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 | Hekts | Approximate ratios |
|---|---|---|---|
| 0 | 0 | 0 | 1/1 |
| 1 | 47.5 | 32.5 | |
| 2 | 95.1 | 65 | 18/17, 19/18, 20/19 |
| 3 | 142.6 | 97.5 | 13/12 |
| 4 | 190.2 | 130 | 19/17 |
| 5 | 237.7 | 162.5 | 23/20 |
| 6 | 285.3 | 195 | 13/11, 20/17 |
| 7 | 332.8 | 227.5 | 17/14, 23/19 |
| 8 | 380.4 | 260 | |
| 9 | 427.9 | 292.5 | 9/7, 23/18 |
| 10 | 475.5 | 325 | |
| 11 | 523 | 357.5 | 19/14, 23/17, 27/20 |
| 12 | 570.6 | 390 | 18/13 |
| 13 | 618.1 | 422.5 | 10/7 |
| 14 | 665.7 | 455 | 28/19 |
| 15 | 713.2 | 487.5 | |
| 16 | 760.8 | 520 | 14/9, 17/11 |
| 17 | 808.3 | 552.5 | |
| 18 | 855.9 | 585 | 18/11, 23/14 |
| 19 | 903.4 | 617.5 | |
| 20 | 951 | 650 | 19/11 |
| 21 | 998.5 | 682.5 | |
| 22 | 1046.1 | 715 | 11/6 |
| 23 | 1093.6 | 747.5 | |
| 24 | 1141.2 | 780 | 27/14, 29/15 |
| 25 | 1188.7 | 812.5 | |
| 26 | 1236.3 | 845 | |
| 27 | 1283.8 | 877.5 | 21/10, 23/11 |
| 28 | 1331.4 | 910 | 13/6, 28/13 |
| 29 | 1378.9 | 942.5 | 20/9 |
| 30 | 1426.5 | 975 | |
| 31 | 1474 | 1007.5 | 7/3 |
| 32 | 1521.6 | 1040 | |
| 33 | 1569.1 | 1072.5 | |
| 34 | 1616.7 | 1105 | 28/11 |
| 35 | 1664.2 | 1137.5 | |
| 36 | 1711.8 | 1170 | |
| 37 | 1759.3 | 1202.5 | |
| 38 | 1806.9 | 1235 | 17/6 |
| 39 | 1854.4 | 1267.5 | |
| 40 | 1902 | 1300 | 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) | |
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