513/512

From Xenharmonic Wiki
Jump to navigation Jump to search
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 comma
FJS name [math]\text{P1}^{19}[/math]
Special properties superparticular,
reduced,
reduced harmonic
Tenney height (log2 n⋅d) 18.0028
Weil height (max(n, d)) 513
Benedetti height (n⋅d) 262656
Harmonic entropy
(Shannon, [math]\sqrt{n\cdot d}[/math])
~2.44811 bits
Comma size unnoticeable
open this interval in xen-calc

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 exceeds 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