118edt

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← 117edt 118edt 119edt →
Prime factorization 2 × 59
Step size 16.1183¢ 
Octave 74\118edt (1192.75¢) (→37\59edt)
Consistency limit 2
Distinct consistency limit 2

118 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 118edt or 118ed3), is a nonoctave tuning system that divides the interval of 3/1 into 118 equal parts of about 16.1 ¢ each. Each step represents a frequency ratio of 31/118, or the 118th root of 3.

Intervals

Steps Cents Approximate Ratios
0 0 1/1
1 16.118
2 32.237
3 48.355
4 64.473
5 80.591 22/21, 43/41, 45/43
6 96.71 37/35
7 112.828
8 128.946 14/13
9 145.064 25/23
10 161.183 45/41
11 177.301 41/37
12 193.419 19/17
13 209.537 35/31, 44/39
14 225.656 33/29, 49/43
15 241.774
16 257.892 29/25
17 274.01 41/35
18 290.129
19 306.247 37/31
20 322.365
21 338.484 45/37
22 354.602 27/22, 43/35
23 370.72 31/25
24 386.838
25 402.957 29/23
26 419.075
27 435.193 9/7
28 451.311 35/27
29 467.43
30 483.548 41/31
31 499.666
32 515.784 31/23
33 531.903
34 548.021
35 564.139 18/13
36 580.257
37 596.376
38 612.494 47/33
39 628.612
40 644.731 45/31
41 660.849
42 676.967 37/25
43 693.085
44 709.204
45 725.322 35/23
46 741.44 23/15
47 757.558
48 773.677
49 789.795 30/19
50 805.913 43/27
51 822.031 37/23
52 838.15
53 854.268
54 870.386
55 886.504
56 902.623
57 918.741 17/10
58 934.859
59 950.978
60 967.096
61 983.214 30/17
62 999.332 41/23
63 1015.451
64 1031.569 49/27
65 1047.687
66 1063.805
67 1079.924
68 1096.042
69 1112.16 19/10
70 1128.278
71 1144.397
72 1160.515 43/22, 45/23
73 1176.633
74 1192.751
75 1208.87
76 1224.988
77 1241.106 43/21
78 1257.224 31/15
79 1273.343
80 1289.461
81 1305.579
82 1321.698
83 1337.816 13/6
84 1353.934
85 1370.052
86 1386.171 49/22
87 1402.289
88 1418.407
89 1434.525
90 1450.644
91 1466.762 7/3
92 1482.88
93 1498.998
94 1515.117
95 1531.235 46/19
96 1547.353 22/9
97 1563.471 37/15
98 1579.59
99 1595.708
100 1611.826
101 1627.945
102 1644.063
103 1660.181
104 1676.299 29/11
105 1692.418
106 1708.536
107 1724.654 46/17
108 1740.772 41/15
109 1756.891
110 1773.009 39/14
111 1789.127
112 1805.245
113 1821.364 43/15
114 1837.482
115 1853.6
116 1869.718
117 1885.837
118 1901.955 3/1

Harmonics

Approximation of harmonics in 118edt
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -7.25 +0.00 +1.62 +2.15 -7.25 -0.11 -5.63 +0.00 -5.10 +7.19 +1.62
Relative (%) -45.0 +0.0 +10.1 +13.3 -45.0 -0.7 -34.9 +0.0 -31.7 +44.6 +10.1
Steps
(reduced)
74
(74)
118
(0)
149
(31)
173
(55)
192
(74)
209
(91)
223
(105)
236
(0)
247
(11)
258
(22)
267
(31)
Approximation of harmonics in 118edt
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -8.01 -7.36 +2.15 +3.24 -5.00 -7.25 -4.14 +3.77 -0.11 -0.05 +3.58
Relative (%) -49.7 -45.6 +13.3 +20.1 -31.0 -45.0 -25.7 +23.4 -0.7 -0.3 +22.2
Steps
(reduced)
275
(39)
283
(47)
291
(55)
298
(62)
304
(68)
310
(74)
316
(80)
322
(86)
327
(91)
332
(96)
337
(101)