5767168/5767125

Interval information

Ratio	5767168/5767125
Factorization	219 × 3-1 × 5-3 × 7-1 × 11 × 13-3
Monzo	[19 -1 -3 -1 1 -3⟩
Size in cents	0.01290813¢
Name	insanisma
Color name	satrithu-alorutriguma, s3u^31org^3M
FJS name	[math]\displaystyle{ \text{P1}^{11}_{5,5,5,7,13,13,13} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	44.9189
Weil norm (log2 max(n, d))	44.9189
Wilson norm (sopfr(nd))	113
Comma size	unnoticeable
S-expression	S64/S65
Open this interval in xen-calc

5767168/5767125, the insanisma, is a 13-limit interval, one of the smallest 13-limit commas. It is an ultraparticular, the difference between 4096/4095 and 4225/4224, or S64/S65 S-expressed.

As an ultraparticular, it is the difference between 22/21 and (65/64)³. It also splits the olympia in three and the ibnsinma in two, each for 4096/4095~4225/4224.

Temperaments

This comma is trivially tempered out in olympic, as 4096/4095 and 4225/4224 are also tempered out there. Thus, any temperament of olympic also tempers it out. See here for a compendium of temperaments and edos that temper out this comma due to being olympian.

Other non-olympian edos that temper out the insanisma by patent val, but not either of S64 and S65 include 35, 40, 49, and some hyperfine edos like 3395 and 8539.

Etymology

This comma was named by Eufalesio in 2026, on the basis that tempering out this comma alone purportedly entails an insane level of precision.