13/9

Interval information

Ratio	13/9
Factorization	3-2 × 13
Monzo	[0 -2 0 0 0 1⟩
Size in cents	636.6177¢
Names	tridecimal diminished fifth, high tritone
Color name	3o5, tho 5th
FJS name	[math]\displaystyle{ \text{d5}^{13} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	6.87036
Weil norm (log2 max(n, d))	7.40088
Wilson norm (sopfr(nd))	19
[sound info]
Open this interval in xen-calc

In 13-limit just intonation, 13/9, the tridecimal diminished fifth is a high tritone measuring about 636.6¢. It appears between the 9th and 13th harmonics of the harmonic series. Its inversion is 18/13, a low tritone.

Approximation

Edo approximations for 13/9 (636.62 ¢)
≤ 80edo, relative error ≤ 10%

Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
2	1\2	600.00	-36.62	-6.10
15	8\15	640.00	+3.38	+4.23
17	9\17	635.29	-1.32	-1.88
19	10\19	631.58	-5.04	-7.98
30	16\30	640.00	+3.38	+8.46
32	17\32	637.50	+0.88	+2.35
34	18\34	635.29	-1.32	-3.75
36	19\36	633.33	-3.28	-9.85
47	25\47	638.30	+1.68	+6.58
49	26\49	636.73	+0.12	+0.48
51	27\51	635.29	-1.32	-5.63
64	34\64	637.50	+0.88	+4.71
66	35\66	636.36	-0.25	-1.40
68	36\68	635.29	-1.32	-7.50
79	42\79	637.97	+1.36	+8.93

See also

• 18/13 – its octave complement
• 27/26 – its fifth complement
• Gallery of just intervals