13/8

Interval information

Ratio	13/8
Subgroup monzo	2.13 [-3 1⟩
Size in cents	840.5277¢
Name	(lesser) tridecimal neutral sixth
Color name	3o6, tho 6th
FJS name	[math]\displaystyle{ \text{m6}^{13} }[/math]
Special properties	reduced, reduced harmonic
Tenney height (log2 nd)	6.70044
Weil height (log2 max(n, d))	7.40088
Wilson height (sopfr(nd))	19
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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