28edf
Division of the just perfect fifth into 28 equal parts (28EDF) is related to 48 edo, but with the 3/2 rather than the 2/1 being just. The octave is about 3.3514 cents stretched and the step size is about 25.0698 cents (corresponding to 47.8663 edo).
| ← 27edf | 28edf | 29edf → |
It is related to the regular temperament which tempers out |187 -159 28> in the 5-limit; 6656/6655, 256000/255879, and 38671875/38614472 in the 13-limit (2.3.5.11.13 subgroup), which is supported by 335, 383, 718, 1053, and 1101 EDOs.
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +3.4 | +3.4 | -3.6 | -9.5 | +10.3 | -3.2 | +8.7 | -8.3 | +11.9 | +11.7 | -3.5 |
| Relative (%) | +13.4 | +13.4 | -14.2 | -37.8 | +41.0 | -12.6 | +34.8 | -33.3 | +47.4 | +46.6 | -13.9 | |
| Steps (reduced) |
48 (20) |
76 (20) |
111 (27) |
134 (22) |
166 (26) |
177 (9) |
196 (0) |
203 (7) |
217 (21) |
233 (9) |
237 (13) | |
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 25.1 | |
| 2 | 50.1 | |
| 3 | 75.2 | 21/20, 23/22, 24/23, 26/25, 27/26 |
| 4 | 100.3 | 17/16, 18/17 |
| 5 | 125.3 | 14/13, 15/14 |
| 6 | 150.4 | 12/11 |
| 7 | 175.5 | 10/9, 11/10, 21/19 |
| 8 | 200.6 | 9/8 |
| 9 | 225.6 | 17/15 |
| 10 | 250.7 | 15/13, 23/20 |
| 11 | 275.8 | 20/17, 27/23 |
| 12 | 300.8 | 25/21 |
| 13 | 325.9 | 6/5 |
| 14 | 351 | 11/9, 27/22 |
| 15 | 376 | 5/4, 26/21 |
| 16 | 401.1 | 19/15 |
| 17 | 426.2 | 23/18 |
| 18 | 451.3 | 13/10, 22/17 |
| 19 | 476.3 | 25/19 |
| 20 | 501.4 | 4/3 |
| 21 | 526.5 | 15/11, 19/14, 23/17, 27/20 |
| 22 | 551.5 | 11/8, 26/19 |
| 23 | 576.6 | 7/5 |
| 24 | 601.7 | 17/12, 24/17 |
| 25 | 626.7 | 10/7, 13/9, 23/16 |
| 26 | 651.8 | 16/11, 19/13 |
| 27 | 676.9 | |
| 28 | 702 | 3/2 |
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