126edt

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← 125edt 126edt 127edt →
Prime factorization 2 × 32 × 7
Step size 15.0949¢ 
Octave 79\126edt (1192.5¢)
Consistency limit 2
Distinct consistency limit 2

126 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 126edt or 126ed3), is a nonoctave tuning system that divides the interval of 3/1 into 126 equal parts of about 15.1 ¢ each. Each step represents a frequency ratio of 31/126, or the 126th root of 3.

Intervals

Steps Cents Approximate ratios
0 0 1/1
1 15.095
2 30.19
3 45.285 38/37, 39/38
4 60.38 30/29
5 75.474 47/45
6 90.569 39/37
7 105.664 50/47
8 120.759
9 135.854
10 150.949
11 166.044 11/10
12 181.139 10/9
13 196.233 37/33
14 211.328 35/31
15 226.423 49/43
16 241.518
17 256.613
18 271.708
19 286.803 46/39
20 301.898
21 316.993
22 332.087 23/19
23 347.182 11/9
24 362.277 37/30
25 377.372 41/33, 46/37, 51/41
26 392.467
27 407.562 19/15, 43/34
28 422.657 37/29
29 437.752
30 452.846 13/10
31 467.941 38/29
32 483.036 41/31
33 498.131
34 513.226 39/29
35 528.321
36 543.416
37 558.511 29/21
38 573.605 46/33
39 588.7
40 603.795
41 618.89 10/7
42 633.985 49/34
43 649.08
44 664.175
45 679.27
46 694.365
47 709.459
48 724.554 41/27
49 739.649 23/15
50 754.744 17/11
51 769.839
52 784.934
53 800.029 27/17, 46/29
54 815.124
55 830.218 21/13
56 845.313
57 860.408 51/31
58 875.503
59 890.598
60 905.693
61 920.788 46/27
62 935.883
63 950.978
64 966.072
65 981.167 37/21
66 996.262
67 1011.357
68 1026.452 38/21
69 1041.547 31/17
70 1056.642 35/19
71 1071.737 13/7
72 1086.831
73 1101.926 17/9
74 1117.021
75 1132.116
76 1147.211 33/17
77 1162.306 45/23
78 1177.401
79 1192.496
80 1207.59
81 1222.685
82 1237.78 47/23
83 1252.875
84 1267.97
85 1283.065 21/10
86 1298.16
87 1313.255
88 1328.35
89 1343.444 50/23
90 1358.539 46/21
91 1373.634
92 1388.729 29/13
93 1403.824
94 1418.919
95 1434.014
96 1449.109 30/13
97 1464.203
98 1479.298
99 1494.393 45/19
100 1509.488 43/18
101 1524.583 41/17
102 1539.678
103 1554.773 27/11
104 1569.868 47/19
105 1584.963
106 1600.057
107 1615.152
108 1630.247
109 1645.342
110 1660.437
111 1675.532 50/19
112 1690.627
113 1705.722
114 1720.816 27/10
115 1735.911 30/11
116 1751.006
117 1766.101
118 1781.196
119 1796.291
120 1811.386 37/13
121 1826.481
122 1841.575 29/10
123 1856.67 38/13
124 1871.765
125 1886.86
126 1901.955 3/1

Harmonics

Approximation of harmonics in 126edt
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -7.50 +0.00 +0.09 +6.24 -7.50 -2.67 -7.42 +0.00 -1.27 -0.23 +0.09
Relative (%) -49.7 +0.0 +0.6 +41.3 -49.7 -17.7 -49.1 +0.0 -8.4 -1.5 +0.6
Steps
(reduced)
79
(79)
126
(0)
159
(33)
185
(59)
205
(79)
223
(97)
238
(112)
252
(0)
264
(12)
275
(23)
285
(33)
Approximation of harmonics in 126edt
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -2.63 +4.92 +6.24 +0.17 +0.88 -7.50 +4.56 +6.33 -2.67 +7.36 +5.88
Relative (%) -17.4 +32.6 +41.3 +1.1 +5.8 -49.7 +30.2 +41.9 -17.7 +48.8 +39.0
Steps
(reduced)
294
(42)
303
(51)
311
(59)
318
(66)
325
(73)
331
(79)
338
(86)
344
(92)
349
(97)
355
(103)
360
(108)