34ed11/5

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34ed11/5

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Prime factorization	2 × 17
Step size	40.1472¢
Octave	30\34ed11/5 (1204.42¢) (→15\17ed11/5)
Twelfth	47\34ed11/5 (1886.92¢)
Consistency limit	3
Distinct consistency limit	2

34 equal divisions of 11/5 (abbreviated 34ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 34 equal parts of about 40.1 ¢ each. Each step represents a frequency ratio of (11/5)^1/34, or the 34th root of 11/5.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	40.147
2	80.294	20/19, 21/20, 22/21, 23/22, 24/23
3	120.442	14/13
4	160.589	11/10, 23/21
5	200.736	19/17
6	240.883	23/20
7	281.03	20/17
8	321.177	6/5
9	361.325	16/13, 21/17
10	401.472	24/19
11	441.619	22/17
12	481.766
13	521.913	19/14, 23/17
14	562.061	25/18
15	602.208	17/12, 24/17
16	642.355
17	682.502
18	722.649
19	762.796
20	802.944	19/12
21	843.091	13/8
22	883.238	5/3
23	923.385	17/10
24	963.532	7/4
25	1003.68
26	1043.827	11/6
27	1083.974
28	1124.121	21/11, 23/12
29	1164.268
30	1204.415	2/1
31	1244.563
32	1284.71	21/10, 23/11
33	1324.857	28/13
34	1365.004	11/5

Harmonics

Approximation of harmonics in 34ed11/5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+4.4	-15.0	+8.8	-16.2	-10.6	+3.5	+13.2	+10.1	-11.7	-16.2	-6.2
	Relative (%)	+11.0	-37.5	+22.0	-40.2	-26.5	+8.8	+33.0	+25.1	-29.2	-40.2	-15.5
Steps (reduced)		30 (30)	47 (13)	60 (26)	69 (1)	77 (9)	84 (16)	90 (22)	95 (27)	99 (31)	103 (1)	107 (5)

Approximation of harmonics in 34ed11/5

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+15.8	+8.0	+9.0	+17.7	-7.0	+14.5	+1.2	-7.3	-11.5	-11.7	-8.4
	Relative (%)	+39.4	+19.8	+22.3	+44.0	-17.4	+36.1	+2.9	-18.3	-28.6	-29.2	-20.9
Steps (reduced)		111 (9)	114 (12)	117 (15)	120 (18)	122 (20)	125 (23)	127 (25)	129 (27)	131 (29)	133 (31)	135 (33)