28ed4/3
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Prime factorization
22 × 7
Step size
17.7873¢
Octave
67\28ed4/3 (1191.75¢)
Twelfth
107\28ed4/3 (1903.24¢)
(semiconvergent)
Consistency limit
2
Distinct consistency limit
2
| ← 27ed4/3 | 28ed4/3 | 29ed4/3 → |
(semiconvergent)
28ed4/3 can be thought of as a 2.3.7.11 subgroup analogue to 20edf or Carlos Gamma. It very closely approximates the intervals of 8/7 (at 13 steps) and 7/6 (at 15 steps), along with 11/8 (at 31 steps); these approximations are related to the temperament in this subgroup tempering out 117649/117612 and 67110351/67108864, which is the subgroup restriction of keenanose. This tuning is close to every other step of 135edo or to 107edt.
Intervals
These are the intervals up to a perfect fourth up.
| Degrees | 2.3.7.11.97 subgroup approximation | Cents |
|---|---|---|
| 1 | 99/98, 98/97, 97/96 | 17.8 |
| 2 | 49/48, 99/97 | 35.6 |
| 3 | 33/32 | 53.4 |
| 4 | 1067/1024, 1617/1552 | 71.1 |
| 5 | 539/512 | 88.9 |
| 6 | 1089/1024 | 106.7 |
| 7 | 8192/7623 | 124.5 |
| 8 | 4096/3773 | 142.3 |
| 9 | 3584/3267 | 160.1 |
| 10 | 256/231 | 177.9 |
| 11 | 384/343, 776/693 | 195.7 |
| 12 | 112/99, 388/343, 768/679 | 213.4 |
| 13 | 8/7 | 231.2 |
| 14 | 97/84, 112/97, 343/297, 396/343 | 249.0 |
| 15 | 7/6 | 266.8 |
| 16 | 33/28 | 284.6 |
| 17 | 231/194, 343/288 | 302.4 |
| 18 | 77/64 | 320.2 |
| 19 | 1089/896 | 338.0 |
| 20 | 3773/3072 | 355.7 |
| 21 | 2541/2048 | 373.5 |
| 22 | 4096/3267 | 391.3 |
| 23 | 2048/1617 | 409.1 |
| 24 | 3072/2401 | 426.9 |
| 25 | 128/99 | 444.7 |
| 26 | 64/49, 388/297 | 462.5 |
| 27 | 128/97, 194/147, 392/297 | 480.3 |
| 28 | 4/3 | 498.0 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -8.25 | +1.29 | +1.29 | +6.30 | -6.96 | -7.02 | -6.96 | +2.58 | -1.95 | -6.87 | +2.58 |
| Relative (%) | -46.4 | +7.2 | +7.2 | +35.4 | -39.1 | -39.5 | -39.1 | +14.5 | -11.0 | -38.6 | +14.5 | |
| Steps (reduced) |
67 (11) |
107 (23) |
135 (23) |
157 (17) |
174 (6) |
189 (21) |
202 (6) |
214 (18) |
224 (0) |
233 (9) |
242 (18) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +6.30 | +2.52 | +7.58 | +2.58 | +4.35 | -5.67 | +7.45 | +7.58 | -5.73 | +2.67 | -3.14 |
| Relative (%) | +35.4 | +14.1 | +42.6 | +14.5 | +24.4 | -31.9 | +41.9 | +42.6 | -32.2 | +15.0 | -17.7 | |
| Steps (reduced) |
250 (26) |
257 (5) |
264 (12) |
270 (18) |
276 (24) |
281 (1) |
287 (7) |
292 (12) |
296 (16) |
301 (21) |
305 (25) | |
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