58edt

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← 57edt58edt59edt →
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 31/58, or the 58th root of 3.

Intervals

Steps Cents Approximate Ratios
0 0 1/1
1 32.792
2 65.585 26/25, 27/26
3 98.377 18/17
4 131.169 27/25
5 163.962 11/10
6 196.754
7 229.546
8 262.339 7/6
9 295.131
10 327.923
11 360.716
12 393.508
13 426.3 23/18
14 459.093 30/23
15 491.885
16 524.677 23/17
17 557.47 29/21
18 590.262
19 623.054 33/23
20 655.847 19/13
21 688.639
22 721.431
23 754.224 17/11
24 787.016 11/7
25 819.808
26 852.601 18/11
27 885.393 5/3
28 918.185 17/10
29 950.978 26/15
30 983.77 30/17
31 1016.562 9/5
32 1049.354 11/6
33 1082.147
34 1114.939 21/11
35 1147.731 33/17
36 1180.524
37 1213.316
38 1246.108
39 1278.901 23/11
40 1311.693
41 1344.485
42 1377.278
43 1410.07
44 1442.862 23/10
45 1475.655
46 1508.447 31/13
47 1541.239
48 1574.032
49 1606.824
50 1639.616 18/7
51 1672.409
52 1705.201
53 1737.993 30/11
54 1770.786 25/9
55 1803.578 17/6
56 1836.37 26/9
57 1869.163
58 1901.955 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)