13/8

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Interval information
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
Tenney height (log2 nd) 6.70044
Weil height (log2 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