5120/5103: Difference between revisions
Correction: 7/5k > 5/7k via the community of sagittal notation |
Dave Keenan (talk | contribs) →Sagittal notation: Changed "simplest ratio" to "simplest interval". Changed colons to slashes and dash. Replaced hair-space with nbhsp template call. |
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{{Infobox Interval | {{Infobox Interval | ||
| Name = hemifamity comma, 5/7-kleisma, aberschisma | |||
| Color name = sry1, saruyo 1sn,<br>Saruyo comma | |||
| Comma = yes | |||
| Name = hemifamity, | |||
| Color name = | |||
| | |||
}} | }} | ||
'''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 [[aberrismic theory]], being the difference between two of the most common aberrismas in just intonation (81/80 and 64/63). | |||
== Notes == | |||
[[Category:Hemifamity]] | [[Category:Hemifamity]] | ||
Latest revision as of 07:02, 10 October 2024
| Interval information |
5/7-kleisma,
aberschisma
Saruyo comma
5120/5103, the hemifamity comma, 5/7-kleisma, or aberschisma, is a small 7-limit comma measuring about 5.8 ¢. 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 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. 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 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 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 hemifamity was given by Gene Ward Smith in 2005 as a contraction of hemififths and amity[1].
An alternate name for the comma, the aberschisma, was given by 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).