2901edo
| ← 2900edo | 2901edo | 2902edo → |
2901 equal divisions of the octave (abbreviated 2901edo or 2901ed2), also called 2901-tone equal temperament (2901tet) or 2901 equal temperament (2901et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2901 equal parts of about 0.414 ¢ each. Each step represents a frequency ratio of 21/2901, or the 2901st root of 2.
Theory
2901edo is consistent in the 17-odd-limit and is otherwise an excellent 31-limit system, with only the pair {19/17, 34/19} being mapped inconsistently in the 31-odd-limit. It provides a good tuning for the jacobin temperament in the 13-limit, the rank-5 temperament tempering out 6656/6655. Alongside jacobin, it tunes the tridecimal quartismic temperament, which also tempers out 123201/123200. It also tunes the monzismic temperament.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.010 | +0.036 | -0.057 | +0.078 | +0.010 | +0.112 | -0.098 | +0.061 | -0.001 | -0.051 |
| Relative (%) | +0.0 | +2.4 | +8.7 | -13.7 | +18.9 | +2.4 | +27.0 | -23.8 | +14.7 | -0.3 | -12.3 | |
| Steps (reduced) |
2901 (0) |
4598 (1697) |
6736 (934) |
8144 (2342) |
10036 (1333) |
10735 (2032) |
11858 (254) |
12323 (719) |
13123 (1519) |
14093 (2489) |
14372 (2768) | |
Subsets and supersets
Since 2901 factors into 3 × 967, 2901edo contains 3edo and 967edo as subsets.
Music
- Demo (2024)