3025/3024
Ratio | 3025/3024 |
Factorization | 2^{-4} × 3^{-3} × 5^{2} × 7^{-1} × 11^{2} |
Monzo | [-4 -3 2 -1 2⟩ |
Size in cents | 0.57240339¢ |
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 (log_{2} nd) | 23.125 |
Weil height (log_{2} 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 |
open this interval in xen-calc |
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]}