13/10
| 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.