77ed4
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Prime factorization
7 × 11
Step size
31.1688¢
Octave
39\77ed4 (1215.58¢)
Twelfth
61\77ed4 (1901.3¢)
Consistency limit
1
Distinct consistency limit
1
 |
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| ← 75ed4 | 77ed4 | 79ed4 → |
77 equal divisions of the 4th harmonic (abbreviated 77ed4) is a nonoctave tuning system that divides the interval of 4/1 into 77 equal parts of about 31.2 ¢ each. Each step represents a frequency ratio of 41/77, or the 77th root of 4.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 31.2 | |
| 2 | 62.3 | 27/26 |
| 3 | 93.5 | 19/18 |
| 4 | 124.7 | 29/27 |
| 5 | 155.8 | 23/21 |
| 6 | 187 | 29/26, 39/35 |
| 7 | 218.2 | 17/15 |
| 8 | 249.4 | 15/13 |
| 9 | 280.5 | 27/23 |
| 10 | 311.7 | |
| 11 | 342.9 | |
| 12 | 374 | |
| 13 | 405.2 | |
| 14 | 436.4 | 9/7 |
| 15 | 467.5 | 17/13 |
| 16 | 498.7 | |
| 17 | 529.9 | 19/14 |
| 18 | 561 | 29/21 |
| 19 | 592.2 | 31/22 |
| 20 | 623.4 | 33/23 |
| 21 | 654.5 | |
| 22 | 685.7 | |
| 23 | 716.9 | |
| 24 | 748.1 | |
| 25 | 779.2 | 11/7 |
| 26 | 810.4 | |
| 27 | 841.6 | |
| 28 | 872.7 | |
| 29 | 903.9 | |
| 30 | 935.1 | |
| 31 | 966.2 | |
| 32 | 997.4 | |
| 33 | 1028.6 | |
| 34 | 1059.7 | |
| 35 | 1090.9 | |
| 36 | 1122.1 | 21/11 |
| 37 | 1153.2 | 37/19 |
| 38 | 1184.4 | |
| 39 | 1215.6 | |
| 40 | 1246.8 | 37/18 |
| 41 | 1277.9 | 23/11 |
| 42 | 1309.1 | |
| 43 | 1340.3 | |
| 44 | 1371.4 | |
| 45 | 1402.6 | |
| 46 | 1433.8 | |
| 47 | 1464.9 | 7/3 |
| 48 | 1496.1 | |
| 49 | 1527.3 | |
| 50 | 1558.4 | |
| 51 | 1589.6 | |
| 52 | 1620.8 | |
| 53 | 1651.9 | 13/5 |
| 54 | 1683.1 | 37/14 |
| 55 | 1714.3 | 35/13 |
| 56 | 1745.5 | |
| 57 | 1776.6 | |
| 58 | 1807.8 | |
| 59 | 1839 | 26/9 |
| 60 | 1870.1 | |
| 61 | 1901.3 | 3/1 |
| 62 | 1932.5 | |
| 63 | 1963.6 | |
| 64 | 1994.8 | 19/6 |
| 65 | 2026 | 29/9 |
| 66 | 2057.1 | 23/7 |
| 67 | 2088.3 | |
| 68 | 2119.5 | 17/5 |
| 69 | 2150.6 | |
| 70 | 2181.8 | |
| 71 | 2213 | |
| 72 | 2244.2 | |
| 73 | 2275.3 | |
| 74 | 2306.5 | |
| 75 | 2337.7 | 27/7 |
| 76 | 2368.8 | |
| 77 | 2400 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +15.6 | -0.7 | +0.0 | -12.3 | +14.9 | -2.6 | +15.6 | -1.3 | +3.3 | -5.9 | -0.7 |
| Relative (%) | +50.0 | -2.1 | +0.0 | -39.4 | +47.9 | -8.3 | +50.0 | -4.2 | +10.6 | -18.8 | -2.1 | |
| Steps (reduced) |
39 (39) |
61 (61) |
77 (0) |
89 (12) |
100 (23) |
108 (31) |
116 (39) |
122 (45) |
128 (51) |
133 (56) |
138 (61) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -14.6 | +13.0 | -12.9 | +0.0 | -11.4 | +14.3 | +14.2 | -12.3 | -3.2 | +9.7 | -4.9 |
| Relative (%) | -46.7 | +41.7 | -41.5 | +0.0 | -36.7 | +45.8 | +45.5 | -39.4 | -10.4 | +31.2 | -15.7 | |
| Steps (reduced) |
142 (65) |
147 (70) |
150 (73) |
154 (0) |
157 (3) |
161 (7) |
164 (10) |
166 (12) |
169 (15) |
172 (18) |
174 (20) | |