66ed7/3
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Prime factorization
2 × 3 × 11
Step size
22.2253¢
Octave
54\66ed7/3 (1200.17¢) (→9\11ed7/3)
Twelfth
86\66ed7/3 (1911.38¢) (→43\33ed7/3)
Consistency limit
4
Distinct consistency limit
4
 |
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| ← 65ed7/3 | 66ed7/3 | 67ed7/3 → |
66 equal divisions of 7/3 (abbreviated 66ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 66 equal parts of about 22.2 ¢ each. Each step represents a frequency ratio of (7/3)1/66, or the 66th root of 7/3.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 22.225 | |
| 2 | 44.451 | |
| 3 | 66.676 | |
| 4 | 88.901 | 20/19 |
| 5 | 111.127 | 16/15 |
| 6 | 133.352 | |
| 7 | 155.577 | 35/32 |
| 8 | 177.803 | |
| 9 | 200.028 | |
| 10 | 222.253 | |
| 11 | 244.478 | 15/13, 23/20 |
| 12 | 266.704 | 7/6 |
| 13 | 288.929 | 13/11 |
| 14 | 311.154 | |
| 15 | 333.38 | 17/14, 23/19 |
| 16 | 355.605 | 16/13 |
| 17 | 377.83 | |
| 18 | 400.056 | 29/23 |
| 19 | 422.281 | |
| 20 | 444.506 | 22/17 |
| 21 | 466.732 | 17/13 |
| 22 | 488.957 | |
| 23 | 511.182 | 35/26 |
| 24 | 533.408 | 15/11 |
| 25 | 555.633 | |
| 26 | 577.858 | |
| 27 | 600.084 | 17/12, 24/17 |
| 28 | 622.309 | |
| 29 | 644.534 | 29/20 |
| 30 | 666.76 | 22/15 |
| 31 | 688.985 | |
| 32 | 711.21 | |
| 33 | 733.435 | 26/17, 29/19 |
| 34 | 755.661 | 17/11, 31/20 |
| 35 | 777.886 | |
| 36 | 800.111 | 35/22 |
| 37 | 822.337 | |
| 38 | 844.562 | 31/19 |
| 39 | 866.787 | 28/17 |
| 40 | 889.013 | |
| 41 | 911.238 | 22/13 |
| 42 | 933.463 | 12/7 |
| 43 | 955.689 | 26/15 |
| 44 | 977.914 | |
| 45 | 1000.139 | |
| 46 | 1022.365 | |
| 47 | 1044.59 | |
| 48 | 1066.815 | |
| 49 | 1089.041 | 15/8 |
| 50 | 1111.266 | 19/10 |
| 51 | 1133.491 | |
| 52 | 1155.716 | |
| 53 | 1177.942 | |
| 54 | 1200.167 | 2/1 |
| 55 | 1222.392 | |
| 56 | 1244.618 | |
| 57 | 1266.843 | |
| 58 | 1289.068 | |
| 59 | 1311.294 | 32/15 |
| 60 | 1333.519 | |
| 61 | 1355.744 | 35/16 |
| 62 | 1377.97 | |
| 63 | 1400.195 | |
| 64 | 1422.42 | |
| 65 | 1444.646 | 23/10, 30/13 |
| 66 | 1466.871 | 7/3 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.17 | +9.42 | +0.33 | -8.15 | +9.59 | +9.42 | +0.50 | -3.38 | -7.98 | +4.82 | +9.76 |
| Relative (%) | +0.8 | +42.4 | +1.5 | -36.7 | +43.1 | +42.4 | +2.3 | -15.2 | -35.9 | +21.7 | +43.9 | |
| Steps (reduced) |
54 (54) |
86 (20) |
108 (42) |
125 (59) |
140 (8) |
152 (20) |
162 (30) |
171 (39) |
179 (47) |
187 (55) |
194 (62) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +4.54 | +9.59 | +1.27 | +0.67 | +6.84 | -3.21 | -7.92 | -7.81 | -3.38 | +4.98 | -5.30 |
| Relative (%) | +20.4 | +43.1 | +5.7 | +3.0 | +30.8 | -14.5 | -35.6 | -35.2 | -15.2 | +22.4 | -23.8 | |
| Steps (reduced) |
200 (2) |
206 (8) |
211 (13) |
216 (18) |
221 (23) |
225 (27) |
229 (31) |
233 (35) |
237 (39) |
241 (43) |
244 (46) | |