195edt

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← 194edt 195edt 196edt →
Prime factorization 3 × 5 × 13
Step size 9.75362 ¢ 
Octave 123\195edt (1199.69 ¢) (→ 41\65edt)
Consistency limit 6
Distinct consistency limit 6

195 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 195edt or 195ed3), is a nonoctave tuning system that divides the interval of 3/1 into 195 equal parts of about 9.75 ¢ each. Each step represents a frequency ratio of 31/195, or the 195th root of 3.

Intervals

Steps Cents Hekts Approximate ratios
0 0 0 1/1
1 9.75 6.67
2 19.51 13.33
3 29.26 20 58/57
4 39.01 26.67 44/43, 45/44, 46/45
5 48.77 33.33 36/35
6 58.52 40 30/29
7 68.28 46.67
8 78.03 53.33 23/22, 45/43, 68/65
9 87.78 60 20/19
10 97.54 66.67
11 107.29 73.33 33/31
12 117.04 80 46/43
13 126.8 86.67
14 136.55 93.33
15 146.3 100 37/34, 62/57
16 156.06 106.67 35/32
17 165.81 113.33 11/10
18 175.57 120 52/47
19 185.32 126.67
20 195.07 133.33 47/42
21 204.83 140 9/8
22 214.58 146.67 43/38
23 224.33 153.33 33/29, 41/36
24 234.09 160
25 243.84 166.67 38/33
26 253.59 173.33 22/19
27 263.35 180
28 273.1 186.67 41/35, 48/41
29 282.85 193.33
30 292.61 200 45/38
31 302.36 206.67 56/47
32 312.12 213.33
33 321.87 220 65/54
34 331.62 226.67 23/19, 63/52
35 341.38 233.33 39/32
36 351.13 240
37 360.88 246.67
38 370.64 253.33 26/21, 57/46
39 380.39 260
40 390.14 266.67
41 399.9 273.33 34/27
42 409.65 280 19/15
43 419.41 286.67 65/51
44 429.16 293.33 41/32
45 438.91 300 58/45
46 448.67 306.67 35/27, 57/44
47 458.42 313.33 43/33
48 468.17 320 38/29
49 477.93 326.67 29/22, 54/41
50 487.68 333.33 57/43
51 497.43 340 4/3
52 507.19 346.67 63/47
53 516.94 353.33 31/23, 58/43
54 526.7 360
55 536.45 366.67 15/11
56 546.2 373.33 37/27, 48/35
57 555.96 380 40/29, 51/37
58 565.71 386.67 43/31
59 575.46 393.33 46/33
60 585.22 400
61 594.97 406.67
62 604.72 413.33
63 614.48 420
64 624.23 426.67 33/23, 43/30
65 633.99 433.33 62/43
66 643.74 440 29/20
67 653.49 446.67 35/24, 54/37
68 663.25 453.33 22/15
69 673 460
70 682.75 466.67 43/29, 46/31
71 692.51 473.33
72 702.26 480 3/2
73 712.01 486.67
74 721.77 493.33 44/29
75 731.52 500 29/19
76 741.27 506.67 66/43
77 751.03 513.33 54/35
78 760.78 520 45/29
79 770.54 526.67 64/41
80 780.29 533.33
81 790.04 540 30/19
82 799.8 546.67 27/17, 46/29
83 809.55 553.33
84 819.3 560
85 829.06 566.67
86 838.81 573.33
87 848.56 580 31/19
88 858.32 586.67 64/39
89 868.07 593.33 33/20
90 877.83 600
91 887.58 606.67
92 897.33 613.33 47/28
93 907.09 620
94 916.84 626.67
95 926.59 633.33 41/24
96 936.35 640
97 946.1 646.67 19/11
98 955.85 653.33 33/19
99 965.61 660
100 975.36 666.67 58/33, 65/37
101 985.12 673.33
102 994.87 680
103 1004.62 686.67
104 1014.38 693.33
105 1024.13 700 47/26
106 1033.88 706.67 20/11
107 1043.64 713.33
108 1053.39 720 57/31, 68/37
109 1063.14 726.67
110 1072.9 733.33
111 1082.65 740 43/23
112 1092.4 746.67 62/33
113 1102.16 753.33 17/9
114 1111.91 760 19/10
115 1121.67 766.67 65/34
116 1131.42 773.33
117 1141.17 780 29/15
118 1150.93 786.67 35/18, 68/35
119 1160.68 793.33 43/22
120 1170.43 800 57/29
121 1180.19 806.67
122 1189.94 813.33
123 1199.69 820 2/1
124 1209.45 826.67
125 1219.2 833.33
126 1228.96 840
127 1238.71 846.67 45/22
128 1248.46 853.33 37/18
129 1258.22 860 60/29
130 1267.97 866.67
131 1277.72 873.33 23/11
132 1287.48 880
133 1297.23 886.67
134 1306.98 893.33
135 1316.74 900
136 1326.49 906.67
137 1336.25 913.33
138 1346 920 37/17
139 1355.75 926.67 35/16
140 1365.51 933.33 11/5
141 1375.26 940
142 1385.01 946.67
143 1394.77 953.33 47/21
144 1404.52 960 9/4
145 1414.27 966.67 43/19
146 1424.03 973.33 41/18, 66/29
147 1433.78 980
148 1443.54 986.67
149 1453.29 993.33 44/19
150 1463.04 1000
151 1472.8 1006.67
152 1482.55 1013.33
153 1492.3 1020 45/19
154 1502.06 1026.67
155 1511.81 1033.33
156 1521.56 1040 65/27
157 1531.32 1046.67 46/19, 63/26
158 1541.07 1053.33
159 1550.82 1060
160 1560.58 1066.67 32/13
161 1570.33 1073.33 52/21, 57/23
162 1580.09 1080
163 1589.84 1086.67
164 1599.59 1093.33 68/27
165 1609.35 1100 38/15
166 1619.1 1106.67
167 1628.85 1113.33 41/16
168 1638.61 1120
169 1648.36 1126.67 57/22
170 1658.11 1133.33
171 1667.87 1140
172 1677.62 1146.67 29/11
173 1687.38 1153.33
174 1697.13 1160 8/3
175 1706.88 1166.67
176 1716.64 1173.33 62/23
177 1726.39 1180
178 1736.14 1186.67 30/11
179 1745.9 1193.33
180 1755.65 1200
181 1765.4 1206.67
182 1775.16 1213.33
183 1784.91 1220
184 1794.67 1226.67 31/11
185 1804.42 1233.33
186 1814.17 1240 57/20
187 1823.93 1246.67 43/15, 66/23
188 1833.68 1253.33
189 1843.43 1260 29/10
190 1853.19 1266.67 35/12
191 1862.94 1273.33 44/15
192 1872.69 1280
193 1882.45 1286.67
194 1892.2 1293.33
195 1901.96 1300 3/1

Harmonics

Approximation of harmonics in 195edt
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -0.31 +0.00 -0.61 +3.22 -0.31 -3.83 -0.92 +0.00 +2.91 +3.72 -0.61
Relative (%) -3.1 +0.0 -6.3 +33.0 -3.1 -39.3 -9.4 +0.0 +29.9 +38.2 -6.3
Steps
(reduced) 		123
(123) 		195
(0) 		246
(51) 		286
(91) 		318
(123) 		345
(150) 		369
(174) 		390
(0) 		409
(19) 		426
(36) 		441
(51)
Approximation of harmonics in 195edt
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -2.63 -4.13 +3.22 -1.22 +1.11 -0.31 +3.63 +2.61 -3.83 +3.42 +4.49
Relative (%) -27.0 -42.4 +33.0 -12.5 +11.4 -3.1 +37.2 +26.8 -39.3 +35.0 +46.0
Steps
(reduced) 		455
(65) 		468
(78) 		481
(91) 		492
(102) 		503
(113) 		513
(123) 		523
(133) 		532
(142) 		540
(150) 		549
(159) 		557
(167)
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