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 Hekts Approximate ratios
0 0 0 1/1
1 16.1 11
2 32.2 22
3 48.4 33.1
4 64.5 44.1
5 80.6 55.1 22/21, 43/41, 45/43
6 96.7 66.1 37/35
7 112.8 77.1
8 128.9 88.1 14/13
9 145.1 99.2 25/23
10 161.2 110.2 45/41
11 177.3 121.2 41/37
12 193.4 132.2 19/17
13 209.5 143.2 35/31, 44/39
14 225.7 154.2 33/29, 49/43
15 241.8 165.3
16 257.9 176.3 29/25
17 274 187.3 41/35
18 290.1 198.3
19 306.2 209.3 37/31
20 322.4 220.3
21 338.5 231.4 45/37
22 354.6 242.4 27/22, 43/35
23 370.7 253.4 31/25
24 386.8 264.4
25 403 275.4 29/23
26 419.1 286.4
27 435.2 297.5 9/7
28 451.3 308.5 35/27
29 467.4 319.5
30 483.5 330.5 41/31
31 499.7 341.5
32 515.8 352.5 31/23
33 531.9 363.6
34 548 374.6
35 564.1 385.6 18/13
36 580.3 396.6
37 596.4 407.6
38 612.5 418.6 47/33
39 628.6 429.7
40 644.7 440.7 45/31
41 660.8 451.7
42 677 462.7 37/25
43 693.1 473.7
44 709.2 484.7
45 725.3 495.8 35/23
46 741.4 506.8 23/15
47 757.6 517.8
48 773.7 528.8
49 789.8 539.8 30/19
50 805.9 550.8 43/27
51 822 561.9 37/23
52 838.1 572.9
53 854.3 583.9
54 870.4 594.9
55 886.5 605.9
56 902.6 616.9
57 918.7 628 17/10
58 934.9 639
59 951 650
60 967.1 661
61 983.2 672 30/17
62 999.3 683.1 41/23
63 1015.5 694.1
64 1031.6 705.1 49/27
65 1047.7 716.1
66 1063.8 727.1
67 1079.9 738.1
68 1096 749.2
69 1112.2 760.2 19/10
70 1128.3 771.2
71 1144.4 782.2
72 1160.5 793.2 43/22, 45/23
73 1176.6 804.2
74 1192.8 815.3
75 1208.9 826.3
76 1225 837.3
77 1241.1 848.3 43/21
78 1257.2 859.3 31/15
79 1273.3 870.3
80 1289.5 881.4
81 1305.6 892.4
82 1321.7 903.4
83 1337.8 914.4 13/6
84 1353.9 925.4
85 1370.1 936.4
86 1386.2 947.5 49/22
87 1402.3 958.5
88 1418.4 969.5
89 1434.5 980.5
90 1450.6 991.5
91 1466.8 1002.5 7/3
92 1482.9 1013.6
93 1499 1024.6
94 1515.1 1035.6
95 1531.2 1046.6 46/19
96 1547.4 1057.6 22/9
97 1563.5 1068.6 37/15
98 1579.6 1079.7
99 1595.7 1090.7
100 1611.8 1101.7
101 1627.9 1112.7
102 1644.1 1123.7
103 1660.2 1134.7
104 1676.3 1145.8 29/11
105 1692.4 1156.8
106 1708.5 1167.8
107 1724.7 1178.8 46/17
108 1740.8 1189.8 41/15
109 1756.9 1200.8
110 1773 1211.9 39/14
111 1789.1 1222.9
112 1805.2 1233.9
113 1821.4 1244.9 43/15
114 1837.5 1255.9
115 1853.6 1266.9
116 1869.7 1278
117 1885.8 1289
118 1902 1300 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)