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