30/17

Interval information

Ratio	30/17
Factorization	2 × 3 × 5 × 17-1
Monzo	[1 1 1 0 0 0 -1⟩
Size in cents	983.3133¢
Name	diatismic minor seventh
Color name	17uy6, suyo 6th
FJS name	[math]\displaystyle{ \text{A6}^{5}_{17} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	8.99435
Weil norm (log2 max(n, d))	9.81378
Wilson norm (sopfr(nd))	27
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In 17-limit just intonation, 30/17 is the diatismic minor seventh, measuring about 983.3 ¢. It falls short of the Pythagorean minor seventh (16/9) by a diatisma (136/135), hence the name. It is the mediant of 7/4 and 23/13. Its inversion is 17/15, the "septendecimal whole tone"; both of these intervals are well approximated in 22edo (18\22, 4\22).

Approximation

Edo approximations for 30/17 (983.31 ¢)
≤ 80edo, relative error ≤ 10%

Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
5	4\5	960.00	-23.31	-9.71
6	5\6	1000.00	+16.69	+8.34
11	9\11	981.82	-1.50	-1.37
17	14\17	988.24	+4.92	+6.97
22	18\22	981.82	-1.50	-2.74
28	23\28	985.71	+2.40	+5.60
33	27\33	981.82	-1.50	-4.11
39	32\39	984.62	+1.30	+4.23
44	36\44	981.82	-1.50	-5.48
50	41\50	984.00	+0.69	+2.86
55	45\55	981.82	-1.50	-6.85
61	50\61	983.61	+0.29	+1.49
66	54\66	981.82	-1.50	-8.22
67	55\67	985.07	+1.76	+9.83
72	59\72	983.33	+0.02	+0.12
77	63\77	981.82	-1.50	-9.59
78	64\78	984.62	+1.30	+8.46

See also

• 17/15 its octave complement
• Gallery of just intervals