1/6-comma meantone - Revision history

Hstraub at 21:24, 15 February 2025

2025-02-15T21:24:02Z

← Older revision		Revision as of 21:24, 15 February 2025
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			{{interwiki
			\| de = Sechstelkomma-mitteltönig
			\| en = 1/6-comma meantone
			\| es =
			\| ja =
			}}
	'''1/6-comma meantone''' is the tuning of [[meantone]] temperament which tunes the fifth as the sixth root of 45/4, or in other words 698.371 [[cent]]s. This means the fifth is flattened by 1/6 of the [[81/80\|syntonic comma (81/80)]] of 21.506 cents, which is to say by 3.584 cents, hence the name 1/6-comma meantone. In 1/6-comma meantone, the diatonic tritone [[45/32]] is tuned justly, and it can be characterized fully as the regular tuning [[tempering out]] 81/80 and tuning 2 and 45/32 justly. [[55edo]] and [[67edo]] approximate it flatly and sharply, respectively, while [[122edo]] using the c val does so near perfectly. Leopold Mozart and Wolfgang Amadeus Mozart recommended this tuning (implemented as 55edo or something close to it), with a subset and further approximation used for keyboard instruments which (apart from an experimental instrument) did not have enough notes per octave to accommodate it in full.<ref>Chesnut, John (1977) ''Mozart's Teaching of Intonation'', '''Journal of the American Musicological Society''' Vol. 30, No. 2 (Summer, 1977), pp. 254-271 (Published By: University of California Press) [https://doi.org/10.2307/831219 doi.org/10.2307/831219], [http://www.jstor.org/stable/831219 https://www.jstor.org/stable/831219]</ref>		'''1/6-comma meantone''' is the tuning of [[meantone]] temperament which tunes the fifth as the sixth root of 45/4, or in other words 698.371 [[cent]]s. This means the fifth is flattened by 1/6 of the [[81/80\|syntonic comma (81/80)]] of 21.506 cents, which is to say by 3.584 cents, hence the name 1/6-comma meantone. In 1/6-comma meantone, the diatonic tritone [[45/32]] is tuned justly, and it can be characterized fully as the regular tuning [[tempering out]] 81/80 and tuning 2 and 45/32 justly. [[55edo]] and [[67edo]] approximate it flatly and sharply, respectively, while [[122edo]] using the c val does so near perfectly. Leopold Mozart and Wolfgang Amadeus Mozart recommended this tuning (implemented as 55edo or something close to it), with a subset and further approximation used for keyboard instruments which (apart from an experimental instrument) did not have enough notes per octave to accommodate it in full.<ref>Chesnut, John (1977) ''Mozart's Teaching of Intonation'', '''Journal of the American Musicological Society''' Vol. 30, No. 2 (Summer, 1977), pp. 254-271 (Published By: University of California Press) [https://doi.org/10.2307/831219 doi.org/10.2307/831219], [http://www.jstor.org/stable/831219 https://www.jstor.org/stable/831219]</ref>

Lucius Chiaraviglio: Fix reference formatting

2024-11-26T23:57:11Z

Fix reference formatting

← Older revision		Revision as of 23:57, 26 November 2024
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	'''1/6-comma meantone''' is the tuning of [[meantone]] temperament which tunes the fifth as the sixth root of 45/4, or in other words 698.371 [[cent]]s. This means the fifth is flattened by 1/6 of the [[81/80\|syntonic comma (81/80)]] of 21.506 cents, which is to say by 3.584 cents, hence the name 1/6-comma meantone. In 1/6-comma meantone, the diatonic tritone [[45/32]] is tuned justly, and it can be characterized fully as the regular tuning [[tempering out]] 81/80 and tuning 2 and 45/32 justly. [[55edo]] and [[67edo]] approximate it flatly and sharply, respectively, while [[122edo]] using the c val does so near perfectly. Leopold Mozart and Wolfgang Amadeus Mozart recommended this tuning (implemented as 55edo or something close to it), with a subset and further approximation used for keyboard instruments which (apart from an experimental instrument) did not have enough notes per octave to accommodate it in full.<ref>''Mozart's Teaching of Intonation'' ~~(John Chesnut, 1977)~~, '''Journal of the American Musicological Society''' Vol. 30, No. 2 (Summer, 1977), pp. 254-271 (Published By: University of California Press) [https://doi.org/10.2307/831219 doi.org/10.2307/831219], [http://www.jstor.org/stable/831219 https://www.jstor.org/stable/831219]</ref>		'''1/6-comma meantone''' is the tuning of [[meantone]] temperament which tunes the fifth as the sixth root of 45/4, or in other words 698.371 [[cent]]s. This means the fifth is flattened by 1/6 of the [[81/80\|syntonic comma (81/80)]] of 21.506 cents, which is to say by 3.584 cents, hence the name 1/6-comma meantone. In 1/6-comma meantone, the diatonic tritone [[45/32]] is tuned justly, and it can be characterized fully as the regular tuning [[tempering out]] 81/80 and tuning 2 and 45/32 justly. [[55edo]] and [[67edo]] approximate it flatly and sharply, respectively, while [[122edo]] using the c val does so near perfectly. Leopold Mozart and Wolfgang Amadeus Mozart recommended this tuning (implemented as 55edo or something close to it), with a subset and further approximation used for keyboard instruments which (apart from an experimental instrument) did not have enough notes per octave to accommodate it in full.<ref>Chesnut, John (1977) ''Mozart's Teaching of Intonation'', '''Journal of the American Musicological Society''' Vol. 30, No. 2 (Summer, 1977), pp. 254-271 (Published By: University of California Press) [https://doi.org/10.2307/831219 doi.org/10.2307/831219], [http://www.jstor.org/stable/831219 https://www.jstor.org/stable/831219]</ref>

	== Tuning profile ==		== Tuning profile ==

Lucius Chiaraviglio: Improve wording

2024-11-26T21:12:40Z

Improve wording

← Older revision		Revision as of 21:12, 26 November 2024
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	'''1/6-comma meantone''' is the tuning of [[meantone]] temperament which tunes the fifth as the sixth root of 45/4, or in other words 698.371 [[cent]]s. This means the fifth is flattened by 1/6 of the [[81/80\|syntonic comma (81/80)]] of 21.506 cents, which is to say by 3.584 cents, hence the name 1/6-comma meantone. In 1/6-comma meantone, the diatonic tritone [[45/32]] is tuned justly, and it can be characterized fully as the regular tuning [[tempering out]] 81/80 and tuning 2 and 45/32 justly. [[55edo]] and [[67edo]] approximate it flatly and sharply, respectively, while [[122edo]] using the c val does so near perfectly. ~~This~~ tuning (implemented as 55edo or something close to it) ~~was favored by Leopold Mozart and Wolfgang Amadeus Mozart~~, with a subset and further approximation used for keyboard instruments which (apart from an experimental instrument) did not have enough notes per octave to accommodate it in full.<ref>''Mozart's Teaching of Intonation'' (John Chesnut, 1977), '''Journal of the American Musicological Society''' Vol. 30, No. 2 (Summer, 1977), pp. 254-271 (Published By: University of California Press) [https://doi.org/10.2307/831219 doi.org/10.2307/831219], [http://www.jstor.org/stable/831219 https://www.jstor.org/stable/831219]</ref>		'''1/6-comma meantone''' is the tuning of [[meantone]] temperament which tunes the fifth as the sixth root of 45/4, or in other words 698.371 [[cent]]s. This means the fifth is flattened by 1/6 of the [[81/80\|syntonic comma (81/80)]] of 21.506 cents, which is to say by 3.584 cents, hence the name 1/6-comma meantone. In 1/6-comma meantone, the diatonic tritone [[45/32]] is tuned justly, and it can be characterized fully as the regular tuning [[tempering out]] 81/80 and tuning 2 and 45/32 justly. [[55edo]] and [[67edo]] approximate it flatly and sharply, respectively, while [[122edo]] using the c val does so near perfectly. Leopold Mozart and Wolfgang Amadeus Mozart recommended this tuning (implemented as 55edo or something close to it), with a subset and further approximation used for keyboard instruments which (apart from an experimental instrument) did not have enough notes per octave to accommodate it in full.<ref>''Mozart's Teaching of Intonation'' (John Chesnut, 1977), '''Journal of the American Musicological Society''' Vol. 30, No. 2 (Summer, 1977), pp. 254-271 (Published By: University of California Press) [https://doi.org/10.2307/831219 doi.org/10.2307/831219], [http://www.jstor.org/stable/831219 https://www.jstor.org/stable/831219]</ref>

	== Tuning profile ==		== Tuning profile ==

Lucius Chiaraviglio: The Mozarts favored 55EDO or something close to it

2024-11-26T21:07:48Z

The Mozarts favored 55EDO or something close to it

← Older revision		Revision as of 21:07, 26 November 2024
Line 1:		Line 1:
	'''1/6-comma meantone''' is the tuning of [[meantone]] temperament which tunes the fifth as the sixth root of 45/4, or in other words 698.371 [[cent]]s. This means the fifth is flattened by 1/6 of the [[81/80\|syntonic comma (81/80)]] of 21.506 cents, which is to say by 3.584 cents, hence the name 1/6-comma meantone. In 1/6-comma meantone, the diatonic tritone [[45/32]] is tuned justly, and it can be characterized fully as the regular tuning [[tempering out]] 81/80 and tuning 2 and 45/32 justly. [[55edo]] and [[67edo]] approximate it flatly and sharply, respectively, while [[122edo]] using the c val does so near perfectly. This tuning (or something ~~very~~ close to it) was favored by Leopold Mozart and Wolfgang Amadeus Mozart, with a subset and approximation used for keyboard instruments which (apart from an experimental instrument) did not have enough notes per octave to accommodate it in full.<ref>''Mozart's Teaching of Intonation'' (John Chesnut, 1977), '''Journal of the American Musicological Society''' Vol. 30, No. 2 (Summer, 1977), pp. 254-271 (Published By: University of California Press) [https://doi.org/10.2307/831219 doi.org/10.2307/831219], [http://www.jstor.org/stable/831219 https://www.jstor.org/stable/831219]</ref>		'''1/6-comma meantone''' is the tuning of [[meantone]] temperament which tunes the fifth as the sixth root of 45/4, or in other words 698.371 [[cent]]s. This means the fifth is flattened by 1/6 of the [[81/80\|syntonic comma (81/80)]] of 21.506 cents, which is to say by 3.584 cents, hence the name 1/6-comma meantone. In 1/6-comma meantone, the diatonic tritone [[45/32]] is tuned justly, and it can be characterized fully as the regular tuning [[tempering out]] 81/80 and tuning 2 and 45/32 justly. [[55edo]] and [[67edo]] approximate it flatly and sharply, respectively, while [[122edo]] using the c val does so near perfectly. This tuning (implemented as 55edo or something close to it) was favored by Leopold Mozart and Wolfgang Amadeus Mozart, with a subset and further approximation used for keyboard instruments which (apart from an experimental instrument) did not have enough notes per octave to accommodate it in full.<ref>''Mozart's Teaching of Intonation'' (John Chesnut, 1977), '''Journal of the American Musicological Society''' Vol. 30, No. 2 (Summer, 1977), pp. 254-271 (Published By: University of California Press) [https://doi.org/10.2307/831219 doi.org/10.2307/831219], [http://www.jstor.org/stable/831219 https://www.jstor.org/stable/831219]</ref>

	== Tuning profile ==		== Tuning profile ==

Lucius Chiaraviglio: Add reference Mozart's Teaching of Intonation, References section

2024-11-26T21:05:10Z

Add reference Mozart's Teaching of Intonation, References section

← Older revision		Revision as of 21:05, 26 November 2024
Line 1:		Line 1:
	'''1/6-comma meantone''' is the tuning of [[meantone]] temperament which tunes the fifth as the sixth root of 45/4, or in other words 698.371 [[cent]]s. This means the fifth is flattened by 1/6 of the [[81/80\|syntonic comma (81/80)]] of 21.506 cents, which is to say by 3.584 cents, hence the name 1/6-comma meantone. In 1/6-comma meantone, the diatonic tritone [[45/32]] is tuned justly, and it can be characterized fully as the regular tuning [[tempering out]] 81/80 and tuning 2 and 45/32 justly. [[55edo]] and [[67edo]] approximate it flatly and sharply, respectively, while [[122edo]] using the c val does so near perfectly.		'''1/6-comma meantone''' is the tuning of [[meantone]] temperament which tunes the fifth as the sixth root of 45/4, or in other words 698.371 [[cent]]s. This means the fifth is flattened by 1/6 of the [[81/80\|syntonic comma (81/80)]] of 21.506 cents, which is to say by 3.584 cents, hence the name 1/6-comma meantone. In 1/6-comma meantone, the diatonic tritone [[45/32]] is tuned justly, and it can be characterized fully as the regular tuning [[tempering out]] 81/80 and tuning 2 and 45/32 justly. [[55edo]] and [[67edo]] approximate it flatly and sharply, respectively, while [[122edo]] using the c val does so near perfectly. This tuning (or something very close to it) was favored by Leopold Mozart and Wolfgang Amadeus Mozart, with a subset and approximation used for keyboard instruments which (apart from an experimental instrument) did not have enough notes per octave to accommodate it in full.<ref>''Mozart's Teaching of Intonation'' (John Chesnut, 1977), '''Journal of the American Musicological Society''' Vol. 30, No. 2 (Summer, 1977), pp. 254-271 (Published By: University of California Press) [https://doi.org/10.2307/831219 doi.org/10.2307/831219], [http://www.jstor.org/stable/831219 https://www.jstor.org/stable/831219]</ref>

	== Tuning profile ==		== Tuning profile ==
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	* ''Baroque Ensemble Tuning in Extended 1/6 Syntonic Comma Meantone'' by [[Ross W. Duffin]] ([https://www.webcitation.org/5zW8FuybZ WebCite])		* ''Baroque Ensemble Tuning in Extended 1/6 Syntonic Comma Meantone'' by [[Ross W. Duffin]] ([https://www.webcitation.org/5zW8FuybZ WebCite])
	* ''Mozart's tuning: 55-EDO and its close relative, 1/6-comma meantone'' by [[Joseph Monzo]] ([https://web.archive.org/web/20120214163510/sonic-arts.org/monzo/55edo/55edo.htm Internet Archive] [https://www.webcitation.org/5zW910Jax WebCite])		* ''Mozart's tuning: 55-EDO and its close relative, 1/6-comma meantone'' by [[Joseph Monzo]] ([https://web.archive.org/web/20120214163510/sonic-arts.org/monzo/55edo/55edo.htm Internet Archive] [https://www.webcitation.org/5zW910Jax WebCite])

			== References ==
			<references />

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

FloraC: Mistuning -> error

2024-11-07T14:30:16Z

Mistuning -> error

← Older revision		Revision as of 14:30, 7 November 2024
Line 17:		Line 17:
	[[Tuning map]]: {{val\| 1200 1898.3706 2793.4825 3383.7062 }}		[[Tuning map]]: {{val\| 1200 1898.3706 2793.4825 3383.7062 }}

	[[~~Mistuning~~ map]]: {{val\| 0 -3.5844 +7.1688 +14.8803 }}		[[Error map]]: {{val\| 0 -3.5844 +7.1688 +14.8803 }}

	== Links ==		== Links ==

FloraC: Rework

2023-10-01T08:03:33Z

Rework

← Older revision		Revision as of 08:03, 1 October 2023
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	'''1/6 comma meantone''' is the tuning of [[~~Meantone family\|~~meantone ~~temperament~~]] which tunes the fifth as the sixth root of 45/4, or in other words 698.371 [[cent]]s. This means the fifth is flattened by 1/6 of the syntonic comma ([[81/80]] ~~ratio)~~ of 21.506 cents, which is to say by 3.584 cents, hence the name 1/6-comma meantone. In 1/6-comma meantone, the diatonic tritone [[45/32]] is tuned justly, and it can be characterized fully as the regular tuning tempering out 81/80 and tuning 2 and 45/32 justly. [[55edo]] and [[67edo]] approximate it flatly and sharply, respectively, while [[122edo]] using the c val does so near perfectly.		'''1/6-comma meantone''' is the tuning of [[meantone]] temperament which tunes the fifth as the sixth root of 45/4, or in other words 698.371 [[cent]]s. This means the fifth is flattened by 1/6 of the [[81/80\|syntonic comma (81/80)]] of 21.506 cents, which is to say by 3.584 cents, hence the name 1/6-comma meantone. In 1/6-comma meantone, the diatonic tritone [[45/32]] is tuned justly, and it can be characterized fully as the regular tuning [[tempering out]] 81/80 and tuning 2 and 45/32 justly. [[55edo]] and [[67edo]] approximate it flatly and sharply, respectively, while [[122edo]] using the c val does so near perfectly.

	== ~~Fractional projection matrix~~ ==		== Tuning profile ==
	~~The~~ [[~~Fractional monzos\|fractional projection matrix~~]] ~~defining [[7-limit]] 1/6 comma meantone is~~		[[Projection map]]:

	{\| class="~~wikitable~~"		{\| class="right-all"
	\|-		\|-
	\| [1		\| [⟨ \|\| 1 \|\| 2/3 \|\| -4/3 \|\| -19/3 \|\| ]
	\| 0
	\| 0
	\| ~~0>~~
	\|-		\|-
	\| [2/3		\| ⟨ \|\| 0 \|\| 1/3 \|\| 4/3 \|\| 10/3 \|\| ]
	\| 1/3
	\| 1/6
	\| ~~0>~~
	\|-		\|-
	\| ~~[-4~~/3		\| ⟨ \|\| 0 \|\| 1/6 \|\| 2/3 \|\| 5/3 \|\| ]
	\| 4/3
	\| 2/3
	\| ~~0>~~
	\|-		\|-
	\| ~~[-19/3~~		\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| ]]
	\| ~~10/3~~
	\| ~~5/3~~
	\| 0~~>~~
	\|}		\|}

			[[Tuning map]]: {{val\| 1200 1898.3706 2793.4825 3383.7062 }}

			[[Mistuning map]]: {{val\| 0 -3.5844 +7.1688 +14.8803 }}

	== Links ==		== Links ==
	* ~~[http://music.case.edu/~rwd/baroquetemp/XMT.intro.html~~ Baroque Ensemble Tuning in Extended 1/6 Syntonic Comma Meantone] by Ross W. Duffin [~~http~~://www.webcitation.org/5zW8FuybZ ~~permalink~~]		* ''Baroque Ensemble Tuning in Extended 1/6 Syntonic Comma Meantone'' by [[Ross W. Duffin]] ([https://www.webcitation.org/5zW8FuybZ WebCite])
	* ~~[http://sonic-arts.org/monzo/55edo/55edo.htm~~ Mozart's tuning: 55-EDO and its close relative, 1/6-comma meantone] by [[Joseph Monzo]] [~~http~~://www.webcitation.org/5zW910Jax ~~permalink~~]		* ''Mozart's tuning: 55-EDO and its close relative, 1/6-comma meantone'' by [[Joseph Monzo]] ([https://web.archive.org/web/20120214163510/sonic-arts.org/monzo/55edo/55edo.htm Internet Archive] [https://www.webcitation.org/5zW910Jax WebCite])

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

FloraC: FloraC moved page 1/6 syntonic comma meantone to 1/6-comma meantone: Syntonic comma is assumed

2023-09-30T07:08:27Z

FloraC moved page 1/6 syntonic comma meantone to 1/6-comma meantone: Syntonic comma is assumed

← Older revision	Revision as of 07:08, 30 September 2023
(No difference)

BudjarnLambeth: Corrected Joe Monzo to Joseph Monzo

2023-08-09T08:38:49Z

Corrected Joe Monzo to Joseph Monzo

← Older revision		Revision as of 08:38, 9 August 2023
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	== Links ==		== Links ==
	* [http://music.case.edu/~rwd/baroquetemp/XMT.intro.html Baroque Ensemble Tuning in Extended 1/6 Syntonic Comma Meantone] by Ross W. Duffin [http://www.webcitation.org/5zW8FuybZ permalink]		* [http://music.case.edu/~rwd/baroquetemp/XMT.intro.html Baroque Ensemble Tuning in Extended 1/6 Syntonic Comma Meantone] by Ross W. Duffin [http://www.webcitation.org/5zW8FuybZ permalink]
	* [http://sonic-arts.org/monzo/55edo/55edo.htm Mozart's tuning: 55-EDO and its close relative, 1/6-comma meantone] by [[~~Joe~~ Monzo]] [http://www.webcitation.org/5zW910Jax permalink]		* [http://sonic-arts.org/monzo/55edo/55edo.htm Mozart's tuning: 55-EDO and its close relative, 1/6-comma meantone] by [[Joseph Monzo]] [http://www.webcitation.org/5zW910Jax permalink]

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

BudjarnLambeth: Added to category "historical"

2023-04-27T01:15:26Z

Added to category "historical"

← Older revision		Revision as of 01:15, 27 April 2023
Line 32:		Line 32:

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