ths equally consonant within a few fractions of a cent. It has divisors 2, 3, 6, 7, 9, 14, 18, 21, 42, and 63.
	{{Harmonics in equal\|126}}		{{Harmonics in equal\|126}}
	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

BudjarnLambeth: Added "harmonics in equal" table

2023-06-24T02:56:25Z

Added "harmonics in equal" table

← Older revision		Revision as of 02:56, 24 June 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	The 126 equal temperament divides the octave into 126 equal parts of 9.524 cents each. It has a distinctly sharp tendency, with the 3, 5, 7 and 11 all sharp. It tempers out 2048/2025 in the 5-limit, 2401/2400 and 4375/4374 in the 7-limit, and 176/175, 1331/1323 and 896/891 in the 11-limit. It provides the optimal patent val for 7- and 11-limit [[Diaschismic_family#Srutal-11-limit\|srutal temperament]]. It also creates an excellent Porcupine [8] scale, mapping the large quills to 17 steps, and the small to 7, which is the precise amount of tempering needed to make the 3rds and 4ths equally consonant within a few fractions of a cent. It has divisors 2, 3, 6, 7, 9, 14, 18, 21, 42, and 63.		The 126 equal temperament divides the octave into 126 equal parts of 9.524 cents each. It has a distinctly sharp tendency, with the 3, 5, 7 and 11 all sharp. It tempers out 2048/2025 in the 5-limit, 2401/2400 and 4375/4374 in the 7-limit, and 176/175, 1331/1323 and 896/891 in the 11-limit. It provides the optimal patent val for 7- and 11-limit [[Diaschismic_family#Srutal-11-limit\|srutal temperament]]. It also creates an excellent Porcupine [8] scale, mapping the large quills to 17 steps, and the small to 7, which is the precise amount of tempering needed to make the 3rds and 4ths equally consonant within a few fractions of a cent. It has divisors 2, 3, 6, 7, 9, 14, 18, 21, 42, and 63.
			{{Harmonics in equal\|126}}
	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

Aura at 18:54, 4 October 2022

2022-10-04T18:54:19Z

← Older revision		Revision as of 18:54, 4 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	The 126 equal temperament divides the octave into 126 equal parts of 9.524 cents each. It has a distinctly sharp tendency, with the 3, 5, 7 and 11 all sharp. It tempers out 2048/2025 in the 5-limit, 2401/2400 and 4375/4374 in the 7-limit, and 176/175, 1331/1323 and 896/891 in the 11-limit. It provides the optimal patent val for 7- and 11-limit [[Diaschismic_family#Srutal-11-limit\|srutal temperament]]. It also creates an excellent Porcupine [8] scale, mapping the large quills to 17 steps, and the small to 7, which is the precise amount of tempering needed to make the 3rds and 4ths equally consonant within a few fractions of a cent. It has divisors 2, 3, 6, 7, 9, 14, 18, 21, 42, and 63.		The 126 equal temperament divides the octave into 126 equal parts of 9.524 cents each. It has a distinctly sharp tendency, with the 3, 5, 7 and 11 all sharp. It tempers out 2048/2025 in the 5-limit, 2401/2400 and 4375/4374 in the 7-limit, and 176/175, 1331/1323 and 896/891 in the 11-limit. It provides the optimal patent val for 7- and 11-limit [[Diaschismic_family#Srutal-11-limit\|srutal temperament]]. It also creates an excellent Porcupine [8] scale, mapping the large quills to 17 steps, and the small to 7, which is the precise amount of tempering needed to make the 3rds and 4ths equally consonant within a few fractions of a cent. It has divisors 2, 3, 6, 7, 9, 14, 18, 21, 42, and 63.

	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

Fredg999 category edits: Categories

2022-07-02T16:26:25Z

← Older revision		Revision as of 09:51, 25 January 2024
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	~~The~~ 126 ~~equal temperament divides the [[octave]] into 126 equal parts of 9.524 cents each. It~~ has a distinctly sharp tendency, with the 3, 5, 7 and 11 all sharp. It tempers out 2048/2025 in the 5-limit, 2401/2400 and 4375/4374 in the 7-limit, and 176/175, 1331/1323 and 896/891 in the 11-limit. It provides the optimal patent val for 7- and 11-limit [[Diaschismic_family#Srutal-11-limit\|srutal temperament]]. It also creates an excellent [[Porcupine]][8] scale, mapping the large quills to 17 steps, and the small to 7, which is the precise amount of tempering needed to make the 3rds and 4ths equally consonant within a few fractions of a cent. It has divisors 2, 3, 6, 7, 9, 14, 18, 21, 42, and 63.		{{EDO intro\|126}}

			126edo has a distinctly sharp tendency, with the 3, 5, 7 and 11 all sharp. It tempers out 2048/2025 in the 5-limit, 2401/2400 and 4375/4374 in the 7-limit, and 176/175, 1331/1323 and 896/891 in the 11-limit. It provides the optimal patent val for 7- and 11-limit [[Diaschismic_family#Srutal-11-limit\|srutal temperament]]. It also creates an excellent [[Porcupine]][8] scale, mapping the large quills to 17 steps, and the small to 7, which is the precise amount of tempering needed to make the 3rds and 4ths equally consonant within a few fractions of a cent. It has divisors 2, 3, 6, 7, 9, 14, 18, 21, 42, and 63.
	{{Harmonics in equal\|126}}		{{Harmonics in equal\|126}}
	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

← Older revision		Revision as of 16:26, 2 July 2022
Line 1:		Line 1:
	The 126 equal temperament divides the octave into 126 equal parts of 9.524 cents each. It has a distinctly sharp tendency, with the 3, 5, 7 and 11 all sharp. It tempers out 2048/2025 in the 5-limit, 2401/2400 and 4375/4374 in the 7-limit, and 176/175, 1331/1323 and 896/891 in the 11-limit. It provides the optimal patent val for 7- and 11-limit [[Diaschismic_family#Srutal-11-limit\|srutal temperament]]. It also creates an excellent Porcupine [8] scale, mapping the large quills to 17 steps, and the small to 7, which is the precise amount of tempering needed to make the 3rds and 4ths equally consonant within a few fractions of a cent. It has divisors 2, 3, 6, 7, 9, 14, 18, 21, 42, and 63.		The 126 equal temperament divides the octave into 126 equal parts of 9.524 cents each. It has a distinctly sharp tendency, with the 3, 5, 7 and 11 all sharp. It tempers out 2048/2025 in the 5-limit, 2401/2400 and 4375/4374 in the 7-limit, and 176/175, 1331/1323 and 896/891 in the 11-limit. It provides the optimal patent val for 7- and 11-limit [[Diaschismic_family#Srutal-11-limit\|srutal temperament]]. It also creates an excellent Porcupine [8] scale, mapping the large quills to 17 steps, and the small to 7, which is the precise amount of tempering needed to make the 3rds and 4ths equally consonant within a few fractions of a cent. It has divisors 2, 3, 6, 7, 9, 14, 18, 21, 42, and 63.

			[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->