Mercator's comma: Difference between revisions
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|-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 | |-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 | ||
<math>\frac{(\ | <math>\frac{\left(\frac{3}{2}\right)^{53}}{2^{31}}</math> | ||
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|53edo]], [[159edo|159edo]], [[212edo|212edo]], [[265edo|265edo]], [[742edo|742edo]], [[954edo|954edo]] and [[1749edo|1749edo]]. | 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|53edo]], [[159edo|159edo]], [[212edo|212edo]], [[265edo|265edo]], [[742edo|742edo]], [[954edo|954edo]] and [[1749edo|1749edo]]. | ||
The comma is named for [http://en.wikipedia.org/wiki/Nicholas_Mercator Nicholas Mercator], who first took note of it as a part of his study of [[53edo|53edo]]. | The comma is named for [http://en.wikipedia.org/wiki/Nicholas_Mercator Nicholas Mercator], who first took note of it as a part of his study of [[53edo|53edo]]. | ||
Revision as of 10:45, 21 June 2020
|-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
[math]\displaystyle{ \frac{\left(\frac{3}{2}\right)^{53}}{2^{31}} }[/math]
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.