13/8
Ratio | 13/8 |
Subgroup monzo | 2.13 [-3 1⟩ |
Size in cents | 840.52766¢ |
Name | (lesser) tridecimal neutral sixth |
Color name | 3o6, tho 6th |
FJS name | [math]\text{m6}^{13}[/math] |
Special properties | reduced, reduced harmonic |
Tenney height (log_{2} nd) | 6.70044 |
Weil height (log_{2} max(n, d)) | 7.40088 |
Wilson height (sopfr (nd)) | 19 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.23596 bits |
[sound info] | |
open this interval in xen-calc |
13/8 is the (lesser) tridecimal neutral sixth, which measures about 840.5¢, falling between the categories of minor sixth and major sixth. In 13-limit just intonation, 13/8, as an octave-reduced 13th harmonic, is treated as a basic component of harmony. In the harmonic series and in chords based on it, 13/8 sits between the more familiar consonances of 3/2 and 7/4, separated from each by the superparticular ratios 13/12 and 14/13, respectively. The word "lesser" is added when necessary to differentiate it from 64/39, another tridecimal neutral sixth. It may also be treated as a type of augmented fifth, as the sum of 5/4 and 13/10.
13/8 differs from the Pythagorean minor sixth 128/81 by 1053/1024, about 48¢, from the classic minor sixth 8/5 by 65/64, about 27¢, from the undecimal neutral sixth 18/11 by 144/143, about 12¢, and from the rastmic neutral sixth 44/27 by 352/351, about 4.9¢.
Approximation
13/8 is a fraction of a cent away from the neutral sixth found in the 10n-edo family (7\10).
This interval is a ratio of two consecutive Fibonacci numbers, therefore it approximates the golden ratio. In this case, 13/8 is ~7.4 ¢ sharp of the golden ratio.
See also
- 16/13 – its octave complement
- 64/39 – the greater tridecimal neutral sixth
- Gallery of just intervals