Mercator's comma: Difference between revisions
→See also: * Mercator’s old comma (It is what Wikipedia calls “Mercator’s comma”, but it is not what most modern musicians or theorists mean by “Mercator’s comma.) |
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== See also == | == See also == | ||
* [[Holdrian comma|Mercator’s old comma]] (It is what Wikipedia calls “Mercator’s comma”, but it is not what most modern musicians or theorists mean by “Mercator’s comma.) | |||
* [[Holdrian comma]] | * [[Holdrian comma]] | ||
* [[Syntonic comma]] | * [[Syntonic comma]] | ||
* [[Unnoticeable comma]] | * [[Unnoticeable comma]] | ||
Revision as of 07:16, 6 November 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 perfect 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, the amount by which a stack of eight apotomes exceeds a 27/16 major sixth, and the amount by which a stack of two Pythagorean countercommas fall short of the mystery comma.
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.
See also
- Mercator’s old comma (It is what Wikipedia calls “Mercator’s comma”, but it is not what most modern musicians or theorists mean by “Mercator’s comma.)
- Holdrian comma
- Syntonic comma
- Unnoticeable comma