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	68.571	26/25, 27/26, 28/27
2	137.143	27/25
3	205.714
4	274.286
5	342.857	11/9, 17/14
6	411.429	14/11
7	480
8	548.571
9	617.143
10	685.714
11	754.286	17/11
12	822.857	21/13
13	891.429	5/3
14	960	26/15
15	1028.571
16	1097.143	17/9
17	1165.714
18	1234.286
19	1302.857
20	1371.429	11/5
21	1440
22	1508.571
23	1577.143
24	1645.714
25	1714.286	27/10
26	1782.857	14/5
27	1851.429
28	1920
29	1988.571
30	2057.143	23/7
31	2125.714	17/5
32	2194.286
33	2262.857
34	2331.429
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)