5120/5103: Difference between revisions
Tristanbay (talk | contribs) Changed the intro to match all the given comma names |
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{{Infobox Interval | {{Infobox Interval | ||
| Name = | | Name = aberschisma | ||
| Color name = sry1, saruyo 1sn,<br> | | Color name = sry1, saruyo 1sn,<br>sryM, saruyoma | ||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
'''5120/5103''', the ''' | '''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 | [[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 | 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 '' | 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 '' | 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, [[ | 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: | [[Category:Aberschismic]] | ||
Latest revision as of 12:39, 6 June 2026
| Interval information |
sryM, saruyoma
5120/5103, the aberschisma (formerly hemifamity comma), is a small 7-limit comma measuring about 5.76 cents. 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 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. Edos that temper it out include 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
In the Sagittal system, the downward version of this comma (possibly tempered) is represented by the 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 . The upward version is called 5/7k or 7/5k up and is represented by .
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[1].
In 2025, 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.