Satanic comma: Difference between revisions
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The '''satanic comma''' ([[monzo]]: {{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. | The '''satanic comma''' ([[monzo]]: {{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{{cent}}. | ||
It is tempered out in [[665edo]] and its multiples ([[1330edo]], etc.), with 665edo itself being an 11-strong 3-2 [[telicity|telic]] system due to tempering this comma out. | It is also the difference between 13 [[Mercator's comma]]s and 2 [[pythagorean comma]]s, 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 [[telicity|telic]] system due to tempering this comma out. The next smallest 3-limit comma is the [[Archangelic comma|190537-comma]], which is orders of magnitude much smaller and complex. | |||
== Etymology == | == Etymology == | ||
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[[Category:Satanic]] | [[Category:Satanic]] | ||
[[Category:Commas named for the intervals they stack]] | |||
Latest revision as of 08:56, 25 December 2025
| Interval information |
reduced harmonic
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 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[1].