70ed7/3

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70ed7/3

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Prime factorization	2 × 5 × 7
Step size	20.9553¢
Octave	57\70ed7/3 (1194.45¢)
Twelfth	91\70ed7/3 (1906.93¢) (→13\10ed7/3)
Consistency limit	2
Distinct consistency limit	2

70 equal divisions of 7/3 (abbreviated 70ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 70 equal parts of about 21 ¢ each. Each step represents a frequency ratio of (7/3)^1/70, or the 70th root of 7/3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	20.955
2	41.911
3	62.866	29/28
4	83.821
5	104.776	33/31, 35/33
6	125.732	14/13
7	146.687	25/23, 37/34
8	167.642	11/10
9	188.598	29/26
10	209.553	26/23, 35/31
11	230.508
12	251.464	15/13, 22/19
13	272.419	34/29
14	293.374
15	314.329	6/5
16	335.285	17/14
17	356.24
18	377.195	36/29
19	398.151	29/23
20	419.106	14/11, 37/29
21	440.061
22	461.017	17/13, 30/23
23	481.972	29/22, 33/25, 37/28
24	502.927
25	523.882	23/17
26	544.838	26/19
27	565.793	18/13, 25/18
28	586.748
29	607.704	37/26
30	628.659	33/23, 36/25
31	649.614
32	670.57	25/17, 28/19, 31/21
33	691.525
34	712.48
35	733.435	26/17, 29/19
36	754.391	17/11
37	775.346	36/23
38	796.301	19/12
39	817.257
40	838.212
41	859.167	23/14
42	880.123
43	901.078	37/22
44	922.033	17/10, 29/17
45	942.988	19/11, 31/18
46	963.944
47	984.899	23/13, 30/17
48	1005.854	25/14, 34/19
49	1026.81
50	1047.765	11/6
51	1068.72	13/7, 37/20
52	1089.676
53	1110.631	19/10
54	1131.586	25/13
55	1152.541	35/18, 37/19
56	1173.497
57	1194.452
58	1215.407
59	1236.363
60	1257.318	29/14, 31/15
61	1278.273	23/11
62	1299.229	36/17
63	1320.184	15/7
64	1341.139	13/6
65	1362.094	11/5
66	1383.05
67	1404.005
68	1424.96	25/11
69	1445.916	30/13
70	1466.871	7/3

Harmonics

Approximation of harmonics in 70ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-5.55	+4.98	+9.86	+0.74	-0.57	+4.98	+4.31	+9.95	-4.81	-2.17	-6.12
	Relative (%)	-26.5	+23.8	+47.0	+3.5	-2.7	+23.8	+20.6	+47.5	-22.9	-10.3	-29.2
Steps (reduced)		57 (57)	91 (21)	115 (45)	133 (63)	148 (8)	161 (21)	172 (32)	182 (42)	190 (50)	198 (58)	205 (65)

Approximation of harmonics in 70ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+2.00	-0.57	+5.72	-1.24	-1.42	+4.41	-5.38	-10.35	+9.95	-7.72	-0.85
	Relative (%)	+9.5	-2.7	+27.3	-5.9	-6.8	+21.0	-25.7	-49.4	+47.5	-36.8	-4.1
Steps (reduced)		212 (2)	218 (8)	224 (14)	229 (19)	234 (24)	239 (29)	243 (33)	247 (37)	252 (42)	255 (45)	259 (49)