5120/5103: Difference between revisions

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{{Infobox Interval

| Name = ~~hemifamity comma, 5/7-kleisma~~

| Name = aberschisma

| Color name = sry1, saruyo 1sn,<br>~~Saruyo comma~~

| Color name = sry1, saruyo 1sn,<br>sryM, saruyoma

| Comma = yes

}}

'''5120/5103''', the '''~~hemifamity comma~~''' or ''~~'5/7-kleisma'~~'', is a [[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]].

'''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 ==

Tempering it out leads to the rank-3 [[~~hemifamity family~~]], 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.

[[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 ~~also ==~~

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.

* [[~~Hemifamity~~ family]], the rank-3 family where it is tempered out

* [[~~Hemifamity~~ temperaments]], a collection of rank-2 temperaments where it is tempered out

* [[Small comma]]

[[Category:~~Hemifamity~~]]

== 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| |( }}.

== Etymology ==

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 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, [[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''.

== References ==

[[Category:Aberschismic]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Name = hemifamity comma, 5/7-kleisma
+| Name = aberschisma
-| Color name = sry1, saruyo 1sn,<br>Saruyo comma
+| Color name = sry1, saruyo 1sn,<br>sryM, saruyoma
 | Comma = yes
 }}
-'''5120/5103''', the '''hemifamity comma''' or '''5/7-kleisma''', is a [[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]].
+'''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 ==
-Tempering it out leads to the rank-3 [[hemifamity family]], 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.
+[[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 also ==
+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.
-* [[Hemifamity family]], the rank-3 family where it is tempered out
-* [[Hemifamity temperaments]], a collection of rank-2 temperaments where it is tempered out
-* [[Small comma]]
-[[Category:Hemifamity]]
+== 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| |( }}.
+== Etymology ==
+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 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, [[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''.
+== References ==
+[[Category:Aberschismic]]