443edo
Jump to navigation
Jump to search
Prime factorization
443 (prime)
Step size
2.7088¢
Fifth
259\443 (701.58¢)
Semitones (A1:m2)
41:34 (111.1¢ : 92.1¢)
Consistency limit
3
Distinct consistency limit
3
| ← 442edo | 443edo | 444edo → |
443 equal divisions of the octave (443edo), or 443-tone equal temperament (443tet), 443 equal temperament (443et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 443 equal parts of about 2.71 ¢ each.
Theory
443et tempers out 67108864/66976875, 6144/6125 and 32805/32768 in the 7-limit; 806736/805255, 35156250/35153041, 759375/758912, 131072/130977, 540/539, 184549376/184528125, 5632/5625, 8019/8000, 160083/160000, 391314/390625, 202397184/201768035, 3294225/3294172 and 20614528/20588575 in the 11-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.00 | -0.37 | +1.05 | +0.93 | +1.28 | -0.80 | +0.69 | +0.46 | +0.17 | -0.23 | +0.79 |
| relative (%) | +0 | -14 | +39 | +34 | +47 | -29 | +25 | +17 | +6 | -9 | +29 | |
| Steps (reduced) |
443 (0) |
702 (259) |
1029 (143) |
1244 (358) |
1533 (204) |
1639 (310) |
1811 (39) |
1882 (110) |
2004 (232) |
2152 (380) |
2195 (423) | |
Subsets and supersets
443edo is the 86th prime edo. 886edo, which doubles it, gives a good correction until the 11-limit.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-702 443⟩ | ⟨443 702] | 0.1183 | 0.1183 | 4.37 |
Rank-2 temperaments
| Periods per 8ve |
Generator (reduced) |
Cents (reduced) |
Associated ratio |
Temperaments |
|---|---|---|---|---|
| 1 | 92\443 | 249.21 | 81/70 | Hemischis (7-limit) |