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	Hekts	Approximate ratios
0	0	0	1/1
1	32.8	22.4
2	65.6	44.8	26/25, 27/26
3	98.4	67.2	18/17
4	131.2	89.7	27/25
5	164	112.1	11/10
6	196.8	134.5
7	229.5	156.9
8	262.3	179.3	7/6
9	295.1	201.7
10	327.9	224.1
11	360.7	246.6
12	393.5	269
13	426.3	291.4	23/18
14	459.1	313.8	30/23
15	491.9	336.2
16	524.7	358.6	23/17
17	557.5	381	29/21
18	590.3	403.4
19	623.1	425.9	33/23
20	655.8	448.3	19/13
21	688.6	470.7
22	721.4	493.1
23	754.2	515.5	17/11
24	787	537.9	11/7
25	819.8	560.3
26	852.6	582.8	18/11
27	885.4	605.2	5/3
28	918.2	627.6	17/10
29	951	650	26/15
30	983.8	672.4	30/17
31	1016.6	694.8	9/5
32	1049.4	717.2	11/6
33	1082.1	739.7
34	1114.9	762.1	21/11
35	1147.7	784.5	33/17
36	1180.5	806.9
37	1213.3	829.3
38	1246.1	851.7
39	1278.9	874.1	23/11
40	1311.7	896.6
41	1344.5	919
42	1377.3	941.4
43	1410.1	963.8
44	1442.9	986.2	23/10
45	1475.7	1008.6
46	1508.4	1031	31/13
47	1541.2	1053.4
48	1574	1075.9
49	1606.8	1098.3
50	1639.6	1120.7	18/7
51	1672.4	1143.1
52	1705.2	1165.5
53	1738	1187.9	30/11
54	1770.8	1210.3	25/9
55	1803.6	1232.8	17/6
56	1836.4	1255.2	26/9
57	1869.2	1277.6
58	1902	1300	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)