51edf
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Prime factorization
3 × 17
Step size
13.7638 ¢
Octave
87\51edf (1197.45 ¢) (→ 29\17edf)
Twelfth
138\51edf (1899.41 ¢) (→ 46\17edf)
Consistency limit
6
Distinct consistency limit
6
| ← 50edf | 51edf | 52edf → |
Division of the just perfect fifth into 51 equal parts (51EDF) is related to 87 edo, but with the 3/2 rather than the 2/1 being just. The octave is compressed by about 2.5474 cents and the step size is about 13.7638 cents (corresponding to 87.1851 edo).
Unlike 87edo, it is only consistent up to the 6-integer-limit, with discrepancy for the 7th harmonic.
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.55 | -2.55 | -6.02 | +3.31 | +5.36 | +5.19 | -5.03 | -4.90 | -5.33 | +6.28 | +0.94 |
| Relative (%) | -18.5 | -18.5 | -43.7 | +24.1 | +38.9 | +37.7 | -36.6 | -35.6 | -38.7 | +45.7 | +6.8 | |
| Steps (reduced) |
87 (36) |
138 (36) |
202 (49) |
245 (41) |
302 (47) |
323 (17) |
356 (50) |
370 (13) |
394 (37) |
424 (16) |
432 (24) | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.57 | -1.36 | -1.23 | -3.82 | -5.36 | +1.67 | -0.99 | +1.76 | -2.29 | +4.68 | +5.57 |
| Relative (%) | -18.7 | -9.9 | -8.9 | -27.7 | -38.9 | +12.1 | -7.2 | +12.8 | -16.6 | +34.0 | +40.4 | |
| Steps (reduced) |
454 (46) |
467 (8) |
473 (14) |
484 (25) |
499 (40) |
513 (3) |
517 (7) |
529 (19) |
536 (26) |
540 (30) |
550 (40) | |
Intervals
| Degree | Cents |
|---|---|
| 0 | |
| 1 | 13.7638 |
| 2 | 27.52765 |
| 3 | 41.2915 |
| 4 | 55.0555 |
| 5 | 68.8191 |
| 6 | 82.5829 |
| 7· | 96.3468 |
| 8 | 110.1106 |
| 9 | 123.8744 |
| 10 | 137.6382 |
| 11 | 151.0206 |
| 12· | 165.1659 |
| 13 | 178.9297 |
| 14 | 192.6935 |
| 15 | 206.45735 |
| 16 | 220.2212 |
| 17· | 233.985 |
| 18 | 248.7488 |
| 19 | 261.51265 |
| 20 | 275.2765 |
| 21 | 289.0403 |
| 22· | 302.8041 |
| 23 | 316.5679 |
| 24 | 330.3318 |
| 25 | 344.0955 |
| 26 | 357.8594 |
| 27 | 371.6232 |
| 28 | 385.3871 |
| 29 | 399.1509 |
| 30 | 412.9147 |
| 31 | 426.6785 |
| 32 | 440.44253 |
| 33 | 455.2062 |
| 34 | 467.97 |
| 35 | 481.7338 |
| 36 | 495.49765 |
| 37 | 509.2615 |
| 38 | 523.0253 |
| 39 | 536.7891 |
| 40 | 550.5529 |
| 41 | 564.3168 |
| 42 | 578.0806 |
| 43 | 591.8444 |
| 44 | 605.6082 |
| 45 | 619.3721 |
| 46 | 633.1359 |
| 47 | 646.8997 |
| 48 | 660.6635 |
| 49 | 674.42735 |
| 50 | 688.1912 |
| 51 | 701.955 |
| 52 | 715.7188 |
| 53 | 729.48365 |
| 54 | 743.2465 |
| 55 | 757.0103 |
| 56 | 770.7741 |
| 57 | 784.5379 |
| 58 | 798.3018 |
| 59 | 812.0656 |
| 60 | 825.8294 |
| 61 | 839.5932 |
| 62 | 853.3571 |
| 63 | 867.1209 |
| 64 | 880.8847 |
| 65 | 894.6485 |
| 66 | 908.41235 |
| 67 | 922.1762 |
| 68 | 935.94 |
| 69 | 949.7038 |
| 70 | 963.46765 |
| 71 | 977.2315 |
| 72 | 990.9952 |
| 73 | 1004.7591 |
| 74 | 1018.5229 |
| 75 | 1032.32868 |
| 76 | 1046.0506 |
| 77 | 1059.8144 |
| 78 | 1073.5782 |
| 79 | 1087.3421 |
| 80 | 1101.1059 |
| 81 | 1114.8697 |
| 82 | 1128.6335 |
| 83 | 1142.39735 |
| 84 | 1156.1612 |
| 85 | 1169.925 |
| 86 | 1183.6888 |
| 87 | 1197.45265 |
| 88 | 1211.2165 |
| 89 | 1224.9803 |
| 90 | 1238.7441 |
| 91 | 1252.5079 |
| 92 | 1266.2718 |
| 93 | 1280.0356 |
| 94 | 1293.7994 |
| 95 | 1307.5632 |
| 96 | 1321.3271 |
| 97 | 1335.0909 |
| 98 | 1348.8547 |
| 99 | 1362.6185 |
| 100 | 1376.3824 |
| 101 | 1390.1462 |
| 102 | 1403.91 |
|
Todo: complete table Add a third column that comments on the intervals, either what JI they approximate, what they are named, or how they can be used musically. |