21/13

Interval information

Ratio	21/13
Factorization	3 × 7 × 13-1
Monzo	[0 1 0 1 0 -1⟩
Size in cents	830.2532¢
Name	tridecimal supraminor sixth
Color name	thuzo 6th, 3uz6
FJS name	[math]\displaystyle{ \text{M6}^{7}_{13} }[/math]
Special properties	reduced
Tenney height (log2 nd)	8.09276
Weil height (log2 max(n, d))	8.78463
Wilson height (sopfr(nd))	23
[sound info]
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21/13, the tridecimal supraminor sixth, is ca. 830 cents in size. It has a very good approximation in 13edo, and notably, 5 of these intervals differ from 11/1 by 4084223/4084101, a comma of a mere 0.052 ¢.

This interval is a ratio of two consecutive Fibonacci numbers and thus a convergent to acoustic phi (the interval of a golden ratio). In this case, 21/13 is ~2.8 ¢ flat of acoustic phi. It differs from 13/8, the previous such convergent, by 169/168, and from the following convergent 34/21 by 442/441.

See also

• 26/21 – its octave complement
• Gallery of just intervals