16/13
Ratio | 16/13 |
Subgroup monzo | 2.13 [4 -1⟩ |
Size in cents | 359.47234¢ |
Names | (greater) tridecimal neutral third, octave-reduced 13th subharmonic |
Color name | 3u3, thu 3rd |
FJS name | [math]\text{M3}_{13}[/math] |
Special properties | reduced, reduced subharmonic |
Tenney height (log_{2} nd) | 7.70044 |
Weil height (log_{2} max(n, d)) | 8 |
Wilson height (sopfr (nd)) | 21 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.2603 bits |
[sound info] | |
open this interval in xen-calc |
In 13-limit just intonation, 16/13, the (greater) tridecimal neutral third, is a 13-limit-based interval measuring about 359.5¢. It is the inversion of 13/8, the 13th harmonic.
16/13 differs from the Pythagorean major third 81/64 by 1053/1024, about 48¢, from the classic major third 5/4 by 65/64, about 27¢, from the undecimal neutral third 11/9 by 144/143, about 12¢, and from the rastmic neutral third 27/22 by 352/351, about 4.9¢. A root-3rd-P5 triad featuring 16/13 is 26:32:39, which introduces another tridecimal neutral third, 39/32, which measures about 342.5¢. The interval between these two intervals is 512/507, about 17¢. While 16/13 is utonal, 39/32 is otonal, as it is the 39th harmonic of the harmonic series.
16/13 is a fraction of a cent away from the neutral third found in the 10n family of edos.
16/13 is near the border-region between neutral thrds and submajor thirds, so it has a bright edge to it compared to narrower neutral thirds, while still sounding slightly darker than a major third like 5/4.