35ed5/2

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35ed5/2

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Prime factorization	5 × 7
Step size	45.3232¢
Octave	26\35ed5/2 (1178.4¢)
Twelfth	42\35ed5/2 (1903.58¢) (→6\5ed5/2)
Consistency limit	2
Distinct consistency limit	2

35 equal divisions of 5/2 (abbreviated 35ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 35 equal parts of about 45.3 ¢ each. Each step represents a frequency ratio of (5/2)^1/35, or the 35th root of 5/2.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	45.3
2	90.6	18/17, 19/18
3	136
4	181.3	21/19
5	226.6
6	271.9	7/6, 27/23
7	317.3	6/5
8	362.6	21/17, 26/21, 27/22
9	407.9	19/15
10	453.2	22/17
11	498.6
12	543.9	26/19
13	589.2	7/5
14	634.5	13/9
15	679.8
16	725.2
17	770.5
18	815.8
19	861.1
20	906.5	22/13
21	951.8	26/15
22	997.1	25/14
23	1042.4
24	1087.8
25	1133.1
26	1178.4
27	1223.7
28	1269.1	23/11, 25/12, 27/13
29	1314.4	15/7
30	1359.7
31	1405
32	1450.3
33	1495.7
34	1541	17/7, 22/9
35	1586.3	5/2

Harmonics

Approximation of harmonics in 35ed5/2

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-21.6	+1.6	+2.1	-21.6	-20.0	-14.9	-19.5	+3.2	+2.1	+18.4	+3.8
	Relative (%)	-47.6	+3.6	+4.7	-47.6	-44.1	-32.9	-42.9	+7.2	+4.7	+40.6	+8.3
Steps (reduced)		26 (26)	42 (7)	53 (18)	61 (26)	68 (33)	74 (4)	79 (9)	84 (14)	88 (18)	92 (22)	95 (25)

Approximation of harmonics in 35ed5/2

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+1.2	+8.8	-20.0	+4.3	-10.0	-18.4	-21.3	-19.5	-13.3	-3.2	+10.5
	Relative (%)	+2.5	+19.5	-44.1	+9.4	-22.2	-40.5	-47.0	-42.9	-29.3	-7.0	+23.2
Steps (reduced)		98 (28)	101 (31)	103 (33)	106 (1)	108 (3)	110 (5)	112 (7)	114 (9)	116 (11)	118 (13)	120 (15)