121edt

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← 120edt121edt122edt →
Prime factorization 112
Step size 15.7186¢ 
Octave 76\121edt (1194.62¢)
Consistency limit 2
Distinct consistency limit 2

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

Approximation of harmonics in 121edt
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)
Approximation of harmonics in 121edt
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)