Satanic comma
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Factorization | 2^{-1054} × 3^{665} |
Monzo | [-1054 665⟩ |
Size in cents | 0.075575483¢ |
Name | satanic comma |
FJS name | [math]\text{95d}{-64}[/math] |
Special properties | reduced |
Tenney height (log_{2} nd) | 2108 |
Weil height (log_{2} max(n, d)) | 2108 |
Wilson height (sopfr (nd)) | 4103 |
Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~2.39833 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]}.