5120/5103: Difference between revisions

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{{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>sryM, saruyoma

| 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]].

'''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 ==

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 ==

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 ''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]]

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).

n 2024 ~~as a~~ reference to groundfault's aberrismic theory, ~~being~~ the difference between two of the most common aberrismas in just intonation (81/80 and 64/63).i

~~in 2024 as a referen to [[groundfault]]<nowiki/>ce~~

~~in 20 as a reference~~ to [[~~groundfault~~]]24

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 ==

[[Category:Hemifamity]]

@@ Line 1: / Line 1: @@
 {{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>sryM, saruyoma
 | 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]].
+'''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 ==
-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 ==
+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 ''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]]
+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).
-n 2024 as a reference to groundfault's aberrismic theory, being the difference between two of the most common aberrismas in just intonation (81/80 and 64/63).i
-in 2024 as a referen to [[groundfault]]<nowiki/>ce
-in 20 as a reference to [[groundfault]]24
+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 ==
 [[Category:Hemifamity]]