28edf
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| ← 27edf | 28edf | 29edf → |
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).
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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