303edo
| ← 302edo | 303edo | 304edo → |
303 equal divisions of the octave (abbreviated 303edo or 303ed2), also called 303-tone equal temperament (303tet) or 303 equal temperament (303et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 303 equal parts of about 3.96 ¢ each. Each step represents a frequency ratio of 21/303, or the 303rd root of 2.
Theory
303edo is inconsistent to the 5-odd-limit with three mappings possible for the 7-limit:
- ⟨303 480 704 851] (patent val)
- ⟨303 480 703 851] (303c val)
- ⟨303 480 703 850] (303cd val)
The patent val tempers out 4294967296/4271484375 and 31381059609/30517578125 in the 5-limit; 3136/3125, 177147/175000 and 10616832/10504375 in the 7-limit, supporting gregorian leap day.
Using the 303c val, it tempers out 15625/15552 and [-83 48 3⟩ in the 5-limit; 225/224, 4375/4374 and [36 -7 5 -13⟩ in the 7-limit, supporting catakleismic
Using the 303cd val, it tempers out 15625/15552 and [-83 48 3⟩ in the 5-limit; 1029/1024 and 43046721/43025920 in the 7-limit, supporting tritikleismic.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -0.96 | +1.81 | +1.47 | -0.82 | -0.92 | +1.98 | -0.48 | +1.43 | +0.13 | -0.48 |
| Relative (%) | +0.0 | -24.4 | +45.6 | +37.1 | -20.8 | -23.3 | +49.9 | -12.2 | +36.1 | +3.2 | -12.1 | |
| Steps (reduced) |
303 (0) |
480 (177) |
704 (98) |
851 (245) |
1048 (139) |
1121 (212) |
1239 (27) |
1287 (75) |
1371 (159) |
1472 (260) |
1501 (289) | |
Subsets and supersets
303 factors into 3 × 101, with 3edo and 101edo as its subset edos. 606edo, which doubles it, gives a good correction to the harmonics 5 and 7.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-160 101⟩ | [⟨303 480]] | 0.3044 | 0.3045 | 7.69 |