Mercator's comma

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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 (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.

See also