40edt
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Prime factorization
23 × 5
Step size
47.5489¢
Octave
25\40edt (1188.72¢) (→5\8edt)
Consistency limit
4
Distinct consistency limit
4
← 39edt | 40edt | 41edt → |
40EDT is the equal division of the third harmonic into 40 parts of 47.5489 cents each, corresponding to 25.2372 edo. It is related to the regular temperament which tempers out |440 -219 -40> in the 5-limit, which is supported by 101, 429, 530, 959, 1388, 1817, 2246 and 2347 EDOs.
Intervals
Steps | Cents | Approximate Ratios |
---|---|---|
0 | 0 | 1/1 |
1 | 47.549 | |
2 | 95.098 | 18/17, 19/18, 20/19 |
3 | 142.647 | 13/12 |
4 | 190.196 | 19/17 |
5 | 237.744 | 23/20 |
6 | 285.293 | 13/11, 20/17 |
7 | 332.842 | 17/14, 23/19 |
8 | 380.391 | |
9 | 427.94 | 9/7, 23/18 |
10 | 475.489 | |
11 | 523.038 | 19/14, 23/17, 27/20 |
12 | 570.587 | 18/13 |
13 | 618.135 | 10/7 |
14 | 665.684 | 28/19 |
15 | 713.233 | |
16 | 760.782 | 14/9, 17/11 |
17 | 808.331 | |
18 | 855.88 | 18/11, 23/14 |
19 | 903.429 | |
20 | 950.978 | 19/11 |
21 | 998.526 | |
22 | 1046.075 | 11/6 |
23 | 1093.624 | |
24 | 1141.173 | 27/14, 29/15 |
25 | 1188.722 | |
26 | 1236.271 | |
27 | 1283.82 | 21/10, 23/11 |
28 | 1331.369 | 13/6, 28/13 |
29 | 1378.917 | 20/9 |
30 | 1426.466 | |
31 | 1474.015 | 7/3 |
32 | 1521.564 | |
33 | 1569.113 | |
34 | 1616.662 | 28/11 |
35 | 1664.211 | |
36 | 1711.76 | |
37 | 1759.308 | |
38 | 1806.857 | 17/6 |
39 | 1854.406 | |
40 | 1901.955 | 3/1 |
Harmonics
Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | -11.3 | +0.0 | +19.1 | +7.1 | -14.6 | -18.5 | -7.4 | -9.8 | -7.7 | +18.9 | -1.4 |
Relative (%) | -23.7 | +0.0 | +40.1 | +15.0 | -30.6 | -38.9 | -15.6 | -20.6 | -16.2 | +39.8 | -3.0 | |
Steps (reduced) |
25 (25) |
40 (0) |
59 (19) |
71 (31) |
87 (7) |
93 (13) |
103 (23) |
107 (27) |
114 (34) |
123 (3) |
125 (5) |
Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | -22.4 | -10.0 | +2.7 | -8.7 | +21.1 | -21.9 | +15.4 | -4.3 | -9.6 | -10.2 | -4.3 |
Relative (%) | -47.2 | -21.0 | +5.6 | -18.2 | +44.3 | -46.1 | +32.5 | -9.1 | -20.2 | -21.4 | -9.0 | |
Steps (reduced) |
131 (11) |
135 (15) |
137 (17) |
140 (20) |
145 (25) |
148 (28) |
150 (30) |
153 (33) |
155 (35) |
156 (36) |
159 (39) |