71ed7/3
Jump to navigation
Jump to search
Prime factorization
71 (prime)
Step size
20.6602¢
Octave
58\71ed7/3 (1198.29¢)
(semiconvergent)
Twelfth
92\71ed7/3 (1900.73¢)
Consistency limit
16
Distinct consistency limit
6
 |
This page is a stub. You can help the Xenharmonic Wiki by expanding it. |
| ← 70ed7/3 | 71ed7/3 | 72ed7/3 → |
(semiconvergent)
71 equal divisions of 7/3 (abbreviated 71ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 71 equal parts of about 20.7 ¢ each. Each step represents a frequency ratio of (7/3)1/71, or the 71st root of 7/3.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 20.7 | |
| 2 | 41.3 | |
| 3 | 62 | 27/26, 28/27, 29/28, 30/29 |
| 4 | 82.6 | 21/20, 22/21 |
| 5 | 103.3 | 17/16, 35/33 |
| 6 | 124 | 29/27 |
| 7 | 144.6 | 25/23 |
| 8 | 165.3 | 11/10 |
| 9 | 185.9 | 10/9, 29/26 |
| 10 | 206.6 | 9/8, 35/31 |
| 11 | 227.3 | 33/29 |
| 12 | 247.9 | 15/13 |
| 13 | 268.6 | 7/6 |
| 14 | 289.2 | 13/11 |
| 15 | 309.9 | 37/31 |
| 16 | 330.6 | 23/19, 29/24 |
| 17 | 351.2 | 27/22 |
| 18 | 371.9 | 26/21, 31/25, 36/29 |
| 19 | 392.5 | |
| 20 | 413.2 | 33/26 |
| 21 | 433.9 | 9/7 |
| 22 | 454.5 | 13/10 |
| 23 | 475.2 | 25/19, 29/22 |
| 24 | 495.8 | 4/3 |
| 25 | 516.5 | 27/20, 31/23, 35/26 |
| 26 | 537.2 | 15/11 |
| 27 | 557.8 | 29/21 |
| 28 | 578.5 | |
| 29 | 599.1 | 24/17 |
| 30 | 619.8 | 10/7 |
| 31 | 640.5 | 29/20 |
| 32 | 661.1 | 22/15 |
| 33 | 681.8 | 37/25 |
| 34 | 702.4 | 3/2 |
| 35 | 723.1 | |
| 36 | 743.8 | 20/13 |
| 37 | 764.4 | 14/9 |
| 38 | 785.1 | 11/7 |
| 39 | 805.7 | 35/22 |
| 40 | 826.4 | 29/18, 37/23 |
| 41 | 847.1 | 31/19 |
| 42 | 867.7 | 33/20 |
| 43 | 888.4 | |
| 44 | 909 | 22/13, 27/16 |
| 45 | 929.7 | 12/7 |
| 46 | 950.4 | 26/15 |
| 47 | 971 | 7/4 |
| 48 | 991.7 | |
| 49 | 1012.3 | |
| 50 | 1033 | 20/11, 29/16 |
| 51 | 1053.7 | |
| 52 | 1074.3 | 13/7 |
| 53 | 1095 | 32/17 |
| 54 | 1115.6 | |
| 55 | 1136.3 | 27/14 |
| 56 | 1157 | 37/19 |
| 57 | 1177.6 | |
| 58 | 1198.3 | 2/1 |
| 59 | 1218.9 | |
| 60 | 1239.6 | |
| 61 | 1260.3 | 29/14, 31/15 |
| 62 | 1280.9 | 21/10 |
| 63 | 1301.6 | 17/8, 36/17 |
| 64 | 1322.2 | 15/7 |
| 65 | 1342.9 | |
| 66 | 1363.6 | 11/5 |
| 67 | 1384.2 | 20/9 |
| 68 | 1404.9 | 9/4 |
| 69 | 1425.6 | |
| 70 | 1446.2 | 30/13 |
| 71 | 1466.9 | 7/3 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.71 | -1.22 | -3.42 | +2.81 | -2.93 | -1.22 | -5.13 | -2.44 | +1.10 | +1.37 | -4.64 |
| Relative (%) | -8.3 | -5.9 | -16.6 | +13.6 | -14.2 | -5.9 | -24.8 | -11.8 | +5.3 | +6.6 | -22.5 | |
| Steps (reduced) |
58 (58) |
92 (21) |
116 (45) |
135 (64) |
150 (8) |
163 (21) |
174 (32) |
184 (42) |
193 (51) |
201 (59) |
208 (66) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.41 | -2.93 | +1.59 | -6.84 | -8.50 | -4.15 | +5.54 | -0.62 | -2.44 | -0.34 | +5.35 |
| Relative (%) | +6.8 | -14.2 | +7.7 | -33.1 | -41.1 | -20.1 | +26.8 | -3.0 | -11.8 | -1.6 | +25.9 | |
| Steps (reduced) |
215 (2) |
221 (8) |
227 (14) |
232 (19) |
237 (24) |
242 (29) |
247 (34) |
251 (38) |
255 (42) |
259 (46) |
263 (50) | |