140edt
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Prime factorization
22 × 5 × 7
Step size
13.5854¢
Octave
88\140edt (1195.51¢) (→22\35edt)
Consistency limit
2
Distinct consistency limit
2
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← 139edt | 140edt | 141edt → |
140 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 140edt or 140ed3), is a nonoctave tuning system that divides the interval of 3/1 into 140 equal parts of about 13.6 ¢ each. Each step represents a frequency ratio of 31/140, or the 140th root of 3.
Intervals
Steps | Cents | Approximate Ratios |
---|---|---|
0 | 0 | 1/1 |
1 | 13.585 | |
2 | 27.171 | |
3 | 40.756 | 42/41, 43/42, 44/43 |
4 | 54.342 | |
5 | 67.927 | 26/25, 51/49 |
6 | 81.512 | 22/21, 43/41 |
7 | 95.098 | 19/18, 37/35 |
8 | 108.683 | 33/31, 49/46 |
9 | 122.269 | 29/27, 44/41 |
10 | 135.854 | |
11 | 149.439 | |
12 | 163.025 | |
13 | 176.61 | 41/37 |
14 | 190.196 | 29/26 |
15 | 203.781 | |
16 | 217.366 | 17/15 |
17 | 230.952 | |
18 | 244.537 | |
19 | 258.122 | 29/25 |
20 | 271.708 | 55/47 |
21 | 285.293 | 46/39 |
22 | 298.879 | 44/37 |
23 | 312.464 | |
24 | 326.049 | 35/29 |
25 | 339.635 | 45/37 |
26 | 353.22 | 27/22 |
27 | 366.806 | 21/17 |
28 | 380.391 | |
29 | 393.976 | 49/39, 54/43 |
30 | 407.562 | 43/34 |
31 | 421.147 | 37/29 |
32 | 434.733 | 9/7 |
33 | 448.318 | 35/27 |
34 | 461.903 | |
35 | 475.489 | 25/19, 54/41 |
36 | 489.074 | |
37 | 502.66 | |
38 | 516.245 | 31/23, 35/26 |
39 | 529.83 | 19/14 |
40 | 543.416 | 26/19 |
41 | 557.001 | 51/37 |
42 | 570.587 | |
43 | 584.172 | 7/5 |
44 | 597.757 | |
45 | 611.343 | 37/26, 47/33 |
46 | 624.928 | 33/23 |
47 | 638.513 | |
48 | 652.099 | 51/35 |
49 | 665.684 | |
50 | 679.27 | 37/25 |
51 | 692.855 | |
52 | 706.44 | |
53 | 720.026 | 47/31 |
54 | 733.611 | 29/19 |
55 | 747.197 | |
56 | 760.782 | 45/29 |
57 | 774.367 | |
58 | 787.953 | 41/26 |
59 | 801.538 | 27/17 |
60 | 815.124 | |
61 | 828.709 | 21/13 |
62 | 842.294 | |
63 | 855.88 | 41/25 |
64 | 869.465 | 43/26 |
65 | 883.051 | 5/3 |
66 | 896.636 | 42/25 |
67 | 910.221 | 22/13 |
68 | 923.807 | 29/17, 46/27 |
69 | 937.392 | 43/25 |
70 | 950.978 | 26/15, 45/26 |
71 | 964.563 | |
72 | 978.148 | 44/25, 51/29 |
73 | 991.734 | 39/22, 55/31 |
74 | 1005.319 | 25/14 |
75 | 1018.904 | 9/5 |
76 | 1032.49 | 49/27 |
77 | 1046.075 | |
78 | 1059.661 | |
79 | 1073.246 | 13/7 |
80 | 1086.831 | |
81 | 1100.417 | 17/9 |
82 | 1114.002 | |
83 | 1127.588 | |
84 | 1141.173 | 29/15 |
85 | 1154.758 | 37/19 |
86 | 1168.344 | |
87 | 1181.929 | |
88 | 1195.515 | |
89 | 1209.1 | |
90 | 1222.685 | |
91 | 1236.271 | 47/23 |
92 | 1249.856 | 35/17 |
93 | 1263.442 | |
94 | 1277.027 | 23/11 |
95 | 1290.612 | |
96 | 1304.198 | |
97 | 1317.783 | 15/7 |
98 | 1331.369 | 41/19 |
99 | 1344.954 | 37/17 |
100 | 1358.539 | 46/21 |
101 | 1372.125 | 42/19 |
102 | 1385.71 | 49/22 |
103 | 1399.295 | |
104 | 1412.881 | 43/19 |
105 | 1426.466 | 41/18 |
106 | 1440.052 | |
107 | 1453.637 | 44/19 |
108 | 1467.222 | 7/3 |
109 | 1480.808 | |
110 | 1494.393 | |
111 | 1507.979 | 43/18, 55/23 |
112 | 1521.564 | |
113 | 1535.149 | 17/7 |
114 | 1548.735 | 22/9 |
115 | 1562.32 | 37/15 |
116 | 1575.906 | |
117 | 1589.491 | |
118 | 1603.076 | |
119 | 1616.662 | |
120 | 1630.247 | |
121 | 1643.833 | |
122 | 1657.418 | |
123 | 1671.003 | |
124 | 1684.589 | 45/17 |
125 | 1698.174 | |
126 | 1711.76 | |
127 | 1725.345 | |
128 | 1738.93 | |
129 | 1752.516 | |
130 | 1766.101 | |
131 | 1779.686 | |
132 | 1793.272 | 31/11 |
133 | 1806.857 | 54/19 |
134 | 1820.443 | |
135 | 1834.028 | 49/17 |
136 | 1847.613 | |
137 | 1861.199 | 41/14 |
138 | 1874.784 | |
139 | 1888.37 | |
140 | 1901.955 | 3/1 |
Harmonics
Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | -4.49 | +0.00 | +4.61 | -1.31 | -4.49 | +0.35 | +0.13 | +0.00 | -5.79 | +5.81 | +4.61 |
Relative (%) | -33.0 | +0.0 | +34.0 | -9.6 | -33.0 | +2.6 | +1.0 | +0.0 | -42.6 | +42.8 | +34.0 | |
Steps (reduced) |
88 (88) |
140 (0) |
177 (37) |
205 (65) |
228 (88) |
248 (108) |
265 (125) |
280 (0) |
293 (13) |
306 (26) |
317 (37) |
Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | +1.90 | -4.13 | -1.31 | -4.36 | -0.63 | -4.49 | -2.99 | +3.31 | +0.35 | +1.33 | +5.88 |
Relative (%) | +14.0 | -30.4 | -9.6 | -32.1 | -4.6 | -33.0 | -22.0 | +24.3 | +2.6 | +9.8 | +43.3 | |
Steps (reduced) |
327 (47) |
336 (56) |
345 (65) |
353 (73) |
361 (81) |
368 (88) |
375 (95) |
382 (102) |
388 (108) |
394 (114) |
400 (120) |