937edo
| ← 936edo | 937edo | 938edo → |
937 equal divisions of the octave (abbreviated 937edo or 937ed2), also called 937-tone equal temperament (937tet) or 937 equal temperament (937et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 937 equal parts of about 1.28 ¢ each. Each step represents a frequency ratio of 21/937, or the 937th root of 2.
Theory
937edo is consistent to the 5-odd-limit, due to its harmonic 7 being about halfway its steps. It can be used in the 2.3.5.17.23.29.47 subgroup, tempering out 2176/2175, 3128/3125, 475136/475065, 16767/16762, 47180151/47104000 and 27103491/27025000. Using the 2.3.17.19.31.37 subgroup, it tempers out 2109/2108.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.141 | +0.453 | -0.630 | -0.281 | -0.624 | -0.400 | +0.312 | +0.061 | -0.395 | +0.510 | +0.541 |
| Relative (%) | -11.0 | +35.3 | -49.2 | -22.0 | -48.7 | -31.2 | +24.4 | +4.7 | -30.8 | +39.9 | +42.2 | |
| Steps (reduced) |
1485 (548) |
2176 (302) |
2630 (756) |
2970 (159) |
3241 (430) |
3467 (656) |
3661 (850) |
3830 (82) |
3980 (232) |
4116 (368) |
4239 (491) | |
Subsets and supersets
937edo is the 159th prime edo. 1874edo, which doubles it, gives a good correction to its harmonic 7.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-1485 937⟩ | [⟨937 1485]] | 0.0444 | 0.0444 | 3.47 |
| 2.3.5 | [-22 30 -11⟩, [85 -17 -25⟩ | [⟨937 1485 2176]] | −0.0354 | 0.1185 | 9.25 |