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{{Infobox ET}} | {{Infobox ET}} | ||
'''[[EDF|Division of the just perfect fifth]] into 51 equal parts''' (51EDF) is related to [[87edo|87 edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 2.5474 cents | '''[[EDF|Division of the just perfect fifth]] into 51 equal parts''' (51EDF) is related to [[87edo|87 edo]], but with the [[3/2]] rather than the [[2/1]] being [[just]]. The octave is [[Octave shrinking|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. | |||
Lookalikes: [[87edo]], [[138edt]] | Lookalikes: [[87edo]], [[138edt]] | ||
== Harmonics == | |||
{{Harmonics in equal|51|3|2|intervals=prime}} | |||
{{Harmonics in equal|51|3|2|intervals=prime|start=12|collapsed=1}} | |||
== Intervals == | == Intervals == | ||
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|1403.91 | |1403.91 | ||
|} | |} | ||
[[ | |||
{{todo|inline=1|complete table|text=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.}} | |||
{{todo|expand}} | |||
Latest revision as of 19:23, 1 August 2025
| ← 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. |