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Interval information
Ratio 513/512
Subgroup monzo 2.3.19 [-9 3 1
Size in cents 3.3780187¢
Names undevicesimal comma,
undevicesimal schisma,
Boethius' comma
Color name L19o1, lano 1sn,
Lano comma
FJS name [math]\text{P1}^{19}[/math]
Special properties superparticular,
Tenney height (log2 nd) 18.0028
Weil height (log2 max(n, d)) 18.0056
Wilson height (sopfr (nd)) 46
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~1.30567 bits
Comma size unnoticeable
open this interval in xen-calc

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.


"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