73ed7/3
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Prime factorization
73 (prime)
Step size
20.0941¢
Octave
60\73ed7/3 (1205.65¢)
Twelfth
95\73ed7/3 (1908.94¢)
Consistency limit
3
Distinct consistency limit
3
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73 equal divisions of 7/3 (abbreviated 73ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 73 equal parts of about 20.1 ¢ each. Each step represents a frequency ratio of (7/3)1/73, or the 73rd root of 7/3.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 20.1 | |
| 2 | 40.2 | |
| 3 | 60.3 | 28/27 |
| 4 | 80.4 | 22/21 |
| 5 | 100.5 | 35/33 |
| 6 | 120.6 | 15/14 |
| 7 | 140.7 | 38/35 |
| 8 | 160.8 | 34/31 |
| 9 | 180.8 | 10/9 |
| 10 | 200.9 | 9/8 |
| 11 | 221 | 25/22 |
| 12 | 241.1 | 38/33 |
| 13 | 261.2 | |
| 14 | 281.3 | 33/28 |
| 15 | 301.4 | 25/21, 31/26 |
| 16 | 321.5 | |
| 17 | 341.6 | |
| 18 | 361.7 | |
| 19 | 381.8 | |
| 20 | 401.9 | 29/23 |
| 21 | 422 | 37/29 |
| 22 | 442.1 | |
| 23 | 462.2 | 17/13 |
| 24 | 482.3 | 33/25 |
| 25 | 502.4 | |
| 26 | 522.4 | 23/17, 27/20 |
| 27 | 542.5 | 26/19 |
| 28 | 562.6 | |
| 29 | 582.7 | 7/5 |
| 30 | 602.8 | |
| 31 | 622.9 | |
| 32 | 643 | |
| 33 | 663.1 | 22/15 |
| 34 | 683.2 | |
| 35 | 703.3 | 3/2 |
| 36 | 723.4 | 38/25 |
| 37 | 743.5 | |
| 38 | 763.6 | 14/9 |
| 39 | 783.7 | 11/7 |
| 40 | 803.8 | 35/22 |
| 41 | 823.9 | 37/23 |
| 42 | 844 | 31/19 |
| 43 | 864 | 33/20 |
| 44 | 884.1 | 5/3 |
| 45 | 904.2 | 27/16 |
| 46 | 924.3 | 29/17 |
| 47 | 944.4 | 19/11 |
| 48 | 964.5 | |
| 49 | 984.6 | 23/13 |
| 50 | 1004.7 | 25/14, 34/19 |
| 51 | 1024.8 | 38/21 |
| 52 | 1044.9 | |
| 53 | 1065 | |
| 54 | 1085.1 | 15/8 |
| 55 | 1105.2 | |
| 56 | 1125.3 | |
| 57 | 1145.4 | |
| 58 | 1165.5 | |
| 59 | 1185.6 | |
| 60 | 1205.6 | |
| 61 | 1225.7 | |
| 62 | 1245.8 | |
| 63 | 1265.9 | |
| 64 | 1286 | 21/10 |
| 65 | 1306.1 | |
| 66 | 1326.2 | |
| 67 | 1346.3 | 37/17 |
| 68 | 1366.4 | 11/5 |
| 69 | 1386.5 | 29/13 |
| 70 | 1406.6 | 9/4 |
| 71 | 1426.7 | |
| 72 | 1446.8 | |
| 73 | 1466.9 | 7/3 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +5.65 | +6.99 | -8.80 | +6.77 | -7.46 | +6.99 | -3.15 | -6.12 | -7.68 | +8.17 | -1.81 |
| Relative (%) | +28.1 | +34.8 | -43.8 | +33.7 | -37.1 | +34.8 | -15.7 | -30.5 | -38.2 | +40.6 | -9.0 | |
| Steps (reduced) |
60 (60) |
95 (22) |
119 (46) |
139 (66) |
154 (8) |
168 (22) |
179 (33) |
189 (43) |
198 (52) |
207 (61) |
214 (68) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.27 | -7.46 | -6.34 | +2.50 | -1.99 | -0.47 | +6.39 | -2.03 | -6.12 | -6.28 | -2.86 |
| Relative (%) | +1.4 | -37.1 | -31.5 | +12.4 | -9.9 | -2.4 | +31.8 | -10.1 | -30.5 | -31.3 | -14.2 | |
| Steps (reduced) |
221 (2) |
227 (8) |
233 (14) |
239 (20) |
244 (25) |
249 (30) |
254 (35) |
258 (39) |
262 (43) |
266 (47) |
270 (51) | |