53ed4
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Prime factorization
53 (prime)
Step size
45.283¢
Octave
27\53ed4 (1222.64¢)
Twelfth
42\53ed4 (1901.89¢)
(convergent)
Consistency limit
1
Distinct consistency limit
1
 |
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| ← 51ed4 | 53ed4 | 55ed4 → |
(convergent)
53 equal divisions of the 4th harmonic (abbreviated 53ed4) is a nonoctave tuning system that divides the interval of 4/1 into 53 equal parts of about 45.3 ¢ each. Each step represents a frequency ratio of 41/53, or the 53rd root of 4.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 45.283 | |
| 2 | 90.566 | 19/18 |
| 3 | 135.849 | |
| 4 | 181.132 | |
| 5 | 226.415 | 25/22, 33/29 |
| 6 | 271.698 | |
| 7 | 316.981 | 6/5 |
| 8 | 362.264 | 21/17 |
| 9 | 407.547 | 19/15, 33/26 |
| 10 | 452.83 | |
| 11 | 498.113 | |
| 12 | 543.396 | 26/19 |
| 13 | 588.679 | |
| 14 | 633.962 | 13/9 |
| 15 | 679.245 | 31/21 |
| 16 | 724.528 | |
| 17 | 769.811 | 14/9 |
| 18 | 815.094 | |
| 19 | 860.377 | 23/14 |
| 20 | 905.66 | |
| 21 | 950.943 | 19/11, 26/15, 33/19 |
| 22 | 996.226 | |
| 23 | 1041.509 | 31/17 |
| 24 | 1086.792 | |
| 25 | 1132.075 | 27/14 |
| 26 | 1177.358 | |
| 27 | 1222.642 | |
| 28 | 1267.925 | 25/12, 27/13 |
| 29 | 1313.208 | |
| 30 | 1358.491 | |
| 31 | 1403.774 | |
| 32 | 1449.057 | |
| 33 | 1494.34 | 26/11 |
| 34 | 1539.623 | 17/7 |
| 35 | 1584.906 | 5/2 |
| 36 | 1630.189 | |
| 37 | 1675.472 | 29/11 |
| 38 | 1720.755 | |
| 39 | 1766.038 | |
| 40 | 1811.321 | |
| 41 | 1856.604 | |
| 42 | 1901.887 | 3/1 |
| 43 | 1947.17 | |
| 44 | 1992.453 | 19/6 |
| 45 | 2037.736 | |
| 46 | 2083.019 | |
| 47 | 2128.302 | |
| 48 | 2173.585 | |
| 49 | 2218.868 | 18/5 |
| 50 | 2264.151 | |
| 51 | 2309.434 | 19/5 |
| 52 | 2354.717 | |
| 53 | 2400 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +22.6 | -0.1 | +0.0 | +21.2 | +22.6 | -17.9 | +22.6 | -0.1 | -1.4 | +14.7 | -0.1 |
| Relative (%) | +50.0 | -0.2 | +0.0 | +46.9 | +49.8 | -39.5 | +50.0 | -0.3 | -3.1 | +32.5 | -0.2 | |
| Steps (reduced) |
27 (27) |
42 (42) |
53 (0) |
62 (9) |
69 (16) |
74 (21) |
80 (27) |
84 (31) |
88 (35) |
92 (39) |
95 (42) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.8 | +4.8 | +21.2 | +0.0 | -14.4 | +22.5 | +19.5 | +21.2 | -18.0 | -7.9 | +5.7 |
| Relative (%) | -6.2 | +10.5 | +46.7 | +0.0 | -31.8 | +49.7 | +43.0 | +46.9 | -39.6 | -17.5 | +12.6 | |
| Steps (reduced) |
98 (45) |
101 (48) |
104 (51) |
106 (0) |
108 (2) |
111 (5) |
113 (7) |
115 (9) |
116 (10) |
118 (12) |
120 (14) | |