40edt

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← 39edt40edt41edt →
Prime factorization 23 × 5
Step size 47.5489¢ 
Octave 25\40edt (1188.72¢) (→5\8edt)
Consistency limit 4
Distinct consistency limit 4

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

Approximation of prime harmonics in 40edt
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)
Approximation of prime harmonics in 40edt
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)