5120/5103: Difference between revisions

(4 intermediate revisions by 3 users not shown)

Line 4:

| 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 '''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.

== 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.

== 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]] in 2024 in reference to [[groundfault]]'s [[~~aberrisma|~~aberrismic theory]], being the difference between two of the most common aberrismas in just intonation (81/80 and 64/63).

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).

== Notes ==

[[Category:Hemifamity]]

@@ Line 4: / Line 4: @@
 | 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 '''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.
 == 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.
+== 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]] in 2024 in reference to [[groundfault]]'s [[aberrisma|aberrismic theory]], being the difference between two of the most common aberrismas in just intonation (81/80 and 64/63).
+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).
 == Notes ==
 [[Category:Hemifamity]]