Mercator's comma: Difference between revisions

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{{Infobox Interval
| Monzo = -84 53
| Name = Mercator's comma, 53-comma
| Comma = yes
}}
{{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>.  
{{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>.  


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== See also ==
== See also ==
* [[Unnoticeable comma]]
* [[Unnoticeable comma]]
[[Category:3-limit]]
[[Category:Small commas]]
[[Category:Unnoticeable commas]]

Revision as of 15:58, 27 October 2022

Interval information
Factorization 2-84 × 353
Monzo [-84 53
Size in cents 3.615046¢
Names Mercator's comma,
53-comma
FJS name [math]\displaystyle{ \text{7d}{-6} }[/math]
Special properties reduced,
reduced harmonic
Tenney norm (log2 nd) 168.003
Weil norm (log2 max(n, d)) 168.006
Wilson norm (sopfr(nd)) 327
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)53/231.

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