437edo
| ← 436edo | 437edo | 438edo → |
437 equal divisions of the octave (abbreviated 437edo or 437ed2), also called 437-tone equal temperament (437tet) or 437 equal temperament (437et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 437 equal parts of about 2.75 ¢ each. Each step represents a frequency ratio of 21/437, or the 437th root of 2.
Theory
437edo is consistent to the 7-odd-limit, but the errors of harmonics 3 and 5 are quite large, giving us the option of treating it as either a full 11-limit temperament, or a 2.9.15.21.13.17 subgroup temperament.
Using the patent val, the equal temperament tempers out 2401/2400 and 4096000/4084101 in the 7-limit; 3025/3024, 41503/41472, 16384/16335, and 151263/151250 in the 11-limit.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.02 | +0.87 | +0.51 | -0.71 | +0.63 | -0.25 | -0.85 | -0.61 | -0.95 | -1.22 | +0.56 |
| Relative (%) | +37.1 | +31.7 | +18.6 | -25.7 | +22.8 | -9.2 | -31.1 | -22.1 | -34.4 | -44.3 | +20.3 | |
| Steps (reduced) |
693 (256) |
1015 (141) |
1227 (353) |
1385 (74) |
1512 (201) |
1617 (306) |
1707 (396) |
1786 (38) |
1856 (108) |
1919 (171) |
1977 (229) | |
Subsets and supersets
Since 437 factors into 19 × 23, 437edo contains 19edo and 23edo as subsets. 874edo, which doubles it, gives a good correction to the harmonic 3.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.9 | [-1385 437⟩ | [⟨437 1385]] | 0.1114 | 0.1114 | 4.06 |