194edt

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← 193edt 194edt 195edt →
Prime factorization 2 × 97
Step size 9.80389 ¢ 
Octave 122\194edt (1196.07 ¢) (→ 61\97edt)
Consistency limit 3
Distinct consistency limit 3

194 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 194edt or 194ed3), is a nonoctave tuning system that divides the interval of 3/1 into 194 equal parts of about 9.8 ¢ each. Each step represents a frequency ratio of 31/194, or the 194th root of 3.

Intervals

Steps Cents Hekts Approximate ratios
0 0 0 1/1
1 9.8 6.7
2 19.61 13.4
3 29.41 20.1 58/57
4 39.22 26.8
5 49.02 33.51
6 58.82 40.21
7 68.63 46.91 26/25
8 78.43 53.61 45/43
9 88.24 60.31
10 98.04 67.01 18/17, 55/52
11 107.84 73.71 33/31
12 117.65 80.41 46/43
13 127.45 87.11 14/13
14 137.25 93.81
15 147.06 100.52
16 156.86 107.22 23/21
17 166.67 113.92
18 176.47 120.62 31/28
19 186.27 127.32 39/35
20 196.08 134.02 28/25
21 205.88 140.72
22 215.69 147.42 17/15
23 225.49 154.12
24 235.29 160.82
25 245.1 167.53 38/33
26 254.9 174.23
27 264.71 180.93
28 274.51 187.63 41/35
29 284.31 194.33 33/28
30 294.12 201.03
31 303.92 207.73 31/26
32 313.72 214.43
33 323.53 221.13 47/39
34 333.33 227.84 57/47
35 343.14 234.54
36 352.94 241.24 38/31
37 362.74 247.94
38 372.55 254.64 31/25
39 382.35 261.34
40 392.16 268.04
41 401.96 274.74 29/23
42 411.76 281.44 33/26
43 421.57 288.14 37/29
44 431.37 294.85
45 441.18 301.55
46 450.98 308.25
47 460.78 314.95
48 470.59 321.65
49 480.39 328.35 33/25
50 490.19 335.05
51 500 341.75
52 509.8 348.45 47/35, 51/38
53 519.61 355.15
54 529.41 361.86 19/14
55 539.21 368.56
56 549.02 375.26
57 558.82 381.96 29/21
58 568.63 388.66 25/18
59 578.43 395.36
60 588.23 402.06
61 598.04 408.76 65/46
62 607.84 415.46 27/19
63 617.65 422.16
64 627.45 428.87
65 637.25 435.57 13/9
66 647.06 442.27
67 656.86 448.97 19/13
68 666.66 455.67 25/17
69 676.47 462.37
70 686.27 469.07 58/39
71 696.08 475.77
72 705.88 482.47
73 715.68 489.18 65/43
74 725.49 495.88 38/25
75 735.29 502.58 26/17
76 745.1 509.28
77 754.9 515.98
78 764.7 522.68 14/9
79 774.51 529.38
80 784.31 536.08
81 794.12 542.78
82 803.92 549.48
83 813.72 556.19
84 823.53 562.89 37/23
85 833.33 569.59 55/34
86 843.13 576.29
87 852.94 582.99 18/11
88 862.74 589.69 28/17, 51/31
89 872.55 596.39
90 882.35 603.09
91 892.15 609.79
92 901.96 616.49
93 911.76 623.2
94 921.57 629.9 46/27, 63/37
95 931.37 636.6
96 941.17 643.3 31/18
97 950.98 650
98 960.78 656.7 47/27, 54/31
99 970.59 663.4
100 980.39 670.1 37/21
101 990.19 676.8
102 1000 683.51 41/23
103 1009.8 690.21
104 1019.6 696.91
105 1029.41 703.61
106 1039.21 710.31 31/17, 51/28
107 1049.02 717.01 11/6
108 1058.82 723.71
109 1068.62 730.41
110 1078.43 737.11
111 1088.23 743.81
112 1098.04 750.52
113 1107.84 757.22
114 1117.64 763.92
115 1127.45 770.62
116 1137.25 777.32 27/14
117 1147.06 784.02
118 1156.86 790.72
119 1166.66 797.42 51/26
120 1176.47 804.12
121 1186.27 810.82
122 1196.07 817.53
123 1205.88 824.23
124 1215.68 830.93
125 1225.49 837.63
126 1235.29 844.33 51/25
127 1245.09 851.03 39/19
128 1254.9 857.73
129 1264.7 864.43 27/13
130 1274.51 871.13
131 1284.31 877.84
132 1294.11 884.54 19/9
133 1303.92 891.24
134 1313.72 897.94
135 1323.53 904.64 58/27
136 1333.33 911.34 54/25
137 1343.13 918.04 63/29
138 1352.94 924.74
139 1362.74 931.44
140 1372.54 938.14 42/19
141 1382.35 944.85
142 1392.15 951.55 38/17
143 1401.96 958.25
144 1411.76 964.95
145 1421.56 971.65 25/11
146 1431.37 978.35
147 1441.17 985.05
148 1450.98 991.75
149 1460.78 998.45
150 1470.58 1005.15
151 1480.39 1011.86
152 1490.19 1018.56 26/11
153 1500 1025.26
154 1509.8 1031.96
155 1519.6 1038.66
156 1529.41 1045.36
157 1539.21 1052.06
158 1549.01 1058.76
159 1558.82 1065.46
160 1568.62 1072.16 47/19
161 1578.43 1078.87
162 1588.23 1085.57
163 1598.03 1092.27
164 1607.84 1098.97
165 1617.64 1105.67 28/11
166 1627.45 1112.37
167 1637.25 1119.07
168 1647.05 1125.77
169 1656.86 1132.47
170 1666.66 1139.18
171 1676.47 1145.88
172 1686.27 1152.58 45/17
173 1696.07 1159.28
174 1705.88 1165.98
175 1715.68 1172.68 35/13
176 1725.48 1179.38
177 1735.29 1186.08
178 1745.09 1192.78 63/23
179 1754.9 1199.48
180 1764.7 1206.19
181 1774.5 1212.89 39/14
182 1784.31 1219.59
183 1794.11 1226.29 31/11
184 1803.92 1232.99 17/6
185 1813.72 1239.69
186 1823.52 1246.39 43/15
187 1833.33 1253.09
188 1843.13 1259.79
189 1852.94 1266.49
190 1862.74 1273.2
191 1872.54 1279.9
192 1882.35 1286.6
193 1892.15 1293.3
194 1901.96 1300 3/1

Harmonics

Approximation of harmonics in 194edt
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -3.93 +0.00 +1.95 -2.01 -3.93 +3.71 -1.97 +0.00 +3.87 -4.27 +1.95
Relative (%) -40.0 +0.0 +19.9 -20.5 -40.0 +37.9 -20.1 +0.0 +39.5 -43.6 +19.9
Steps
(reduced) 		122
(122) 		194
(0) 		245
(51) 		284
(90) 		316
(122) 		344
(150) 		367
(173) 		388
(0) 		407
(19) 		423
(35) 		439
(51)
Approximation of harmonics in 194edt
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +0.64 -0.21 -2.01 +3.91 -3.01 -3.93 +0.51 -0.05 +3.71 +1.61 +3.08
Relative (%) +6.5 -2.2 -20.5 +39.9 -30.7 -40.0 +5.2 -0.6 +37.9 +16.4 +31.4
Steps
(reduced) 		453
(65) 		466
(78) 		478
(90) 		490
(102) 		500
(112) 		510
(122) 		520
(132) 		529
(141) 		538
(150) 		546
(158) 		554
(166)
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