2897edo
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Prime factorization
2897 (prime)
Step size
0.414222¢
Fifth
1695\2897 (702.106¢)
Semitones (A1:m2)
277:216 (114.7¢ : 89.47¢)
Dual sharp fifth
1695\2897 (702.106¢)
Dual flat fifth
1694\2897 (701.691¢)
Dual major 2nd
492\2897 (203.797¢)
Consistency limit
7
Distinct consistency limit
7
| ← 2896edo | 2897edo | 2898edo → |
2897 equal divisions of the octave (abbreviated 2897edo or 2897ed2), also called 2897-tone equal temperament (2897tet) or 2897 equal temperament (2897et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2897 equal parts of about 0.414 ¢ each. Each step represents a frequency ratio of 21/2897, or the 2897th root of 2.
Theory
Although 2897edo is a dual-fifth system which only has a consistency limit of 7, one of its multiples, 31867edo, is not only a denominator in the series of convergents for log23, but is also consistent to the 21-odd-limit.
Prime harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.151 | +0.155 | +0.038 | -0.113 | +0.011 | -0.072 | -0.109 | -0.157 | -0.102 | +0.189 | +0.100 |
| Relative (%) | +36.4 | +37.4 | +9.3 | -27.3 | +2.7 | -17.4 | -26.2 | -38.0 | -24.6 | +45.6 | +24.1 | |
| Steps (reduced) |
4592 (1695) |
6727 (933) |
8133 (2339) |
9183 (492) |
10022 (1331) |
10720 (2029) |
11318 (2627) |
11841 (253) |
12306 (718) |
12725 (1137) |
13105 (1517) | |
|
Todo: explain its xenharmonic value |