3025/3024: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = lehmerisma | | Name = lehmerisma | ||
| Color name = | | Color name = 1ooryy-2, Loloruyoyo comma | ||
| | | Comma = yes | ||
}} | }} | ||
'''3025/3024''', the '''lehmerisma''', is an [[unnoticeable comma|unnoticeable]] [[11-limit]] [[comma]] measuring about 0.57{{cent}}. It is the difference between [[55/54]] and [[56/55]], between [[121/120]] and [[126/125]], between [[225/224]] and [[243/242]], and between [[385/384]] and [[441/440]], as well as the amount by which two [[12/11]] neutral seconds falls short of [[25/21]], the quasi-tempered minor third. | |||
It factors into the two smallest superparticular commas in the 11-limit: 3025/3024 = ([[4375/4374]])([[9801/9800]]). | |||
Tempering | == Temperaments == | ||
[[Tempering out]] this comma leads to the '''lehmerismic temperament''', which splits [[28/27]] into two equal parts, each representing 55/54~56/55. See [[Rank-4 temperament #Lehmerismic (3025/3024)]] for some technical details. See [[Lehmerismic temperaments]] for a collection of rank-3 temperaments where it is tempered out. | |||
== Etymology == | |||
This comma was named by [[Gene Ward Smith]] in 2004 after the American mathematician [[wikipedia: D. H. Lehmer|D. H. Lehmer]]. | |||
<blockquote> | |||
Or perhaps 3025/3024 is a better lehmerisma, as Lehmer mentions it on the first page of his paper. […] He was a wonderful gentlemen and a hell of a mathematician, and deserves | |||
a comma as much as anyone. | |||
</blockquote> | |||
—Gene Ward Smith<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10130.html Yahoo! Tuning Group | ''Re: {{lbrack}}tuning-math{{rbrack}} Digest Number 1011'']</ref> | |||
== See also == | == See also == | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
== Notes == | |||
[[Category:Lehmerismic]] | [[Category:Lehmerismic]] | ||
[[Category:Commas named after mathematicians]] | |||
Latest revision as of 11:29, 5 November 2024
| Interval information |
reduced
S22 / S24
3025/3024, the lehmerisma, is an unnoticeable 11-limit comma measuring about 0.57 ¢. It is the difference between 55/54 and 56/55, between 121/120 and 126/125, between 225/224 and 243/242, and between 385/384 and 441/440, as well as the amount by which two 12/11 neutral seconds falls short of 25/21, the quasi-tempered minor third.
It factors into the two smallest superparticular commas in the 11-limit: 3025/3024 = (4375/4374)(9801/9800).
Temperaments
Tempering out this comma leads to the lehmerismic temperament, which splits 28/27 into two equal parts, each representing 55/54~56/55. See Rank-4 temperament #Lehmerismic (3025/3024) for some technical details. See Lehmerismic temperaments for a collection of rank-3 temperaments where it is tempered out.
Etymology
This comma was named by Gene Ward Smith in 2004 after the American mathematician D. H. Lehmer.
Or perhaps 3025/3024 is a better lehmerisma, as Lehmer mentions it on the first page of his paper. […] He was a wonderful gentlemen and a hell of a mathematician, and deserves a comma as much as anyone.
—Gene Ward Smith[1]