513/512

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 height (log2 nd)	18.0028
Weil height (log2 max(n, d))	18.0056
Wilson height (sopfr(nd))	46
Comma size	unnoticeable
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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). It is significant in Functional Just System and Helmholtz-Ellis notation as the formal comma to translate a Pythagorean interval to a nearby undevicesimal interval.

Temperaments

"Boethius" redirects here. For the medieval Roman platonist, see Wikipedia: 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 also

• Unnoticeable comma
• List of superparticular intervals