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
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
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513/512, the undevicesimal comma, undevicesimal schisma or Boethius' comma, is a 19-limit (also 2.3.19 subgroup) unnoticeable comma. It is the amount by which 19/16 falls short of the Pythagorean minor third (32/27). By tempering it out is defined the boethius temperament, which enables the boethius chords. 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.

See also

• Unnoticeable comma
• List of superparticular intervals