34ed5/4

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34ed5/4

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Prime factorization	2 × 17
Step size	11.3622¢
Octave	106\34ed5/4 (1204.39¢) (→53\17ed5/4)
Twelfth	167\34ed5/4 (1897.48¢)
Consistency limit	2
Distinct consistency limit	2

34 equal divisions of 5/4 (abbreviated 34ed5/4) is a nonoctave tuning system that divides the interval of 5/4 into 34 equal parts of about 11.4 ¢ each. Each step represents a frequency ratio of (5/4)^1/34, or the 34th root of 5/4.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	11.362
2	22.724
3	34.087
4	45.449
5	56.811
6	68.173
7	79.535	23/22, 24/23
8	90.897	18/17, 20/19
9	102.26	19/18
10	113.622	15/14
11	124.984	14/13, 27/25
12	136.346	13/12, 25/23
13	147.708
14	159.07	11/10, 12/11
15	170.433
16	181.795
17	193.157	19/17
18	204.519	28/25
19	215.881	25/22, 26/23
20	227.243
21	238.606	23/20
22	249.968	22/19
23	261.33	7/6
24	272.692
25	284.054	20/17
26	295.416	13/11
27	306.779	25/21
28	318.141	6/5
29	329.503	23/19
30	340.865	17/14, 28/23
31	352.227	11/9
32	363.589
33	374.952
34	386.314

Harmonics

Approximation of harmonics in 34ed5/4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+4.39	-4.47	-2.58	-2.58	-0.08	-5.62	+1.81	+2.42	+1.81	-4.13	+4.31
	Relative (%)	+38.6	-39.4	-22.7	-22.7	-0.7	-49.5	+15.9	+21.3	+15.9	-36.3	+37.9
Steps (reduced)		106 (4)	167 (31)	211 (7)	245 (7)	273 (1)	296 (24)	317 (11)	335 (29)	351 (11)	365 (25)	379 (5)

Approximation of harmonics in 34ed5/4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+2.08	-1.23	+4.31	-5.17	+3.50	-4.56	+4.10	-5.17	+1.27	+0.26	+2.84
	Relative (%)	+18.3	-10.9	+37.9	-45.5	+30.8	-40.1	+36.1	-45.5	+11.1	+2.3	+25.0
Steps (reduced)		391 (17)	402 (28)	413 (5)	422 (14)	432 (24)	440 (32)	449 (7)	456 (14)	464 (22)	471 (29)	478 (2)