58ed7/3

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58ed7/3

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Prime factorization	2 × 29
Step size	25.2909¢
Octave	47\58ed7/3 (1188.67¢)
Twelfth	75\58ed7/3 (1896.82¢)
Consistency limit	3
Distinct consistency limit	3

58 equal divisions of 7/3 (abbreviated 58ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 58 equal parts of about 25.3 ¢ each. Each step represents a frequency ratio of (7/3)^1/58, or the 58th root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	25.3
2	50.6	34/33
3	75.9	22/21
4	101.2
5	126.5
6	151.7
7	177
8	202.3
9	227.6
10	252.9
11	278.2
12	303.5	25/21, 31/26
13	328.8	23/19
14	354.1	27/22
15	379.4
16	404.7	29/23
17	429.9
18	455.2
19	480.5	33/25
20	505.8
21	531.1	34/25
22	556.4
23	581.7	7/5
24	607
25	632.3
26	657.6	19/13
27	682.9
28	708.1
29	733.4	26/17, 29/19
30	758.7
31	784	11/7
32	809.3
33	834.6	34/21
34	859.9
35	885.2	5/3
36	910.5
37	935.8
38	961.1
39	986.3	23/13
40	1011.6
41	1036.9	31/17
42	1062.2
43	1087.5
44	1112.8
45	1138.1	27/14
46	1163.4
47	1188.7
48	1214
49	1239.3
50	1264.5
51	1289.8
52	1315.1	15/7
53	1340.4
54	1365.7	11/5
55	1391	29/13
56	1416.3	34/15
57	1441.6
58	1466.9	7/3

Harmonics

Approximation of harmonics in 58ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-11.3	-5.1	+2.6	-4.3	+8.8	-5.1	-8.7	-10.3	+9.6	-3.6	-2.5
	Relative (%)	-44.8	-20.3	+10.4	-17.1	+34.9	-20.3	-34.4	-40.6	+38.1	-14.3	-9.9
Steps (reduced)		47 (47)	75 (17)	95 (37)	110 (52)	123 (7)	133 (17)	142 (26)	150 (34)	158 (42)	164 (48)	170 (54)

Approximation of harmonics in 58ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+10.7	+8.8	-9.5	+5.3	+1.5	+3.7	+11.2	-1.7	-10.3	+10.3	+9.3
	Relative (%)	+42.2	+34.9	-37.4	+20.8	+5.8	+14.6	+44.5	-6.7	-40.6	+40.9	+36.6
Steps (reduced)		176 (2)	181 (7)	185 (11)	190 (16)	194 (20)	198 (24)	202 (28)	205 (31)	208 (34)	212 (38)	215 (41)