35ed7/4

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35ed7/4

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Prime factorization	5 × 7
Step size	27.6807¢
Octave	43\35ed7/4 (1190.27¢)
Twelfth	69\35ed7/4 (1909.97¢)
Consistency limit	2
Distinct consistency limit	2

35 equal divisions of 7/4 (abbreviated 35ed7/4) is a nonoctave tuning system that divides the interval of 7/4 into 35 equal parts of about 27.7⁠ ⁠¢ each. Each step represents a frequency ratio of (7/4)^1/35, or the 35th root of 7/4.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	27.7
2	55.4
3	83	20/19, 23/22
4	110.7
5	138.4	13/12, 27/25
6	166.1	11/10
7	193.8	19/17
8	221.4
9	249.1	22/19, 23/20
10	276.8	20/17
11	304.5	25/21
12	332.2	17/14, 23/19, 28/23
13	359.8
14	387.5
15	415.2	14/11
16	442.9	9/7, 22/17
17	470.6	17/13
18	498.3
19	525.9	19/14, 23/17
20	553.6
21	581.3	7/5
22	609	17/12
23	636.7
24	664.3	19/13, 28/19
25	692
26	719.7
27	747.4	17/11, 20/13
28	775.1	11/7
29	802.7	19/12
30	830.4
31	858.1	18/11, 23/14, 28/17
32	885.8	5/3
33	913.5	17/10, 22/13
34	941.1	19/11
35	968.8

Harmonics

Approximation of harmonics in 35ed7/4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-9.7	+8.0	+8.2	+9.4	-1.7	+8.2	-1.5	-11.6	-0.3	+0.8	-11.4
	Relative (%)	-35.1	+29.0	+29.7	+34.1	-6.2	+29.7	-5.4	-42.1	-1.0	+2.9	-41.3
Steps (reduced)		43 (8)	69 (34)	87 (17)	101 (31)	112 (7)	122 (17)	130 (25)	137 (32)	144 (4)	150 (10)	155 (15)

Approximation of harmonics in 35ed7/4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-11.6	-1.5	-10.2	-11.2	-5.5	+6.3	-4.3	-10.0	-11.4	-8.9	-2.8
	Relative (%)	-41.9	-5.4	-36.9	-40.6	-19.7	+22.8	-15.4	-36.2	-41.3	-32.3	-10.3
Steps (reduced)		160 (20)	165 (25)	169 (29)	173 (33)	177 (2)	181 (6)	184 (9)	187 (12)	190 (15)	193 (18)	196 (21)