35ed4

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35ed4

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Prime factorization	5 × 7
Step size	68.5714¢
Octave	18\35ed4 (1234.29¢)
Twelfth	28\35ed4 (1920¢) (→4\5ed4)
Consistency limit	1
Distinct consistency limit	1

35 equal divisions of the 4th harmonic (abbreviated 35ed4) is a nonoctave tuning system that divides the interval of 4/1 into 35 equal parts of about 68.6 ¢ each. Each step represents a frequency ratio of 4^1/35, or the 35th root of 4.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	68.6	26/25, 27/26, 28/27
2	137.1	27/25
3	205.7
4	274.3
5	342.9	11/9, 17/14
6	411.4	14/11
7	480
8	548.6
9	617.1
10	685.7
11	754.3	17/11
12	822.9	21/13
13	891.4	5/3
14	960	26/15
15	1028.6
16	1097.1	17/9
17	1165.7
18	1234.3
19	1302.9
20	1371.4	11/5
21	1440
22	1508.6
23	1577.1
24	1645.7
25	1714.3	27/10
26	1782.9	14/5
27	1851.4
28	1920
29	1988.6
30	2057.1	23/7
31	2125.7	17/5
32	2194.3
33	2262.9
34	2331.4
35	2400

Harmonics

Approximation of harmonics in 35ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+34.3	+18.0	+0.0	+25.1	-16.2	-8.8	+34.3	-32.5	-9.2	+31.5	+18.0
	Relative (%)	+50.0	+26.3	+0.0	+36.6	-23.7	-12.9	+50.0	-47.4	-13.4	+46.0	+26.3
Steps (reduced)		18 (18)	28 (28)	35 (0)	41 (6)	45 (10)	49 (14)	53 (18)	55 (20)	58 (23)	61 (26)	63 (28)

Approximation of harmonics in 35ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+16.6	+25.5	-25.4	+0.0	+32.2	+1.8	-23.2	+25.1	+9.2	-2.7	-11.1
	Relative (%)	+24.2	+37.1	-37.1	+0.0	+46.9	+2.6	-33.9	+36.6	+13.4	-4.0	-16.2
Steps (reduced)		65 (30)	67 (32)	68 (33)	70 (0)	72 (2)	73 (3)	74 (4)	76 (6)	77 (7)	78 (8)	79 (9)