Satanic comma
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| Factorization | 2-1054 × 3665 |
| Monzo | [-1054 665⟩ |
| Size in cents | 0.075575483¢ |
| 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 | |
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].