63edt
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Prime factorization
32 × 7
Step size
30.1898¢
Octave
40\63edt (1207.59¢)
Consistency limit
2
Distinct consistency limit
2
 |
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| ← 62edt | 63edt | 64edt → |
63 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 63edt or 63ed3), is a nonoctave tuning system that divides the interval of 3/1 into 63 equal parts of about 30.2 ¢ each. Each step represents a frequency ratio of 31/63, or the 63rd root of 3.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 30.2 | |
| 2 | 60.4 | 30/29, 31/30 |
| 3 | 90.6 | 19/18, 20/19 |
| 4 | 120.8 | 29/27 |
| 5 | 150.9 | 12/11 |
| 6 | 181.1 | 10/9 |
| 7 | 211.3 | 26/23, 35/31 |
| 8 | 241.5 | 23/20, 31/27 |
| 9 | 271.7 | 34/29 |
| 10 | 301.9 | 31/26 |
| 11 | 332.1 | 23/19 |
| 12 | 362.3 | |
| 13 | 392.5 | |
| 14 | 422.7 | 23/18 |
| 15 | 452.8 | 13/10, 35/27 |
| 16 | 483 | |
| 17 | 513.2 | 31/23, 35/26 |
| 18 | 543.4 | 26/19 |
| 19 | 573.6 | |
| 20 | 603.8 | |
| 21 | 634 | 13/9 |
| 22 | 664.2 | 25/17 |
| 23 | 694.4 | |
| 24 | 724.6 | 35/23 |
| 25 | 754.7 | 31/20 |
| 26 | 784.9 | 11/7 |
| 27 | 815.1 | |
| 28 | 845.3 | 31/19 |
| 29 | 875.5 | |
| 30 | 905.7 | |
| 31 | 935.9 | 12/7 |
| 32 | 966.1 | 7/4 |
| 33 | 996.3 | |
| 34 | 1026.5 | |
| 35 | 1056.6 | 35/19 |
| 36 | 1086.8 | |
| 37 | 1117 | 21/11 |
| 38 | 1147.2 | 35/18 |
| 39 | 1177.4 | |
| 40 | 1207.6 | |
| 41 | 1237.8 | |
| 42 | 1268 | 27/13 |
| 43 | 1298.2 | |
| 44 | 1328.3 | |
| 45 | 1358.5 | |
| 46 | 1388.7 | 29/13 |
| 47 | 1418.9 | 34/15 |
| 48 | 1449.1 | 30/13 |
| 49 | 1479.3 | |
| 50 | 1509.5 | |
| 51 | 1539.7 | |
| 52 | 1569.9 | |
| 53 | 1600.1 | |
| 54 | 1630.2 | |
| 55 | 1660.4 | 34/13 |
| 56 | 1690.6 | |
| 57 | 1720.8 | 27/10 |
| 58 | 1751 | 11/4 |
| 59 | 1781.2 | |
| 60 | 1811.4 | |
| 61 | 1841.6 | 29/10 |
| 62 | 1871.8 | |
| 63 | 1902 | 3/1 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +7.6 | +0.0 | -15.0 | -8.9 | +7.6 | +12.4 | -7.4 | +0.0 | -1.3 | +14.9 | -15.0 |
| Relative (%) | +25.1 | +0.0 | -49.7 | -29.3 | +25.1 | +41.2 | -24.6 | +0.0 | -4.2 | +49.3 | -49.7 | |
| Steps (reduced) |
40 (40) |
63 (0) |
79 (16) |
92 (29) |
103 (40) |
112 (49) |
119 (56) |
126 (0) |
132 (6) |
138 (12) |
142 (16) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.6 | -10.2 | -8.9 | +0.2 | -14.2 | +7.6 | +4.6 | +6.3 | +12.4 | -7.7 | +5.9 |
| Relative (%) | -8.7 | -33.7 | -29.3 | +0.6 | -47.1 | +25.1 | +15.1 | +21.0 | +41.2 | -25.6 | +19.5 | |
| Steps (reduced) |
147 (21) |
151 (25) |
155 (29) |
159 (33) |
162 (36) |
166 (40) |
169 (43) |
172 (46) |
175 (49) |
177 (51) |
180 (54) | |