13/12

From Xenharmonic Wiki
Jump to navigation Jump to search
Interval information
Ratio 13/12
Factorization 2-2 × 3-1 × 13
Monzo [-2 -1 0 0 0 1
Size in cents 138.5727¢
Name (lesser) tridecimal neutral second
Color name 3o2, tho 2nd
FJS name [math]\displaystyle{ \text{m2}^{13} }[/math]
Special properties superparticular,
reduced
Tenney height (log2 nd) 7.2854
Weil height (log2 max(n, d)) 7.40088
Wilson height (sopfr(nd)) 20
Harmonic entropy
(Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])
~4.25344 bits

[sound info]
Open this interval in xen-calc

In 13-limit just intonation, 13/12 is the (lesser) tridecimal neutral second of about 138.6¢. It is a superparticular interval, as it is found in the harmonic series between the 13th and the 12th harmonics (between 13/8 and 3/2 in the octave). It is flat of the 11-limit lesser neutral second of 12/11 by 144/143 (about 12.1¢), and sharp of the 13-limit large semitone of 14/13 by 169/168 (about 10.3¢).

Temperaments

Todo: expand

Approximation

It is approximated to within about 0.11 cents by the 3-step interval of 26edo.

See also