Mercator's comma

|-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.