39/32
| Ratio | 39/32 |
| Factorization | 2-5 × 3 × 13 |
| Monzo | [-5 1 0 0 0 1⟩ |
| Size in cents | 342.48266¢ |
| Names | lesser tridecimal neutral third, octave-reduced 39th harmonic |
| Color name | 3o3, tho 3rd |
| FJS name | [math]\text{m3}^{13}[/math] |
| Special properties | reduced, reduced harmonic |
| Tenney height (log2 nd) | 10.2854 |
| Weil height (log2 max(n, d)) | 10.5708 |
| Wilson height (sopfr (nd)) | 26 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.2507 bits |
[sound info] | |
| open this interval in xen-calc | |
In 13-limit just intonation, 39/32, the (lesser) tridecimal neutral third, is the otonal combination of primes 13 and 3 octave-reduced. It is the fifth complement of 16/13, which measures about 359.5¢.
39/32 differs from the Pythagorean minor third 32/27 by 1053/1024, about 48¢, from the classic minor third 6/5 by 65/64, about 27¢, from the rastmic neutral third 27/22 by 144/143, about 12¢, and from the undecimal neutral third 11/9 by 352/351, about 4.9¢.
39/32 is a fraction of a cent away from the neutral third found in the 7n family of edos.
39/32 is near the border-region between neutral thirds and supraminor thirds, so it has a dark edge to it compared to wider neutral thirds, while still sounding slightly brighter than a minor third like 6/5.