Mercator's comma: Difference between revisions

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The comma with the ~~Monzo~~ of {{monzo|-84 53}}, known as '''Mercator's comma''' or the '''53-comma''', is a small comma of 3.615 cents which is the amount by which 53 [[perfect fifth]]s exceed 31 [[octave]]s, in other words (3/2)53/231. It is also the amount by which a stack of four [[Pythagorean comma]]s exceeds a [[Pythagorean limma]], the amount by which a stack of eight [[apotome]]s exceeds a [[27/16]] major sixth, and the amount by which a stack of two [[Pythagorean countercomma]]s fall short of the [[mystery comma]].

The comma with the monzo of {{monzo|-84 53}}, known as '''Mercator's comma''' or the '''53-comma''', is a small comma of 3.615 cents which is the amount by which 53 [[perfect fifth]]s exceed 31 [[octave]]s, in other words (3/2)53/231. It is also the amount by which a stack of four [[Pythagorean comma]]s exceeds a [[Pythagorean limma]], the amount by which a stack of eight [[apotome]]s exceeds a [[27/16]] major sixth, and the amount by which a stack of two [[Pythagorean countercomma]]s fall short of the [[mystery comma]].

The comma is named for [[Nicholas Mercator]], who first took note of it as a part of his study of [[53edo]].

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== See also ==

* [[Holdrian comma|~~Mercator’s~~ old comma]] (It is what Wikipedia calls ~~“Mercator’s comma”~~, but it is not what most modern musicians or theorists mean by ~~“Mercator’s~~ comma.)

* [[Holdrian comma#Mercator's comma, Mercator’s old comma, and the Holdrian comma|Mercator's old comma]] (It is what Wikipedia calls "Mercator's comma", but it is not what most modern musicians or theorists mean by "Mercator's comma".)

* [[Holdrian comma]]

* [[Syntonic comma]]

* [[Small comma]]

* [[Unnoticeable comma]]

[[Category:Commas named after mathematicians]]

[[Category:Commas named after music theorists]]

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-The comma with the Monzo of {{monzo|-84 53}}, known as '''Mercator's comma''' or the '''53-comma''', is a small comma of 3.615 cents which is the amount by which 53 [[perfect fifth]]s exceed 31 [[octave]]s, in other words (3/2)<sup>53</sup>/2<sup>31</sup>.  It is also the amount by which a stack of four [[Pythagorean comma]]s exceeds a [[Pythagorean limma]], the amount by which a stack of eight [[apotome]]s exceeds a [[27/16]] major sixth, and the amount by which a stack of two [[Pythagorean countercomma]]s fall short of the [[mystery comma]].
+The comma with the monzo of {{monzo|-84 53}}, known as '''Mercator's comma''' or the '''53-comma''', is a small comma of 3.615 cents which is the amount by which 53 [[perfect fifth]]s exceed 31 [[octave]]s, in other words (3/2)<sup>53</sup>/2<sup>31</sup>.  It is also the amount by which a stack of four [[Pythagorean comma]]s exceeds a [[Pythagorean limma]], the amount by which a stack of eight [[apotome]]s exceeds a [[27/16]] major sixth, and the amount by which a stack of two [[Pythagorean countercomma]]s fall short of the [[mystery comma]].
 The comma is named for [[Nicholas Mercator]], who first took note of it as a part of his study of [[53edo]].
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 == See also ==
-* [[Holdrian comma|Mercator’s old comma]] (It is what Wikipedia calls “Mercator’s comma”, but it is not what most modern musicians or theorists mean by “Mercator’s comma.)
+* [[Holdrian comma#Mercator's comma, Mercator’s old comma, and the Holdrian comma|Mercator's old comma]] (It is what Wikipedia calls "Mercator's comma", but it is not what most modern musicians or theorists mean by "Mercator's comma".)
 * [[Holdrian comma]]
-* [[Syntonic comma]]
-* [[Small comma]]
-* [[Unnoticeable comma]]
 [[Category:Commas named after mathematicians]]
 [[Category:Commas named after music theorists]]