Harmonic class - Revision history

FloraC: Fix redirect

2026-05-22T07:57:12Z

Fix redirect

← Older revision		Revision as of 07:57, 22 May 2026
Line 1:		Line 1:
	#REDIRECT [[Harmonic limit#~~Harmonic class~~]]		#REDIRECT [[Harmonic limit #Proper harmonic limit]]

	[[Category:Terms]]		[[Category:Terms]]

FloraC: +category

2025-04-24T04:51:37Z

+category

← Older revision		Revision as of 04:51, 24 April 2025
Line 1:		Line 1:
	#REDIRECT [[Harmonic limit#Harmonic class]]		#REDIRECT [[Harmonic limit#Harmonic class]]

			[[Category:Terms]]

Sintel: Redirected page to Harmonic limit#Harmonic class

2025-04-23T19:34:04Z

Redirected page to Harmonic limit#Harmonic class

← Older revision		Revision as of 19:34, 23 April 2025
Line 1:		Line 1:
	'''Harmonic class''' ('''HC''') classifies [[JI]] [[ratio]]s based on the highest [[prime interval\|prime]] they contain in either the numerator or denominator. HC tells us that the ratio must contain the prime of whatever class it falls into and will contain no higher prime.		#REDIRECT [[Harmonic limit#Harmonic class]]

	[[Harmonic limit]] refers to the highest prime allowed in the ratios and includes all simpler ratios of lower limit, but HC only contains those which contain that prime. For example, while 5/4 falls into the 7-limit, it is not considered a HC7 interval because the highest prime it contains is 5 not 7. Therefore, HC7 must contain a 7 and no higher prime. 9/7 however would be considered HC7 because 9 is not prime but rather a multiple of 3. Therefore, HC9 does not exist.

	~~It has been criticized by some schools that the sound of JI is not well characterized by this classification system. Specifically, it is believed that each harmonic~~ class lacks a consistent sound quality. Rather, [[primodality]] classifies intervals by their common denominator, and meanwhile, the [[2.3-equivalent class and Pythagorean-commatic interval naming system\|2.3-equivalent class]] may be used as an enhancement suitable for traditional JI and/or [[regular temperament theory]].

	~~[[Category:Prime limit]]~~
	~~[[Category:Interval complexity measures~~]]

FloraC: Recategorize

2023-11-26T11:14:05Z

Recategorize

← Older revision		Revision as of 11:14, 26 November 2023
Line 6:		Line 6:

	[[Category:Prime limit]]		[[Category:Prime limit]]
	[[Category:Interval complexity ~~measure~~]]		[[Category:Interval complexity measures]]

FloraC: Improve linking and categories

2023-09-29T10:19:42Z

Improve linking and categories

← Older revision		Revision as of 10:19, 29 September 2023
Line 1:		Line 1:
	'''Harmonic class''' ('''HC''') classifies JI ~~ratios~~ based on the highest [[prime interval\|prime]] they contain in either the numerator or denominator. HC tells us that the ratio must contain the prime of whatever class it falls into and will contain no higher prime.		'''Harmonic class''' ('''HC''') classifies [[JI]] [[ratio]]s based on the highest [[prime interval\|prime]] they contain in either the numerator or denominator. HC tells us that the ratio must contain the prime of whatever class it falls into and will contain no higher prime.

	[[Harmonic limit]] refers to the highest prime allowed in the ratios and includes all simpler ratios of lower limit, but HC only contains those which contain that prime. For example, while 5/4 falls into the 7-limit, it is not considered a HC7 interval because the highest prime it contains is 5 not 7. Therefore, HC7 must contain a 7 and no higher prime. 9/7 however would be considered HC7 because 9 is not prime but rather a multiple of 3. Therefore, HC9 does not exist.		[[Harmonic limit]] refers to the highest prime allowed in the ratios and includes all simpler ratios of lower limit, but HC only contains those which contain that prime. For example, while 5/4 falls into the 7-limit, it is not considered a HC7 interval because the highest prime it contains is 5 not 7. Therefore, HC7 must contain a 7 and no higher prime. 9/7 however would be considered HC7 because 9 is not prime but rather a multiple of 3. Therefore, HC9 does not exist.
Line 5:		Line 5:
	It has been criticized by some schools that the sound of JI is not well characterized by this classification system. Specifically, it is believed that each harmonic class lacks a consistent sound quality. Rather, [[primodality]] classifies intervals by their common denominator, and meanwhile, the [[2.3-equivalent class and Pythagorean-commatic interval naming system\|2.3-equivalent class]] may be used as an enhancement suitable for traditional JI and/or [[regular temperament theory]].		It has been criticized by some schools that the sound of JI is not well characterized by this classification system. Specifically, it is believed that each harmonic class lacks a consistent sound quality. Rather, [[primodality]] classifies intervals by their common denominator, and meanwhile, the [[2.3-equivalent class and Pythagorean-commatic interval naming system\|2.3-equivalent class]] may be used as an enhancement suitable for traditional JI and/or [[regular temperament theory]].

	[[Category:~~Class~~]]		[[Category:Prime limit]]
	[[Category:~~Harmonic]]~~		[[Category:Interval complexity measure]]
	~~[[Category:Limit~~]]

Mousemambo: link to 2.3-equivalent_class_and_Pythagorean-commatic_interval_naming_system

2023-09-18T04:13:57Z

link to 2.3-equivalent_class_and_Pythagorean-commatic_interval_naming_system

← Older revision		Revision as of 04:13, 18 September 2023
Line 3:		Line 3:
	[[Harmonic limit]] refers to the highest prime allowed in the ratios and includes all simpler ratios of lower limit, but HC only contains those which contain that prime. For example, while 5/4 falls into the 7-limit, it is not considered a HC7 interval because the highest prime it contains is 5 not 7. Therefore, HC7 must contain a 7 and no higher prime. 9/7 however would be considered HC7 because 9 is not prime but rather a multiple of 3. Therefore, HC9 does not exist.		[[Harmonic limit]] refers to the highest prime allowed in the ratios and includes all simpler ratios of lower limit, but HC only contains those which contain that prime. For example, while 5/4 falls into the 7-limit, it is not considered a HC7 interval because the highest prime it contains is 5 not 7. Therefore, HC7 must contain a 7 and no higher prime. 9/7 however would be considered HC7 because 9 is not prime but rather a multiple of 3. Therefore, HC9 does not exist.

	It has been criticized by some schools that the sound of JI is not well characterized by this classification system. Specifically, it is believed that each harmonic class lacks a consistent sound quality. Rather, [[primodality]] classifies intervals by their common denominator, and meanwhile, the 2.3-equivalent class may be used as an enhancement suitable for traditional JI and/or [[regular temperament theory]].		It has been criticized by some schools that the sound of JI is not well characterized by this classification system. Specifically, it is believed that each harmonic class lacks a consistent sound quality. Rather, [[primodality]] classifies intervals by their common denominator, and meanwhile, the [[2.3-equivalent class and Pythagorean-commatic interval naming system\|2.3-equivalent class]] may be used as an enhancement suitable for traditional JI and/or [[regular temperament theory]].

	[[Category:Class]]		[[Category:Class]]
	[[Category:Harmonic]]		[[Category:Harmonic]]
	[[Category:Limit]]		[[Category:Limit]]

BudjarnLambeth: Moved from category "overtone" to "harmonic"

2023-04-28T09:20:34Z

Moved from category "overtone" to "harmonic"

← Older revision		Revision as of 09:20, 28 April 2023
Line 6:		Line 6:

	[[Category:Class]]		[[Category:Class]]
	[[Category:~~Overtone~~]]		[[Category:Harmonic]]
	[[Category:Limit]]		[[Category:Limit]]

FloraC: +criticisms

2023-01-02T09:07:30Z

+criticisms

← Older revision		Revision as of 09:07, 2 January 2023
Line 2:		Line 2:

	[[Harmonic limit]] refers to the highest prime allowed in the ratios and includes all simpler ratios of lower limit, but HC only contains those which contain that prime. For example, while 5/4 falls into the 7-limit, it is not considered a HC7 interval because the highest prime it contains is 5 not 7. Therefore, HC7 must contain a 7 and no higher prime. 9/7 however would be considered HC7 because 9 is not prime but rather a multiple of 3. Therefore, HC9 does not exist.		[[Harmonic limit]] refers to the highest prime allowed in the ratios and includes all simpler ratios of lower limit, but HC only contains those which contain that prime. For example, while 5/4 falls into the 7-limit, it is not considered a HC7 interval because the highest prime it contains is 5 not 7. Therefore, HC7 must contain a 7 and no higher prime. 9/7 however would be considered HC7 because 9 is not prime but rather a multiple of 3. Therefore, HC9 does not exist.

			It has been criticized by some schools that the sound of JI is not well characterized by this classification system. Specifically, it is believed that each harmonic class lacks a consistent sound quality. Rather, [[primodality]] classifies intervals by their common denominator, and meanwhile, the 2.3-equivalent class may be used as an enhancement suitable for traditional JI and/or [[regular temperament theory]].

	[[Category:Class]]		[[Category:Class]]
	[[Category:Overtone]]		[[Category:Overtone]]
	[[Category:Limit]]		[[Category:Limit]]

FloraC: That list isn't useful cuz HC contains infinitely many intervals and examples are already given in the first paragraph

2023-01-02T09:06:16Z

That list isn't useful cuz HC contains infinitely many intervals and examples are already given in the first paragraph

← Older revision		Revision as of 09:06, 2 January 2023
Line 1:		Line 1:
	'''Harmonic ~~Class~~''' ('''HC''') classifies JI ratios based on the highest [[prime interval\|prime]] they contain in either the numerator or denominator. HC tells us that the ratio must contain the prime of whatever class it falls into and will contain no higher prime. [[Harmonic limit]] refers to the highest prime allowed in the ratios and includes all simpler ratios of lower limit, but HC only contains those which contain that prime. For example, while 5/4 falls into the 7-limit, it is not considered a HC7 interval because the highest prime it contains is 5 not 7. Therefore, HC7 must contain a 7 and no higher prime. 9/7 however would be considered HC7 because 9 is not prime but rather a multiple of 3. Therefore, HC9 does not exist.		'''Harmonic class''' ('''HC''') classifies JI ratios based on the highest [[prime interval\|prime]] they contain in either the numerator or denominator. HC tells us that the ratio must contain the prime of whatever class it falls into and will contain no higher prime.

	~~== List~~ of ~~harmonic classes ==~~		[[Harmonic limit]] refers to the highest prime allowed in the ratios and includes all simpler ratios of lower limit, but HC only contains those which contain that prime. For example, while 5/4 falls into the 7-limit, it is not considered a HC7 interval because the highest prime it contains is 5 not 7. Therefore, HC7 must contain a 7 and no higher prime. 9/7 however would be considered HC7 because 9 is not prime but rather a multiple of 3. Therefore, HC9 does not exist.
	* HC1 - 1/1, ~~2/1~~
	* HC3 - 9/8, 3/2, 4~~/3, 16/9, 3/1~~
	* HC5 - ~~10/9~~, 6/5, ~~5/4, 8/5, 5/3~~
	* HC7 ~~- 8/~~7~~, 7/6,~~ 9/7~~, 7/5, 10/7, 12/7, 7/4~~
	* HC11 - 12/11, 11/10, 11/9, ~~14/11, 11/8, 16/11, 11/7, 18/11, 20/11, 11/6~~
	* HC13 -

	[[Category:Class]]		[[Category:Class]]
	[[Category:Overtone]]		[[Category:Overtone]]
	[[Category:Limit]]		[[Category:Limit]]

FloraC: Cleanup

2023-01-02T07:58:11Z

Cleanup

← Older revision		Revision as of 07:58, 2 January 2023
Line 1:		Line 1:
	~~=Definition=~~		'''Harmonic Class''' ('''HC''') classifies JI ratios based on the highest [[prime interval\|prime]] they contain in either the numerator or denominator. HC tells us that the ratio must contain the prime of whatever class it falls into and will contain no higher prime. [[Harmonic limit]] refers to the highest prime allowed in the ratios and includes all simpler ratios of lower limit, but HC only contains those which contain that prime. For example, while 5/4 falls into the 7-limit, it is not considered a HC7 interval because the highest prime it contains is 5 not 7. Therefore, HC7 must contain a 7 and no higher prime. 9/7 however would be considered HC7 because 9 is not prime but rather a multiple of 3. Therefore, HC9 does not exist.
	Harmonic Class or HC classifies JI ratios based on the highest prime they contain in either the numerator or denominator. HC tells us that the ratio must contain the prime of whatever class it falls into and will contain no higher prime. Harmonic ~~Limit~~ refers to the highest prime allowed in the ratios and includes all simpler ratios of lower limit but HC only contains those which contain that prime. For example, while 5/4 falls into the 7-limit, it is not considered a HC7 interval because the highest prime it contains is 5 not 7. Therefore, HC7 must contain a 7 and no higher prime. 9/7 however would be considered HC7 because 9 is not prime but rather a multiple of 3. Therefore, HC9 ~~doesn't~~ exist.

	=List of ~~Harmonic Classes~~=		== List of harmonic classes ==
			* HC1 - 1/1, 2/1
			* HC3 - 9/8, 3/2, 4/3, 16/9, 3/1
			* HC5 - 10/9, 6/5, 5/4, 8/5, 5/3
			* HC7 - 8/7, 7/6, 9/7, 7/5, 10/7, 12/7, 7/4
			* HC11 - 12/11, 11/10, 11/9, 14/11, 11/8, 16/11, 11/7, 18/11, 20/11, 11/6
			* HC13 -

	<ul><li>HC1 - 1/1, 2/1</li><li>HC3 - 9/8, 3/2, 4/3, 16/9, 3/1</li><li>HC5 - 10/9, 6/5, 5/4, 8/5, 5/3</li><li>HC7 - 8/7, 7/6, 9/7, 7/5, 10/7, 12/7, 7/4</li><li>HC11 - 12/11, 11/10, 11/9, 14/11, 11/8, 16/11, 11/7, 18/11, 20/11, 11/6</li><li>HC13 -</li></ul> [[Category:~~class~~]]		[[Category:Class]]
	[[Category:Overtone]]		[[Category:Overtone]]
	[[Category:~~limit~~]]		[[Category:Limit]]