69edt
Jump to navigation
Jump to search
Prime factorization
3 × 23
Step size
27.5646¢
Octave
44\69edt (1212.84¢)
Consistency limit
2
Distinct consistency limit
2
 |
This page is a stub. You can help the Xenharmonic Wiki by expanding it. |
| ← 68edt | 69edt | 70edt → |
69 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 69edt or 69ed3), is a nonoctave tuning system that divides the interval of 3/1 into 69 equal parts of about 27.6 ¢ each. Each step represents a frequency ratio of 31/69, or the 69th root of 3.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 27.6 | |
| 2 | 55.1 | 31/30, 34/33 |
| 3 | 82.7 | |
| 4 | 110.3 | 33/31 |
| 5 | 137.8 | |
| 6 | 165.4 | 11/10 |
| 7 | 193 | 19/17 |
| 8 | 220.5 | 17/15 |
| 9 | 248.1 | 15/13 |
| 10 | 275.6 | 27/23 |
| 11 | 303.2 | 25/21, 31/26, 37/31 |
| 12 | 330.8 | 23/19 |
| 13 | 358.3 | |
| 14 | 385.9 | |
| 15 | 413.5 | 33/26 |
| 16 | 441 | |
| 17 | 468.6 | |
| 18 | 496.2 | |
| 19 | 523.7 | 23/17 |
| 20 | 551.3 | |
| 21 | 578.9 | 7/5 |
| 22 | 606.4 | 27/19 |
| 23 | 634 | 13/9 |
| 24 | 661.5 | |
| 25 | 689.1 | |
| 26 | 716.7 | |
| 27 | 744.2 | |
| 28 | 771.8 | |
| 29 | 799.4 | 27/17 |
| 30 | 826.9 | 21/13 |
| 31 | 854.5 | 18/11 |
| 32 | 882.1 | 5/3 |
| 33 | 909.6 | |
| 34 | 937.2 | |
| 35 | 964.8 | |
| 36 | 992.3 | |
| 37 | 1019.9 | 9/5 |
| 38 | 1047.5 | 11/6 |
| 39 | 1075 | 13/7 |
| 40 | 1102.6 | 17/9 |
| 41 | 1130.1 | 25/13 |
| 42 | 1157.7 | |
| 43 | 1185.3 | |
| 44 | 1212.8 | |
| 45 | 1240.4 | |
| 46 | 1268 | 27/13 |
| 47 | 1295.5 | 19/9 |
| 48 | 1323.1 | 15/7 |
| 49 | 1350.7 | |
| 50 | 1378.2 | 31/14 |
| 51 | 1405.8 | |
| 52 | 1433.4 | |
| 53 | 1460.9 | |
| 54 | 1488.5 | 26/11 |
| 55 | 1516.1 | |
| 56 | 1543.6 | |
| 57 | 1571.2 | |
| 58 | 1598.7 | |
| 59 | 1626.3 | 23/9 |
| 60 | 1653.9 | 13/5 |
| 61 | 1681.4 | 37/14 |
| 62 | 1709 | |
| 63 | 1736.6 | 30/11 |
| 64 | 1764.1 | |
| 65 | 1791.7 | 31/11 |
| 66 | 1819.3 | |
| 67 | 1846.8 | |
| 68 | 1874.4 | |
| 69 | 1902 | 3/1 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +12.8 | +0.0 | -1.9 | -2.3 | +12.8 | -5.9 | +11.0 | +0.0 | +10.5 | +10.9 | -1.9 |
| Relative (%) | +46.6 | +0.0 | -6.8 | -8.3 | +46.6 | -21.6 | +39.8 | +0.0 | +38.3 | +39.7 | -6.8 | |
| Steps (reduced) |
44 (44) |
69 (0) |
87 (18) |
101 (32) |
113 (44) |
122 (53) |
131 (62) |
138 (0) |
145 (7) |
151 (13) |
156 (18) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.6 | +6.9 | -2.3 | -3.8 | +1.5 | +12.8 | +1.9 | -4.2 | -5.9 | -3.8 | +1.9 |
| Relative (%) | -9.6 | +25.0 | -8.3 | -13.7 | +5.6 | +46.6 | +7.0 | -15.1 | -21.6 | -13.8 | +7.1 | |
| Steps (reduced) |
161 (23) |
166 (28) |
170 (32) |
174 (36) |
178 (40) |
182 (44) |
185 (47) |
188 (50) |
191 (53) |
194 (56) |
197 (59) | |