64edt
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Prime factorization
26
Step size
29.718¢
Octave
40\64edt (1188.72¢) (→5\8edt)
Consistency limit
2
Distinct consistency limit
2
 |
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| ← 63edt | 64edt | 65edt → |
64 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 64edt or 64ed3), is a nonoctave tuning system that divides the interval of 3/1 into 64 equal parts of about 29.7 ¢ each. Each step represents a frequency ratio of 31/64, or the 64th root of 3.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 29.7 | |
| 2 | 59.4 | 30/29, 31/30 |
| 3 | 89.2 | |
| 4 | 118.9 | 31/29 |
| 5 | 148.6 | |
| 6 | 178.3 | 10/9 |
| 7 | 208 | 35/31 |
| 8 | 237.7 | 31/27 |
| 9 | 267.5 | 7/6 |
| 10 | 297.2 | |
| 11 | 326.9 | 23/19, 35/29 |
| 12 | 356.6 | 27/22 |
| 13 | 386.3 | |
| 14 | 416.1 | |
| 15 | 445.8 | 22/17, 35/27 |
| 16 | 475.5 | 25/19, 29/22 |
| 17 | 505.2 | |
| 18 | 534.9 | 15/11 |
| 19 | 564.6 | 18/13 |
| 20 | 594.4 | 31/22 |
| 21 | 624.1 | 33/23 |
| 22 | 653.8 | |
| 23 | 683.5 | |
| 24 | 713.2 | |
| 25 | 743 | 20/13, 23/15 |
| 26 | 772.7 | |
| 27 | 802.4 | 27/17, 35/22 |
| 28 | 832.1 | 21/13, 34/21 |
| 29 | 861.8 | |
| 30 | 891.5 | |
| 31 | 921.3 | 17/10, 29/17 |
| 32 | 951 | |
| 33 | 980.7 | 30/17 |
| 34 | 1010.4 | |
| 35 | 1040.1 | 31/17 |
| 36 | 1069.8 | 13/7 |
| 37 | 1099.6 | 17/9 |
| 38 | 1129.3 | |
| 39 | 1159 | |
| 40 | 1188.7 | |
| 41 | 1218.4 | |
| 42 | 1248.2 | 35/17 |
| 43 | 1277.9 | 23/11 |
| 44 | 1307.6 | |
| 45 | 1337.3 | 13/6 |
| 46 | 1367 | 11/5 |
| 47 | 1396.7 | |
| 48 | 1426.5 | |
| 49 | 1456.2 | |
| 50 | 1485.9 | |
| 51 | 1515.6 | |
| 52 | 1545.3 | 22/9 |
| 53 | 1575.1 | |
| 54 | 1604.8 | |
| 55 | 1634.5 | 18/7 |
| 56 | 1664.2 | 34/13 |
| 57 | 1693.9 | |
| 58 | 1723.6 | 27/10 |
| 59 | 1753.4 | |
| 60 | 1783.1 | |
| 61 | 1812.8 | |
| 62 | 1842.5 | 29/10 |
| 63 | 1872.2 | |
| 64 | 1902 | 3/1 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -11.3 | +0.0 | +7.2 | +7.2 | -11.3 | -10.7 | -4.1 | +0.0 | -4.1 | +9.2 | +7.2 |
| Relative (%) | -38.0 | +0.0 | +24.1 | +24.2 | -38.0 | -36.0 | -13.9 | +0.0 | -13.8 | +31.0 | +24.1 | |
| Steps (reduced) |
40 (40) |
64 (0) |
81 (17) |
94 (30) |
104 (40) |
113 (49) |
121 (57) |
128 (0) |
134 (6) |
140 (12) |
145 (17) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -12.5 | +7.8 | +7.2 | +14.3 | -1.5 | -11.3 | +14.0 | +14.3 | -10.7 | -2.1 | +10.1 |
| Relative (%) | -42.2 | +26.1 | +24.2 | +48.2 | -5.0 | -38.0 | +47.1 | +48.3 | -36.0 | -7.0 | +34.1 | |
| Steps (reduced) |
149 (21) |
154 (26) |
158 (30) |
162 (34) |
165 (37) |
168 (40) |
172 (44) |
175 (47) |
177 (49) |
180 (52) |
183 (55) | |