Mercator's comma
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Factorization | 2^{-84} × 3^{53} |
Monzo | [-84 53⟩ |
Size in cents | 3.6150459¢ |
Names | Mercator's comma, 53-comma |
Color name | Wa-53 comma |
FJS name | [math]\text{7d}{-6}[/math] |
Special properties | reduced, reduced harmonic |
Tenney height (log_{2} nd) | 168.003 |
Weil height (log_{2} max(n, d)) | 168.006 |
Wilson height (sopfr (nd)) | 327 |
Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~2.45434 bits |
Comma size | small |
open this interval in xen-calc |
[-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}/2^{31}.
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 edos 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.