35/29

35/29, the doublewide minor third, is a minor third in 29-limit just intonation. It is sharp of 32/27, the Pythagorean minor third, by 945/928, and sharp of 6/5, the classical minor third, by 175/174. It is flat by 29/24, another 29-limit minor third, by 841/840 (S29), a comma 2.06 ¢ in size.

Interval information

Ratio	35/29
Subgroup monzo	5.7.29 [1 1 -1⟩
Size in cents	325.5624¢
Name	doublewide minor third
Color name	29uzy3, twenuzoyo 3rd
FJS name	[math]\displaystyle{ \text{M3}^{5,7}_{29} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	9.98726
Weil norm (log2 max(n, d))	10.2586
Wilson norm (sopfr(nd))	41
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Approximation

Edo approximations for 35/29 (325.56 ¢)
≤ 80edo, relative error ≤ 10%

Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
4	1\4	300.00	-25.56	-8.52
11	3\11	327.27	+1.71	+1.57
15	4\15	320.00	-5.56	-6.95
22	6\22	327.27	+1.71	+3.14
26	7\26	323.08	-2.49	-5.39
33	9\33	327.27	+1.71	+4.70
37	10\37	324.32	-1.24	-3.82
44	12\44	327.27	+1.71	+6.27
48	13\48	325.00	-0.56	-2.25
55	15\55	327.27	+1.71	+7.84
59	16\59	325.42	-0.14	-0.68
63	17\63	323.81	-1.75	-9.20
66	18\66	327.27	+1.71	+9.41
70	19\70	325.71	+0.15	+0.89
74	20\74	324.32	-1.24	-7.63

Temperaments

The 35/29 interval gives an excellent generator for the doublewide temperament with a half octave. It lies between 16\59 (32\118) and 3\11 (6\22), which may also serve as generators for doublewide.