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