35ed7/3

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35ed7/3

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Prime factorization	5 × 7
Step size	41.9106¢
Octave	29\35ed7/3 (1215.41¢)
Twelfth	45\35ed7/3 (1885.98¢) (→9\7ed7/3)
Consistency limit	2
Distinct consistency limit	2

35 equal divisions of 7/3 (abbreviated 35ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 35 equal parts of about 41.9 ¢ each. Each step represents a frequency ratio of (7/3)^1/35, or the 35th root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	41.911
2	83.821	20/19, 23/22
3	125.732	14/13, 27/25
4	167.642	11/10
5	209.553	26/23
6	251.464	22/19
7	293.374	13/11
8	335.285	17/14, 23/19, 28/23
9	377.195
10	419.106	14/11
11	461.017	13/10, 17/13
12	502.927
13	544.838	26/19
14	586.748	7/5
15	628.659
16	670.57	28/19
17	712.48
18	754.391	17/11
19	796.301	19/12
20	838.212
21	880.123	5/3
22	922.033	17/10
23	963.944
24	1005.854
25	1047.765	11/6
26	1089.676
27	1131.586	23/12
28	1173.497
29	1215.407
30	1257.318
31	1299.229
32	1341.139	13/6
33	1383.05
34	1424.96
35	1466.871	7/3

Harmonics

Approximation of harmonics in 35ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+15.4	-16.0	-11.1	-20.2	-0.6	-16.0	+4.3	+10.0	-4.8	-2.2	+14.8
	Relative (%)	+36.8	-38.1	-26.5	-48.2	-1.4	-38.1	+10.3	+23.8	-11.5	-5.2	+35.4
Steps (reduced)		29 (29)	45 (10)	57 (22)	66 (31)	74 (4)	80 (10)	86 (16)	91 (21)	95 (25)	99 (29)	103 (33)

Approximation of harmonics in 35ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+2.0	-0.6	+5.7	+19.7	-1.4	-16.5	+15.6	+10.6	+10.0	+13.2	+20.1
	Relative (%)	+4.8	-1.4	+13.6	+47.0	-3.4	-39.5	+37.2	+25.3	+23.8	+31.6	+48.0
Steps (reduced)		106 (1)	109 (4)	112 (7)	115 (10)	117 (12)	119 (14)	122 (17)	124 (19)	126 (21)	128 (23)	130 (25)