20/17

Interval information

Ratio	20/17
Factorization	22 × 5 × 17-1
Monzo	[2 0 1 0 0 0 -1⟩
Size in cents	281.3583¢
Name	diatismic minor third
Color name	17uy2, suyo 2nd
FJS name	[math]\displaystyle{ \text{A2}^{5}_{17} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	8.40939
Weil norm (log2 max(n, d))	8.64386
Wilson norm (sopfr(nd))	26
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In 17-limit just intonation, 20/17 is the diatismic minor third, measuring about 281.4 ¢. It falls short of the Pythagorean minor third (32/27) by a diatisma (136/135), hence the name. It is the mediant of 7/6 and 13/11, as it is (7 + 13)/(6 + 11). It is found in the harmonic series between the 17th and 20th harmonics.

Approximation

Edo approximations for 20/17 (281.36 ¢)
≤ 80edo, relative error ≤ 10%

Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
4	1\4	300.00	+18.64	+6.21
13	3\13	276.92	-4.44	-4.80
17	4\17	282.35	+0.99	+1.41
21	5\21	285.71	+4.36	+7.62
26	6\26	276.92	-4.44	-9.61
30	7\30	280.00	-1.36	-3.40
34	8\34	282.35	+0.99	+2.82
38	9\38	284.21	+2.85	+9.03
43	10\43	279.07	-2.29	-8.20
47	11\47	280.85	-0.51	-1.99
51	12\51	282.35	+0.99	+4.23
60	14\60	280.00	-1.36	-6.79
64	15\64	281.25	-0.11	-0.58
68	16\68	282.35	+0.99	+5.64
77	18\77	280.52	-0.84	-5.38

See also

• 17/10 – its octave complement
• 51/40 – its fifth complement
• 17/15 – its fourth complement
• 4\17 (282.353 cents)
• Gallery of just intervals