From Xenharmonic Wiki
Jump to navigation Jump to search
Interval information
Ratio 15/13
Factorization 3 × 5 × 13-1
Monzo [0 1 1 0 0 -1
Size in cents 247.74105¢
Name tridecimal semifourth
Color name 3uy2, thuyo 2nd
FJS name [math]\text{A2}^{5}_{13}[/math]
Special properties reduced
Tenney height (log2 nd) 7.60733
Weil height (log2 max(n, d)) 7.81378
Wilson height (sopfr (nd)) 21
Harmonic entropy
(Shannon, [math]\sqrt{n\cdot d}[/math])
~4.55413 bits

[sound info]
open this interval in xen-calc

In 13-limit just intonation, 15/13, the tridecimal semifourth is an interval measuring about 247.7¢. In the language of Margo Schulter, 15/13 is an instance of an interseptimal interval, as it falls in an ambiguous zone between two septimal extremes – namely the large major second 8/7 and the small minor third 7/6. (15/13)×(13/10) = 3/2, which implies that 15/13 and 13/10 make a 3/2 perfect fifth. Thus you can make a root-3rd-P5 triad that goes 26:30:39, with a 15/13 inframinor third up from the root. When being used as type of second, it is given the name ultramajor second as it is even sharper than 8/7 which is often called a "supermajor second".

See also