34ed7/4

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34ed7/4

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Prime factorization	2 × 17
Step size	28.4949¢
Octave	42\34ed7/4 (1196.78¢) (→21\17ed7/4)
Twelfth	67\34ed7/4 (1909.16¢)
Consistency limit	6
Distinct consistency limit	3

34 equal divisions of 7/4 (abbreviated 34ed7/4) is a nonoctave tuning system that divides the interval of 7/4 into 34 equal parts of about 28.5 ¢ each. Each step represents a frequency ratio of (7/4)^1/34, or the 34th root of 7/4.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	28.495
2	56.99
3	85.485	19/18, 20/19, 21/20, 22/21
4	113.98
5	142.474	12/11, 13/12
6	170.969	11/10, 21/19
7	199.464	19/17
8	227.959	8/7, 25/22
9	256.454	15/13, 22/19
10	284.949	13/11, 20/17
11	313.444	6/5
12	341.939	11/9, 17/14, 28/23
13	370.433	21/17, 26/21
14	398.928	24/19
15	427.423
16	455.918	13/10, 17/13
17	484.413
18	512.908
19	541.403	15/11, 26/19
20	569.898	18/13, 25/18
21	598.392	17/12, 24/17
22	626.887	23/16
23	655.382	19/13, 22/15
24	683.877
25	712.372
26	740.867	20/13, 26/17
27	769.362
28	797.857	19/12
29	826.352	21/13
30	854.846	18/11, 23/14
31	883.341	5/3
32	911.836	17/10, 22/13
33	940.331	12/7, 19/11
34	968.826	7/4

Harmonics

Approximation of harmonics in 34ed7/4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-3.2	+7.2	-6.4	+6.2	+4.0	-6.4	-9.6	-14.1	+3.0	+8.9	+0.8
	Relative (%)	-11.3	+25.3	-22.6	+21.7	+14.0	-22.6	-33.8	-49.5	+10.4	+31.4	+2.7
Steps (reduced)		42 (8)	67 (33)	84 (16)	98 (30)	109 (7)	118 (16)	126 (24)	133 (31)	140 (4)	146 (10)	151 (15)

Approximation of harmonics in 34ed7/4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+4.7	-9.6	+13.4	-12.9	-3.8	+11.2	+3.1	-0.2	+0.8	+5.7	-14.2
	Relative (%)	+16.4	-33.8	+47.0	-45.1	-13.5	+39.3	+10.8	-0.9	+2.7	+20.1	-50.0
Steps (reduced)		156 (20)	160 (24)	165 (29)	168 (32)	172 (2)	176 (6)	179 (9)	182 (12)	185 (15)	188 (18)	190 (20)