58edt

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58edt

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Prime factorization	2 × 29
Step size	32.7923¢
Octave	37\58edt (1213.32¢)
Consistency limit	2
Distinct consistency limit	2

58 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 58edt or 58ed3), is a nonoctave tuning system that divides the interval of 3/1 into 58 equal parts of about 32.8 ¢ each. Each step represents a frequency ratio of 3^1/58, or the 58th root of 3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	32.8
2	65.6	26/25, 27/26
3	98.4	18/17
4	131.2	27/25
5	164	11/10
6	196.8
7	229.5
8	262.3	7/6
9	295.1
10	327.9
11	360.7
12	393.5
13	426.3	23/18
14	459.1	30/23
15	491.9
16	524.7	23/17
17	557.5	29/21
18	590.3
19	623.1	33/23
20	655.8	19/13
21	688.6
22	721.4
23	754.2	17/11
24	787	11/7
25	819.8
26	852.6	18/11
27	885.4	5/3
28	918.2	17/10
29	951	26/15
30	983.8	30/17
31	1016.6	9/5
32	1049.4	11/6
33	1082.1
34	1114.9	21/11
35	1147.7	33/17
36	1180.5
37	1213.3
38	1246.1
39	1278.9	23/11
40	1311.7
41	1344.5
42	1377.3
43	1410.1
44	1442.9	23/10
45	1475.7
46	1508.4	31/13
47	1541.2
48	1574
49	1606.8
50	1639.6	18/7
51	1672.4
52	1705.2
53	1738	30/11
54	1770.8	25/9
55	1803.6	17/6
56	1836.4	26/9
57	1869.2
58	1902	3/1

Harmonics

Approximation of harmonics in 58edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+13.3	+0.0	-6.2	+1.0	+13.3	+8.8	+7.2	+0.0	+14.4	+13.3	-6.2
	Relative (%)	+40.6	+0.0	-18.8	+3.2	+40.6	+26.8	+21.8	+0.0	+43.8	+40.6	-18.8
Steps (reduced)		37 (37)	58 (0)	73 (15)	85 (27)	95 (37)	103 (45)	110 (52)	116 (0)	122 (6)	127 (11)	131 (15)

Approximation of harmonics in 58edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-13.6	-10.7	+1.0	-12.3	+13.9	+13.3	-14.7	-5.1	+8.8	-6.2	+15.3
	Relative (%)	-41.4	-32.6	+3.2	-37.6	+42.4	+40.6	-44.8	-15.6	+26.8	-18.8	+46.5
Steps (reduced)		135 (19)	139 (23)	143 (27)	146 (30)	150 (34)	153 (37)	155 (39)	158 (42)	161 (45)	163 (47)	166 (50)