226edo
Theory
226et tempers out 2029/2024 in the 7-limit; 243/242 and 117440512/117406179 in the 11-limit; as well as 364/363 and 729/728, in the 13-limit.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.07 | +1.30 | -2.45 | -2.14 | +0.89 | -1.59 | +0.23 | +1.24 | -0.17 | +1.79 | -1.73 |
| Relative (%) | -20.2 | +24.4 | -46.2 | -40.3 | +16.8 | -29.9 | +4.3 | +23.3 | -3.2 | +33.6 | -32.5 | |
| Steps (reduced) |
358 (132) |
525 (73) |
634 (182) |
716 (38) |
782 (104) |
836 (158) |
883 (205) |
924 (20) |
960 (56) |
993 (89) |
1022 (118) | |
Subsets and supersets
226 factors into 2 × 113, with 2edo and 113edo as its subset edos. 904edo, which quadruples it, gives a good correction to the harmonic 7.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-179 113⟩ | ⟨226 358] | 0.3376 | 0.3377 | 6.36 |
| 2.3.5 | [17 1 -8⟩, [-32 29 -6⟩ | 0.0386 | 0.5044 | 9.50 | |
Rank-2 temperaments
| Periods per 8ve |
Generator (reduced) |
Cents (reduced) |
Associated ratio |
Temperaments |
|---|---|---|---|---|
| 1 | 73\226 | 387.61 | 5/4 | Würschmidt |
| 2 | 23\226 | 122.12 | 15/14 | Lagaca |