249edo
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Prime factorization
3 × 83
Step size
4.81928¢
Fifth
146\249 (703.614¢)
Semitones (A1:m2)
26:17 (125.3¢ : 81.93¢)
Dual sharp fifth
146\249 (703.614¢)
Dual flat fifth
145\249 (698.795¢)
Dual major 2nd
42\249 (202.41¢) (→14\83)
Consistency limit
3
Distinct consistency limit
3
| ← 248edo | 249edo | 250edo → |
249 equal divisions of the octave (abbreviated 249edo or 249ed2), also called 249-tone equal temperament (249tet) or 249 equal temperament (249et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 249 equal parts of about 4.82 ¢ each. Each step represents a frequency ratio of 21/249, or the 249th root of 2.
249edo is inconsistent in the 5-odd-limit and there are a number of mappings to be considered, in particular, a sharp tending mapping for the 2.3.5.7.17.19 subgroup, and a flat-tending mapping for the 2.9.5.7.11.13 subgroup.
In the 249bcee val, it is a tuning for the diesic temperament.
It is part of the optimal ET sequence for the diesic and undecimal magic temperaments.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.66 | -0.77 | -0.15 | -1.50 | -1.92 | -1.97 | +0.89 | +1.07 | +1.28 | +1.51 | -1.77 |
| Relative (%) | +34.4 | -16.0 | -3.1 | -31.1 | -39.8 | -40.9 | +18.4 | +22.2 | +26.6 | +31.3 | -36.7 | |
| Steps (reduced) |
395 (146) |
578 (80) |
699 (201) |
789 (42) |
861 (114) |
921 (174) |
973 (226) |
1018 (22) |
1058 (62) |
1094 (98) |
1126 (130) | |