34/27

Interval information

Ratio	34/27
Subgroup monzo	2.3.17 [1 -3 1⟩
Size in cents	399.0904¢
Names	septendecimal quasi-tempered major third, septendecimal tendomean major third
Color name	17o4, iso 4th
FJS name	[math]\displaystyle{ \text{d4}^{17} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	9.84235
Weil norm (log2 max(n, d))	10.1749
Wilson norm (sopfr(nd))	28
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34/27, the septendecimal quasi-tempered major third, is a 17-limit interval that is extremely well-approximated by 1\3 by direct approximation, although 12edo is the first multiple thereof that maps it correctly (as 4\12).

Approximation

Edo approximations for 34/27 (399.09 ¢)
≤ 80edo, relative error ≤ 10%

Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
3	1\3	400.00	+0.91	+0.23
6	2\6	400.00	+0.91	+0.45
9	3\9	400.00	+0.91	+0.68
12	4\12	400.00	+0.91	+0.91
15	5\15	400.00	+0.91	+1.14
18	6\18	400.00	+0.91	+1.36
21	7\21	400.00	+0.91	+1.59
24	8\24	400.00	+0.91	+1.82
27	9\27	400.00	+0.91	+2.05
30	10\30	400.00	+0.91	+2.27
33	11\33	400.00	+0.91	+2.50
36	12\36	400.00	+0.91	+2.73
39	13\39	400.00	+0.91	+2.96
42	14\42	400.00	+0.91	+3.18
45	15\45	400.00	+0.91	+3.41
48	16\48	400.00	+0.91	+3.64
51	17\51	400.00	+0.91	+3.87
54	18\54	400.00	+0.91	+4.09
57	19\57	400.00	+0.91	+4.32
60	20\60	400.00	+0.91	+4.55
63	21\63	400.00	+0.91	+4.78
66	22\66	400.00	+0.91	+5.00
69	23\69	400.00	+0.91	+5.23
72	24\72	400.00	+0.91	+5.46
75	25\75	400.00	+0.91	+5.68
78	26\78	400.00	+0.91	+5.91

See also

• 27/17 – its octave complement