13/8
| Interval information |
reduced harmonic
(Shannon, [math]\sqrt{nd}[/math])
[sound info]
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