103ed7/3
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Prime factorization
103 (prime)
Step size
14.2415¢
Octave
84\103ed7/3 (1196.28¢)
Twelfth
134\103ed7/3 (1908.36¢)
Consistency limit
2
Distinct consistency limit
2
 |
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| ← 102ed7/3 | 103ed7/3 | 104ed7/3 → |
103 equal divisions of 7/3 (abbreviated 103ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 103 equal parts of about 14.2 ¢ each. Each step represents a frequency ratio of (7/3)1/103, or the 103rd root of 7/3.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 14.241 | |
| 2 | 28.483 | |
| 3 | 42.724 | 41/40 |
| 4 | 56.966 | |
| 5 | 71.207 | |
| 6 | 85.449 | |
| 7 | 99.69 | |
| 8 | 113.932 | 31/29 |
| 9 | 128.173 | 14/13 |
| 10 | 142.415 | |
| 11 | 156.656 | |
| 12 | 170.898 | |
| 13 | 185.139 | 39/35 |
| 14 | 199.381 | 37/33 |
| 15 | 213.622 | 26/23, 43/38 |
| 16 | 227.863 | |
| 17 | 242.105 | 23/20, 38/33 |
| 18 | 256.346 | |
| 19 | 270.588 | |
| 20 | 284.829 | 33/28 |
| 21 | 299.071 | |
| 22 | 313.312 | 6/5 |
| 23 | 327.554 | 29/24 |
| 24 | 341.795 | 28/23 |
| 25 | 356.037 | |
| 26 | 370.278 | |
| 27 | 384.52 | |
| 28 | 398.761 | |
| 29 | 413.002 | 33/26 |
| 30 | 427.244 | |
| 31 | 441.485 | 31/24, 40/31 |
| 32 | 455.727 | 13/10 |
| 33 | 469.968 | 38/29 |
| 34 | 484.21 | 37/28, 41/31 |
| 35 | 498.451 | |
| 36 | 512.693 | |
| 37 | 526.934 | 19/14 |
| 38 | 541.176 | 26/19 |
| 39 | 555.417 | 40/29 |
| 40 | 569.659 | 25/18 |
| 41 | 583.9 | 7/5 |
| 42 | 598.142 | 24/17, 41/29 |
| 43 | 612.383 | 37/26 |
| 44 | 626.624 | 33/23 |
| 45 | 640.866 | |
| 46 | 655.107 | 19/13 |
| 47 | 669.349 | 28/19 |
| 48 | 683.59 | 43/29 |
| 49 | 697.832 | |
| 50 | 712.073 | |
| 51 | 726.315 | |
| 52 | 740.556 | 43/28 |
| 53 | 754.798 | 17/11 |
| 54 | 769.039 | 39/25 |
| 55 | 783.281 | |
| 56 | 797.522 | 19/12 |
| 57 | 811.764 | |
| 58 | 826.005 | |
| 59 | 840.246 | |
| 60 | 854.488 | |
| 61 | 868.729 | 33/20, 38/23, 43/26 |
| 62 | 882.971 | 5/3 |
| 63 | 897.212 | 42/25 |
| 64 | 911.454 | |
| 65 | 925.695 | 29/17, 41/24 |
| 66 | 939.937 | |
| 67 | 954.178 | 33/19 |
| 68 | 968.42 | |
| 69 | 982.661 | |
| 70 | 996.903 | |
| 71 | 1011.144 | 43/24 |
| 72 | 1025.385 | |
| 73 | 1039.627 | 31/17 |
| 74 | 1053.868 | |
| 75 | 1068.11 | |
| 76 | 1082.351 | 43/23 |
| 77 | 1096.593 | |
| 78 | 1110.834 | 19/10 |
| 79 | 1125.076 | 23/12 |
| 80 | 1139.317 | |
| 81 | 1153.559 | 35/18, 37/19 |
| 82 | 1167.8 | |
| 83 | 1182.042 | |
| 84 | 1196.283 | |
| 85 | 1210.525 | |
| 86 | 1224.766 | |
| 87 | 1239.007 | |
| 88 | 1253.249 | |
| 89 | 1267.49 | |
| 90 | 1281.732 | |
| 91 | 1295.973 | |
| 92 | 1310.215 | |
| 93 | 1324.456 | 43/20 |
| 94 | 1338.698 | 13/6 |
| 95 | 1352.939 | 24/11 |
| 96 | 1367.181 | |
| 97 | 1381.422 | |
| 98 | 1395.664 | |
| 99 | 1409.905 | |
| 100 | 1424.147 | |
| 101 | 1438.388 | |
| 102 | 1452.629 | |
| 103 | 1466.871 | 7/3 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -3.72 | +6.40 | +6.81 | +5.01 | +2.68 | +6.40 | +3.09 | -1.44 | +1.30 | -7.05 | -1.03 |
| Relative (%) | -26.1 | +44.9 | +47.8 | +35.2 | +18.8 | +44.9 | +21.7 | -10.1 | +9.1 | -49.5 | -7.3 | |
| Steps (reduced) |
84 (84) |
134 (31) |
169 (66) |
196 (93) |
218 (12) |
237 (31) |
253 (47) |
267 (61) |
280 (74) |
291 (85) |
302 (96) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +2.81 | +2.68 | -2.83 | -0.63 | -5.89 | -5.16 | +0.93 | -2.42 | -1.44 | +3.47 | -2.28 |
| Relative (%) | +19.7 | +18.8 | -19.8 | -4.4 | -41.4 | -36.2 | +6.5 | -17.0 | -10.1 | +24.4 | -16.0 | |
| Steps (reduced) |
312 (3) |
321 (12) |
329 (20) |
337 (28) |
344 (35) |
351 (42) |
358 (49) |
364 (55) |
370 (61) |
376 (67) |
381 (72) | |