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Interval information
Ratio 3025/3024
Factorization 2-4 × 3-3 × 52 × 7-1 × 112
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,
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
open this interval in xen-calc

3025/3024, the lehmerisma, is an 11-limit unnoticeable 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 two superparticular commas: (4375/4374)(9801/9800).


Tempering it out 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.


This comma was named by Gene Ward Smith in 2004 after the American mathematician D. H. Lehmer[1].

See also