59ed4
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Prime factorization
59 (prime)
Step size
40.678¢
Octave
30\59ed4 (1220.34¢)
Twelfth
47\59ed4 (1911.86¢)
Consistency limit
1
Distinct consistency limit
1
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← 57ed4 | 59ed4 | 61ed4 → |
59 equal divisions of the 4th harmonic (abbreviated 59ed4) is a nonoctave tuning system that divides the interval of 4/1 into 59 equal parts of about 40.7 ¢ each. Each step represents a frequency ratio of 41/59, or the 59th root of 4.
Intervals
Steps | Cents | Approximate ratios |
---|---|---|
0 | 0 | 1/1 |
1 | 40.7 | |
2 | 81.4 | 21/20, 22/21 |
3 | 122 | |
4 | 162.7 | 11/10 |
5 | 203.4 | |
6 | 244.1 | 15/13 |
7 | 284.7 | 13/11, 20/17 |
8 | 325.4 | |
9 | 366.1 | 21/17, 26/21 |
10 | 406.8 | 19/15 |
11 | 447.5 | 22/17 |
12 | 488.1 | |
13 | 528.8 | |
14 | 569.5 | |
15 | 610.2 | |
16 | 650.8 | |
17 | 691.5 | |
18 | 732.2 | 26/17, 29/19 |
19 | 772.9 | |
20 | 813.6 | |
21 | 854.2 | |
22 | 894.9 | |
23 | 935.6 | |
24 | 976.3 | |
25 | 1016.9 | |
26 | 1057.6 | |
27 | 1098.3 | 17/9 |
28 | 1139 | 27/14, 29/15 |
29 | 1179.7 | |
30 | 1220.3 | |
31 | 1261 | 31/15 |
32 | 1301.7 | |
33 | 1342.4 | |
34 | 1383.1 | 20/9 |
35 | 1423.7 | |
36 | 1464.4 | 7/3 |
37 | 1505.1 | 31/13 |
38 | 1545.8 | 22/9 |
39 | 1586.4 | |
40 | 1627.1 | |
41 | 1667.8 | |
42 | 1708.5 | |
43 | 1749.2 | |
44 | 1789.8 | 31/11 |
45 | 1830.5 | |
46 | 1871.2 | |
47 | 1911.9 | |
48 | 1952.5 | |
49 | 1993.2 | |
50 | 2033.9 | |
51 | 2074.6 | |
52 | 2115.3 | |
53 | 2155.9 | |
54 | 2196.6 | |
55 | 2237.3 | |
56 | 2278 | |
57 | 2318.6 | |
58 | 2359.3 | |
59 | 2400 |
Harmonics
Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | +20.3 | +9.9 | +0.0 | -20.2 | -10.4 | +7.4 | +20.3 | +19.8 | +0.1 | -2.2 | +9.9 |
Relative (%) | +50.0 | +24.4 | +0.0 | -49.7 | -25.6 | +18.3 | +50.0 | +48.7 | +0.3 | -5.3 | +24.4 | |
Steps (reduced) |
30 (30) |
47 (47) |
59 (0) |
68 (9) |
76 (17) |
83 (24) |
89 (30) |
94 (35) |
98 (39) |
102 (43) |
106 (47) |
Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | -6.6 | -12.9 | -10.3 | +0.0 | +17.1 | -0.5 | -12.8 | -20.2 | +17.4 | +18.2 | -18.1 |
Relative (%) | -16.3 | -31.7 | -25.3 | +0.0 | +42.0 | -1.3 | -31.4 | -49.7 | +42.7 | +44.7 | -44.5 | |
Steps (reduced) |
109 (50) |
112 (53) |
115 (56) |
118 (0) |
121 (3) |
123 (5) |
125 (7) |
127 (9) |
130 (12) |
132 (14) |
133 (15) |