49ed7/3
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Prime factorization
72
Step size
29.9361¢
Octave
40\49ed7/3 (1197.45¢)
(semiconvergent)
Twelfth
64\49ed7/3 (1915.91¢)
Consistency limit
2
Distinct consistency limit
2
 |
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| ← 48ed7/3 | 49ed7/3 | 50ed7/3 → |
(semiconvergent)
49 equal divisions of 7/3 (abbreviated 49ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 49 equal parts of about 29.9 ¢ each. Each step represents a frequency ratio of (7/3)1/49, or the 49th root of 7/3.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 29.936 | |
| 2 | 59.872 | 29/28, 30/29, 31/30 |
| 3 | 89.808 | 20/19 |
| 4 | 119.745 | 15/14, 31/29 |
| 5 | 149.681 | 12/11, 25/23 |
| 6 | 179.617 | 31/28 |
| 7 | 209.553 | 26/23 |
| 8 | 239.489 | 23/20 |
| 9 | 269.425 | 7/6 |
| 10 | 299.361 | 19/16 |
| 11 | 329.298 | 23/19, 29/24 |
| 12 | 359.234 | 16/13 |
| 13 | 389.17 | 5/4 |
| 14 | 419.106 | 14/11 |
| 15 | 449.042 | 13/10, 22/17 |
| 16 | 478.978 | 25/19, 29/22 |
| 17 | 508.914 | |
| 18 | 538.851 | 15/11, 26/19 |
| 19 | 568.787 | 32/23 |
| 20 | 598.723 | 17/12, 24/17, 31/22 |
| 21 | 628.659 | 23/16 |
| 22 | 658.595 | 19/13, 22/15 |
| 23 | 688.531 | |
| 24 | 718.467 | |
| 25 | 748.404 | 17/11, 20/13 |
| 26 | 778.34 | 11/7 |
| 27 | 808.276 | 8/5 |
| 28 | 838.212 | 13/8 |
| 29 | 868.148 | 28/17 |
| 30 | 898.084 | 32/19 |
| 31 | 928.02 | 12/7, 29/17 |
| 32 | 957.957 | |
| 33 | 987.893 | 23/13, 30/17 |
| 34 | 1017.829 | |
| 35 | 1047.765 | 11/6 |
| 36 | 1077.701 | 28/15 |
| 37 | 1107.637 | 19/10 |
| 38 | 1137.573 | 25/13, 29/15 |
| 39 | 1167.509 | |
| 40 | 1197.446 | 2/1 |
| 41 | 1227.382 | |
| 42 | 1257.318 | 29/14, 31/15 |
| 43 | 1287.254 | |
| 44 | 1317.19 | 15/7 |
| 45 | 1347.126 | 24/11 |
| 46 | 1377.062 | 31/14 |
| 47 | 1406.999 | |
| 48 | 1436.935 | 23/10 |
| 49 | 1466.871 | 7/3 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.6 | +14.0 | -5.1 | -2.3 | +11.4 | +14.0 | -7.7 | -2.0 | -4.8 | +9.8 | +8.8 |
| Relative (%) | -8.5 | +46.6 | -17.1 | -7.5 | +38.1 | +46.6 | -25.6 | -6.7 | -16.1 | +32.8 | +29.6 | |
| Steps (reduced) |
40 (40) |
64 (15) |
80 (31) |
93 (44) |
104 (6) |
113 (15) |
120 (22) |
127 (29) |
133 (35) |
139 (41) |
144 (46) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -10.0 | +11.4 | +11.7 | -10.2 | +4.6 | -4.6 | -8.4 | -7.4 | -2.0 | +7.3 | -9.8 |
| Relative (%) | -33.3 | +38.1 | +39.1 | -34.1 | +15.3 | -15.3 | -28.0 | -24.6 | -6.7 | +24.2 | -32.8 | |
| Steps (reduced) |
148 (1) |
153 (6) |
157 (10) |
160 (13) |
164 (17) |
167 (20) |
170 (23) |
173 (26) |
176 (29) |
179 (32) |
181 (34) | |