5120/5103 - Revision history

FloraC: - self link; consistently use the name aberschisma (rather than an equation); remove the ratio for the reciprocal of the septischisma (not important)

2026-08-30T13:34:51Z

- self link; consistently use the name *aberschisma* (rather than an equation); remove the ratio for the reciprocal of the septischisma (not important)

← Older revision		Revision as of 13:34, 30 August 2026
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	'''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]].		'''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]].

	In terms of smaller commas, it is the difference between the [[marvel comma]] and the [[32805/32768\|schisma]], as well as the sum of the schisma and the [[septischisma]]. In terms of [[S-expression]]s, this can be seen through the fact that one way of expressing the schisma is {{nowrap~~\| [[225/224~~\|S15]]/(~~[[5120/5103\|~~S8/S9]]) }} while the septischisma can be expressed as {{nowrap\| (S8/S9)<sup>2</sup>/S15 }}, that is, the reciprocal of the septischisma~~, 33480783/33554432,~~ is ~~{{nowrap\| S8/S9 {{=}} 5120/5103 }}~~ below the schisma.		In terms of smaller commas, it is the difference between the [[marvel comma]] and the [[32805/32768\|schisma]], as well as the sum of the schisma and the [[septischisma]]. In terms of [[S-expression]]s, this can be seen through the fact that one way of expressing the schisma is {{nowrap\| S15/(S8/S9) }} while the septischisma can be expressed as {{nowrap\| (S8/S9)<sup>2</sup>/S15 }}, that is, the reciprocal of the septischisma is an aberschisma below the schisma.

	== Temperaments ==		== Temperaments ==

Godtone: this fact appears interesting when viewed from S-expressions

2026-08-30T13:20:07Z

this fact appears interesting when viewed from S-expressions

← Older revision		Revision as of 13:20, 30 August 2026
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	'''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]].		'''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]].

	In terms of smaller commas, it is the difference between the [[marvel comma]] and the [[32805/32768\|schisma]], as well as the sum of the schisma and the [[septischisma]].		In terms of smaller commas, it is the difference between the [[marvel comma]] and the [[32805/32768\|schisma]], as well as the sum of the schisma and the [[septischisma]]. In terms of [[S-expression]]s, this can be seen through the fact that one way of expressing the schisma is {{nowrap\| [[225/224\|S15]]/([[5120/5103\|S8/S9]]) }} while the septischisma can be expressed as {{nowrap\| (S8/S9)<sup>2</sup>/S15 }}, that is, the reciprocal of the septischisma, 33480783/33554432, is {{nowrap\| S8/S9 {{=}} 5120/5103 }} below the schisma.

	== Temperaments ==		== Temperaments ==

FloraC: Note that it's the sum of the schisma and septischisma, significant for the fact that these are commas of 2.3.5 and 2.3.7, respectively

2026-08-30T07:58:46Z

Note that it's the sum of the schisma and septischisma, significant for the fact that these are commas of 2.3.5 and 2.3.7, respectively

← Older revision		Revision as of 07:58, 30 August 2026
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	\| Comma = yes		\| Comma = yes
	}}		}}
	'''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.		'''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]].

			In terms of smaller commas, it is the difference between the [[marvel comma]] and the [[32805/32768\|schisma]], as well as the sum of the schisma and the [[septischisma]].

	== Temperaments ==		== Temperaments ==

FloraC: + categories

2026-08-27T02:27:06Z

+ categories

← Older revision		Revision as of 02:27, 27 August 2026
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	[[Category:Aberschismic]]		[[Category:Aberschismic]]
			[[Category:Commas named for their regular temperament properties]]
			[[Category:Commas named by translating something into another language]]

FloraC: /* Temperaments */

2026-08-03T04:30:18Z

Temperaments

← Older revision		Revision as of 04:30, 3 August 2026
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	[[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.		[[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.		See [[Aberschismic family]] for the [[family]] of rank-3 temperaments where it is tempered out. See [[Aberschismic temperaments]] for a collection of rank-2 temperaments where it is tempered out.

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

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 ==