204edt

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← 203edt 204edt 205edt →
Prime factorization 22 × 3 × 17
Step size 9.32331 ¢ 
Octave 129\204edt (1202.71 ¢) (→ 43\68edt)
Consistency limit 3
Distinct consistency limit 3

204 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 204edt or 204ed3), is a nonoctave tuning system that divides the interval of 3/1 into 204 equal parts of about 9.32 ¢ each. Each step represents a frequency ratio of 31/204, or the 204th root of 3.

Intervals

Steps Cents Hekts Approximate ratios
0 0 0 1/1
1 9.32 6.37
2 18.65 12.75
3 27.97 19.12
4 37.29 25.49 46/45, 47/46
5 46.62 31.86 37/36, 38/37
6 55.94 38.24 31/30
7 65.26 44.61 27/26
8 74.59 50.98 47/45
9 83.91 57.35
10 93.23 63.73 19/18
11 102.56 70.1 35/33, 69/65
12 111.88 76.47
13 121.2 82.84 44/41
14 130.53 89.22 41/38, 55/51
15 139.85 95.59
16 149.17 101.96
17 158.5 108.33 23/21, 57/52
18 167.82 114.71
19 177.14 121.08 31/28, 41/37
20 186.47 127.45 39/35
21 195.79 133.82 28/25, 47/42
22 205.11 140.2
23 214.44 146.57
24 223.76 152.94 33/29
25 233.08 159.31
26 242.41 165.69
27 251.73 172.06
28 261.05 178.43
29 270.38 184.8
30 279.7 191.18
31 289.02 197.55 13/11
32 298.35 203.92
33 307.67 210.29
34 316.99 216.67
35 326.32 223.04 35/29
36 335.64 229.41 17/14
37 344.96 235.78
38 354.29 242.16 27/22
39 363.61 248.53 37/30, 58/47
40 372.93 254.9 31/25
41 382.26 261.27
42 391.58 267.65 69/55
43 400.9 274.02 29/23
44 410.23 280.39 19/15
45 419.55 286.76 65/51
46 428.87 293.14
47 438.2 299.51
48 447.52 305.88 57/44
49 456.84 312.25
50 466.17 318.63 55/42
51 475.49 325 25/19
52 484.81 331.37 41/31, 45/34
53 494.14 337.75
54 503.46 344.12
55 512.78 350.49 39/29
56 522.11 356.86 50/37
57 531.43 363.24 34/25
58 540.75 369.61 41/30, 56/41
59 550.08 375.98
60 559.4 382.35 29/21
61 568.72 388.73 25/18
62 578.05 395.1
63 587.37 401.47 66/47
64 596.69 407.84
65 606.02 414.22 44/31
66 615.34 420.59
67 624.66 426.96 33/23
68 633.99 433.33
69 643.31 439.71
70 652.63 446.08 51/35
71 661.95 452.45 63/43
72 671.28 458.82 28/19
73 680.6 465.2
74 689.92 471.57 70/47
75 699.25 477.94
76 708.57 484.31
77 717.89 490.69 56/37
78 727.22 497.06 35/23
79 736.54 503.43 26/17
80 745.86 509.8
81 755.19 516.18 65/42
82 764.51 522.55 14/9
83 773.83 528.92
84 783.16 535.29 11/7
85 792.48 541.67
86 801.8 548.04 27/17
87 811.13 554.41
88 820.45 560.78 45/28
89 829.77 567.16 21/13
90 839.1 573.53
91 848.42 579.9 31/19
92 857.74 586.27
93 867.07 592.65
94 876.39 599.02 68/41
95 885.71 605.39
96 895.04 611.76 52/31, 57/34
97 904.36 618.14
98 913.68 624.51 39/23
99 923.01 630.88 46/27
100 932.33 637.25
101 941.65 643.63 31/18
102 950.98 650
103 960.3 656.37 47/27, 54/31
104 969.62 662.75
105 978.95 669.12 44/25
106 988.27 675.49 23/13
107 997.59 681.86
108 1006.92 688.24 34/19
109 1016.24 694.61
110 1025.56 700.98 47/26
111 1034.89 707.35
112 1044.21 713.73
113 1053.53 720.1 57/31, 68/37
114 1062.86 726.47
115 1072.18 732.84 13/7
116 1081.5 739.22 28/15
117 1090.83 745.59
118 1100.15 751.96 17/9
119 1109.47 758.33
120 1118.8 764.71 21/11
121 1128.12 771.08
122 1137.44 777.45 27/14
123 1146.77 783.82
124 1156.09 790.2
125 1165.41 796.57 51/26
126 1174.74 802.94 69/35
127 1184.06 809.31
128 1193.38 815.69
129 1202.71 822.06
130 1212.03 828.43
131 1221.35 834.8
132 1230.68 841.18 57/28
133 1240 847.55 43/21
134 1249.32 853.92 35/17
135 1258.65 860.29
136 1267.97 866.67 52/25
137 1277.29 873.04 23/11
138 1286.62 879.41
139 1295.94 885.78
140 1305.26 892.16
141 1314.59 898.53 47/22
142 1323.91 904.9 58/27
143 1333.23 911.27 54/25
144 1342.56 917.65 63/29
145 1351.88 924.02
146 1361.2 930.39
147 1370.53 936.76
148 1379.85 943.14
149 1389.17 949.51 29/13
150 1398.5 955.88
151 1407.82 962.25
152 1417.14 968.63 34/15
153 1426.47 975 57/25
154 1435.79 981.37
155 1445.11 987.75
156 1454.44 994.12 44/19
157 1463.76 1000.49
158 1473.08 1006.86
159 1482.41 1013.24
160 1491.73 1019.61 45/19
161 1501.05 1025.98 69/29
162 1510.38 1032.35 55/23
163 1519.7 1038.73
164 1529.02 1045.1
165 1538.35 1051.47
166 1547.67 1057.84 22/9
167 1556.99 1064.22
168 1566.32 1070.59 42/17
169 1575.64 1076.96
170 1584.96 1083.33
171 1594.29 1089.71
172 1603.61 1096.08
173 1612.93 1102.45 33/13
174 1622.26 1108.82
175 1631.58 1115.2
176 1640.9 1121.57
177 1650.23 1127.94 70/27
178 1659.55 1134.31
179 1668.87 1140.69
180 1678.2 1147.06 29/11
181 1687.52 1153.43
182 1696.84 1159.8
183 1706.17 1166.18
184 1715.49 1172.55 35/13
185 1724.81 1178.92
186 1734.14 1185.29
187 1743.46 1191.67 52/19, 63/23
188 1752.78 1198.04
189 1762.11 1204.41
190 1771.43 1210.78
191 1780.75 1217.16
192 1790.08 1223.53
193 1799.4 1229.9 65/23
194 1808.72 1236.27 54/19
195 1818.05 1242.65
196 1827.37 1249.02
197 1836.69 1255.39 26/9
198 1846.02 1261.76
199 1855.34 1268.14
200 1864.66 1274.51
201 1873.99 1280.88
202 1883.31 1287.25
203 1892.63 1293.63
204 1901.96 1300 3/1

Harmonics

Approximation of harmonics in 204edt
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +2.71 +0.00 -3.91 +1.36 +2.71 -3.11 -1.20 +0.00 +4.06 -2.45 -3.91
Relative (%) +29.0 +0.0 -41.9 +14.5 +29.0 -33.4 -12.9 +0.0 +43.6 -26.2 -41.9
Steps
(reduced) 		129
(129) 		204
(0) 		257
(53) 		299
(95) 		333
(129) 		361
(157) 		386
(182) 		408
(0) 		428
(20) 		445
(37) 		461
(53)
Approximation of harmonics in 204edt
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -2.63 -0.40 +1.36 +1.50 -0.89 +2.71 +2.34 -2.55 -3.11 +0.26 -2.11
Relative (%) -28.2 -4.3 +14.5 +16.1 -9.6 +29.0 +25.1 -27.4 -33.4 +2.8 -22.6
Steps
(reduced) 		476
(68) 		490
(82) 		503
(95) 		515
(107) 		526
(118) 		537
(129) 		547
(139) 		556
(148) 		565
(157) 		574
(166) 		582
(174)
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