16/9

Interval information

Ratio	16/9
Factorization	24 × 3-2
Monzo	[4 -2⟩
Size in cents	996.09¢
Name	Pythagorean minor seventh
Color name	w7, wa 7th
FJS name	[math]\displaystyle{ \text{m7} }[/math]
Special properties	reduced, reduced subharmonic
Tenney norm (log2 nd)	7.16993
Weil norm (log2 max(n, d))	8
Wilson norm (sopfr(nd))	14
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Minor seventh

In 3-limit just intonation, 16/9 is the Pythagorean minor seventh, at about 996.1 cents. It is equal to two perfect fourths, or (4/3)×(4/3), and is thus the octave reduced form of the ninth subharmonic. It differs from the nearby 5-limit minor seventh 9/5 (~1017.6 cents) by the syntonic comma of 81/80 (~21.5 cents), and the 7-limit minor seventh 7/4 (~968.8 cents) by the septimal comma of 64/63 (~27.3 cents).

Approximation

Edo approximations for 16/9 (996.09 ¢)
≤ 80edo, relative error ≤ 10%

Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
6	5\6	1000.00	+3.91	+1.96
12	10\12	1000.00	+3.91	+3.91
18	15\18	1000.00	+3.91	+5.87
23	19\23	991.30	-4.79	-9.17
24	20\24	1000.00	+3.91	+7.82
29	24\29	993.10	-2.99	-7.22
30	25\30	1000.00	+3.91	+9.78
35	29\35	994.29	-1.80	-5.26
41	34\41	995.12	-0.97	-3.31
47	39\47	995.74	-0.35	-1.35
53	44\53	996.23	+0.14	+0.60
59	49\59	996.61	+0.52	+2.56
65	54\65	996.92	+0.83	+4.51
71	59\71	997.18	+1.09	+6.47
76	63\76	994.74	-1.35	-8.57
77	64\77	997.40	+1.31	+8.42

See also

• 9/8 – its octave complement
• Ed16/9
• Gallery of just intervals