User:MisterShafXen/52ed7/6
| ← 51ed7/6 | 52ed7/6 | 53ed7/6 → |
52 equal divisions of 7/6 (abbreviated 52ed7/6) is a nonoctave tuning system that divides the interval of 7/6 into 52 equal parts of about 5.13 ¢ each. Each step represents a frequency ratio of (7/6)1/52, or the 52nd root of 7/6.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 5.1 | |
| 2 | 10.3 | |
| 3 | 15.4 | |
| 4 | 20.5 | |
| 5 | 25.7 | |
| 6 | 30.8 | |
| 7 | 35.9 | |
| 8 | 41.1 | |
| 9 | 46.2 | |
| 10 | 51.3 | 33/32 |
| 11 | 56.5 | |
| 12 | 61.6 | 29/28, 30/29 |
| 13 | 66.7 | 25/24, 26/25 |
| 14 | 71.8 | |
| 15 | 77 | 23/22, 24/23 |
| 16 | 82.1 | 21/20, 22/21 |
| 17 | 87.2 | |
| 18 | 92.4 | 20/19 |
| 19 | 97.5 | |
| 20 | 102.6 | 17/16, 18/17 |
| 21 | 107.8 | |
| 22 | 112.9 | 16/15, 31/29, 33/31 |
| 23 | 118 | |
| 24 | 123.2 | 15/14 |
| 25 | 128.3 | 14/13 |
| 26 | 133.4 | 13/12 |
| 27 | 138.6 | |
| 28 | 143.7 | 25/23 |
| 29 | 148.8 | |
| 30 | 154 | 12/11 |
| 31 | 159.1 | 23/21 |
| 32 | 164.2 | 11/10 |
| 33 | 169.4 | |
| 34 | 174.5 | 21/19, 31/28, 32/29 |
| 35 | 179.6 | 10/9 |
| 36 | 184.8 | |
| 37 | 189.9 | 19/17, 29/26 |
| 38 | 195 | 28/25 |
| 39 | 200.2 | |
| 40 | 205.3 | 9/8 |
| 41 | 210.4 | 26/23 |
| 42 | 215.5 | 17/15 |
| 43 | 220.7 | 25/22 |
| 44 | 225.8 | 33/29 |
| 45 | 230.9 | |
| 46 | 236.1 | 8/7 |
| 47 | 241.2 | 23/20 |
| 48 | 246.3 | |
| 49 | 251.5 | 15/13 |
| 50 | 256.6 | 22/19, 29/25 |
| 51 | 261.7 | 7/6 |
| 52 | 266.9 |
Commas
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43 | 47 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.92 | +2.07 | +0.43 | -2.15 | +0.58 | -1.23 | +1.36 | -1.31 | +1.52 | +0.53 | -2.03 | -0.41 | +1.50 | +1.16 | +1.13 |
| Relative (%) | +17.9 | +40.3 | +8.5 | -41.8 | +11.3 | -24.0 | +26.6 | -25.4 | +29.7 | +10.2 | -39.5 | -7.9 | +29.2 | +22.6 | +22.1 | |
| Steps (reduced) |
234 (26) |
371 (7) |
543 (23) |
656 (32) |
809 (29) |
865 (33) |
956 (20) |
993 (5) |
1058 (18) |
1136 (44) |
1158 (14) |
1218 (22) |
1253 (5) |
1269 (21) |
1299 (51) | |
| Harmonic | 53 | 59 | 61 | 67 | 71 | 73 | 79 | 83 | 89 | 97 | 101 | 103 | 107 | 109 | 113 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.58 | -2.49 | +1.38 | -1.94 | +0.31 | -1.59 | +0.23 | +1.96 | -0.83 | -1.01 | +0.88 | -2.28 | -1.52 | +2.35 | +1.54 |
| Relative (%) | -30.8 | -48.5 | +27.0 | -37.9 | +6.0 | -31.0 | +4.4 | +38.2 | -16.2 | -19.8 | +17.1 | -44.4 | -29.6 | +45.7 | +29.9 | |
| Steps (reduced) |
1339 (39) |
1375 (23) |
1387 (35) |
1418 (14) |
1438 (34) |
1447 (43) |
1474 (18) |
1491 (35) |
1514 (6) |
1543 (35) |
1557 (49) |
1563 (3) |
1576 (16) |
1583 (23) |
1595 (35) | |