328edo
| ← 327edo | 328edo | 329edo → |
Theory
328edo is enfactored in the 5-limit, with the same tuning as 164edo. It tempers out 2401/2400, 3136/3125, and 6144/6125 in the 7-limit, 9801/9800, 16384/16335 and 19712/19683 in the 11-limit, 676/675, 1001/1000, 1716/1715 and 2080/2079 in the 13-limit, 936/935, 1156/1155 and 2601/2600 in the 17-limit, so that it supports würschmidt and hemiwürschmidt, and provides the optimal patent val for 7-limit hemiwürschmidt, 11- and 13-limit semihemiwür, and 13-limit semiporwell.
Prime harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.48 | +1.49 | +0.69 | +0.97 | +1.12 | +0.94 | -1.68 | +1.14 | -1.17 | +1.17 | +0.99 |
| Relative (%) | +13.2 | +40.8 | +18.8 | +26.5 | +30.6 | +25.6 | -46.0 | +31.2 | -32.0 | +32.0 | +27.2 | |
| Steps (reduced) |
520 (192) |
762 (106) |
921 (265) |
1040 (56) |
1135 (151) |
1214 (230) |
1281 (297) |
1341 (29) |
1393 (81) |
1441 (129) |
1484 (172) | |
Divisors
Since 328 factors into 23 × 41, it has subset edos 2, 4, 8, 41, 82, and 164.
Regular temperament properties
| Subgroup | Comma list | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3.5.7 | 2401/2400, 3136/3125, 589824/588245 | [⟨328 520 762 921]] | -0.298 | 0.229 | 6.27 |
| 2.3.5.7.11 | 2401/2400, 3136/3125, 9801/9800, 19712/19683 | [⟨328 520 762 921 1135]] | -0.303 | 0.205 | 5.61 |
| 2.3.5.7.11.13 | 676/675, 1001/1000, 1716/1715, 3136/3125, 10648/10647 | [⟨328 520 762 921 1135 1214]] | -0.295 | 0.188 | 5.15 |
| 2.3.5.7.11.13.17 | 676/675, 936/935, 1001/1000, 1156/1155, 1716/1715, 3136/3125 | [⟨328 520 762 921 1135 1214 1341]] | -0.293 | 0.174 | 4.77 |
Rank-2 temperaments
Note: 5-limit temperaments supported by 164et are not listed.
| Periods per 8ve |
Generator (Reduced) |
Cents (Reduced) |
Associated Ratio |
Temperaments |
|---|---|---|---|---|
| 1 | 53\328 | 193.90 | 28/25 | Hemiwürschmidt |
| 1 | 117\328 | 428.05 | 2800/2187 | Osiris |
| 2 | 17\328 | 62.20 | 28/27 | Eagle |
| 2 | 111\328 (53\328) |
406.10 (193.90) |
495/392 (28/25) |
Semihemiwürschmidt |
| 8 | 136\328 (13\328) |
497.56 (47.56) |
4/3 (36/35) |
Twilight |
| 41 | 49\328 (1\328) |
179.27 (3.66) |
567/512 (352/351) |
Hemicountercomp |