42ed7/3
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Prime factorization
2 × 3 × 7
Step size
34.9255¢
Octave
34\42ed7/3 (1187.47¢) (→17\21ed7/3)
Twelfth
54\42ed7/3 (1885.98¢) (→9\7ed7/3)
Consistency limit
3
Distinct consistency limit
3
 |
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| ← 41ed7/3 | 42ed7/3 | 43ed7/3 → |
42 equal divisions of 7/3 (abbreviated 42ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 42 equal parts of about 34.9 ¢ each. Each step represents a frequency ratio of (7/3)1/42, or the 42nd root of 7/3.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 34.925 | |
| 2 | 69.851 | |
| 3 | 104.776 | |
| 4 | 139.702 | |
| 5 | 174.627 | |
| 6 | 209.553 | 9/8, 26/23 |
| 7 | 244.478 | 15/13, 23/20 |
| 8 | 279.404 | 20/17 |
| 9 | 314.329 | |
| 10 | 349.255 | |
| 11 | 384.18 | |
| 12 | 419.106 | |
| 13 | 454.031 | 13/10, 30/23 |
| 14 | 488.957 | |
| 15 | 523.882 | 23/17 |
| 16 | 558.808 | |
| 17 | 593.733 | |
| 18 | 628.659 | |
| 19 | 663.584 | 19/13, 22/15 |
| 20 | 698.51 | 3/2 |
| 21 | 733.435 | 23/15, 26/17, 29/19 |
| 22 | 768.361 | 14/9 |
| 23 | 803.286 | |
| 24 | 838.212 | |
| 25 | 873.137 | |
| 26 | 908.063 | 22/13, 27/16 |
| 27 | 942.988 | 19/11 |
| 28 | 977.914 | 30/17 |
| 29 | 1012.839 | |
| 30 | 1047.765 | |
| 31 | 1082.69 | |
| 32 | 1117.616 | 19/10 |
| 33 | 1152.541 | |
| 34 | 1187.467 | |
| 35 | 1222.392 | |
| 36 | 1257.318 | |
| 37 | 1292.243 | |
| 38 | 1327.169 | |
| 39 | 1362.094 | 11/5 |
| 40 | 1397.02 | |
| 41 | 1431.945 | |
| 42 | 1466.871 | 7/3 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -12.5 | -16.0 | +9.9 | +7.7 | +6.4 | -16.0 | -2.7 | +3.0 | -4.8 | +4.8 | -6.1 |
| Relative (%) | -35.9 | -45.7 | +28.2 | +22.1 | +18.4 | -45.7 | -7.7 | +8.5 | -13.8 | +13.8 | -17.5 | |
| Steps (reduced) |
34 (34) |
54 (12) |
69 (27) |
80 (38) |
89 (5) |
96 (12) |
103 (19) |
109 (25) |
114 (30) |
119 (35) |
123 (39) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -5.0 | +6.4 | -8.3 | -15.2 | -15.4 | -9.6 | +1.6 | -17.3 | +3.0 | -7.7 | -14.8 |
| Relative (%) | -14.3 | +18.4 | -23.6 | -43.5 | -44.1 | -27.4 | +4.6 | -49.6 | +8.5 | -22.1 | -42.4 | |
| Steps (reduced) |
127 (1) |
131 (5) |
134 (8) |
137 (11) |
140 (14) |
143 (17) |
146 (20) |
148 (22) |
151 (25) |
153 (27) |
155 (29) | |