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	25.291
2	50.582	34/33
3	75.873	22/21
4	101.164
5	126.454
6	151.745
7	177.036
8	202.327
9	227.618
10	252.909
11	278.2
12	303.491	25/21, 31/26
13	328.781	23/19
14	354.072	27/22
15	379.363
16	404.654	29/23
17	429.945
18	455.236
19	480.527	33/25
20	505.818
21	531.108	34/25
22	556.399
23	581.69	7/5
24	606.981
25	632.272
26	657.563	19/13
27	682.854
28	708.145
29	733.435	26/17, 29/19
30	758.726
31	784.017	11/7
32	809.308
33	834.599	34/21
34	859.89
35	885.181	5/3
36	910.472
37	935.762
38	961.053
39	986.344	23/13
40	1011.635
41	1036.926	31/17
42	1062.217
43	1087.508
44	1112.799
45	1138.089	27/14
46	1163.38
47	1188.671
48	1213.962
49	1239.253
50	1264.544
51	1289.835
52	1315.126	15/7
53	1340.417
54	1365.707	11/5
55	1390.998	29/13
56	1416.289	34/15
57	1441.58
58	1466.871	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)