101ed4
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Prime factorization
101 (prime)
Step size
23.7624¢
Octave
51\101ed4 (1211.88¢)
Twelfth
80\101ed4 (1900.99¢)
Consistency limit
1
Distinct consistency limit
1
 |
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| ← 99ed4 | 101ed4 | 103ed4 → |
101 equal divisions of the 4th harmonic (abbreviated 101ed4) is a nonoctave tuning system that divides the interval of 4/1 into 101 equal parts of about 23.8 ¢ each. Each step represents a frequency ratio of 41/101, or the 101st root of 4.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 23.762 | |
| 2 | 47.525 | |
| 3 | 71.287 | |
| 4 | 95.05 | 19/18, 37/35 |
| 5 | 118.812 | |
| 6 | 142.574 | 25/23 |
| 7 | 166.337 | 11/10 |
| 8 | 190.099 | |
| 9 | 213.861 | |
| 10 | 237.624 | 31/27, 39/34 |
| 11 | 261.386 | 43/37 |
| 12 | 285.149 | |
| 13 | 308.911 | |
| 14 | 332.673 | |
| 15 | 356.436 | 43/35 |
| 16 | 380.198 | |
| 17 | 403.96 | |
| 18 | 427.723 | |
| 19 | 451.485 | 35/27 |
| 20 | 475.248 | |
| 21 | 499.01 | |
| 22 | 522.772 | 23/17 |
| 23 | 546.535 | 37/27 |
| 24 | 570.297 | |
| 25 | 594.059 | |
| 26 | 617.822 | 10/7 |
| 27 | 641.584 | |
| 28 | 665.347 | 25/17 |
| 29 | 689.109 | |
| 30 | 712.871 | |
| 31 | 736.634 | |
| 32 | 760.396 | 45/29 |
| 33 | 784.158 | 11/7 |
| 34 | 807.921 | 43/27 |
| 35 | 831.683 | 21/13 |
| 36 | 855.446 | |
| 37 | 879.208 | |
| 38 | 902.97 | |
| 39 | 926.733 | 29/17 |
| 40 | 950.495 | |
| 41 | 974.257 | |
| 42 | 998.02 | |
| 43 | 1021.782 | |
| 44 | 1045.545 | |
| 45 | 1069.307 | 13/7 |
| 46 | 1093.069 | |
| 47 | 1116.832 | |
| 48 | 1140.594 | 29/15 |
| 49 | 1164.356 | 45/23 |
| 50 | 1188.119 | |
| 51 | 1211.881 | |
| 52 | 1235.644 | |
| 53 | 1259.406 | |
| 54 | 1283.168 | 21/10 |
| 55 | 1306.931 | |
| 56 | 1330.693 | 41/19 |
| 57 | 1354.455 | |
| 58 | 1378.218 | |
| 59 | 1401.98 | |
| 60 | 1425.743 | 41/18 |
| 61 | 1449.505 | 30/13 |
| 62 | 1473.267 | |
| 63 | 1497.03 | |
| 64 | 1520.792 | |
| 65 | 1544.554 | |
| 66 | 1568.317 | |
| 67 | 1592.079 | |
| 68 | 1615.842 | |
| 69 | 1639.604 | |
| 70 | 1663.366 | 34/13 |
| 71 | 1687.129 | 45/17 |
| 72 | 1710.891 | |
| 73 | 1734.653 | 30/11 |
| 74 | 1758.416 | |
| 75 | 1782.178 | |
| 76 | 1805.941 | |
| 77 | 1829.703 | |
| 78 | 1853.465 | |
| 79 | 1877.228 | |
| 80 | 1900.99 | 3/1 |
| 81 | 1924.752 | |
| 82 | 1948.515 | |
| 83 | 1972.277 | |
| 84 | 1996.04 | 19/6 |
| 85 | 2019.802 | |
| 86 | 2043.564 | |
| 87 | 2067.327 | 33/10 |
| 88 | 2091.089 | |
| 89 | 2114.851 | |
| 90 | 2138.614 | |
| 91 | 2162.376 | |
| 92 | 2186.139 | |
| 93 | 2209.901 | |
| 94 | 2233.663 | |
| 95 | 2257.426 | |
| 96 | 2281.188 | |
| 97 | 2304.95 | |
| 98 | 2328.713 | |
| 99 | 2352.475 | 35/9 |
| 100 | 2376.238 | |
| 101 | 2400 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +11.9 | -1.0 | +0.0 | -6.1 | +10.9 | +5.4 | +11.9 | -1.9 | +5.8 | +7.1 | -1.0 |
| Relative (%) | +50.0 | -4.1 | +0.0 | -25.7 | +45.9 | +22.9 | +50.0 | -8.1 | +24.3 | +29.9 | -4.1 | |
| Steps (reduced) |
51 (51) |
80 (80) |
101 (0) |
117 (16) |
131 (30) |
142 (41) |
152 (51) |
160 (59) |
168 (67) |
175 (74) |
181 (80) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +3.0 | -6.4 | -7.1 | +0.0 | -9.9 | +10.0 | +11.4 | -6.1 | +4.5 | -4.8 | -10.5 |
| Relative (%) | +12.8 | -27.1 | -29.8 | +0.0 | -41.7 | +41.9 | +48.0 | -25.7 | +18.8 | -20.1 | -44.0 | |
| Steps (reduced) |
187 (86) |
192 (91) |
197 (96) |
202 (0) |
206 (4) |
211 (9) |
215 (13) |
218 (16) |
222 (20) |
225 (23) |
228 (26) | |