55ed4
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Prime factorization
5 × 11
Step size
43.6364¢
Octave
28\55ed4 (1221.82¢)
Twelfth
44\55ed4 (1920¢) (→4\5ed4)
Consistency limit
1
Distinct consistency limit
1
 |
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| ← 53ed4 | 55ed4 | 57ed4 → |
55 equal divisions of the 4th harmonic (abbreviated 55ed4) is a nonoctave tuning system that divides the interval of 4/1 into 55 equal parts of about 43.6 ¢ each. Each step represents a frequency ratio of 41/55, or the 55th root of 4.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 43.6 | |
| 2 | 87.3 | |
| 3 | 130.9 | 14/13 |
| 4 | 174.5 | 21/19 |
| 5 | 218.2 | 25/22 |
| 6 | 261.8 | 29/25 |
| 7 | 305.5 | 25/21 |
| 8 | 349.1 | |
| 9 | 392.7 | |
| 10 | 436.4 | |
| 11 | 480 | 25/19, 29/22, 33/25 |
| 12 | 523.6 | 23/17, 27/20 |
| 13 | 567.3 | |
| 14 | 610.9 | |
| 15 | 654.5 | 19/13 |
| 16 | 698.2 | 3/2 |
| 17 | 741.8 | |
| 18 | 785.5 | 11/7 |
| 19 | 829.1 | 21/13 |
| 20 | 872.7 | |
| 21 | 916.4 | |
| 22 | 960 | 33/19 |
| 23 | 1003.6 | 25/14 |
| 24 | 1047.3 | |
| 25 | 1090.9 | |
| 26 | 1134.5 | 25/13 |
| 27 | 1178.2 | |
| 28 | 1221.8 | |
| 29 | 1265.5 | 29/14 |
| 30 | 1309.1 | |
| 31 | 1352.7 | |
| 32 | 1396.4 | |
| 33 | 1440 | |
| 34 | 1483.6 | 33/14 |
| 35 | 1527.3 | |
| 36 | 1570.9 | |
| 37 | 1614.5 | 33/13 |
| 38 | 1658.2 | 13/5 |
| 39 | 1701.8 | |
| 40 | 1745.5 | |
| 41 | 1789.1 | 31/11 |
| 42 | 1832.7 | 26/9 |
| 43 | 1876.4 | |
| 44 | 1920 | |
| 45 | 1963.6 | 28/9 |
| 46 | 2007.3 | |
| 47 | 2050.9 | |
| 48 | 2094.5 | |
| 49 | 2138.2 | |
| 50 | 2181.8 | |
| 51 | 2225.5 | |
| 52 | 2269.1 | |
| 53 | 2312.7 | 19/5 |
| 54 | 2356.4 | |
| 55 | 2400 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +21.8 | +18.0 | +0.0 | +6.4 | -3.8 | -8.8 | +21.8 | -7.5 | -15.4 | -5.9 | +18.0 |
| Relative (%) | +50.0 | +41.4 | +0.0 | +14.7 | -8.6 | -20.2 | +50.0 | -17.3 | -35.3 | -13.4 | +41.4 | |
| Steps (reduced) |
28 (28) |
44 (44) |
55 (0) |
64 (9) |
71 (16) |
77 (22) |
83 (28) |
87 (32) |
91 (36) |
95 (40) |
99 (44) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +10.4 | +13.0 | -19.2 | +0.0 | -17.7 | +14.3 | +7.9 | +6.4 | +9.2 | +16.0 | -17.4 |
| Relative (%) | +23.8 | +29.8 | -43.9 | +0.0 | -40.5 | +32.7 | +18.2 | +14.7 | +21.1 | +36.6 | -39.8 | |
| Steps (reduced) |
102 (47) |
105 (50) |
107 (52) |
110 (0) |
112 (2) |
115 (5) |
117 (7) |
119 (9) |
121 (11) |
123 (13) |
124 (14) | |