Satanic comma
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Factorization
2-1054 × 3665
Monzo
[-1054 665⟩
Size in cents
0.07557548¢
Name
satanic comma
FJS name
[math]\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]\sqrt{nd}[/math])
~1.19987 bits
Comma size
unnoticeable
open this interval in xen-calc
Interval information |
reduced harmonic
(Shannon, [math]\sqrt{nd}[/math])
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[1].