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. 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 ==

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[[Category:Satanic]]

[[Category:Commas named for ~~their regular temperament properties~~]]

[[Category:Commas named for the intervals they stack]]

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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.  This difference is inaudible, at only 0.076{{cent}}.
+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 ==
@@ Line 14: / Line 16: @@
 [[Category:Satanic]]
-[[Category:Commas named for their regular temperament properties]]
+[[Category:Commas named for the intervals they stack]]