56ed7/3
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Prime factorization
23 × 7
Step size
26.1941¢
Octave
46\56ed7/3 (1204.93¢) (→23\28ed7/3)
Twelfth
73\56ed7/3 (1912.17¢)
Consistency limit
4
Distinct consistency limit
4
 |
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| ← 55ed7/3 | 56ed7/3 | 57ed7/3 → |
56 equal divisions of 7/3 (abbreviated 56ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 56 equal parts of about 26.2 ¢ each. Each step represents a frequency ratio of (7/3)1/56, or the 56th root of 7/3.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 26.194 | |
| 2 | 52.388 | 31/30, 34/33 |
| 3 | 78.582 | 23/22 |
| 4 | 104.776 | 33/31 |
| 5 | 130.971 | 14/13 |
| 6 | 157.165 | 34/31 |
| 7 | 183.359 | |
| 8 | 209.553 | |
| 9 | 235.747 | 8/7 |
| 10 | 261.941 | |
| 11 | 288.135 | |
| 12 | 314.329 | |
| 13 | 340.524 | |
| 14 | 366.718 | 26/21 |
| 15 | 392.912 | |
| 16 | 419.106 | |
| 17 | 445.3 | 22/17 |
| 18 | 471.494 | 21/16 |
| 19 | 497.688 | 4/3 |
| 20 | 523.882 | 19/14, 23/17 |
| 21 | 550.077 | |
| 22 | 576.271 | |
| 23 | 602.465 | |
| 24 | 628.659 | 33/23 |
| 25 | 654.853 | 19/13 |
| 26 | 681.047 | 34/23 |
| 27 | 707.241 | |
| 28 | 733.435 | 29/19, 32/21 |
| 29 | 759.63 | 31/20 |
| 30 | 785.824 | |
| 31 | 812.018 | |
| 32 | 838.212 | 13/8 |
| 33 | 864.406 | 33/20 |
| 34 | 890.6 | |
| 35 | 916.794 | 17/10 |
| 36 | 942.988 | |
| 37 | 969.183 | 7/4 |
| 38 | 995.377 | 16/9 |
| 39 | 1021.571 | |
| 40 | 1047.765 | |
| 41 | 1073.959 | 13/7 |
| 42 | 1100.153 | |
| 43 | 1126.347 | |
| 44 | 1152.541 | 33/17 |
| 45 | 1178.736 | |
| 46 | 1204.93 | |
| 47 | 1231.124 | |
| 48 | 1257.318 | 29/14, 31/15 |
| 49 | 1283.512 | |
| 50 | 1309.706 | |
| 51 | 1335.9 | 13/6 |
| 52 | 1362.094 | 11/5 |
| 53 | 1388.289 | 29/13 |
| 54 | 1414.483 | 34/15 |
| 55 | 1440.677 | 23/10 |
| 56 | 1466.871 | 7/3 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +4.9 | +10.2 | +9.9 | -9.7 | -11.0 | +10.2 | -11.4 | -5.8 | -4.8 | -12.6 | -6.1 |
| Relative (%) | +18.8 | +39.0 | +37.6 | -37.2 | -42.2 | +39.0 | -43.5 | -22.0 | -18.4 | -48.3 | -23.4 | |
| Steps (reduced) |
46 (46) |
73 (17) |
92 (36) |
106 (50) |
118 (6) |
129 (17) |
137 (25) |
145 (33) |
152 (40) |
158 (46) |
164 (52) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +12.5 | -11.0 | +0.5 | -6.5 | -6.7 | -0.8 | +10.3 | +0.1 | -5.8 | -7.7 | -6.1 |
| Relative (%) | +47.6 | -42.2 | +1.8 | -24.7 | -25.4 | -3.2 | +39.5 | +0.5 | -22.0 | -29.5 | -23.3 | |
| Steps (reduced) |
170 (2) |
174 (6) |
179 (11) |
183 (15) |
187 (19) |
191 (23) |
195 (27) |
198 (30) |
201 (33) |
204 (36) |
207 (39) | |