3025/3024: Difference between revisions
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'''3025/3024''', the '''lehmerisma''', is an [[11-limit]] [[ | '''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 two superparticular commas: ([[4375/4374]])([[9801/9800]]). | It factors into the two smallest superparticular commas in the 11-limit: 3025/3024 = ([[4375/4374]])([[9801/9800]]). | ||
== Temperaments == | == Temperaments == | ||
Tempering | [[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 == | == Etymology == | ||
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]