443edo
| ← 442edo | 443edo | 444edo → |
443 equal divisions of the octave (abbreviated 443edo or 443ed2), also called 443-tone equal temperament (443tet) or 443 equal temperament (443et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 443 equal parts of about 2.709 ¢ each. Each step represents a frequency ratio of 21/443, or the 443rd root of 2.
Theory
443edo is inconsistent to the 5-odd-limit and the error of harmonic 5 is quite large. To start with, the patent val ⟨443 702 1029 1244 1533] as well as the 443cde val ⟨443 702 1028 1243 1532] are worth considering.
Using the patent val, the equal temperament tempers out 6144/6125, 32805/32768, and 67108864/66976875 in the 7-limit; 540/539, 5632/5625, 8019/8000, and 131072/130977 in the 11-limit. It supports hemischis, the 130 & 313 temperament.
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* | Cents* | Associated Ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 92\443 | 249.21 | 15/13 | Hemischis (443) |
* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct