104ed7/3
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Prime factorization
23 × 13
Step size
14.1045¢
Octave
85\104ed7/3 (1198.88¢)
(semiconvergent)
Twelfth
135\104ed7/3 (1904.11¢)
Consistency limit
4
Distinct consistency limit
4
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(semiconvergent)
104 equal divisions of 7/3 (abbreviated 104ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 104 equal parts of about 14.1 ¢ each. Each step represents a frequency ratio of (7/3)1/104, or the 104th root of 7/3.
Intervals
Steps | Cents | Approximate Ratios |
---|---|---|
0 | 0 | 1/1 |
1 | 14.105 | |
2 | 28.209 | |
3 | 42.314 | 40/39, 41/40, 42/41, 43/42 |
4 | 56.418 | 32/31 |
5 | 70.523 | |
6 | 84.627 | 21/20, 41/39, 43/41 |
7 | 98.732 | 18/17 |
8 | 112.836 | |
9 | 126.941 | 14/13, 43/40 |
10 | 141.045 | |
11 | 155.15 | 23/21 |
12 | 169.254 | 32/29, 43/39 |
13 | 183.359 | 10/9 |
14 | 197.463 | 37/33, 46/41 |
15 | 211.568 | 26/23 |
16 | 225.672 | 33/29, 41/36 |
17 | 239.777 | 23/20, 39/34 |
18 | 253.882 | 22/19 |
19 | 267.986 | 7/6 |
20 | 282.091 | 20/17, 33/28 |
21 | 296.195 | 19/16 |
22 | 310.3 | |
23 | 324.404 | 41/34 |
24 | 338.509 | 28/23 |
25 | 352.613 | 38/31 |
26 | 366.718 | 21/17 |
27 | 380.822 | |
28 | 394.927 | |
29 | 409.031 | |
30 | 423.136 | 23/18, 37/29 |
31 | 437.24 | 9/7 |
32 | 451.345 | 35/27 |
33 | 465.449 | 17/13 |
34 | 479.554 | 29/22 |
35 | 493.658 | |
36 | 507.763 | |
37 | 521.868 | 23/17, 27/20 |
38 | 535.972 | |
39 | 550.077 | 11/8 |
40 | 564.181 | 18/13 |
41 | 578.286 | |
42 | 592.39 | 31/22 |
43 | 606.495 | 44/31 |
44 | 620.599 | |
45 | 634.704 | 13/9 |
46 | 648.808 | 16/11 |
47 | 662.913 | |
48 | 677.017 | 34/23 |
49 | 691.122 | |
50 | 705.226 | |
51 | 719.331 | |
52 | 733.435 | 26/17, 29/19 |
53 | 747.54 | 20/13, 37/24 |
54 | 761.645 | |
55 | 775.749 | 36/23 |
56 | 789.854 | 41/26 |
57 | 803.958 | 43/27 |
58 | 818.063 | |
59 | 832.167 | 21/13, 34/21 |
60 | 846.272 | 31/19 |
61 | 860.376 | 23/14 |
62 | 874.481 | |
63 | 888.585 | |
64 | 902.69 | 32/19 |
65 | 916.794 | 17/10 |
66 | 930.899 | 12/7 |
67 | 945.003 | 19/11 |
68 | 959.108 | 40/23 |
69 | 973.212 | |
70 | 987.317 | 23/13 |
71 | 1001.421 | 41/23 |
72 | 1015.526 | 9/5 |
73 | 1029.631 | 29/16 |
74 | 1043.735 | 42/23 |
75 | 1057.84 | |
76 | 1071.944 | 13/7 |
77 | 1086.049 | |
78 | 1100.153 | 17/9 |
79 | 1114.258 | 40/21 |
80 | 1128.362 | 23/12 |
81 | 1142.467 | |
82 | 1156.571 | 39/20, 41/21 |
83 | 1170.676 | |
84 | 1184.78 | |
85 | 1198.885 | 2/1 |
86 | 1212.989 | |
87 | 1227.094 | |
88 | 1241.198 | 41/20, 43/21 |
89 | 1255.303 | 33/16 |
90 | 1269.408 | |
91 | 1283.512 | 21/10 |
92 | 1297.617 | 36/17 |
93 | 1311.721 | |
94 | 1325.826 | 43/20 |
95 | 1339.93 | 13/6 |
96 | 1354.035 | |
97 | 1368.139 | |
98 | 1382.244 | 20/9 |
99 | 1396.348 | |
100 | 1410.453 | |
101 | 1424.557 | 41/18 |
102 | 1438.662 | 39/17 |
103 | 1452.766 | 37/16, 44/19 |
104 | 1466.871 | 7/3 |
Harmonics
Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | -1.12 | +2.16 | -2.23 | +6.38 | +1.04 | +2.16 | -3.35 | +4.31 | +5.27 | -4.59 | -0.07 |
Relative (%) | -7.9 | +15.3 | -15.8 | +45.3 | +7.4 | +15.3 | -23.7 | +30.6 | +37.3 | -32.5 | -0.5 | |
Steps (reduced) |
85 (85) |
135 (31) |
170 (66) |
198 (94) |
220 (12) |
239 (31) |
255 (47) |
270 (62) |
283 (75) |
294 (86) |
305 (97) |
Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | +2.40 | +1.04 | -5.57 | -4.46 | +3.42 | +3.20 | -5.78 | +4.15 | +4.31 | -5.70 | +1.97 |
Relative (%) | +17.0 | +7.4 | -39.5 | -31.6 | +24.2 | +22.7 | -41.0 | +29.4 | +30.6 | -40.4 | +14.0 | |
Steps (reduced) |
315 (3) |
324 (12) |
332 (20) |
340 (28) |
348 (36) |
355 (43) |
361 (49) |
368 (56) |
374 (62) |
379 (67) |
385 (73) |