4/9-comma meantone - Revision history

BudjarnLambeth: Mathematical interest

2025-08-10T22:13:05Z

Mathematical interest

← Older revision		Revision as of 22:13, 10 August 2025
Line 1:		Line 1:
	{{~~Niche~~}}		{{Mathematical interest}}

	'''4/9-comma meantone''' is a tuning of [[meantone]] where the [[3/2\|fifth]] is flattened by 4/9 of the [[81/80\|syntonic comma]], producing a fifth of 692.396649¢ cents. This is approximated well by [[26edo]] (15\26 is 692.307692¢, which is flatter by 0.088957¢, for a cumulative error of only 2.312882¢ for proceeding all the way around the 26edo circle of fifths). The [[eigenmonzo]] is [[2500/2187]] (231.569849¢), which is only a ragisma ([[4375/4374]], 0.395756¢) sharp of [[8/7]] (231.174094¢).		'''4/9-comma meantone''' is a tuning of [[meantone]] where the [[3/2\|fifth]] is flattened by 4/9 of the [[81/80\|syntonic comma]], producing a fifth of 692.396649¢ cents. This is approximated well by [[26edo]] (15\26 is 692.307692¢, which is flatter by 0.088957¢, for a cumulative error of only 2.312882¢ for proceeding all the way around the 26edo circle of fifths). The [[eigenmonzo]] is [[2500/2187]] (231.569849¢), which is only a ragisma ([[4375/4374]], 0.395756¢) sharp of [[8/7]] (231.174094¢).

Lériendil: changed novelty to niche

2025-03-18T11:42:05Z

changed novelty to niche

← Older revision		Revision as of 11:42, 18 March 2025
Line 1:		Line 1:
	{{~~Novelty~~}}		{{Niche}}

	'''4/9-comma meantone''' is a tuning of [[meantone]] where the [[3/2\|fifth]] is flattened by 4/9 of the [[81/80\|syntonic comma]], producing a fifth of 692.396649¢ cents. This is approximated well by [[26edo]] (15\26 is 692.307692¢, which is flatter by 0.088957¢, for a cumulative error of only 2.312882¢ for proceeding all the way around the 26edo circle of fifths). The [[eigenmonzo]] is [[2500/2187]] (231.569849¢), which is only a ragisma ([[4375/4374]], 0.395756¢) sharp of [[8/7]] (231.174094¢).		'''4/9-comma meantone''' is a tuning of [[meantone]] where the [[3/2\|fifth]] is flattened by 4/9 of the [[81/80\|syntonic comma]], producing a fifth of 692.396649¢ cents. This is approximated well by [[26edo]] (15\26 is 692.307692¢, which is flatter by 0.088957¢, for a cumulative error of only 2.312882¢ for proceeding all the way around the 26edo circle of fifths). The [[eigenmonzo]] is [[2500/2187]] (231.569849¢), which is only a ragisma ([[4375/4374]], 0.395756¢) sharp of [[8/7]] (231.174094¢).

Lucius Chiaraviglio: Add ragisma = 4375/4374

2024-11-13T06:26:35Z

Add ragisma = 4375/4374

← Older revision		Revision as of 06:26, 13 November 2024
Line 1:		Line 1:
	{{Novelty}}		{{Novelty}}

	'''4/9-comma meantone''' is a tuning of [[meantone]] where the [[3/2\|fifth]] is flattened by 4/9 of the [[81/80\|syntonic comma]], producing a fifth of 692.396649¢ cents. This is approximated well by [[26edo]] (15\26 is 692.307692¢, which is flatter by 0.088957¢, for a cumulative error of only 2.312882¢ for proceeding all the way around the 26edo circle of fifths). The [[eigenmonzo]] is [[2500/2187]] (231.569849¢), which is only 0.~~395755¢~~ sharp of [[8/7]] (231.174094¢).		'''4/9-comma meantone''' is a tuning of [[meantone]] where the [[3/2\|fifth]] is flattened by 4/9 of the [[81/80\|syntonic comma]], producing a fifth of 692.396649¢ cents. This is approximated well by [[26edo]] (15\26 is 692.307692¢, which is flatter by 0.088957¢, for a cumulative error of only 2.312882¢ for proceeding all the way around the 26edo circle of fifths). The [[eigenmonzo]] is [[2500/2187]] (231.569849¢), which is only a ragisma ([[4375/4374]], 0.395756¢) sharp of [[8/7]] (231.174094¢).

	The most accurate choice for extending 4/9-comma meantone into the [[7-limit]], [[11-limit]] or [[13-limit]] is [[flattone]] temperament.		The most accurate choice for extending 4/9-comma meantone into the [[7-limit]], [[11-limit]] or [[13-limit]] is [[flattone]] temperament.

Lucius Chiaraviglio: Add note about how close 15\26 is to the 4/9-comma meantone fifth; add ToDo tag (intended for 11-limit, 13-limit extensions)

2024-11-13T06:23:23Z

Add note about how close 15\26 is to the 4/9-comma meantone fifth; add ToDo tag (intended for 11-limit, 13-limit extensions)

← Older revision		Revision as of 06:23, 13 November 2024
Line 1:		Line 1:
	{{Novelty}}		{{Novelty}}

	'''4/9-comma meantone''' is a tuning of [[meantone]] where the [[3/2\|fifth]] is flattened by 4/9 of the [[81/80\|syntonic comma]], producing a fifth of 692.~~397~~ cents. This is approximated well by [[26edo]]. The [[eigenmonzo]] is [[2500/2187]] (231.569849¢), which is only 0.~~396¢~~ sharp of [[8/7]] (231.174094¢).		'''4/9-comma meantone''' is a tuning of [[meantone]] where the [[3/2\|fifth]] is flattened by 4/9 of the [[81/80\|syntonic comma]], producing a fifth of 692.396649¢ cents. This is approximated well by [[26edo]] (15\26 is 692.307692¢, which is flatter by 0.088957¢, for a cumulative error of only 2.312882¢ for proceeding all the way around the 26edo circle of fifths). The [[eigenmonzo]] is [[2500/2187]] (231.569849¢), which is only 0.395755¢ sharp of [[8/7]] (231.174094¢).

	The most accurate choice for extending 4/9-comma meantone into the [[7-limit]], [[11-limit]] or [[13-limit]] is [[flattone]] temperament.		The most accurate choice for extending 4/9-comma meantone into the [[7-limit]], [[11-limit]] or [[13-limit]] is [[flattone]] temperament.

	[[Category:Meantone]]		[[Category:Meantone]]
			[[category:todo:expand]]

BudjarnLambeth: Link

2024-11-13T05:12:13Z

Link

← Older revision		Revision as of 05:12, 13 November 2024
Line 1:		Line 1:
	{{Novelty}}		{{Novelty}}

	'''4/9-comma meantone''' is a tuning of meantone where the [[3/2\|fifth]] is flattened by 4/9 of the [[81/80\|syntonic comma]], producing a fifth of 692.397 cents. This is approximated well by [[26edo]]. The [[eigenmonzo]] is [[2500/2187]] (231.569849¢), which is only 0.396¢ sharp of [[8/7]] (231.174094¢).		'''4/9-comma meantone''' is a tuning of [[meantone]] where the [[3/2\|fifth]] is flattened by 4/9 of the [[81/80\|syntonic comma]], producing a fifth of 692.397 cents. This is approximated well by [[26edo]]. The [[eigenmonzo]] is [[2500/2187]] (231.569849¢), which is only 0.396¢ sharp of [[8/7]] (231.174094¢).

	The most accurate choice for extending 4/9-comma meantone into the [[7-limit]], [[11-limit]] or [[13-limit]] is [[flattone]] temperament.		The most accurate choice for extending 4/9-comma meantone into the [[7-limit]], [[11-limit]] or [[13-limit]] is [[flattone]] temperament.

	[[Category:Meantone]]		[[Category:Meantone]]

BudjarnLambeth: Add link

2024-11-13T05:11:34Z

Add link

← Older revision		Revision as of 05:11, 13 November 2024
Line 1:		Line 1:
	{{Novelty}}		{{Novelty}}

	'''4/9-comma meantone''' is a tuning of meantone where the [[3/2\|fifth]] is flattened by 4/9 of the [[81/80\|syntonic comma]], producing a fifth of 692.397 cents. This is approximated well by [[26edo]]. The eigenmonzo is [[2500/2187]] (231.569849¢), which is only 0.396¢ sharp of [[8/7]] (231.174094¢).		'''4/9-comma meantone''' is a tuning of meantone where the [[3/2\|fifth]] is flattened by 4/9 of the [[81/80\|syntonic comma]], producing a fifth of 692.397 cents. This is approximated well by [[26edo]]. The [[eigenmonzo]] is [[2500/2187]] (231.569849¢), which is only 0.396¢ sharp of [[8/7]] (231.174094¢).

	The most accurate choice for extending 4/9-comma meantone into the [[7-limit]], [[11-limit]] or [[13-limit]] is [[flattone]] temperament.		The most accurate choice for extending 4/9-comma meantone into the [[7-limit]], [[11-limit]] or [[13-limit]] is [[flattone]] temperament.

	[[Category:Meantone]]		[[Category:Meantone]]

Lucius Chiaraviglio: Add eigenmonzo 2500/2187 and nearest useful approximation 8/7. Recommend (but did not do) removing Novelty tag.

2024-11-12T16:23:24Z

Add eigenmonzo 2500/2187 and nearest useful approximation 8/7. Recommend (but did not do) removing Novelty tag.

← Older revision		Revision as of 16:23, 12 November 2024
Line 1:		Line 1:
	{{Novelty}}		{{Novelty}}

	'''4/9-comma meantone''' is a tuning of meantone where the [[3/2\|fifth]] is flattened by 4/9 of the [[81/80\|syntonic comma]], producing a fifth of 692.397 cents. This is approximated well by [[26edo]].		'''4/9-comma meantone''' is a tuning of meantone where the [[3/2\|fifth]] is flattened by 4/9 of the [[81/80\|syntonic comma]], producing a fifth of 692.397 cents. This is approximated well by [[26edo]]. The eigenmonzo is [[2500/2187]] (231.569849¢), which is only 0.396¢ sharp of [[8/7]] (231.174094¢).

	The most accurate choice for extending 4/9-comma meantone into the [[7-limit]], [[11-limit]] or [[13-limit]] is [[flattone]] temperament.		The most accurate choice for extending 4/9-comma meantone into the [[7-limit]], [[11-limit]] or [[13-limit]] is [[flattone]] temperament.

	[[Category:Meantone]]		[[Category:Meantone]]

Fitzgerald Lee at 13:21, 19 October 2024

2024-10-19T13:21:42Z

← Older revision		Revision as of 13:21, 19 October 2024
Line 3:		Line 3:
	'''4/9-comma meantone''' is a tuning of meantone where the [[3/2\|fifth]] is flattened by 4/9 of the [[81/80\|syntonic comma]], producing a fifth of 692.397 cents. This is approximated well by [[26edo]].		'''4/9-comma meantone''' is a tuning of meantone where the [[3/2\|fifth]] is flattened by 4/9 of the [[81/80\|syntonic comma]], producing a fifth of 692.397 cents. This is approximated well by [[26edo]].

	The most accurate choice for extending 4/9-comma meantone into the [[7-limit]], [[11-limit]] or [[13-limit]] is [[flattone]].		The most accurate choice for extending 4/9-comma meantone into the [[7-limit]], [[11-limit]] or [[13-limit]] is [[flattone]] temperament.

	[[Category:Meantone]]		[[Category:Meantone]]

Fitzgerald Lee at 13:16, 19 October 2024

2024-10-19T13:16:53Z

← Older revision		Revision as of 13:16, 19 October 2024
Line 3:		Line 3:
	'''4/9-comma meantone''' is a tuning of meantone where the [[3/2\|fifth]] is flattened by 4/9 of the [[81/80\|syntonic comma]], producing a fifth of 692.397 cents. This is approximated well by [[26edo]].		'''4/9-comma meantone''' is a tuning of meantone where the [[3/2\|fifth]] is flattened by 4/9 of the [[81/80\|syntonic comma]], producing a fifth of 692.397 cents. This is approximated well by [[26edo]].

	The most accurate choice for extending 4/9-comma meantone into the [[7-limit]], [[11-limit]] or [[13-limit]] is ~~the~~ [[flattone]] ~~temperament~~.		The most accurate choice for extending 4/9-comma meantone into the [[7-limit]], [[11-limit]] or [[13-limit]] is [[flattone]].

	[[Category:Meantone]]		[[Category:Meantone]]

Fitzgerald Lee at 13:15, 19 October 2024

2024-10-19T13:15:58Z

← Older revision		Revision as of 13:15, 19 October 2024
Line 3:		Line 3:
	'''4/9-comma meantone''' is a tuning of meantone where the [[3/2\|fifth]] is flattened by 4/9 of the [[81/80\|syntonic comma]], producing a fifth of 692.397 cents. This is approximated well by [[26edo]].		'''4/9-comma meantone''' is a tuning of meantone where the [[3/2\|fifth]] is flattened by 4/9 of the [[81/80\|syntonic comma]], producing a fifth of 692.397 cents. This is approximated well by [[26edo]].

	The most accurate choice for extending 4/9-comma meantone into the [[7-limit]], [[11-limit]] or [[13-limit]] is [[flattone]] temperament.		The most accurate choice for extending 4/9-comma meantone into the [[7-limit]], [[11-limit]] or [[13-limit]] is the [[flattone]] temperament.

	[[Category:Meantone]]		[[Category:Meantone]]