Satanic comma

The satanic comma (monzo: [-1054 665⟩) is the difference between 666 perfect fifths (octave-reduced) and a single perfect fifth. Equivalently, it is the difference between 665 perfect fifths (octave-reduced) and the unison – but that would not be as devilishly intriguing. This difference is inaudible, at only 0.076 ¢.

Interval information

Factorization	2-1054 × 3665
Monzo	[-1054 665⟩
Size in cents	0.07557548¢
Name	satanic comma
FJS name	[math]\displaystyle{ \text{95d}{-64} }[/math]
Special properties	reduced, reduced harmonic
Tenney norm (log2 nd)	2108
Weil norm (log2 max(n, d))	2108
Wilson norm (sopfr(nd))	4103
Comma size	unnoticeable
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It is also the difference between 13 Mercator's commas and 2 pythagorean commas, or put simply, the difference between the 359-comma and the 306-comma.

It is tempered out in 665edo and its multiples (1330edo, etc.), with 665edo itself being an 11-strong 3-2 telic system due to tempering this comma out. The next smallest 3-limit comma is the 190537-comma, which is orders of magnitude much smaller and complex.

Etymology

This comma was named by Marc Jones in 1990.