187edt

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← 186edt 187edt 188edt →
Prime factorization 11 × 17
Step size 10.1709 ¢ 
Octave 118\187edt (1200.16 ¢)
Consistency limit 12
Distinct consistency limit 12

187 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 187edt or 187ed3), is a nonoctave tuning system that divides the interval of 3/1 into 187 equal parts of about 10.2 ¢ each. Each step represents a frequency ratio of 31/187, or the 187th root of 3.

Intervals

Steps Cents Hekts Approximate ratios
0 0 0 1/1
1 10.17 6.95
2 20.34 13.9
3 30.51 20.86 56/55, 57/56, 58/57
4 40.68 27.81 42/41, 43/42, 44/43
5 50.85 34.76 34/33, 35/34
6 61.03 41.71 29/28, 57/55
7 71.2 48.66 25/24, 49/47
8 81.37 55.61 22/21, 43/41, 65/62
9 91.54 62.57 39/37, 58/55
10 101.71 69.52 35/33
11 111.88 76.47 16/15
12 122.05 83.42 44/41
13 132.22 90.37 27/25, 41/38
14 142.39 97.33 38/35, 51/47, 63/58
15 152.56 104.28
16 162.73 111.23 56/51
17 172.91 118.18 21/19
18 183.08 125.13 10/9
19 193.25 132.09 19/17
20 203.42 139.04 9/8
21 213.59 145.99 43/38
22 223.76 152.94 33/29, 58/51
23 233.93 159.89 63/55
24 244.1 166.84 38/33
25 254.27 173.8 22/19
26 264.44 180.75
27 274.61 187.7 34/29, 41/35
28 284.78 194.65 33/28, 46/39
29 294.96 201.6 32/27, 51/43
30 305.13 208.56 31/26, 37/31
31 315.3 215.51 6/5
32 325.47 222.46 35/29
33 335.64 229.41 17/14
34 345.81 236.36
35 355.98 243.32 43/35
36 366.15 250.27 21/17
37 376.32 257.22 41/33, 46/37
38 386.49 264.17 5/4
39 396.66 271.12 39/31, 44/35
40 406.84 278.07 43/34
41 417.01 285.03 14/11
42 427.18 291.98 32/25, 55/43
43 437.35 298.93
44 447.52 305.88 22/17, 57/44
45 457.69 312.83 43/33, 56/43
46 467.86 319.79 38/29, 55/42
47 478.03 326.74 29/22
48 488.2 333.69 57/43
49 498.37 340.64 4/3
50 508.54 347.59 51/38, 55/41
51 518.72 354.55 27/20, 58/43
52 528.89 361.5 19/14
53 539.06 368.45 56/41
54 549.23 375.4
55 559.4 382.35 29/21, 47/34
56 569.57 389.3 25/18, 57/41
57 579.74 396.26
58 589.91 403.21 45/32, 52/37
59 600.08 410.16 41/29, 58/41
60 610.25 417.11 37/26, 64/45
61 620.42 424.06 63/44
62 630.59 431.02 36/25
63 640.77 437.97 42/29, 55/38
64 650.94 444.92 51/35
65 661.11 451.87 41/28, 63/43
66 671.28 458.82 28/19
67 681.45 465.78 40/27, 43/29
68 691.62 472.73
69 701.79 479.68 3/2
70 711.96 486.63
71 722.13 493.58 41/27, 44/29
72 732.3 500.53 29/19
73 742.47 507.49 43/28, 66/43
74 752.65 514.44 17/11
75 762.82 521.39
76 772.99 528.34 25/16
77 783.16 535.29 11/7
78 793.33 542.25
79 803.5 549.2 35/22, 62/39
80 813.67 556.15 8/5
81 823.84 563.1 37/23, 66/41
82 834.01 570.05 34/21
83 844.18 577.01 57/35
84 854.35 583.96
85 864.53 590.91 28/17
86 874.7 597.86 58/35, 63/38
87 884.87 604.81 5/3
88 895.04 611.76 52/31, 57/34
89 905.21 618.72 27/16
90 915.38 625.67 39/23, 56/33
91 925.55 632.62 29/17
92 935.72 639.57
93 945.89 646.52 19/11
94 956.06 653.48 33/19
95 966.23 660.43
96 976.4 667.38 51/29, 58/33, 65/37
97 986.58 674.33 23/13
98 996.75 681.28 16/9
99 1006.92 688.24 34/19
100 1017.09 695.19 9/5
101 1027.26 702.14 38/21
102 1037.43 709.09 51/28
103 1047.6 716.04
104 1057.77 722.99 35/19
105 1067.94 729.95 50/27, 63/34
106 1078.11 736.9 41/22
107 1088.28 743.85 15/8
108 1098.46 750.8 66/35
109 1108.63 757.75 55/29
110 1118.8 764.71 21/11
111 1128.97 771.66 48/25
112 1139.14 778.61 56/29
113 1149.31 785.56 33/17
114 1159.48 792.51 43/22
115 1169.65 799.47 55/28, 57/29
116 1179.82 806.42
117 1189.99 813.37
118 1200.16 820.32 2/1
119 1210.34 827.27
120 1220.51 834.22
121 1230.68 841.18 55/27, 57/28
122 1240.85 848.13 43/21
123 1251.02 855.08 35/17
124 1261.19 862.03 29/14
125 1271.36 868.98 25/12
126 1281.53 875.94 44/21, 65/31
127 1291.7 882.89
128 1301.87 889.84
129 1312.04 896.79 32/15
130 1322.21 903.74
131 1332.39 910.7 41/19, 54/25
132 1342.56 917.65 63/29
133 1352.73 924.6
134 1362.9 931.55
135 1373.07 938.5 42/19
136 1383.24 945.45 20/9
137 1393.41 952.41 38/17
138 1403.58 959.36 9/4
139 1413.75 966.31 43/19
140 1423.92 973.26 66/29
141 1434.09 980.21
142 1444.27 987.17
143 1454.44 994.12 44/19, 51/22
144 1464.61 1001.07
145 1474.78 1008.02
146 1484.95 1014.97 33/14
147 1495.12 1021.93 64/27
148 1505.29 1028.88 31/13
149 1515.46 1035.83 12/5
150 1525.63 1042.78
151 1535.8 1049.73 17/7
152 1545.97 1056.68
153 1556.15 1063.64
154 1566.32 1070.59 42/17
155 1576.49 1077.54
156 1586.66 1084.49 5/2
157 1596.83 1091.44
158 1607 1098.4 43/17
159 1617.17 1105.35 28/11
160 1627.34 1112.3 64/25
161 1637.51 1119.25
162 1647.68 1126.2 57/22
163 1657.85 1133.16
164 1668.02 1140.11 55/21
165 1678.2 1147.06 29/11
166 1688.37 1154.01
167 1698.54 1160.96 8/3
168 1708.71 1167.91 51/19
169 1718.88 1174.87 27/10
170 1729.05 1181.82 19/7
171 1739.22 1188.77
172 1749.39 1195.72
173 1759.56 1202.67 47/17, 58/21
174 1769.73 1209.63 25/9
175 1779.9 1216.58
176 1790.08 1223.53 45/16
177 1800.25 1230.48
178 1810.42 1237.43 37/13
179 1820.59 1244.39 63/22
180 1830.76 1251.34
181 1840.93 1258.29 55/19
182 1851.1 1265.24
183 1861.27 1272.19 41/14
184 1871.44 1279.14 56/19
185 1881.61 1286.1
186 1891.78 1293.05
187 1901.96 1300 3/1

Harmonics

Approximation of harmonics in 187edt
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +0.16 +0.00 +0.33 +0.51 +0.16 -2.26 +0.49 +0.00 +0.67 -1.60 +0.33
Relative (%) +1.6 +0.0 +3.2 +5.0 +1.6 -22.3 +4.8 +0.0 +6.6 -15.7 +3.2
Steps
(reduced) 		118
(118) 		187
(0) 		236
(49) 		274
(87) 		305
(118) 		331
(144) 		354
(167) 		374
(0) 		392
(18) 		408
(34) 		423
(49)
Approximation of harmonics in 187edt
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +4.15 -2.10 +0.51 +0.66 -2.59 +0.16 -1.90 +0.84 -2.26 -1.43 +2.98
Relative (%) +40.8 -20.6 +5.0 +6.5 -25.5 +1.6 -18.7 +8.2 -22.3 -14.1 +29.3
Steps
(reduced) 		437
(63) 		449
(75) 		461
(87) 		472
(98) 		482
(108) 		492
(118) 		501
(127) 		510
(136) 		518
(144) 		526
(152) 		534
(160)
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