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)<sup>53</sup>/2<sup>31</sup>. | {{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>. | ||
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 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]]. | |||
== See also == | == See also == | ||
Revision as of 04:49, 13 March 2021
[-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.
The comma is named for 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 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.