Satanic comma

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 height (log2 nd)	2108
Weil height (log2 max(n, d))	2108
Wilson height (sopfr(nd))	4103
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~1.19987 bits
Comma size	unnoticeable
Open this interval in xen-calc

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 ¢.

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.

Etymology

This comma was named by Marc Jones in 1990.