2029edo
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Prime factorization
2029 (prime)
Step size
0.591424¢
Fifth
1187\2029 (702.021¢)
Semitones (A1:m2)
193:152 (114.1¢ : 89.9¢)
Consistency limit
15
Distinct consistency limit
15
| ← 2028edo | 2029edo | 2030edo → |
2029 equal divisions of the octave (abbreviated 2029edo or 2029ed2), also called 2029-tone equal temperament (2029tet) or 2029 equal temperament (2029et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2029 equal parts of about 0.591 ¢ each. Each step represents a frequency ratio of 21/2029, or the 2029th root of 2.
2029edo is consistent in the 15-odd-limit and it is also a good 23-limit system (particularly a no-17s 23-limit system), with all prime harmonics from 3 through 23 tuned flat.
In the 29-limit, despite inconsistency, it does provide a strong tuning for the rank-9 bronxismic temperament, tempering out 10472/10469.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.066 | -0.114 | -0.073 | -0.110 | -0.114 | -0.273 | -0.027 | -0.182 | +0.093 | -0.038 |
| Relative (%) | +0.0 | +11.1 | -19.2 | -12.3 | -18.7 | -19.2 | -46.2 | -4.5 | -30.7 | +15.7 | -6.4 | |
| Steps (reduced) |
2029 (0) |
3216 (1187) |
4711 (653) |
5696 (1638) |
7019 (932) |
7508 (1421) |
8293 (177) |
8619 (503) |
9178 (1062) |
9857 (1741) |
10052 (1936) | |