63ed4
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Prime factorization
32 × 7
Step size
38.0952¢
Octave
32\63ed4 (1219.05¢)
Twelfth
50\63ed4 (1904.76¢)
Consistency limit
1
Distinct consistency limit
1
 |
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| ← 61ed4 | 63ed4 | 65ed4 → |
63 equal divisions of the 4th harmonic (abbreviated 63ed4) is a nonoctave tuning system that divides the interval of 4/1 into 63 equal parts of about 38.1 ¢ each. Each step represents a frequency ratio of 41/63, or the 63rd root of 4.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 38.095 | |
| 2 | 76.19 | |
| 3 | 114.286 | 31/29 |
| 4 | 152.381 | |
| 5 | 190.476 | 19/17 |
| 6 | 228.571 | |
| 7 | 266.667 | |
| 8 | 304.762 | 25/21 |
| 9 | 342.857 | |
| 10 | 380.952 | |
| 11 | 419.048 | 14/11 |
| 12 | 457.143 | 13/10 |
| 13 | 495.238 | |
| 14 | 533.333 | 15/11 |
| 15 | 571.429 | |
| 16 | 609.524 | 27/19 |
| 17 | 647.619 | |
| 18 | 685.714 | |
| 19 | 723.81 | 35/23 |
| 20 | 761.905 | 14/9 |
| 21 | 800 | 27/17 |
| 22 | 838.095 | |
| 23 | 876.19 | |
| 24 | 914.286 | 22/13 |
| 25 | 952.381 | 33/19 |
| 26 | 990.476 | |
| 27 | 1028.571 | |
| 28 | 1066.667 | |
| 29 | 1104.762 | 17/9 |
| 30 | 1142.857 | 29/15 |
| 31 | 1180.952 | |
| 32 | 1219.048 | |
| 33 | 1257.143 | 29/14, 31/15 |
| 34 | 1295.238 | 19/9 |
| 35 | 1333.333 | |
| 36 | 1371.429 | |
| 37 | 1409.524 | |
| 38 | 1447.619 | 30/13 |
| 39 | 1485.714 | 33/14 |
| 40 | 1523.81 | |
| 41 | 1561.905 | |
| 42 | 1600 | |
| 43 | 1638.095 | |
| 44 | 1676.19 | 29/11 |
| 45 | 1714.286 | |
| 46 | 1752.381 | |
| 47 | 1790.476 | 31/11 |
| 48 | 1828.571 | |
| 49 | 1866.667 | |
| 50 | 1904.762 | 3/1 |
| 51 | 1942.857 | |
| 52 | 1980.952 | |
| 53 | 2019.048 | |
| 54 | 2057.143 | 23/7 |
| 55 | 2095.238 | |
| 56 | 2133.333 | |
| 57 | 2171.429 | |
| 58 | 2209.524 | |
| 59 | 2247.619 | 11/3 |
| 60 | 2285.714 | |
| 61 | 2323.81 | |
| 62 | 2361.905 | |
| 63 | 2400 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +19.0 | +2.8 | +0.0 | -5.4 | -16.2 | -16.4 | +19.0 | +5.6 | +13.7 | +1.1 | +2.8 |
| Relative (%) | +50.0 | +7.4 | +0.0 | -14.1 | -42.6 | -43.2 | +50.0 | +14.7 | +35.9 | +2.8 | +7.4 | |
| Steps (reduced) |
32 (32) |
50 (50) |
63 (0) |
73 (10) |
81 (18) |
88 (25) |
95 (32) |
100 (37) |
105 (42) |
109 (46) |
113 (50) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +16.6 | +2.6 | -2.6 | +0.0 | +9.3 | -13.4 | +7.2 | -5.4 | -13.6 | -18.0 | -18.8 |
| Relative (%) | +43.6 | +6.8 | -6.7 | +0.0 | +24.5 | -35.3 | +19.0 | -14.1 | -35.8 | -47.2 | -49.2 | |
| Steps (reduced) |
117 (54) |
120 (57) |
123 (60) |
126 (0) |
129 (3) |
131 (5) |
134 (8) |
136 (10) |
138 (12) |
140 (14) |
142 (16) | |