Mercator's comma: Difference between revisions
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{{monzo|-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)<sup>53</sup>/2<sup>31</sup>. It is also the amount by which a stack of | {{monzo|-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)<sup>53</sup>/2<sup>31</sup>. It is also the amount by which a stack of four [[Pythagorean comma]]s exceeds a [[Pythagorean limma]], and the amount by which a stack of eight [[apotome]]s exceeds a [[27/16]] major sixth. | ||
The comma is named for [[Wikipedia: Nicholas Mercator|Nicholas Mercator]], who first took note of it as a part of his study of [[53edo]]. | The comma is named for [[Wikipedia: Nicholas Mercator|Nicholas Mercator]], who first took note of it as a part of his study of [[53edo]]. | ||
Revision as of 22:48, 14 October 2024
| Interval information |
53-comma
reduced harmonic
[-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. It is also the amount by which a stack of four Pythagorean commas exceeds a Pythagorean limma, and the amount by which a stack of eight apotomes exceeds a 27/16 major sixth.
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.