Pythagorean comma: Difference between revisions

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The '''Pythagorean''' or '''ditonic comma''' (about 23.460[[Cent|¢]]) is the interval 531441/524288 or {{Monzo| -19 12 }} in [[monzo]] notation. 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]].
{{Infobox Interval
| JI glyph =
| Ratio = 531441/524288
| Monzo = -19 12
| Cents = 23.46001
| Name = Pythagorean comma, <br>ditonic comma
| Color name =
| FJS name =
| Sound =
}}
 
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]].


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

Revision as of 01:11, 8 November 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 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)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