73709edo
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Prime factorization
73709 (prime)
Step size
0.0162802¢
Fifth
43117\73709 (701.955¢)
Semitones (A1:m2)
6983:5542 (113.7¢ : 90.23¢)
Consistency limit
11
Distinct consistency limit
11
| ← 73708edo | 73709edo | 73710edo → |
73709 equal divisions of the octave (abbreviated 73709edo or 73709ed2), also called 73709-tone equal temperament (73709tet) or 73709 equal temperament (73709et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 73709 equal parts of about 0.0163 ¢ each. Each step represents a frequency ratio of 21/73709, or the 73709th root of 2.
While it is distinctly consistent through the 11-odd-limit, its notability stems from the fact that it is a very strong 5-limit division, with lower 5-limit relative error than any smaller edo. However, 78005edo, only slightly larger, beats it. It tempers out [21 290 -207⟩ and [-573 237 85⟩ (quark) in the 5-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00000 | -0.00002 | +0.00003 | -0.00527 | -0.00399 | +0.00470 | +0.00328 | -0.00796 | -0.00372 | +0.00128 | +0.00235 |
| Relative (%) | +0.0 | -0.1 | +0.2 | -32.4 | -24.5 | +28.9 | +20.1 | -48.9 | -22.8 | +7.9 | +14.4 | |
| Steps (reduced) |
73709 (0) |
116826 (43117) |
171147 (23729) |
206927 (59509) |
254991 (33864) |
272756 (51629) |
301283 (6447) |
313110 (18274) |
333427 (38591) |
358077 (63241) |
365169 (70333) | |