27ed8/3
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27 equal divisions of 8/3 (abbreviated 27ed8/3) is a nonoctave tuning system that divides the interval of 8/3 into 27 equal parts of about 62.9 ¢ each. Each step represents a frequency ratio of (8/3)1/27, or the 27th root of 8/3.
Interval table
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 62.9 | 24/23, 25/24 |
| 2 | 125.8 | 14/13 |
| 3 | 188.7 | 10/9, 19/17 |
| 4 | 251.6 | 22/19, 23/20 |
| 5 | 314.5 | 6/5 |
| 6 | 377.3 | 5/4, 26/21 |
| 7 | 440.2 | 22/17 |
| 8 | 503.1 | 4/3 |
| 9 | 566 | 25/18 |
| 10 | 628.9 | 23/16 |
| 11 | 691.8 | 3/2 |
| 12 | 754.7 | 17/11 |
| 13 | 817.6 | 8/5 |
| 14 | 880.5 | 5/3 |
| 15 | 943.4 | 19/11 |
| 16 | 1006.2 | 9/5, 16/9 |
| 17 | 1069.1 | 13/7 |
| 18 | 1132 | 23/12 |
| 19 | 1194.9 | 2/1 |
| 20 | 1257.8 | |
| 21 | 1320.7 | |
| 22 | 1383.6 | 20/9 |
| 23 | 1446.5 | 23/10 |
| 24 | 1509.4 | 12/5 |
| 25 | 1572.3 | |
| 26 | 1635.2 | 23/9 |
| 27 | 1698 | 8/3 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -5.1 | -15.2 | -10.2 | -19.1 | -20.3 | +27.3 | -15.2 | -30.5 | -24.2 | -0.5 | -25.4 |
| Relative (%) | -8.1 | -24.2 | -16.2 | -30.4 | -32.3 | +43.4 | -24.2 | -48.5 | -38.5 | -0.9 | -40.4 | |
| Steps (reduced) |
19 (19) |
30 (3) |
38 (11) |
44 (17) |
49 (22) |
54 (0) |
57 (3) |
60 (6) |
63 (9) |
66 (12) |
68 (14) | |