513/512

513/512, the undevicesimal comma, undevicesimal schisma or Boethius' comma, is an unnoticeable 19-limit (also 2.3.19 subgroup) comma. It is the amount by which 19/16 exceeds the Pythagorean minor third (32/27).

Interval information

Ratio	513/512
Subgroup monzo	2.3.19 [-9 3 1⟩
Size in cents	3.378019¢
Names	undevicesimal comma, undevicesimal schisma, Boethius' comma
Color name	L19o1, lano 1sn, Lano comma
FJS name	[math]\displaystyle{ \text{P1}^{19} }[/math]
Special properties	superparticular, reduced, reduced harmonic
Tenney norm (log2 nd)	18.0028
Weil norm (log2 max(n, d))	18.0056
Wilson norm (sopfr(nd))	46
Comma size	unnoticeable
Open this interval in xen-calc

Temperaments

"Boethius" redirects here. For the medieval Roman platonist, see Anicius Manlius Severinus Boethius.

By tempering out this comma in the 19-limit is defined the boethius temperament, or in the 2.3.19 subgroup, the boethian temperament. Both enables the boethius chords. See No-fives subgroup temperaments #Boethian.

Notation

This comma is significant in Functional Just System and Helmholtz-Ellis notation as the formal comma to translate a Pythagorean interval to a nearby undevicesimal interval.

Sagittal notation

In the Sagittal system, this comma (possibly tempered) is represented by the sagittal  and is called the 19 schisma, or 19s for short, because the simplest interval it notates is 19/1 (equiv 19/16), as for example in D-F⁠ ⁠. The downward version is called 1/19s or 19s down and is represented by .

See also

• List of superparticular intervals