Pythagorean comma: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
Arseniiv (talk | contribs)
m infoboxified
Xenwolf (talk | contribs)
bold redirect lemma
Line 16: Line 16:
}}
}}


The '''Pythagorean''' or '''ditonic comma''' is the interval 531441/524288. It could also be called the 12-comma as it is the amount by which twelve fifths exceed seven octaves, or in other words (3/2)<sup>12</sup>/2<sup>7</sup> and it also can be written as the ratio between the apotome and the Pythagorean minor second, ([[2187/2048]])/([[256/243]]). For EDOs up to 300, it is tempered out if and only if the EDO is a multiple of 12, and hence for instance by [[12edo]], [[24edo]], [[72edo]] and [[84edo]].
The '''Pythagorean''' or '''ditonic comma''' is the interval with the ratio '''531441/524288''' (={{Monzo| -19 12 }}). It could also be called the 12-comma as it is the amount by which twelve fifths exceed seven octaves, or in other words (3/2)<sup>12</sup>/2<sup>7</sup> and it also can be written as the ratio between the apotome and the Pythagorean minor second, ([[2187/2048]])/([[256/243]]). For EDOs up to 300, it is tempered out if and only if the EDO is a multiple of 12, and hence for instance by [[12edo]], [[24edo]], [[72edo]] and [[84edo]].


== See also ==
== See also ==

Revision as of 14:00, 20 December 2020

Interval information
Ratio 531441/524288
Factorization 2-19 × 312
Monzo [-19 12
Size in cents 23.46001¢
Names Pythagorean comma,
ditonic comma
FJS name [math]\displaystyle{ \text{d}{-2} }[/math]
Special properties reduced,
reduced harmonic
Tenney norm (log2 nd) 38.0196
Weil norm (log2 max(n, d)) 38.0391
Wilson norm (sopfr(nd)) 74
Open this interval in xen-calc

The Pythagorean or ditonic comma is the interval with the ratio 531441/524288 (=[-19 12). It could also be called the 12-comma as it is the amount by which twelve fifths exceed seven octaves, or in other words (3/2)12/27 and it also can be written as the ratio between the apotome and the Pythagorean minor second, (2187/2048)/(256/243). For EDOs up to 300, it is tempered out if and only if the EDO is a multiple of 12, and hence for instance by 12edo, 24edo, 72edo and 84edo.

See also