Mercator's comma - Revision history

FloraC: + category

2026-09-10T06:57:33Z

+ category

← Older revision		Revision as of 06:57, 10 September 2026
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	* [[Unnoticeable comma]] (its size often considered to be a threshold for it.)		* [[Unnoticeable comma]] (its size often considered to be a threshold for it.)

			[[Category:Mercator]]
	[[Category:Commas named after mathematicians]]		[[Category:Commas named after mathematicians]]
	[[Category:Commas named after music theorists]]		[[Category:Commas named after music theorists]]

FloraC: Various cleanup

2026-09-10T06:57:19Z

Various cleanup

← Older revision		Revision as of 06:57, 10 September 2026
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	\| Comma = yes		\| Comma = yes
	}}		}}
	~~The comma with the monzo of {{monzo\|-84 53}}, known as~~ '''Mercator's comma''', '''mercator 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]].		'''Mercator's comma''', '''mercator comma''', or systematically the '''53-comma''', is a [[small comma\|small]] [[3-limit]] [[comma]] of about 3.62 [[cent]]s. It is the amount by which 53 [[3/2\|perfect fifths]] 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 [[Pythagorean 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]].		The comma is named for [[Nicholas Mercator]], who first took note of it as a part of his study of [[53edo]].

	== ~~Temperament~~ ==		== Temperaments ==
	Tempering out this comma leads to the [[~~Mercator family~~]] ~~of temperaments~~. For edos N up to [[8745edo\|8745]], the comma is tempered out if and only if 53 divides N. Examples of such ~~EDOs~~ include [[53edo]], [[159edo]], [[212edo]], [[265edo]], [[742edo]], [[954edo]] and [[1749edo]].		[[Tempering out]] this comma leads to the [[mercator]] temperament. For edos ''N'' up to [[8745edo\|8745]], the comma is tempered out if and only if 53 divides ''N''. Examples of such edos include [[53edo]], [[159edo]], [[212edo]], [[265edo]], [[742edo]], [[954edo]] and [[1749edo]].

			See [[Mercator family]] for the [[family of temperaments]] where it is tempered out.

	== See also ==		== See also ==
	* [[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 #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]]		* [[Holdrian comma]]
	* [[Unnoticeable comma]] (~~Despite not being an unnoticeable comma by itself,~~ it~~'s mentioned in the intro of this page~~.)		* [[Unnoticeable comma]] (its size often considered to be a threshold for it.)

	[[Category:Commas named after mathematicians]]		[[Category:Commas named after mathematicians]]
	[[Category:Commas named after music theorists]]		[[Category:Commas named after music theorists]]

FilterNashi: /* See also */

2026-06-24T18:59:26Z

FilterNashi: /* See also */

2026-06-24T18:59:04Z

Eufalesio: Updated color notation

2026-05-01T14:45:27Z

Updated color notation

← Older revision		Revision as of 14:45, 1 May 2026
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	\| Monzo = -84 53		\| Monzo = -84 53
	\| Name = Mercator's comma, 53-comma		\| Name = Mercator's comma, 53-comma
	\| Color name = ~~Wa-53 comma~~		\| Color name = 53wM, fithewama
	\| Comma = yes		\| Comma = yes
	}}		}}

FloraC: Undo revision 211176 by M1k1 H2tsun2 (talk)

2025-09-27T12:01:29Z

Undo revision 211176 by M1k1 H2tsun2 (talk)

← Older revision		Revision as of 12:01, 27 September 2025
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	{{Infobox Interval		{{Infobox Interval
	\| Monzo = -84 53		\| Monzo = -84 53
	\| Name = ~~Threerish 53-tone's comma,~~ Mercator's comma, 53-comma		\| Name = Mercator's comma, 53-comma
	\| Color name = Wa-53 comma		\| Color name = Wa-53 comma
	\| Comma = yes		\| Comma = yes

M1k1 H2tsun2: add it them

2025-09-27T11:59:21Z

add it them

← Older revision		Revision as of 11:59, 27 September 2025
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	{{Infobox Interval		{{Infobox Interval
	\| Monzo = -84 53		\| Monzo = -84 53
	\| Name = Mercator's comma, 53-comma		\| Name = Threerish 53-tone's comma, Mercator's comma, 53-comma
	\| Color name = Wa-53 comma		\| Color name = Wa-53 comma
	\| Comma = yes		\| Comma = yes

VectorGraphics at 03:02, 9 September 2025

2025-09-09T03:02:48Z

← Older revision		Revision as of 03:02, 9 September 2025
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	\| Comma = yes		\| Comma = yes
	}}		}}
	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''', '''mercator 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]].		The comma is named for [[Nicholas Mercator]], who first took note of it as a part of his study of [[53edo]].

FilterNashi at 12:28, 12 June 2025

2025-06-12T12:28:47Z

← Older revision		Revision as of 12:28, 12 June 2025
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	== See also ==		== 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]]		* [[Holdrian comma]]

	[[Category:Commas named after mathematicians]]		[[Category:Commas named after mathematicians]]
	[[Category:Commas named after music theorists]]		[[Category:Commas named after music theorists]]

FilterNashi at 12:25, 12 June 2025

2025-06-12T12:25:11Z

← Older revision		Revision as of 12:25, 12 June 2025
Line 13:		Line 13:

	== See also ==		== See also ==
	* [[Holdrian comma\|Mercator's old comma]] (~~Known as Holdrian 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 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]]

	[[Category:Commas named after mathematicians]]		[[Category:Commas named after mathematicians]]
	[[Category:Commas named after music theorists]]		[[Category:Commas named after music theorists]]

← Older revision		Revision as of 18:59, 24 June 2026
Line 15:		Line 15:
	* [[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#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]]		* [[Holdrian comma]]
	* [[~~unnoticeable~~ comma]] (Despite not being an unnoticeable comma by itself, it's mentioned in the intro of this page.)		* [[Unnoticeable comma]] (Despite not being an unnoticeable comma by itself, it's mentioned in the intro of this page.)

	[[Category:Commas named after mathematicians]]		[[Category:Commas named after mathematicians]]
	[[Category:Commas named after music theorists]]		[[Category:Commas named after music theorists]]