121edt
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Prime factorization
112
Step size
15.7186¢
Octave
76\121edt (1194.62¢)
Consistency limit
2
Distinct consistency limit
2
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121 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 121edt or 121ed3), is a nonoctave tuning system that divides the interval of 3/1 into 121 equal parts of about 15.7 ¢ each. Each step represents a frequency ratio of 31/121, or the 121st root of 3.
Intervals
Steps | Cents | Approximate Ratios |
---|---|---|
0 | 0 | 1/1 |
1 | 15.719 | |
2 | 31.437 | |
3 | 47.156 | 36/35 |
4 | 62.875 | |
5 | 78.593 | 22/21, 23/22, 45/43 |
6 | 94.312 | 19/18 |
7 | 110.03 | 33/31, 49/46 |
8 | 125.749 | |
9 | 141.468 | 38/35 |
10 | 157.186 | 23/21 |
11 | 172.905 | 21/19 |
12 | 188.624 | 29/26 |
13 | 204.342 | |
14 | 220.061 | 25/22 |
15 | 235.78 | 47/41 |
16 | 251.498 | |
17 | 267.217 | 7/6 |
18 | 282.935 | |
19 | 298.654 | |
20 | 314.373 | 6/5 |
21 | 330.091 | 23/19 |
22 | 345.81 | 11/9 |
23 | 361.529 | |
24 | 377.247 | 41/33 |
25 | 392.966 | |
26 | 408.685 | 19/15 |
27 | 424.403 | 23/18 |
28 | 440.122 | 49/38 |
29 | 455.84 | |
30 | 471.559 | 46/35 |
31 | 487.278 | |
32 | 502.996 | |
33 | 518.715 | 31/23 |
34 | 534.434 | 49/36 |
35 | 550.152 | |
36 | 565.871 | 43/31 |
37 | 581.59 | 7/5 |
38 | 597.308 | |
39 | 613.027 | 47/33 |
40 | 628.745 | |
41 | 644.464 | 45/31 |
42 | 660.183 | |
43 | 675.901 | 31/21, 34/23 |
44 | 691.62 | |
45 | 707.339 | |
46 | 723.057 | 38/25, 41/27 |
47 | 738.776 | 23/15 |
48 | 754.495 | 17/11 |
49 | 770.213 | |
50 | 785.932 | |
51 | 801.65 | 27/17 |
52 | 817.369 | |
53 | 833.088 | 34/21 |
54 | 848.806 | 31/19, 49/30 |
55 | 864.525 | |
56 | 880.244 | |
57 | 895.962 | |
58 | 911.681 | |
59 | 927.4 | |
60 | 943.118 | |
61 | 958.837 | 47/27 |
62 | 974.555 | |
63 | 990.274 | |
64 | 1005.993 | 34/19 |
65 | 1021.711 | |
66 | 1037.43 | |
67 | 1053.149 | |
68 | 1068.867 | |
69 | 1084.586 | 43/23 |
70 | 1100.305 | 17/9 |
71 | 1116.023 | |
72 | 1131.742 | |
73 | 1147.46 | 33/17 |
74 | 1163.179 | 45/23, 49/25 |
75 | 1178.898 | |
76 | 1194.616 | |
77 | 1210.335 | |
78 | 1226.054 | |
79 | 1241.772 | 43/21 |
80 | 1257.491 | 31/15 |
81 | 1273.21 | |
82 | 1288.928 | |
83 | 1304.647 | |
84 | 1320.365 | 15/7 |
85 | 1336.084 | |
86 | 1351.803 | |
87 | 1367.521 | |
88 | 1383.24 | |
89 | 1398.959 | |
90 | 1414.677 | 43/19 |
91 | 1430.396 | |
92 | 1446.115 | |
93 | 1461.833 | |
94 | 1477.552 | |
95 | 1493.27 | 45/19 |
96 | 1508.989 | 43/18 |
97 | 1524.708 | 41/17 |
98 | 1540.426 | |
99 | 1556.145 | 27/11 |
100 | 1571.864 | |
101 | 1587.582 | 5/2 |
102 | 1603.301 | |
103 | 1619.02 | |
104 | 1634.738 | 18/7 |
105 | 1650.457 | |
106 | 1666.175 | |
107 | 1681.894 | |
108 | 1697.613 | |
109 | 1713.331 | |
110 | 1729.05 | 19/7 |
111 | 1744.769 | |
112 | 1760.487 | 47/17 |
113 | 1776.206 | |
114 | 1791.925 | 31/11 |
115 | 1807.643 | |
116 | 1823.362 | 43/15 |
117 | 1839.08 | |
118 | 1854.799 | 35/12 |
119 | 1870.518 | |
120 | 1886.236 | |
121 | 1901.955 | 3/1 |
Harmonics
Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | -5.38 | +0.00 | +4.95 | -4.12 | -5.38 | -5.04 | -0.43 | +0.00 | +6.22 | -1.60 | +4.95 |
Relative (%) | -34.3 | +0.0 | +31.5 | -26.2 | -34.3 | -32.0 | -2.8 | +0.0 | +39.6 | -10.2 | +31.5 | |
Steps (reduced) |
76 (76) |
121 (0) |
153 (32) |
177 (56) |
197 (76) |
214 (93) |
229 (108) |
242 (0) |
254 (12) |
264 (22) |
274 (32) |
Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | +7.85 | +5.30 | -4.12 | -5.82 | -0.74 | -5.38 | -4.67 | +0.84 | -5.04 | -6.98 | -5.34 |
Relative (%) | +49.9 | +33.7 | -26.2 | -37.0 | -4.7 | -34.3 | -29.7 | +5.3 | -32.0 | -44.4 | -34.0 | |
Steps (reduced) |
283 (41) |
291 (49) |
298 (56) |
305 (63) |
312 (70) |
318 (76) |
324 (82) |
330 (88) |
335 (93) |
340 (98) |
345 (103) |