131edt

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← 130edt 131edt 132edt →
Prime factorization 131 (prime)
Step size 14.5187¢ 
Octave 83\131edt (1205.06¢)
Consistency limit 2
Distinct consistency limit 2

131edt is the equal division of the third harmonic into 131 parts of 14.5187 cents each, corresponding to 82.6520 edo (similar to every third step of 248edo). It is notable for consistency to the no-evens 25-throdd limit. Furthermore, several higher primes, including 29, 31, 37, 43, and 53, lie at close to halfway between 131edt's steps; therefore 262edt, which doubles it, improves representation of a large spectrum of primes, though it loses consistency of a few intervals of 19.

131edt is the 16th no-twos zeta peak EDT.

Intervals

Steps Cents Approximate Ratios
0 0 1/1
1 14.519
2 29.037
3 43.556 39/38
4 58.075 30/29
5 72.594 49/47
6 87.112 41/39
7 101.631 35/33
8 116.15
9 130.669 41/38
10 145.187 25/23, 37/34
11 159.706 45/41
12 174.225 21/19
13 188.744 29/26, 39/35
14 203.262
15 217.781 17/15, 42/37
16 232.3
17 246.819 15/13
18 261.337
19 275.856 27/23, 34/29
20 290.375 13/11
21 304.894
22 319.412
23 333.931
24 348.45 11/9
25 362.969 37/30
26 377.487 41/33, 46/37, 51/41
27 392.006
28 406.525
29 421.043 37/29
30 435.562 9/7
31 450.081 35/27
32 464.6 17/13
33 479.118 29/22, 33/25
34 493.637
35 508.156 51/38
36 522.675 23/17, 50/37
37 537.193 15/11
38 551.712
39 566.231 43/31
40 580.75 7/5
41 595.268
42 609.787 27/19, 37/26
43 624.306 33/23
44 638.825
45 653.343 51/35
46 667.862 25/17
47 682.381
48 696.9
49 711.418
50 725.937 35/23, 38/25
51 740.456 23/15
52 754.975 17/11
53 769.493 39/25
54 784.012 11/7
55 798.531 46/29
56 813.049
57 827.568
58 842.087
59 856.606 41/25
60 871.124
61 885.643 5/3
62 900.162 37/22
63 914.681 39/23
64 929.199
65 943.718 50/29
66 958.237 47/27
67 972.756
68 987.274 23/13
69 1001.793 41/23
70 1016.312 9/5
71 1030.831 49/27
72 1045.349
73 1059.868
74 1074.387
75 1088.906
76 1103.424
77 1117.943 21/11
78 1132.462 25/13
79 1146.98 33/17
80 1161.499 45/23
81 1176.018
82 1190.537
83 1205.055
84 1219.574
85 1234.093 51/25
86 1248.612 35/17, 37/18
87 1263.13
88 1277.649 23/11
89 1292.168 19/9
90 1306.687
91 1321.205 15/7
92 1335.724
93 1350.243
94 1364.762 11/5
95 1379.28 51/23
96 1393.799 38/17, 47/21
97 1408.318
98 1422.837 25/11
99 1437.355 39/17
100 1451.874
101 1466.393 7/3
102 1480.912
103 1495.43
104 1509.949
105 1524.468 41/17
106 1538.986
107 1553.505 27/11
108 1568.024 47/19
109 1582.543
110 1597.061
111 1611.58 33/13
112 1626.099 23/9
113 1640.618 49/19
114 1655.136 13/5
115 1669.655
116 1684.174 37/14, 45/17
117 1698.693
118 1713.211 35/13
119 1727.73 19/7
120 1742.249 41/15
121 1756.768
122 1771.286
123 1785.805
124 1800.324
125 1814.843
126 1829.361
127 1843.88 29/10
128 1858.399 38/13
129 1872.918
130 1887.436
131 1901.955 3/1

Harmonics

Approximation of prime harmonics in 131edt
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +5.06 +0.00 +1.28 -0.48 +1.04 +2.21 +2.38 -1.44 +1.73
Relative (%) +34.8 +0.0 +8.8 -3.3 +7.2 +15.2 +16.4 -9.9 +11.9
Steps
(reduced)
83
(83)
131
(0)
192
(61)
232
(101)
286
(24)
306
(44)
338
(76)
351
(89)
374
(112)
Approximation of odd harmonics in 131edt
Harmonic 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53
Error Absolute (¢) +2.57 +0.00 +6.96 -6.87 +1.04 +0.81 +6.23 +2.21 +2.74 -7.12 +1.28 -1.40 -0.96 +2.38 -6.14
Relative (%) +17.7 +0.0 +47.9 -47.3 +7.2 +5.6 +42.9 +15.2 +18.9 -49.1 +8.8 -9.7 -6.6 +16.4 -42.3
Steps
(reduced)
384
(122)
393
(0)
402
(9)
409
(16)
417
(24)
424
(31)
431
(38)
437
(44)
443
(50)
448
(55)
454
(61)
459
(66)
464
(71)
469
(76)
473
(80)