352/351 - Revision history

FloraC: Hyphenation

2026-10-10T08:27:33Z

Hyphenation

← Older revision		Revision as of 08:27, 10 October 2026
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	== Temperaments ==		== Temperaments ==
	[[Tempering out]] this comma leads to a form of '''major minthmic ~~temperament~~''' (full 13-limit rank-5) or '''majorminth ~~temperament~~''' (2.3.11.13-subgroup rank-3), which enables [[major minthmic chords]]. Mintha was a nymph turned into a mint plant by a goddess whom she got in the way of<ref>[https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0104%3Aalphabetic+letter%3DM%3Aentry+group%3D26%3Aentry%3Dmintha-bio-1 ''Dictionary of Greek and Roman Biography and Mythology''] – William Smith (1849)</ref><ref>[https://web.archive.org/web/20221230130135/http://mythandreligion.upatras.gr/english/__trashed/ ''Dictionary of Classical Mythology''] – M. R. Wright (2012)</ref><ref>[https://www.greekboston.com/culture/mythology/minthe ''All About Minthe – Myth of Greek Mythology''] – Greek Boston (2024)</ref>, and major minthmic tempering has the slightly sharp, minty-fresh fifths some people appreciate. [[Margo Schulter]] has expressed great fondness for this comma, for example.		[[Tempering out]] this comma leads to a form of '''major-minthmic''' temperament (full 13-limit rank-5) or '''majorminth''' temperament (2.3.11.13-subgroup rank-3), which enables [[major-minthmic chords]]. Mintha was a nymph turned into a mint plant by a goddess whom she got in the way of<ref>[https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0104%3Aalphabetic+letter%3DM%3Aentry+group%3D26%3Aentry%3Dmintha-bio-1 ''Dictionary of Greek and Roman Biography and Mythology''] – William Smith (1849)</ref><ref>[https://web.archive.org/web/20221230130135/http://mythandreligion.upatras.gr/english/__trashed/ ''Dictionary of Classical Mythology''] – M. R. Wright (2012)</ref><ref>[https://www.greekboston.com/culture/mythology/minthe ''All About Minthe – Myth of Greek Mythology''] – Greek Boston (2024)</ref>, and major minthmic tempering has the slightly sharp, minty-fresh fifths some people appreciate. [[Margo Schulter]] has expressed great fondness for this comma, for example.

	It is tempered out in a large number of notable temperaments such as [[meanpop]], [[srutal]], [[countercata]], [[cassandra]], [[diaschismic]], [[hemififths]], [[amity]], [[rodan]], [[buzzard]] and higher rank temperaments like [[parapyth]], [[Aberschismic family#Overview to extensions\|aberschismic extensions]], [[gentle]], [[Catalog of rank-4 temperaments#Akua (352/351, 847/845)\|akua]] or [[valinorsmic]].		It is tempered out in a large number of notable temperaments such as [[meanpop]], [[srutal]], [[countercata]], [[cassandra]], [[diaschismic]], [[hemififths]], [[amity]], [[rodan]], [[buzzard]] and higher rank temperaments like [[parapyth]], [[Aberschismic family#Overview to extensions\|aberschismic extensions]], [[gentle]], [[Catalog of rank-4 temperaments#Akua (352/351, 847/845)\|akua]] or [[valinorsmic]].

FloraC: Chain of fourths -> chain of fifths; - complex interval relations

2026-10-09T12:31:29Z

Chain of fourths -> chain of fifths; - complex interval relations

← Older revision		Revision as of 12:31, 9 October 2026
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	\| Comma = yes		\| Comma = yes
	}}		}}
	'''352/351''', the '''major minthma''' or '''major gentle comma''' is a [[small comma\|small]] [[13-limit]] (also 2.3.11.13 [[subgroup]]) [[comma]] measuring about 4.9{{cent}}. This comma can be described in a number of ways. First, it is the difference between the tridecimal minor third of [[13/11]] and the Pythagorean minor third of [[32/27]]~~, hence the name ''11/13''-kleisma~~. This means that ~~when this comma is~~ [[~~tempering out~~\|~~tempered out~~]], 11/8 ~~plus three perfect fourths~~ octave ~~reduces to 13/8~~; as such, this comma can be understood as relating harmonics 11 and 13 by a chain of ~~fourths~~. Second, it is the difference between various tridecimal intervals and their adjacent undecimal intervals such as:		'''352/351''', the '''major minthma''' or '''major gentle comma''' is a [[small comma\|small]] [[13-limit]] (also 2.3.11.13 [[subgroup]]) [[comma]] measuring about 4.9{{cent}}. This comma can be described in a number of ways. First, it is the difference between the tridecimal minor third of [[13/11]] and the Pythagorean minor third of [[32/27]]. This means that [[13/8]] plus three [[3/2\|perfect fifths]] differs from [[11/8]] by exactly this comma up to [[octave equivalence]]; as such, this comma can be understood as relating harmonics 11 and 13 by a [[chain of fifths]]. Second, it is the difference between various tridecimal intervals and their adjacent undecimal intervals such as between [[11/9]] and [[39/32]], between [[16/13]] and [[27/22]], and between the tridecimal quartertone of [[1053/1024]] and the undecimal quartertone of [[33/32]].
	* The tridecimal quartertone of [[1053/1024]] and the undecimal quartertone of [[33/32]];
	* [[88/81]] and [[13/12]];
	* [[128/117]] and [[12/11]];
	* [[11/9]] and [[39/32]];
	* [[16/13]] and [[27/22]];
	* [[11/8]] and [[~~351~~/~~256]];~~
	* [[243/176]] and [[18/~~13]];~~
	~~And their [[octave complement~~]]~~<nowiki/>s~~.

	352/351 and [[351/350]], the ratwolfsma, are extremely close in size and make up a consecutive pair of 13-limit [[superparticular]] commas. Their difference is ~~[[chalmersia\|~~123201/123200]], the chalmersia, the smallest 13-limit superparticular comma; their sum is [[176/175]], the valinorsma, an 11-limit superparticular comma.		352/351 and [[351/350]], the ratwolfsma, are extremely close in size and make up a consecutive pair of 13-limit [[superparticular]] commas. Their difference is 123201/123200, the [[chalmersia]], the smallest 13-limit superparticular comma; their sum is 176/175, the [[valinorsma]], an 11-limit superparticular comma.

	== Temperaments ==		== Temperaments ==
	Tempering out this comma leads to a form of '''major minthmic temperament''' (full 13-limit rank-5) or '''majorminth temperament''' (2.3.11.13 subgroup rank-3), which enables [[major minthmic chords]]. Mintha was a nymph turned into a mint plant by a goddess whom she got in the way of<ref>[https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0104%3Aalphabetic+letter%3DM%3Aentry+group%3D26%3Aentry%3Dmintha-bio-1 ''Dictionary of Greek and Roman Biography and Mythology''] – William Smith (1849)</ref><ref>[https://web.archive.org/web/20221230130135/http://mythandreligion.upatras.gr/english/__trashed/ ''Dictionary of Classical Mythology''] – M. R. Wright (2012)</ref><ref>[https://www.greekboston.com/culture/mythology/minthe ''All About Minthe – Myth of Greek Mythology''] – Greek Boston (2024)</ref>, and major minthmic tempering has the slightly sharp, minty-fresh fifths some people appreciate. [[Margo Schulter]] has expressed great fondness for this comma, for example.		[[Tempering out]] this comma leads to a form of '''major minthmic temperament''' (full 13-limit rank-5) or '''majorminth temperament''' (2.3.11.13-subgroup rank-3), which enables [[major minthmic chords]]. Mintha was a nymph turned into a mint plant by a goddess whom she got in the way of<ref>[https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0104%3Aalphabetic+letter%3DM%3Aentry+group%3D26%3Aentry%3Dmintha-bio-1 ''Dictionary of Greek and Roman Biography and Mythology''] – William Smith (1849)</ref><ref>[https://web.archive.org/web/20221230130135/http://mythandreligion.upatras.gr/english/__trashed/ ''Dictionary of Classical Mythology''] – M. R. Wright (2012)</ref><ref>[https://www.greekboston.com/culture/mythology/minthe ''All About Minthe – Myth of Greek Mythology''] – Greek Boston (2024)</ref>, and major minthmic tempering has the slightly sharp, minty-fresh fifths some people appreciate. [[Margo Schulter]] has expressed great fondness for this comma, for example.

	It is tempered out in a large number of notable temperaments such as [[meanpop]], [[srutal]], [[countercata]], [[cassandra]], [[diaschismic]], [[hemififths]], [[amity]], [[rodan]], [[buzzard]] and higher rank temperaments like [[parapyth]], [[Aberschismic family#Overview to extensions\|aberschismic extensions]], [[gentle]], [[Catalog of rank-4 temperaments#Akua (352/351, 847/845)\|akua]] or [[valinorsmic]].		It is tempered out in a large number of notable temperaments such as [[meanpop]], [[srutal]], [[countercata]], [[cassandra]], [[diaschismic]], [[hemififths]], [[amity]], [[rodan]], [[buzzard]] and higher rank temperaments like [[parapyth]], [[Aberschismic family#Overview to extensions\|aberschismic extensions]], [[gentle]], [[Catalog of rank-4 temperaments#Akua (352/351, 847/845)\|akua]] or [[valinorsmic]].
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	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]

	== ~~Notes~~ ==		== References ==

	[[Category:Major minthmic]]		[[Category:Major minthmic]]
	[[Category:Commas named for the intervals they stack]]		[[Category:Commas named for the intervals they stack]]
	[[Category:Commas named for the generator of their temperament]]		[[Category:Commas named for the generator of their temperament]]

FloraC: - 11/13-kleisma (no need, covered by the Sagittal section)

2026-10-09T12:21:20Z

- 11/13-kleisma (no need, covered by the Sagittal section)

← Older revision		Revision as of 12:21, 9 October 2026
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	{{Infobox Interval		{{Infobox Interval
	\| Name = major minthma, major gentle comma~~, 11/13-kleisma~~		\| Name = major minthma, major gentle comma
	\| Color name = 3u1oM, thuloma		\| Color name = 3u1oM, thuloma
	\| Comma = yes		\| Comma = yes
	}}		}}
	'''352/351''', the '''major minthma''', '''major gentle comma~~''' or '''11/13-kleisma~~''' is a [[small comma\|small]] [[13-limit]] (also 2.3.11.13 [[subgroup]]) [[comma]] measuring about 4.9{{cent}}. This comma can be described in a number of ways. First, it is the difference between the tridecimal minor third of [[13/11]] and the Pythagorean minor third of [[32/27]], hence the name ''11/13''-kleisma. This means that when this comma is [[tempering out\|tempered out]], 11/8 plus three perfect fourths octave reduces to 13/8; as such, this comma can be understood as relating harmonics 11 and 13 by a chain of fourths. Second, it is the difference between various tridecimal intervals and their adjacent undecimal intervals such as:		'''352/351''', the '''major minthma''' or '''major gentle comma''' is a [[small comma\|small]] [[13-limit]] (also 2.3.11.13 [[subgroup]]) [[comma]] measuring about 4.9{{cent}}. This comma can be described in a number of ways. First, it is the difference between the tridecimal minor third of [[13/11]] and the Pythagorean minor third of [[32/27]], hence the name ''11/13''-kleisma. This means that when this comma is [[tempering out\|tempered out]], 11/8 plus three perfect fourths octave reduces to 13/8; as such, this comma can be understood as relating harmonics 11 and 13 by a chain of fourths. Second, it is the difference between various tridecimal intervals and their adjacent undecimal intervals such as:
	* The tridecimal quartertone of [[1053/1024]] and the undecimal quartertone of [[33/32]];		* The tridecimal quartertone of [[1053/1024]] and the undecimal quartertone of [[33/32]];
	* [[88/81]] and [[13/12]];		* [[88/81]] and [[13/12]];

Eufalesio: Small expansion

2026-08-23T12:15:44Z

Small expansion

← Older revision		Revision as of 12:15, 23 August 2026
Line 5:		Line 5:
	}}		}}
	'''352/351''', the '''major minthma''', '''major gentle comma''' or '''11/13-kleisma''' is a [[small comma\|small]] [[13-limit]] (also 2.3.11.13 [[subgroup]]) [[comma]] measuring about 4.9{{cent}}. This comma can be described in a number of ways. First, it is the difference between the tridecimal minor third of [[13/11]] and the Pythagorean minor third of [[32/27]], hence the name ''11/13''-kleisma. This means that when this comma is [[tempering out\|tempered out]], 11/8 plus three perfect fourths octave reduces to 13/8; as such, this comma can be understood as relating harmonics 11 and 13 by a chain of fourths. Second, it is the difference between various tridecimal intervals and their adjacent undecimal intervals such as:		'''352/351''', the '''major minthma''', '''major gentle comma''' or '''11/13-kleisma''' is a [[small comma\|small]] [[13-limit]] (also 2.3.11.13 [[subgroup]]) [[comma]] measuring about 4.9{{cent}}. This comma can be described in a number of ways. First, it is the difference between the tridecimal minor third of [[13/11]] and the Pythagorean minor third of [[32/27]], hence the name ''11/13''-kleisma. This means that when this comma is [[tempering out\|tempered out]], 11/8 plus three perfect fourths octave reduces to 13/8; as such, this comma can be understood as relating harmonics 11 and 13 by a chain of fourths. Second, it is the difference between various tridecimal intervals and their adjacent undecimal intervals such as:
	* ~~Between the~~ tridecimal quartertone of [[1053/1024]] and the undecimal quartertone of [[33/32]];		* The tridecimal quartertone of [[1053/1024]] and the undecimal quartertone of [[33/32]];
	* ~~Between~~ [[16/13]] and [[27/22]]; and		* [[88/81]] and [[13/12]];
	* ~~Between~~ [[39/32]] and [[11/9]].		* [[128/117]] and [[12/11]];
			* [[11/9]] and [[39/32]];
			* [[16/13]] and [[27/22]];
			* [[11/8]] and [[351/256]];
			* [[243/176]] and [[18/13]];
			And their [[octave complement]]<nowiki/>s.

	352/351 and [[351/350]], the ratwolfsma, are extremely close in size and make up a consecutive pair of 13-limit [[superparticular]] commas. Their difference is [[chalmersia\|123201/123200]], the chalmersia, the smallest 13-limit superparticular comma; their sum is [[176/175]], the valinorsma, an 11-limit superparticular comma.		352/351 and [[351/350]], the ratwolfsma, are extremely close in size and make up a consecutive pair of 13-limit [[superparticular]] commas. Their difference is [[chalmersia\|123201/123200]], the chalmersia, the smallest 13-limit superparticular comma; their sum is [[176/175]], the valinorsma, an 11-limit superparticular comma.
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	== Temperaments ==		== Temperaments ==
	Tempering out this comma leads to a form of '''major minthmic temperament''' (full 13-limit rank-5) or '''majorminth temperament''' (2.3.11.13 subgroup rank-3), which enables [[major minthmic chords]]. Mintha was a nymph turned into a mint plant by a goddess whom she got in the way of<ref>[https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0104%3Aalphabetic+letter%3DM%3Aentry+group%3D26%3Aentry%3Dmintha-bio-1 ''Dictionary of Greek and Roman Biography and Mythology''] – William Smith (1849)</ref><ref>[https://web.archive.org/web/20221230130135/http://mythandreligion.upatras.gr/english/__trashed/ ''Dictionary of Classical Mythology''] – M. R. Wright (2012)</ref><ref>[https://www.greekboston.com/culture/mythology/minthe ''All About Minthe – Myth of Greek Mythology''] – Greek Boston (2024)</ref>, and major minthmic tempering has the slightly sharp, minty-fresh fifths some people appreciate. [[Margo Schulter]] has expressed great fondness for this comma, for example.		Tempering out this comma leads to a form of '''major minthmic temperament''' (full 13-limit rank-5) or '''majorminth temperament''' (2.3.11.13 subgroup rank-3), which enables [[major minthmic chords]]. Mintha was a nymph turned into a mint plant by a goddess whom she got in the way of<ref>[https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0104%3Aalphabetic+letter%3DM%3Aentry+group%3D26%3Aentry%3Dmintha-bio-1 ''Dictionary of Greek and Roman Biography and Mythology''] – William Smith (1849)</ref><ref>[https://web.archive.org/web/20221230130135/http://mythandreligion.upatras.gr/english/__trashed/ ''Dictionary of Classical Mythology''] – M. R. Wright (2012)</ref><ref>[https://www.greekboston.com/culture/mythology/minthe ''All About Minthe – Myth of Greek Mythology''] – Greek Boston (2024)</ref>, and major minthmic tempering has the slightly sharp, minty-fresh fifths some people appreciate. [[Margo Schulter]] has expressed great fondness for this comma, for example.

			It is tempered out in a large number of notable temperaments such as [[meanpop]], [[srutal]], [[countercata]], [[cassandra]], [[diaschismic]], [[hemififths]], [[amity]], [[rodan]], [[buzzard]] and higher rank temperaments like [[parapyth]], [[Aberschismic family#Overview to extensions\|aberschismic extensions]], [[gentle]], [[Catalog of rank-4 temperaments#Akua (352/351, 847/845)\|akua]] or [[valinorsmic]].

	== Notation ==		== Notation ==

Eufalesio: Color name

2026-07-17T16:08:14Z

Color name

← Older revision		Revision as of 16:08, 17 July 2026
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	{{Infobox Interval		{{Infobox Interval
	\| Name = major minthma, major gentle comma, 11/13-kleisma		\| Name = major minthma, major gentle comma, 11/13-kleisma
	\| Color name = ~~3u1o1~~, ~~thulo 1sn, <br>Thulo comma~~		\| Color name = 3u1oM, thuloma
	\| Comma = yes		\| Comma = yes
	}}		}}

FloraC: Move relevant temp info from the chords page

2025-03-20T14:34:24Z

Move relevant temp info from the chords page

← Older revision		Revision as of 14:34, 20 March 2025
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	== Temperaments ==		== Temperaments ==
	Tempering out this comma leads to a form of '''major minthmic temperament''' (full 13-limit rank-5) or '''majorminth temperament''' (2.3.11.13 subgroup rank-3), which enables [[major minthmic chords]].		Tempering out this comma leads to a form of '''major minthmic temperament''' (full 13-limit rank-5) or '''majorminth temperament''' (2.3.11.13 subgroup rank-3), which enables [[major minthmic chords]]. Mintha was a nymph turned into a mint plant by a goddess whom she got in the way of<ref>[https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0104%3Aalphabetic+letter%3DM%3Aentry+group%3D26%3Aentry%3Dmintha-bio-1 ''Dictionary of Greek and Roman Biography and Mythology''] – William Smith (1849)</ref><ref>[https://web.archive.org/web/20221230130135/http://mythandreligion.upatras.gr/english/__trashed/ ''Dictionary of Classical Mythology''] – M. R. Wright (2012)</ref><ref>[https://www.greekboston.com/culture/mythology/minthe ''All About Minthe – Myth of Greek Mythology''] – Greek Boston (2024)</ref>, and major minthmic tempering has the slightly sharp, minty-fresh fifths some people appreciate. [[Margo Schulter]] has expressed great fondness for this comma, for example.

	== Notation ==		== Notation ==
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	== See also ==		== See also ==
	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]

			== Notes ==

	[[Category:Major minthmic]]		[[Category:Major minthmic]]
	[[Category:Commas named for the intervals they stack]]		[[Category:Commas named for the intervals they stack]]
	[[Category:Commas named for the generator of their temperament]]		[[Category:Commas named for the generator of their temperament]]

FloraC: Duh, grammar

2024-11-26T07:55:07Z

Duh, grammar

← Older revision		Revision as of 07:55, 26 November 2024
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	This comma was known as the ''minthma'' from 2011. The word ''minthma'' is a contraction of ''minor thirds comma'' into a single word. In 2022, [[Margo Schulter]] requested it should be changed to ''major''/''greater minthma'' to distinguish it from [[364/363]], which would gain the name ''minor''/''lesser minthma''.		This comma was known as the ''minthma'' from 2011. The word ''minthma'' is a contraction of ''minor thirds comma'' into a single word. In 2022, [[Margo Schulter]] requested it should be changed to ''major''/''greater minthma'' to distinguish it from [[364/363]], which would gain the name ''minor''/''lesser minthma''.

	The ''major gentle comma'' was also added to this comma in contrast to the ''minor gentle comma'' of 364/363. Both commas were essential to define the [[gentle]] temperament. Gentle is named for the [[gentle region\|gentle fifth]], a mild version of the [[superpyth]] fifth.		The ''major gentle comma'' was also added to this comma in contrast to the ''minor gentle comma'' of 364/363. Both commas were essential to define the [[gentle]] temperament. Gentle was named for the [[gentle region\|gentle fifth]], a mild version of the [[superpyth]] fifth.

	== See also ==		== See also ==

FloraC: Rework

2024-11-26T07:54:29Z

Rework

← Older revision		Revision as of 07:54, 26 November 2024
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	Tempering out this comma leads to a form of '''major minthmic temperament''' (full 13-limit rank-5) or '''majorminth temperament''' (2.3.11.13 subgroup rank-3), which enables [[major minthmic chords]].		Tempering out this comma leads to a form of '''major minthmic temperament''' (full 13-limit rank-5) or '''majorminth temperament''' (2.3.11.13 subgroup rank-3), which enables [[major minthmic chords]].

	== Sagittal notation ==		== Notation ==
			=== Sagittal notation ===
	In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented (in a secondary role) by the sagittal {{sagittal \| !( }} and is called the '''13/11 kleisma''', or '''13/11k''' for short, because the simplest interval it notates is 13/11, as for example in D-F{{nbhsp}}{{sagittal \| !( }}. The primary role of {{ sagittal \| !( }} is [[5120/5103#Sagittal notation \| 5103/5120]] (7/5k). The upward version is called '''11/13k''' or '''13/11k up''' and is represented (in a secondary role) by {{sagittal\| \|( }}.		In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented (in a secondary role) by the sagittal {{sagittal \| !( }} and is called the '''13/11 kleisma''', or '''13/11k''' for short, because the simplest interval it notates is 13/11, as for example in D-F{{nbhsp}}{{sagittal \| !( }}. The primary role of {{ sagittal \| !( }} is [[5120/5103#Sagittal notation \| 5103/5120]] (7/5k). The upward version is called '''11/13k''' or '''13/11k up''' and is represented (in a secondary role) by {{sagittal\| \|( }}.

Line 20:		Line 21:
	This comma was known as the ''minthma'' from 2011. The word ''minthma'' is a contraction of ''minor thirds comma'' into a single word. In 2022, [[Margo Schulter]] requested it should be changed to ''major''/''greater minthma'' to distinguish it from [[364/363]], which would gain the name ''minor''/''lesser minthma''.		This comma was known as the ''minthma'' from 2011. The word ''minthma'' is a contraction of ''minor thirds comma'' into a single word. In 2022, [[Margo Schulter]] requested it should be changed to ''major''/''greater minthma'' to distinguish it from [[364/363]], which would gain the name ''minor''/''lesser minthma''.

	The ''major gentle comma'' was also added to this comma in contrast to the ''minor gentle comma'' of 364/363. Both commas were essential to define the [[gentle]] temperament. ~~The reason why~~ the ~~temperament was named “gentle” in~~ the ~~first place does not appear to be written down anywhere~~.		The ''major gentle comma'' was also added to this comma in contrast to the ''minor gentle comma'' of 364/363. Both commas were essential to define the [[gentle]] temperament. Gentle is named for the [[gentle region\|gentle fifth]], a mild version of the [[superpyth]] fifth.

	== See also ==		== See also ==
	* [[Small comma]]
	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]

	[[Category:Major minthmic]]		[[Category:Major minthmic]]
	[[Category:Commas named for the intervals they stack]]		[[Category:Commas named for the intervals they stack]]
	[[Category:Commas ~~with unknown etymology~~]]		[[Category:Commas named for the generator of their temperament]]

FloraC: Style and wording

2024-11-26T07:45:15Z

Style and wording

← Older revision		Revision as of 07:45, 26 November 2024
Line 4:		Line 4:
	\| Comma = yes		\| Comma = yes
	}}		}}
	'''352/351''', the '''major minthma''', '''major gentle comma''' or '''11/13-kleisma''' is a [[small comma\|small]] [[13-limit]] (also 2.3.11.13 [[subgroup]]) [[comma]] measuring about 4.9{{cent}}. This comma can be described in a number of ways. First, it is the difference between the tridecimal minor third of [[13/11]] and the Pythagorean minor third of [[32/27]], hence the name ''11/13''-kleisma. (This means that when this comma is tempered, 11/8 plus three perfect fourths octave reduces to 13/8; as such, this comma can be understood as relating harmonics 11 and 13 by a chain of fourths.) Second, it is the difference between various tridecimal intervals and their adjacent undecimal intervals such as:		'''352/351''', the '''major minthma''', '''major gentle comma''' or '''11/13-kleisma''' is a [[small comma\|small]] [[13-limit]] (also 2.3.11.13 [[subgroup]]) [[comma]] measuring about 4.9{{cent}}. This comma can be described in a number of ways. First, it is the difference between the tridecimal minor third of [[13/11]] and the Pythagorean minor third of [[32/27]], hence the name ''11/13''-kleisma. This means that when this comma is [[tempering out\|tempered out]], 11/8 plus three perfect fourths octave reduces to 13/8; as such, this comma can be understood as relating harmonics 11 and 13 by a chain of fourths. Second, it is the difference between various tridecimal intervals and their adjacent undecimal intervals such as:
	* Between the tridecimal quartertone of [[1053/1024]] and the undecimal quartertone of [[33/32]];		* Between the tridecimal quartertone of [[1053/1024]] and the undecimal quartertone of [[33/32]];
	* Between [[16/13]] and [[27/22]]; and		* Between [[16/13]] and [[27/22]]; and

CellularAutomaton: made a hopefully useful detail more explicit

2024-11-26T01:09:13Z

made a hopefully useful detail more explicit

← Older revision		Revision as of 01:09, 26 November 2024
Line 4:		Line 4:
	\| Comma = yes		\| Comma = yes
	}}		}}
	'''352/351''', the '''major minthma''', '''major gentle comma''' or '''11/13-kleisma''' is a [[small comma\|small]] [[13-limit]] (also 2.3.11.13 [[subgroup]]) [[comma]] measuring about 4.9{{cent}}. This comma can be described in a number of ways. First, it is the difference between the tridecimal minor third of [[13/11]] and the Pythagorean minor third of [[32/27]], hence the name ''11/13''-kleisma. Second, it is the difference between various tridecimal intervals and their adjacent undecimal intervals such as:		'''352/351''', the '''major minthma''', '''major gentle comma''' or '''11/13-kleisma''' is a [[small comma\|small]] [[13-limit]] (also 2.3.11.13 [[subgroup]]) [[comma]] measuring about 4.9{{cent}}. This comma can be described in a number of ways. First, it is the difference between the tridecimal minor third of [[13/11]] and the Pythagorean minor third of [[32/27]], hence the name ''11/13''-kleisma. (This means that when this comma is tempered, 11/8 plus three perfect fourths octave reduces to 13/8; as such, this comma can be understood as relating harmonics 11 and 13 by a chain of fourths.) Second, it is the difference between various tridecimal intervals and their adjacent undecimal intervals such as:
	* Between the tridecimal quartertone of [[1053/1024]] and the undecimal quartertone of [[33/32]];		* Between the tridecimal quartertone of [[1053/1024]] and the undecimal quartertone of [[33/32]];
	* Between [[16/13]] and [[27/22]]; and		* Between [[16/13]] and [[27/22]]; and