Mercator's comma: Difference between revisions

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{{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 ~~fifths~~ exceed 31 ~~octaves~~, in other words (3/2)53/231.

{{Infobox Interval

| Monzo = -84 53

| Name = Mercator's comma, 53-comma

| Color name = Wa-53 comma

| 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)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]].

~~For equal divisions N up to 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~~]].

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~~ [[~~Wikipedia:Nicholas_Mercator~~|~~Nicholas Mercator~~]], ~~who first took note of it as a part of his study~~ of [[53edo]].

== Temperament ==

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]].

== See also ==

* [[~~Unnoticeable~~ 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]]

[[Category:~~3-limit~~]]

[[Category:Commas named after mathematicians]]

[[Category:~~Comma]]~~

[[Category:Commas named after music theorists]]

~~[[Category:Unnoticeable comma~~]]

@@ Line 1: / Line 1: @@
-{{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 fifths exceed 31 octaves, in other words (3/2)<sup>53</sup>/2<sup>31</sup>.
+{{Infobox Interval
+| Monzo = -84 53
+| Name = Mercator's comma, 53-comma
+| Color name = Wa-53 comma
+| 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]].
-For equal divisions N up to 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]].
+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 [[Wikipedia:Nicholas_Mercator|Nicholas Mercator]], who first took note of it as a part of his study of [[53edo]].
+== Temperament ==
+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]].
 == See also ==
-* [[Unnoticeable 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]]
-[[Category:3-limit]]
+[[Category:Commas named after mathematicians]]
-[[Category:Comma]]
+[[Category:Commas named after music theorists]]
-[[Category:Unnoticeable comma]]