18/13

In 13-limit just intonation, 18/13, the tridecimal augmented fourth is a low tritone measuring about 563.4¢. It represents the interval between the 13th and 18th harmonics of the harmonic series.

Interval information

Ratio	18/13
Factorization	2 × 32 × 13-1
Monzo	[1 2 0 0 0 -1⟩
Size in cents	563.3823¢
Names	tridecimal augmented fourth, low tritone
Color name	3u4, thu 4th
FJS name	[math]\displaystyle{ \text{A4}_{13} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	7.87036
Weil norm (log2 max(n, d))	8.33985
Wilson norm (sopfr(nd))	21
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The low tritone in 17edo approximates 18/13 quite well, while 17edo's approximations of 13/8 and 9/8 are both a little sharp. The inversion of 18/13 is 13/9, a high tritone measuring about 636.6¢; the interval between these two tridecimal (13-based) tritones is 169/162, approximately 73.2¢.

Approximation

Edo approximations for 18/13 (563.38 ¢)
≤ 80edo, relative error ≤ 10%

Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
2	1\2	600.00	+36.62	+6.10
15	7\15	560.00	-3.38	-4.23
17	8\17	564.71	+1.32	+1.88
19	9\19	568.42	+5.04	+7.98
30	14\30	560.00	-3.38	-8.46
32	15\32	562.50	-0.88	-2.35
34	16\34	564.71	+1.32	+3.75
36	17\36	566.67	+3.28	+9.85
47	22\47	561.70	-1.68	-6.58
49	23\49	563.27	-0.12	-0.48
51	24\51	564.71	+1.32	+5.63
64	30\64	562.50	-0.88	-4.71
66	31\66	563.64	+0.25	+1.40
68	32\68	564.71	+1.32	+7.50
79	37\79	562.03	-1.36	-8.93

See also

• 13/9 – its octave complement
• 13/12 – its fifth complement
• Gallery of just intervals