66edt
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Prime factorization
2 × 3 × 11
Step size
28.8175¢
Octave
42\66edt (1210.34¢) (→7\11edt)
Consistency limit
2
Distinct consistency limit
2
 |
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| ← 65edt | 66edt | 67edt → |
66 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 66edt or 66ed3), is a nonoctave tuning system that divides the interval of 3/1 into 66 equal parts of about 28.8 ¢ each. Each step represents a frequency ratio of 31/66, or the 66th root of 3.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 28.818 | |
| 2 | 57.635 | |
| 3 | 86.453 | |
| 4 | 115.27 | 31/29 |
| 5 | 144.088 | |
| 6 | 172.905 | 21/19 |
| 7 | 201.723 | |
| 8 | 230.54 | |
| 9 | 259.358 | |
| 10 | 288.175 | 13/11 |
| 11 | 316.993 | 6/5 |
| 12 | 345.81 | 11/9 |
| 13 | 374.628 | |
| 14 | 403.445 | 29/23 |
| 15 | 432.263 | 9/7 |
| 16 | 461.08 | 17/13 |
| 17 | 489.898 | |
| 18 | 518.715 | 31/23 |
| 19 | 547.533 | |
| 20 | 576.35 | |
| 21 | 605.168 | 27/19 |
| 22 | 633.985 | 13/9, 36/25 |
| 23 | 662.803 | 22/15 |
| 24 | 691.62 | |
| 25 | 720.438 | |
| 26 | 749.255 | |
| 27 | 778.073 | |
| 28 | 806.89 | 35/22 |
| 29 | 835.708 | 34/21 |
| 30 | 864.525 | |
| 31 | 893.343 | |
| 32 | 922.16 | 29/17 |
| 33 | 950.978 | 26/15 |
| 34 | 979.795 | |
| 35 | 1008.613 | 34/19 |
| 36 | 1037.43 | 31/17 |
| 37 | 1066.248 | |
| 38 | 1095.065 | |
| 39 | 1123.883 | |
| 40 | 1152.7 | 35/18 |
| 41 | 1181.518 | |
| 42 | 1210.335 | |
| 43 | 1239.153 | |
| 44 | 1267.97 | 25/12, 27/13 |
| 45 | 1296.788 | 19/9 |
| 46 | 1325.605 | |
| 47 | 1354.423 | |
| 48 | 1383.24 | |
| 49 | 1412.058 | |
| 50 | 1440.875 | |
| 51 | 1469.693 | 7/3 |
| 52 | 1498.51 | |
| 53 | 1527.328 | |
| 54 | 1556.145 | 27/11 |
| 55 | 1584.963 | 5/2 |
| 56 | 1613.78 | 33/13 |
| 57 | 1642.598 | |
| 58 | 1671.415 | |
| 59 | 1700.233 | |
| 60 | 1729.05 | 19/7 |
| 61 | 1757.868 | |
| 62 | 1786.685 | |
| 63 | 1815.503 | |
| 64 | 1844.32 | |
| 65 | 1873.138 | |
| 66 | 1901.955 | 3/1 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +10.3 | +0.0 | -8.1 | +9.0 | +10.3 | +2.8 | +2.2 | +0.0 | -9.5 | -1.6 | -8.1 |
| Relative (%) | +35.9 | +0.0 | -28.3 | +31.2 | +35.9 | +9.8 | +7.6 | +0.0 | -33.0 | -5.5 | -28.3 | |
| Steps (reduced) |
42 (42) |
66 (0) |
83 (17) |
97 (31) |
108 (42) |
117 (51) |
125 (59) |
132 (0) |
138 (6) |
144 (12) |
149 (17) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.6 | +13.2 | +9.0 | +12.5 | -6.0 | +10.3 | +3.2 | +0.8 | +2.8 | +8.7 | -10.6 |
| Relative (%) | -9.1 | +45.7 | +31.2 | +43.5 | -20.8 | +35.9 | +11.1 | +2.9 | +9.8 | +30.3 | -36.7 | |
| Steps (reduced) |
154 (22) |
159 (27) |
163 (31) |
167 (35) |
170 (38) |
174 (42) |
177 (45) |
180 (48) |
183 (51) |
186 (54) |
188 (56) | |