34ed5/2

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34ed5/2

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Prime factorization	2 × 17
Step size	46.6563¢
Octave	26\34ed5/2 (1213.06¢) (→13\17ed5/2)
Twelfth	41\34ed5/2 (1912.91¢)
Consistency limit	3
Distinct consistency limit	3

34 equal divisions of 5/2 (abbreviated 34ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 34 equal parts of about 46.7 ¢ each. Each step represents a frequency ratio of (5/2)^1/34, or the 34th root of 5/2.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	46.656
2	93.313
3	139.969	27/25
4	186.625	10/9, 19/17
5	233.281
6	279.938
7	326.594	23/19
8	373.25	21/17, 26/21
9	419.907	14/11
10	466.563	17/13
11	513.219	27/20
12	559.875
13	606.532
14	653.188	19/13
15	699.844	3/2
16	746.501	17/11
17	793.157
18	839.813
19	886.469	5/3
20	933.126
21	979.782	23/13
22	1026.438
23	1073.095	13/7, 28/15
24	1119.751	21/11
25	1166.407
26	1213.063
27	1259.72
28	1306.376
29	1353.032
30	1399.689	9/4
31	1446.345
32	1493.001	26/11
33	1539.657	17/7, 22/9
34	1586.314	5/2

Harmonics

Approximation of harmonics in 34ed5/2

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+13.1	+11.0	-20.5	+13.1	-22.6	-9.6	-7.5	+21.9	-20.5	+1.1	-9.6
	Relative (%)	+28.0	+23.5	-44.0	+28.0	-48.5	-20.5	-16.0	+47.0	-44.0	+2.3	-20.5
Steps (reduced)		26 (26)	41 (7)	51 (17)	60 (26)	66 (32)	72 (4)	77 (9)	82 (14)	85 (17)	89 (21)	92 (24)

Approximation of harmonics in 34ed5/2

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-8.2	+3.5	-22.6	+5.6	-6.0	-11.7	-12.0	-7.5	+1.4	+14.2	-16.1
	Relative (%)	-17.5	+7.5	-48.5	+12.0	-13.0	-25.1	-25.7	-16.0	+3.0	+30.3	-34.6
Steps (reduced)		95 (27)	98 (30)	100 (32)	103 (1)	105 (3)	107 (5)	109 (7)	111 (9)	113 (11)	115 (13)	116 (14)