From Xenharmonic Wiki
Jump to navigation Jump to search
Interval information
Ratio 13/10
Factorization 2-1 × 5-1 × 13
Monzo [-1 0 -1 0 0 1
Size in cents 454.21395¢
Names Barbados third,
tridecimal semisixth
Color name 3og4, thogu 4th
FJS name [math]\text{d4}^{13}_{5}[/math]
Special properties reduced
Tenney height (log2 nd) 7.02237
Weil height (log2 max(n, d)) 7.40088
Wilson height (sopfr (nd)) 20
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~4.2437 bits

[sound info]
open this interval in xen-calc

In 13-limit just intonation, 13/10, the tridecimal semisixth is an interseptimal interval measuring about 454.2¢. It falls in an ambiguous zone between a wide major third such as 9/7 and a flat perfect fourth such as 21/16. The descriptor "interseptimal" comes from Margo Schulter, and indicates its position between those two septimal (7-based) extremes. 13/10 appears between the 10th and 13th overtones of the harmonic series and appears in such chords as 8:10:13, a quasi-augmented triad. 13/10 also appears in the relatively-simple 10:13:15 triad, which consists of an interseptimal ultramajor third (13/10) and an interseptimal inframinor third (15/13) which stack to make a 3/2 perfect fifth. It is well-approximated in 16edo, 21edo, 24edo, 29edo, 37edo, and of course, infinitely many other EDO systems.

See also