34edf
Jump to navigation
Jump to search
Prime factorization
2 × 17
Step size
20.6457¢
Octave
58\34edf (1197.45¢) (→29\17edf)
Twelfth
92\34edf (1899.41¢) (→46\17edf)
Consistency limit
15
Distinct consistency limit
9
| ← 33edf | 34edf | 35edf → |
Division of the just perfect fifth into 34 equal parts (34EDF) is related to 58edo, 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 20.6457 cents (corresponding to 58.1234 edo).
The patent val has a generally flat tendency for harmonics up to 16, with the exception for 5. Unlike 58edo, it is only consistent up to the 15-integer-limit, with discrepancy for the 16th harmonic (four octaves).
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.55 | -2.55 | +0.86 | -3.57 | -1.53 | -1.69 | +8.73 | +1.98 | +1.55 | -7.48 | +0.94 |
| Relative (%) | -12.3 | -12.3 | +4.2 | -17.3 | -7.4 | -8.2 | +42.3 | +9.6 | +7.5 | -36.2 | +4.5 | |
| Steps (reduced) |
58 (24) |
92 (24) |
135 (33) |
163 (27) |
201 (31) |
215 (11) |
238 (0) |
247 (9) |
263 (25) |
282 (10) |
288 (16) | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +4.31 | -8.24 | -8.11 | +3.07 | +1.53 | +1.67 | +5.89 | +8.64 | -9.17 | +4.68 | -8.20 |
| Relative (%) | +20.9 | -39.9 | -39.3 | +14.8 | +7.4 | +8.1 | +28.5 | +41.8 | -44.4 | +22.6 | -39.7 | |
| Steps (reduced) |
303 (31) |
311 (5) |
315 (9) |
323 (17) |
333 (27) |
342 (2) |
345 (5) |
353 (13) |
357 (17) |
360 (20) |
366 (26) | |
Intervals
| Degree | Cents | Approx. ratios |
|---|---|---|
| 0 | 1/1 | |
| 1 | 20.6457 | 56/55, 64/63, 81/80, 128/125 |
| 2 | 41.2915 | 6/35, 49/48, 50/49, 55/54 |
| 3 | 61.9372 | 25/24, 26/25, 27/26, 28/27, 33/32 |
| 4 | 82.5829 | 21/20, 22/21 |
| 5 | 103.2287 | 16/15, 17/16, 18/17 |
| 6 | 123.8744 | 15/14, 14/13 |
| 7· | 144.52015 | 12/11, 13/12 |
| 8 | 165.1659 | 11/10 |
| 9 | 185.8116 | 10/9 |
| 10 | 206.45735 | 9/8 |
| 11 | 227.1031 | 8/7 |
| 12· | 248.7488 | 15/13 |
| 13 | 268.3946 | 7/6 |
| 14 | 289.0403 | 13/11, 20/17 |
| 15 | 309.686 | 6/5 |
| 16 | 330.3318 | 17/14 |
| 17· | 350.9775 | 11/9, 16/13 |
| 18 | 371.6232 | 21/17 |
| 19 | 392.269 | 5/4 |
| 20 | 412.9147 | 14/11 |
| 21 | 433.5604 | 9/7 |
| 22· | 455.2062 | 13/10, 17/13, 22/17 |
| 23 | 474.8519 | 21/16 |
| 24 | 495.49765 | 4/3 |
| 25 | 516.1434 | 27/20 |
| 26 | 536.7891 | 15/11 |
| 27 | 557.43485 | 11/8, 18/13 |
| 28 | 578.0806 | 7/5 |
| 29 | 598.7263 | 17/12, 24/17 |
| 30 | 619.3721 | 10/7 |
| 31 | 640.0178 | 13/9, 16/11 |
| 32 | 660.6635 | 22/15 |
| 33 | 681.3093 | 40/27 |
| 34 | 701.955 | 3/2 |
| 35 | 722.6007 | 32/21 |
| 36 | 743.2465 | 20/13, 26/17, 17/11 |
| 37 | 763.8922 | 14/9 |
| 38 | 784.5379 | 11/7 |
| 39 | 805.1837 | 8/5 |
| 40 | 825.8294 | 34/21 |
| 41 | 846.47515 | 13/8, 18/11 |
| 42 | 867.1209 | 28/17 |
| 43 | 887.7666 | 5/3, |
| 44 | 908.41235 | 22/13, 17/10 |
| 45 | 929.0581 | 12/7 |
| 46 | 949.7038 | 26/15 |
| 47 | 970.35 | 7/4 |
| 48 | 990.9952 | 16/9 |
| 49 | 1011.641 | 9/5 |
| 50 | 1032.32868 | 20/11 |
| 51 | 1052.9235 | 11/6, 24/13 |
| 52 | 1073.5782 | 28/15, 13/7 |
| 53 | 1094.224 | 15/8, 32/17, 17/9 |
| 54 | 1114.8697 | 40/21, 21/11 |
| 55 | 1135.5154 | 48/25, 25/13, 52/27, 27/14, 64/33 |
| 56 | 1156.1612 | 35/18, 96/49, 49/25, 108/55 |
| 57 | 1176.8069 | 55/28, 63/32, 160/81, 125/64 |
| 58 | 1197.45265 | 2/1 |
| 59 | 1218.0984 | 112/55, 128/63, 81/40, 256/125 |
| 60 | 1238.7441 | 72/35, 49/24, 100/49, 55/27 |
| 61 | 1259.38985 | 25/12, 52/25, 27/13, 56/27, 33/16 |
| 62 | 1280.0356 | 21/10, 44/21 |
| 63 | 1300.6813 | 32/15, 17/8, 36/17 |
| 64 | 1321.3271 | 15/7, 28/13 |
| 65 | 1341.9728 | 24/11, 13/5 |
| 66 | 1362.6185 | 11/10 |
| 67 | 1383.3643 | 20/9 |
| 68 | 1403.91 | 9/4 |