3025/3024

Interval information

Ratio	3025/3024
Factorization	2-4 × 3-3 × 52 × 7-1 × 112
Monzo	[-4 -3 2 -1 2⟩
Size in cents	0.5724034¢
Name	lehmerisma
Color name	1ooryy-2, Loloruyoyo comma
FJS name	[math]\text{m}{-2}^{5,5,11,11}_{7}[/math]
Special properties	square superparticular, reduced
Tenney height (log2 nd)	23.125
Weil height (log2 max(n, d))	23.1254
Wilson height (sopfr(nd))	56
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.20127 bits
Comma size	unnoticeable
S-expressions	S55, S22 / S24
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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

See also

• List of superparticular intervals