54ed7/3
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Prime factorization
2 × 33
Step size
27.1643¢
Octave
44\54ed7/3 (1195.23¢) (→22\27ed7/3)
Twelfth
70\54ed7/3 (1901.5¢) (→35\27ed7/3)
Consistency limit
4
Distinct consistency limit
4
 |
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| ← 53ed7/3 | 54ed7/3 | 55ed7/3 → |
54 equal divisions of 7/3 (abbreviated 54ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 54 equal parts of about 27.2 ¢ each. Each step represents a frequency ratio of (7/3)1/54, or the 54th root of 7/3.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 27.2 | |
| 2 | 54.3 | 30/29, 31/30 |
| 3 | 81.5 | 21/20, 22/21, 23/22 |
| 4 | 108.7 | 33/31 |
| 5 | 135.8 | 13/12 |
| 6 | 163 | 11/10 |
| 7 | 190.1 | 19/17 |
| 8 | 217.3 | 17/15 |
| 9 | 244.5 | 23/20 |
| 10 | 271.6 | 7/6 |
| 11 | 298.8 | |
| 12 | 326 | 23/19 |
| 13 | 353.1 | 27/22 |
| 14 | 380.3 | |
| 15 | 407.5 | 19/15 |
| 16 | 434.6 | 9/7 |
| 17 | 461.8 | 30/23 |
| 18 | 489 | |
| 19 | 516.1 | 27/20, 31/23 |
| 20 | 543.3 | |
| 21 | 570.4 | |
| 22 | 597.6 | 31/22 |
| 23 | 624.8 | 33/23 |
| 24 | 651.9 | |
| 25 | 679.1 | 31/21 |
| 26 | 706.3 | 3/2 |
| 27 | 733.4 | 29/19 |
| 28 | 760.6 | 14/9, 31/20 |
| 29 | 787.8 | 30/19 |
| 30 | 814.9 | |
| 31 | 842.1 | 13/8 |
| 32 | 869.3 | 33/20 |
| 33 | 896.4 | |
| 34 | 923.6 | 17/10, 29/17 |
| 35 | 950.7 | 19/11, 33/19 |
| 36 | 977.9 | |
| 37 | 1005.1 | |
| 38 | 1032.2 | 20/11 |
| 39 | 1059.4 | 24/13 |
| 40 | 1086.6 | |
| 41 | 1113.7 | 19/10 |
| 42 | 1140.9 | 27/14, 29/15 |
| 43 | 1168.1 | |
| 44 | 1195.2 | 2/1 |
| 45 | 1222.4 | |
| 46 | 1249.6 | |
| 47 | 1276.7 | 23/11 |
| 48 | 1303.9 | |
| 49 | 1331 | 28/13 |
| 50 | 1358.2 | |
| 51 | 1385.4 | 20/9 |
| 52 | 1412.5 | |
| 53 | 1439.7 | 23/10 |
| 54 | 1466.9 | 7/3 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -4.8 | -0.5 | -9.5 | +11.6 | -5.2 | -0.5 | +12.8 | -0.9 | +6.8 | +4.8 | -10.0 |
| Relative (%) | -17.6 | -1.7 | -35.1 | +42.7 | -19.2 | -1.7 | +47.3 | -3.4 | +25.2 | +17.7 | -36.8 | |
| Steps (reduced) |
44 (44) |
70 (16) |
88 (34) |
103 (49) |
114 (6) |
124 (16) |
133 (25) |
140 (32) |
147 (39) |
153 (45) |
158 (50) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -12.8 | -5.2 | +11.2 | +8.1 | +11.8 | -5.7 | +9.4 | +2.1 | -0.9 | +0.0 | +4.6 |
| Relative (%) | -46.9 | -19.2 | +41.1 | +29.7 | +43.4 | -20.9 | +34.5 | +7.6 | -3.4 | +0.2 | +16.9 | |
| Steps (reduced) |
163 (1) |
168 (6) |
173 (11) |
177 (15) |
181 (19) |
184 (22) |
188 (26) |
191 (29) |
194 (32) |
197 (35) |
200 (38) | |