34/21

Interval information

Ratio	34/21
Factorization	2 × 3-1 × 7-1 × 17
Monzo	[1 -1 0 -1 0 0 1⟩
Size in cents	834.1745¢
Name	septendecimal supraminor sixth
Color name	17or6, soru 6th
FJS name	[math]\displaystyle{ \text{m6}^{17}_{7} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	9.47978
Weil norm (log2 max(n, d))	10.1749
Wilson norm (sopfr(nd))	29
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34/21 is the septendecimal supraminor sixth.

This interval is a ratio of two consecutive Fibonacci numbers, therefore it approximates the golden ratio. In this case, 34/21 is ~1.1 ¢ sharp of the golden ratio. Two fall short of 21/8 and three of them fall short of 17/4 by 9261/9248, which becomes particularly significant in Sephiroth temperament.

Approximation

Edo approximations for 34/21 (834.17 ¢)
≤ 80edo, relative error ≤ 10%

Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
3	2\3	800.00	-34.17	-8.54
10	7\10	840.00	+5.83	+4.85
13	9\13	830.77	-3.41	-3.69
20	14\20	840.00	+5.83	+9.71
23	16\23	834.78	+0.61	+1.17
26	18\26	830.77	-3.41	-7.38
33	23\33	836.36	+2.19	+6.02
36	25\36	833.33	-0.84	-2.52
46	32\46	834.78	+0.61	+2.33
49	34\49	832.65	-1.52	-6.21
56	39\56	835.71	+1.54	+7.19
59	41\59	833.90	-0.28	-1.36
62	43\62	832.26	-1.92	-9.90
69	48\69	834.78	+0.61	+3.50
72	50\72	833.33	-0.84	-5.05
79	55\79	835.44	+1.27	+8.35

See also

• 21/17 – its octave complement
• Gallery of just intervals