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 16.1
2 32.2
3 48.4
4 64.5
5 80.6 22/21, 43/41, 45/43
6 96.7 37/35
7 112.8
8 128.9 14/13
9 145.1 25/23
10 161.2 45/41
11 177.3 41/37
12 193.4 19/17
13 209.5 35/31, 44/39
14 225.7 33/29, 49/43
15 241.8
16 257.9 29/25
17 274 41/35
18 290.1
19 306.2 37/31
20 322.4
21 338.5 45/37
22 354.6 27/22, 43/35
23 370.7 31/25
24 386.8
25 403 29/23
26 419.1
27 435.2 9/7
28 451.3 35/27
29 467.4
30 483.5 41/31
31 499.7
32 515.8 31/23
33 531.9
34 548
35 564.1 18/13
36 580.3
37 596.4
38 612.5 47/33
39 628.6
40 644.7 45/31
41 660.8
42 677 37/25
43 693.1
44 709.2
45 725.3 35/23
46 741.4 23/15
47 757.6
48 773.7
49 789.8 30/19
50 805.9 43/27
51 822 37/23
52 838.1
53 854.3
54 870.4
55 886.5
56 902.6
57 918.7 17/10
58 934.9
59 951
60 967.1
61 983.2 30/17
62 999.3 41/23
63 1015.5
64 1031.6 49/27
65 1047.7
66 1063.8
67 1079.9
68 1096
69 1112.2 19/10
70 1128.3
71 1144.4
72 1160.5 43/22, 45/23
73 1176.6
74 1192.8
75 1208.9
76 1225
77 1241.1 43/21
78 1257.2 31/15
79 1273.3
80 1289.5
81 1305.6
82 1321.7
83 1337.8 13/6
84 1353.9
85 1370.1
86 1386.2 49/22
87 1402.3
88 1418.4
89 1434.5
90 1450.6
91 1466.8 7/3
92 1482.9
93 1499
94 1515.1
95 1531.2 46/19
96 1547.4 22/9
97 1563.5 37/15
98 1579.6
99 1595.7
100 1611.8
101 1627.9
102 1644.1
103 1660.2
104 1676.3 29/11
105 1692.4
106 1708.5
107 1724.7 46/17
108 1740.8 41/15
109 1756.9
110 1773 39/14
111 1789.1
112 1805.2
113 1821.4 43/15
114 1837.5
115 1853.6
116 1869.7
117 1885.8
118 1902 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)