61ed4
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Prime factorization
61 (prime)
Step size
39.3443¢
Octave
31\61ed4 (1219.67¢)
Twelfth
48\61ed4 (1888.52¢)
Consistency limit
1
Distinct consistency limit
1
 |
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| ← 59ed4 | 61ed4 | 63ed4 → |
61 equal divisions of the 4th harmonic (abbreviated 61ed4) is a nonoctave tuning system that divides the interval of 4/1 into 61 equal parts of about 39.3 ¢ each. Each step represents a frequency ratio of 41/61, or the 61st root of 4.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 39.344 | |
| 2 | 78.689 | |
| 3 | 118.033 | 31/29 |
| 4 | 157.377 | 23/21 |
| 5 | 196.721 | 19/17 |
| 6 | 236.066 | |
| 7 | 275.41 | |
| 8 | 314.754 | 6/5 |
| 9 | 354.098 | |
| 10 | 393.443 | |
| 11 | 432.787 | |
| 12 | 472.131 | 25/19 |
| 13 | 511.475 | 35/26 |
| 14 | 550.82 | |
| 15 | 590.164 | |
| 16 | 629.508 | |
| 17 | 668.852 | 25/17 |
| 18 | 708.197 | |
| 19 | 747.541 | |
| 20 | 786.885 | 11/7, 30/19 |
| 21 | 826.23 | 21/13, 29/18 |
| 22 | 865.574 | |
| 23 | 904.918 | |
| 24 | 944.262 | 19/11, 31/18 |
| 25 | 983.607 | 23/13, 30/17 |
| 26 | 1022.951 | |
| 27 | 1062.295 | |
| 28 | 1101.639 | |
| 29 | 1140.984 | 29/15 |
| 30 | 1180.328 | |
| 31 | 1219.672 | |
| 32 | 1259.016 | 31/15 |
| 33 | 1298.361 | |
| 34 | 1337.705 | 13/6 |
| 35 | 1377.049 | |
| 36 | 1416.393 | |
| 37 | 1455.738 | |
| 38 | 1495.082 | |
| 39 | 1534.426 | 17/7 |
| 40 | 1573.77 | |
| 41 | 1613.115 | 33/13 |
| 42 | 1652.459 | 13/5 |
| 43 | 1691.803 | |
| 44 | 1731.148 | 19/7 |
| 45 | 1770.492 | |
| 46 | 1809.836 | |
| 47 | 1849.18 | 35/12 |
| 48 | 1888.525 | |
| 49 | 1927.869 | |
| 50 | 1967.213 | |
| 51 | 2006.557 | 35/11 |
| 52 | 2045.902 | |
| 53 | 2085.246 | |
| 54 | 2124.59 | |
| 55 | 2163.934 | |
| 56 | 2203.279 | 25/7 |
| 57 | 2242.623 | |
| 58 | 2281.967 | |
| 59 | 2321.311 | |
| 60 | 2360.656 | |
| 61 | 2400 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +19.7 | -13.4 | +0.0 | +7.1 | +6.2 | +14.8 | +19.7 | +12.5 | -12.5 | +19.2 | -13.4 |
| Relative (%) | +50.0 | -34.1 | +0.0 | +18.1 | +15.9 | +37.6 | +50.0 | +31.7 | -31.9 | +48.7 | -34.1 | |
| Steps (reduced) |
31 (31) |
48 (48) |
61 (0) |
71 (10) |
79 (18) |
86 (25) |
92 (31) |
97 (36) |
101 (40) |
106 (45) |
109 (48) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +5.4 | -4.9 | -6.3 | +0.0 | +13.1 | -7.2 | +17.2 | +7.1 | +1.4 | -0.5 | +1.2 |
| Relative (%) | +13.7 | -12.4 | -16.0 | +0.0 | +33.2 | -18.3 | +43.8 | +18.1 | +3.4 | -1.3 | +3.1 | |
| Steps (reduced) |
113 (52) |
116 (55) |
119 (58) |
122 (0) |
125 (3) |
127 (5) |
130 (8) |
132 (10) |
134 (12) |
136 (14) |
138 (16) | |