140edt

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← 139edt140edt141edt →
Prime factorization 22 × 5 × 7
Step size 13.5854¢ 
Octave 88\140edt (1195.51¢) (→22\35edt)
Consistency limit 2
Distinct consistency limit 2

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

Approximation of harmonics in 140edt
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)
Approximation of harmonics in 140edt
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)