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]]. | ||