5120/5103 - Revision history

FloraC: Text replacement - "Category:Hemifamity" to "Category:Aberschismic"

2026-06-06T12:39:15Z

Text replacement - "Category:Hemifamity" to "Category:Aberschismic"

← Older revision		Revision as of 12:39, 6 June 2026
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	== References ==		== References ==

	[[Category:~~Hemifamity~~]]		[[Category:Aberschismic]]

FloraC: Officialize the name aberschisma (see talk)

2026-06-06T12:23:14Z

Officialize the name aberschisma (see talk)

← Older revision		Revision as of 12:23, 6 June 2026
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	{{Infobox Interval		{{Infobox Interval
	\| Name = ~~argent comma, 5/7-kleisma~~		\| Name = aberschisma
	\| Color name = sry1, saruyo 1sn,<br>sryM, saruyoma		\| Color name = sry1, saruyo 1sn,<br>sryM, saruyoma
	\| Comma = yes		\| Comma = yes
	}}		}}
	'''5120/5103''', the '''~~argent comma~~'''~~, '''5/7-kleisma''', '~~''hemifamity comma''~~', or '''aberschisma'''~~, is a [[small comma\|small]] [[7-limit]] [[comma]] measuring about ~~{{frac\|~~5~~\|3\|4}}{{~~cent}}. It is the difference between [[7/5]] (small septimal tritone) and [[1024/729]] (Pythagorean diminished fifth), or between [[10/7]] (large septimal tritone) and [[729/512]] (Pythagorean augmented fourth). It is also the difference between [[15/14]] and [[2187/2048]], between [[21/20]] and [[256/243]], between [[80/63]] and [[81/64]], etc., hence, between the septimal comma of [[64/63]] and the syntonic comma of [[81/80]], as well as between [[~~schisma\|32805~~/~~32768~~]], the ~~schisma~~, and [[~~225~~/~~224~~]], the ~~marvel comma~~.		'''5120/5103''', the '''aberschisma''' (formerly ''hemifamity comma''), is a [[small comma\|small]] [[7-limit]] [[comma]] measuring about 5.76 [[cent]]s. It is the difference between [[7/5]] (small septimal tritone) and [[1024/729]] (Pythagorean diminished fifth), or between [[10/7]] (large septimal tritone) and [[729/512]] (Pythagorean augmented fourth). It is also the difference between [[15/14]] and [[2187/2048]], between [[21/20]] and [[256/243]], between [[80/63]] and [[81/64]], etc., hence, between the septimal comma of [[64/63]] and the syntonic comma of [[81/80]], as well as between [[225/224]], the marvel comma, and [[32805/32768]], the schisma.

	== Temperaments ==		== Temperaments ==
	Tempering it out leads to the rank-3 [[~~hemifamity~~]] temperament, which splits the septimal quartertone [[36/35]] into two equal parts, each representing 81/80~64/63. Rank-2 temperaments that temper it out include [[hemififths]], [[amity]], and [[garibaldi]] to name three. [[Edo]]s that temper it out include ~~[[12edo\|12]],~~ {{EDOs\| 29, 34, 41, 46, 53, 58, 87, 94, 99, 111, 140, 145, 152, 239, 292, 391 }}, etc. See [[~~Hemifamity~~ family]] for the rank-3 family where it is tempered out. See [[~~Hemifamity~~ temperaments]] for a collection of rank-2 temperaments where it is tempered out.		[[Tempering out]] this comma in the 7-limit leads to the rank-3 [[aberschismic]] temperament, which splits the septimal quartertone [[36/35]] into two equal parts, each representing 81/80~64/63. Rank-2 temperaments that temper it out include [[hemififths]], [[amity]], and [[garibaldi]] to name three. [[Edo]]s that temper it out include {{EDOs\| 12, 29, 34, 41, 46, 53, 58, 87, 94, 99, 111, 140, 145, 152, 239, 292, 391 }}, etc.

			See [[Aberschismic family]] for the rank-3 [[family]] where it is tempered out. See [[Aberschismic temperaments]] for a collection of rank-2 temperaments where it is tempered out.

	== Sagittal notation ==		== Sagittal notation ==
	In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented by the sagittal {{sagittal \| !( }} and is called the '''7/5 kleisma''', or '''7/5k''' for short, because the simplest interval it notates is 7/5, as for example in ~~B-F~~{{nbhsp}}{{sagittal \| !( }}. The upward version is called '''5/7k''' or '''7/5k up''' and is represented by {{sagittal\| \|( }}.		In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented by the sagittal {{sagittal \| !( }} and is called the '''7/5 kleisma''', or '''7/5k''' for short, because the simplest interval it notates is 7/5, as for example in B–F{{nbhsp}}{{sagittal \| !( }}. The upward version is called '''5/7k''' or '''7/5k up''' and is represented by {{sagittal\| \|( }}.

	== Etymology ==		== Etymology ==
	The name ''~~hemifamity~~'' was ~~given~~ by [[~~Gene Ward Smith~~]] in ~~2005 as a contraction of~~ '~~'hemififths'' and ''amity''<ref>~~[~~https:~~//~~yahootuninggroupsultimatebackup.github.io~~/~~tuning-math/topicId_12900~~.~~html Yahoo! Tuning Group \| ''Seven limit~~ comma ~~names from pairs of temperament names'']</ref>~~.		The name ''aberschisma'' was coined by [[Tristan Bay]] in 2024 in reference to [[groundfault]]'s [[aberrismic theory]], since 5120/5103 is the difference between two of the most common aberrismas in just intonation (81/80 and 64/63). By 2026, this is the most widely used name for the comma.

	The name ''~~aberschisma~~'', was ~~coined~~ by [[~~User:Tristanbay\|Tristan Bay~~]] in ~~2024 in reference to [[groundfault]]~~'s [~~[aberrismic theory]], since 5120~~/~~5103 is the difference between two~~ of ~~the most common aberrismas in just intonation (81/80 and 64~~/~~63)~~.		The formerly official name ''hemifamity'' was given by [[Gene Ward Smith]] in 2005 as a contraction of ''hemififths'' and ''amity''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_12900.html Yahoo! Tuning Group \| ''Seven limit comma names from pairs of temperament names'']</ref>.

	In 2025, [[~~User:FloraC~~\|FloraC]] et al. gave this comma the name ''argent comma'' due to the fifth size from the [[argent ~~temperament~~]] being essentially optimal for tuning the full 7-limit ~~temperament (~~and ~~the~~ 2.3.7/5 subgroup temperament) that ~~tempers~~ only it out.		In 2025, [[Flora Canou\|FloraC]] et al. gave this comma the name ''argent comma'' due to the fifth size from the [[argent tuning]] being essentially optimal for tuning the full 7-limit and 2.3.7/5-subgroup temperament that temper only it out. While not gaining community-wide support over ''aberschisma'', the name has since been reused for the 2.3.7/5-subgroup temperament in the form ''argentic''.

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

	[[Category:Hemifamity]]		[[Category:Hemifamity]]

TallKite: updated the comma color name

2026-04-29T04:08:31Z

updated the comma color name

← Older revision		Revision as of 04:08, 29 April 2026
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	{{Infobox Interval		{{Infobox Interval
	\| Name = argent comma, 5/7-kleisma		\| Name = argent comma, 5/7-kleisma
	\| Color name = sry1, saruyo 1sn,<br>~~Saruyo comma~~		\| Color name = sry1, saruyo 1sn,<br>sryM, saruyoma
	\| Comma = yes		\| Comma = yes
	}}		}}

Tristanbay: /* Temperaments */ Mentioned garibaldi

2025-10-14T07:06:22Z

Temperaments: Mentioned garibaldi

← Older revision		Revision as of 07:06, 14 October 2025
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	== Temperaments ==		== Temperaments ==
	Tempering it out leads to the rank-3 [[hemifamity]] temperament, which splits the septimal quartertone [[36/35]] into two equal parts, each representing 81/80~64/63. Rank-2 temperaments that temper it out include [[hemififths]] ~~and~~ [[amity]], to name ~~two~~. [[Edo]]s that temper it out include [[12edo\|12]], {{EDOs\| 29, 34, 41, 46, 53, 58, 87, 94, 99, 111, 140, 145, 152, 239, 292, 391 }}, etc. See [[Hemifamity family]] for the rank-3 family where it is tempered out. See [[Hemifamity temperaments]] for a collection of rank-2 temperaments where it is tempered out.		Tempering it out leads to the rank-3 [[hemifamity]] temperament, which splits the septimal quartertone [[36/35]] into two equal parts, each representing 81/80~64/63. Rank-2 temperaments that temper it out include [[hemififths]], [[amity]], and [[garibaldi]] to name three. [[Edo]]s that temper it out include [[12edo\|12]], {{EDOs\| 29, 34, 41, 46, 53, 58, 87, 94, 99, 111, 140, 145, 152, 239, 292, 391 }}, etc. See [[Hemifamity family]] for the rank-3 family where it is tempered out. See [[Hemifamity temperaments]] for a collection of rank-2 temperaments where it is tempered out.

	== Sagittal notation ==		== Sagittal notation ==

Tristanbay: Changed cent approximation to fraction

2025-10-14T07:03:31Z

Changed cent approximation to fraction

← Older revision		Revision as of 07:03, 14 October 2025
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	\| Comma = yes		\| Comma = yes
	}}		}}
	'''5120/5103''', the '''argent comma''', '''5/7-kleisma''', '''hemifamity comma''', or '''aberschisma''', is a [[small comma\|small]] [[7-limit]] [[comma]] measuring about 5.8{{cent}}. It is the difference between [[7/5]] (small septimal tritone) and [[1024/729]] (Pythagorean diminished fifth), or between [[10/7]] (large septimal tritone) and [[729/512]] (Pythagorean augmented fourth). It is also the difference between [[15/14]] and [[2187/2048]], between [[21/20]] and [[256/243]], between [[80/63]] and [[81/64]], etc., hence, between the septimal comma of [[64/63]] and the syntonic comma of [[81/80]], as well as between [[schisma\|32805/32768]], the schisma, and [[225/224]], the marvel comma.		'''5120/5103''', the '''argent comma''', '''5/7-kleisma''', '''hemifamity comma''', or '''aberschisma''', is a [[small comma\|small]] [[7-limit]] [[comma]] measuring about {{frac\|5\|3\|4}}{{cent}}. It is the difference between [[7/5]] (small septimal tritone) and [[1024/729]] (Pythagorean diminished fifth), or between [[10/7]] (large septimal tritone) and [[729/512]] (Pythagorean augmented fourth). It is also the difference between [[15/14]] and [[2187/2048]], between [[21/20]] and [[256/243]], between [[80/63]] and [[81/64]], etc., hence, between the septimal comma of [[64/63]] and the syntonic comma of [[81/80]], as well as between [[schisma\|32805/32768]], the schisma, and [[225/224]], the marvel comma.

	== Temperaments ==		== Temperaments ==

Tristanbay: Changed the intro to match all the given comma names

2025-10-14T07:01:31Z

Changed the intro to match all the given comma names

← Older revision		Revision as of 07:01, 14 October 2025
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	\| Comma = yes		\| Comma = yes
	}}		}}
	'''5120/5103''', the '''~~hemifamity~~ comma''', '''5/7-kleisma''', or '''aberschisma''', is a [[small comma\|small]] [[7-limit]] [[comma]] measuring about 5.8{{cent}}. It is the difference between [[7/5]] (small septimal tritone) and [[1024/729]] (Pythagorean diminished fifth), or between [[10/7]] (large septimal tritone) and [[729/512]] (Pythagorean augmented fourth). It is also the difference between [[15/14]] and [[2187/2048]], between [[21/20]] and [[256/243]], between [[80/63]] and [[81/64]], etc., hence, between the septimal comma of [[64/63]] and the syntonic comma of [[81/80]], as well as between [[schisma\|32805/32768]], the schisma, and [[225/224]], the marvel comma.		'''5120/5103''', the '''argent comma''', '''5/7-kleisma''', '''hemifamity comma''', or '''aberschisma''', is a [[small comma\|small]] [[7-limit]] [[comma]] measuring about 5.8{{cent}}. It is the difference between [[7/5]] (small septimal tritone) and [[1024/729]] (Pythagorean diminished fifth), or between [[10/7]] (large septimal tritone) and [[729/512]] (Pythagorean augmented fourth). It is also the difference between [[15/14]] and [[2187/2048]], between [[21/20]] and [[256/243]], between [[80/63]] and [[81/64]], etc., hence, between the septimal comma of [[64/63]] and the syntonic comma of [[81/80]], as well as between [[schisma\|32805/32768]], the schisma, and [[225/224]], the marvel comma.

	== Temperaments ==		== Temperaments ==

Tristanbay: Made "argent comma" the top name in the infobox and removed 2 of the other names from it, but those names are still mentioned in "Etymology"

2025-10-14T06:58:52Z

Made "argent comma" the top name in the infobox and removed 2 of the other names from it, but those names are still mentioned in "Etymology"

← Older revision		Revision as of 06:58, 14 October 2025
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	{{Infobox Interval		{{Infobox Interval
	\| Name = ~~hemifamity~~ comma, 5/7-kleisma~~, aberschisma~~		\| Name = argent comma, 5/7-kleisma
	\| Color name = sry1, saruyo 1sn,<br>Saruyo comma		\| Color name = sry1, saruyo 1sn,<br>Saruyo comma
	\| Comma = yes		\| Comma = yes
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	The name ''hemifamity'' was given by [[Gene Ward Smith]] in 2005 as a contraction of ''hemififths'' and ''amity''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_12900.html Yahoo! Tuning Group \| ''Seven limit comma names from pairs of temperament names'']</ref>.		The name ''hemifamity'' was given by [[Gene Ward Smith]] in 2005 as a contraction of ''hemififths'' and ''amity''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_12900.html Yahoo! Tuning Group \| ''Seven limit comma names from pairs of temperament names'']</ref>.

	~~An alternate~~ name ~~for the comma, the~~ ''aberschisma'', was ~~given~~ by [[User:Tristanbay\|Tristan Bay]] in 2024 in reference to [[groundfault]]'s [[aberrismic theory]], ~~being~~ the difference between two of the most common aberrismas in just intonation (81/80 and 64/63).		The name ''aberschisma'', was coined by [[User:Tristanbay\|Tristan Bay]] in 2024 in reference to [[groundfault]]'s [[aberrismic theory]], since 5120/5103 is the difference between two of the most common aberrismas in just intonation (81/80 and 64/63).

			In 2025, [[User:FloraC\|FloraC]] et al. gave this comma the name ''argent comma'' due to the fifth size from the [[argent temperament]] being essentially optimal for tuning the full 7-limit temperament (and the 2.3.7/5 subgroup temperament) that tempers only it out.

	== Notes ==		== Notes ==

	[[Category:Hemifamity]]		[[Category:Hemifamity]]

Dave Keenan: /* Sagittal notation */ Changed "simplest ratio" to "simplest interval". Changed colons to slashes and dash. Replaced hair-space with nbhsp template call.

2024-10-10T07:02:47Z

Sagittal notation: Changed "simplest ratio" to "simplest interval". Changed colons to slashes and dash. Replaced hair-space with nbhsp template call.

← Older revision		Revision as of 07:02, 10 October 2024
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	== Sagittal notation ==		== Sagittal notation ==
	In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented by the sagittal {{sagittal \| !( }} and is called the '''7/5 kleisma''', or '''7/5k''' for short, because the simplest ~~ratio~~ it notates is 5:7, as for example in B:F~~ ~~{{sagittal \| !( }}. The upward version is called '''5/7k''' or '''7/5k up''' and is represented by {{sagittal\| \|( }}.		In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented by the sagittal {{sagittal \| !( }} and is called the '''7/5 kleisma''', or '''7/5k''' for short, because the simplest interval it notates is 7/5, as for example in B-F{{nbhsp}}{{sagittal \| !( }}. The upward version is called '''5/7k''' or '''7/5k up''' and is represented by {{sagittal\| \|( }}.

	== Etymology ==		== Etymology ==

Dave Keenan: /* Sagittal notation */ Added upward version

2024-10-09T13:12:18Z

Sagittal notation: Added upward version

← Older revision		Revision as of 13:12, 9 October 2024
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	== Sagittal notation ==		== Sagittal notation ==
	In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented by the sagittal {{sagittal \| !( }} and is called the '''7/5 kleisma''', or '''7/5k''' for short, because the simplest ratio it notates is 5:7, as for example in B:F{{sagittal \| !( }}.		In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented by the sagittal {{sagittal \| !( }} and is called the '''7/5 kleisma''', or '''7/5k''' for short, because the simplest ratio it notates is 5:7, as for example in B:F {{sagittal \| !( }}. The upward version is called '''5/7k''' or '''7/5k up''' and is represented by {{sagittal\| \|( }}.

	== Etymology ==		== Etymology ==

Cmloegcmluin: add section for this comma's use in Sagittal notation

2024-10-09T05:18:48Z

add section for this comma's use in Sagittal notation

← Older revision		Revision as of 05:18, 9 October 2024
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	== Temperaments ==		== Temperaments ==
	Tempering it out leads to the rank-3 [[hemifamity]] temperament, which splits the septimal quartertone [[36/35]] into two equal parts, each representing 81/80~64/63. Rank-2 temperaments that temper it out include [[hemififths]] and [[amity]], to name two. [[Edo]]s that temper it out include [[12edo\|12]], {{EDOs\| 29, 34, 41, 46, 53, 58, 87, 94, 99, 111, 140, 145, 152, 239, 292, 391 }}, etc. See [[Hemifamity family]] for the rank-3 family where it is tempered out. See [[Hemifamity temperaments]] for a collection of rank-2 temperaments where it is tempered out.		Tempering it out leads to the rank-3 [[hemifamity]] temperament, which splits the septimal quartertone [[36/35]] into two equal parts, each representing 81/80~64/63. Rank-2 temperaments that temper it out include [[hemififths]] and [[amity]], to name two. [[Edo]]s that temper it out include [[12edo\|12]], {{EDOs\| 29, 34, 41, 46, 53, 58, 87, 94, 99, 111, 140, 145, 152, 239, 292, 391 }}, etc. See [[Hemifamity family]] for the rank-3 family where it is tempered out. See [[Hemifamity temperaments]] for a collection of rank-2 temperaments where it is tempered out.

			== Sagittal notation ==
			In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented by the sagittal {{sagittal \| !( }} and is called the '''7/5 kleisma''', or '''7/5k''' for short, because the simplest ratio it notates is 5:7, as for example in B:F{{sagittal \| !( }}.

	== Etymology ==		== Etymology ==