73ed5
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Prime factorization
73 (prime)
Step size
38.1687¢
Octave
31\73ed5 (1183.23¢)
Twelfth
50\73ed5 (1908.43¢)
Consistency limit
2
Distinct consistency limit
2
| ← 72ed5 | 73ed5 | 74ed5 → |
73 equal divisions of the 5th harmonic (abbreviated 73ed5) is a nonoctave tuning system that divides the interval of 5/1 into 73 equal parts of about 38.2 ¢ each. Each step represents a frequency ratio of 51/73, or the 73rd root of 5.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 38.2 | |
| 2 | 76.3 | 23/22 |
| 3 | 114.5 | 31/29 |
| 4 | 152.7 | |
| 5 | 190.8 | 19/17 |
| 6 | 229 | |
| 7 | 267.2 | 7/6 |
| 8 | 305.3 | 25/21, 37/31 |
| 9 | 343.5 | |
| 10 | 381.7 | |
| 11 | 419.9 | 37/29 |
| 12 | 458 | 30/23 |
| 13 | 496.2 | |
| 14 | 534.4 | 15/11, 34/25 |
| 15 | 572.5 | |
| 16 | 610.7 | 27/19 |
| 17 | 648.9 | |
| 18 | 687 | |
| 19 | 725.2 | 35/23, 38/25 |
| 20 | 763.4 | |
| 21 | 801.5 | 27/17, 35/22 |
| 22 | 839.7 | |
| 23 | 877.9 | |
| 24 | 916 | |
| 25 | 954.2 | 33/19 |
| 26 | 992.4 | |
| 27 | 1030.6 | |
| 28 | 1068.7 | 13/7 |
| 29 | 1106.9 | |
| 30 | 1145.1 | 33/17 |
| 31 | 1183.2 | |
| 32 | 1221.4 | |
| 33 | 1259.6 | 31/15 |
| 34 | 1297.7 | |
| 35 | 1335.9 | 13/6 |
| 36 | 1374.1 | |
| 37 | 1412.2 | |
| 38 | 1450.4 | 30/13 |
| 39 | 1488.6 | |
| 40 | 1526.7 | |
| 41 | 1564.9 | 37/15 |
| 42 | 1603.1 | |
| 43 | 1641.3 | |
| 44 | 1679.4 | 29/11 |
| 45 | 1717.6 | 35/13 |
| 46 | 1755.8 | |
| 47 | 1793.9 | 31/11 |
| 48 | 1832.1 | |
| 49 | 1870.3 | |
| 50 | 1908.4 | |
| 51 | 1946.6 | |
| 52 | 1984.8 | 22/7 |
| 53 | 2022.9 | 29/9 |
| 54 | 2061.1 | 23/7 |
| 55 | 2099.3 | 37/11 |
| 56 | 2137.4 | |
| 57 | 2175.6 | |
| 58 | 2213.8 | |
| 59 | 2252 | 11/3 |
| 60 | 2290.1 | |
| 61 | 2328.3 | 23/6 |
| 62 | 2366.5 | |
| 63 | 2404.6 | |
| 64 | 2442.8 | |
| 65 | 2481 | 21/5 |
| 66 | 2519.1 | 30/7 |
| 67 | 2557.3 | |
| 68 | 2595.5 | |
| 69 | 2633.6 | |
| 70 | 2671.8 | |
| 71 | 2710 | |
| 72 | 2748.1 | |
| 73 | 2786.3 | 5/1 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -16.8 | +6.5 | +4.6 | +0.0 | -10.3 | -10.0 | -12.1 | +13.0 | -16.8 | +9.1 | +11.1 |
| Relative (%) | -43.9 | +17.0 | +12.1 | +0.0 | -27.0 | -26.2 | -31.8 | +33.9 | -43.9 | +23.8 | +29.1 | |
| Steps (reduced) |
31 (31) |
50 (50) |
63 (63) |
73 (0) |
81 (8) |
88 (15) |
94 (21) |
100 (27) |
104 (31) |
109 (36) |
113 (40) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -13.0 | +11.4 | +6.5 | +9.3 | +18.8 | -3.8 | +17.1 | +4.6 | -3.5 | -7.7 | -8.3 |
| Relative (%) | -34.0 | +29.9 | +17.0 | +24.2 | +49.3 | -10.0 | +44.8 | +12.1 | -9.2 | -20.2 | -21.8 | |
| Steps (reduced) |
116 (43) |
120 (47) |
123 (50) |
126 (53) |
129 (56) |
131 (58) |
134 (61) |
136 (63) |
138 (65) |
140 (67) |
142 (69) | |
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