47ed7/3
Jump to navigation
Jump to search
Prime factorization
47 (prime)
Step size
31.21¢
Octave
38\47ed7/3 (1185.98¢)
Twelfth
61\47ed7/3 (1903.81¢)
Consistency limit
2
Distinct consistency limit
2
 |
This page is a stub. You can help the Xenharmonic Wiki by expanding it. |
| ← 46ed7/3 | 47ed7/3 | 48ed7/3 → |
47 equal divisions of 7/3 (abbreviated 47ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 47 equal parts of about 31.2 ¢ each. Each step represents a frequency ratio of (7/3)1/47, or the 47th root of 7/3.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 31.21 | |
| 2 | 62.42 | 26/25, 31/30 |
| 3 | 93.63 | 18/17, 19/18 |
| 4 | 124.84 | 14/13, 15/14, 29/27 |
| 5 | 156.05 | 23/21 |
| 6 | 187.26 | 19/17 |
| 7 | 218.47 | 17/15, 25/22 |
| 8 | 249.68 | 15/13, 22/19 |
| 9 | 280.89 | 27/23 |
| 10 | 312.1 | 6/5 |
| 11 | 343.31 | 11/9 |
| 12 | 374.52 | 31/25 |
| 13 | 405.73 | 19/15, 29/23 |
| 14 | 436.94 | 9/7 |
| 15 | 468.15 | 17/13 |
| 16 | 499.36 | |
| 17 | 530.57 | 19/14 |
| 18 | 561.78 | 18/13, 29/21 |
| 19 | 592.99 | 31/22 |
| 20 | 624.2 | |
| 21 | 655.41 | 19/13 |
| 22 | 686.62 | |
| 23 | 717.83 | |
| 24 | 749.04 | 17/11 |
| 25 | 780.25 | 11/7 |
| 26 | 811.461 | |
| 27 | 842.671 | 31/19 |
| 28 | 873.881 | |
| 29 | 905.091 | 22/13 |
| 30 | 936.301 | 31/18 |
| 31 | 967.511 | |
| 32 | 998.721 | 25/14 |
| 33 | 1029.931 | |
| 34 | 1061.141 | |
| 35 | 1092.351 | |
| 36 | 1123.561 | 21/11 |
| 37 | 1154.771 | |
| 38 | 1185.981 | |
| 39 | 1217.191 | |
| 40 | 1248.401 | |
| 41 | 1279.611 | 23/11 |
| 42 | 1310.821 | |
| 43 | 1342.031 | 13/6 |
| 44 | 1373.241 | 31/14 |
| 45 | 1404.451 | |
| 46 | 1435.661 | |
| 47 | 1466.871 | 7/3 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -14.0 | +1.9 | +3.2 | -8.6 | -12.2 | +1.9 | -10.8 | +3.7 | +8.6 | -0.4 | +5.0 |
| Relative (%) | -44.9 | +5.9 | +10.2 | -27.6 | -39.0 | +5.9 | -34.8 | +11.9 | +27.5 | -1.2 | +16.1 | |
| Steps (reduced) |
38 (38) |
61 (14) |
77 (30) |
89 (42) |
99 (5) |
108 (14) |
115 (21) |
122 (28) |
128 (34) |
133 (39) |
138 (44) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -8.7 | -12.2 | -6.8 | +6.3 | -5.0 | -10.3 | -10.3 | -5.5 | +3.7 | -14.4 | +2.3 |
| Relative (%) | -27.9 | -39.0 | -21.7 | +20.3 | -16.0 | -33.0 | -32.9 | -17.5 | +11.9 | -46.2 | +7.3 | |
| Steps (reduced) |
142 (1) |
146 (5) |
150 (9) |
154 (13) |
157 (16) |
160 (19) |
163 (22) |
166 (25) |
169 (28) |
171 (30) |
174 (33) | |