55ed7/3
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Prime factorization
5 × 11
Step size
26.6704¢
Octave
45\55ed7/3 (1200.17¢) (→9\11ed7/3)
Twelfth
71\55ed7/3 (1893.6¢)
Consistency limit
8
Distinct consistency limit
5
 |
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| ← 54ed7/3 | 55ed7/3 | 56ed7/3 → |
55 equal divisions of 7/3 (abbreviated 55ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 55 equal parts of about 26.7 ¢ each. Each step represents a frequency ratio of (7/3)1/55, or the 55th root of 7/3.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 26.67 | |
| 2 | 53.341 | 32/31, 33/32 |
| 3 | 80.011 | 21/20, 23/22 |
| 4 | 106.682 | 17/16, 33/31 |
| 5 | 133.352 | 27/25 |
| 6 | 160.022 | |
| 7 | 186.693 | 10/9 |
| 8 | 213.363 | |
| 9 | 240.033 | |
| 10 | 266.704 | 7/6 |
| 11 | 293.374 | 19/16 |
| 12 | 320.045 | 6/5 |
| 13 | 346.715 | |
| 14 | 373.385 | 26/21 |
| 15 | 400.056 | 24/19, 29/23 |
| 16 | 426.726 | |
| 17 | 453.396 | 13/10 |
| 18 | 480.067 | 29/22 |
| 19 | 506.737 | |
| 20 | 533.408 | 19/14 |
| 21 | 560.078 | 18/13 |
| 22 | 586.748 | 7/5 |
| 23 | 613.419 | 10/7 |
| 24 | 640.089 | 13/9 |
| 25 | 666.76 | 28/19 |
| 26 | 693.43 | |
| 27 | 720.1 | |
| 28 | 746.771 | 20/13 |
| 29 | 773.441 | |
| 30 | 800.111 | 19/12 |
| 31 | 826.782 | 21/13 |
| 32 | 853.452 | |
| 33 | 880.123 | 5/3 |
| 34 | 906.793 | 32/19 |
| 35 | 933.463 | 12/7 |
| 36 | 960.134 | 33/19 |
| 37 | 986.804 | |
| 38 | 1013.474 | 9/5 |
| 39 | 1040.145 | 31/17 |
| 40 | 1066.815 | 13/7 |
| 41 | 1093.486 | 32/17 |
| 42 | 1120.156 | |
| 43 | 1146.826 | 31/16, 33/17 |
| 44 | 1173.497 | |
| 45 | 1200.167 | 2/1 |
| 46 | 1226.837 | |
| 47 | 1253.508 | 33/16 |
| 48 | 1280.178 | 21/10, 23/11 |
| 49 | 1306.849 | 17/8 |
| 50 | 1333.519 | |
| 51 | 1360.189 | |
| 52 | 1386.86 | 20/9 |
| 53 | 1413.53 | |
| 54 | 1440.201 | |
| 55 | 1466.871 | 7/3 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.2 | -8.4 | +0.3 | -12.6 | -8.2 | -8.4 | +0.5 | +10.0 | -12.4 | +9.3 | -8.0 |
| Relative (%) | +0.6 | -31.3 | +1.3 | -47.2 | -30.7 | -31.3 | +1.9 | +37.3 | -46.6 | +34.7 | -30.1 | |
| Steps (reduced) |
45 (45) |
71 (16) |
90 (35) |
104 (49) |
116 (6) |
126 (16) |
135 (25) |
143 (33) |
149 (39) |
156 (46) |
161 (51) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -13.2 | -8.2 | +5.7 | +0.7 | +2.4 | +10.1 | -3.5 | -12.3 | +10.0 | +9.4 | +12.5 |
| Relative (%) | -49.7 | -30.7 | +21.4 | +2.5 | +9.0 | +38.0 | -13.0 | -46.0 | +37.3 | +35.4 | +46.8 | |
| Steps (reduced) |
166 (1) |
171 (6) |
176 (11) |
180 (15) |
184 (19) |
188 (23) |
191 (26) |
194 (29) |
198 (33) |
201 (36) |
204 (39) | |