2549edo
| ← 2548edo | 2549edo | 2550edo → |
2549 equal divisions of the octave (abbreviated 2549edo or 2549ed2), also called 2549-tone equal temperament (2549tet) or 2549 equal temperament (2549et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2549 equal parts of about 0.471 ¢ each. Each step represents a frequency ratio of 21/2549, or the 2549th root of 2.
Theory
2549edo is consistent to the 7-odd-limit, tempering out 43046721/43025920, [28 7 -12 -4⟩ and [-14 4 -10 11⟩. It is strong in the 2.3.7.11.17.19.29 subgroup, tempering out 5832/5831, 23409/23408, 69632/69629, 2910897/2910208, 19267919/19267584 and 424589/424536. Using the 2.3.7.11.17.19.41 subgroup, it tempers out 8569/8568.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.033 | +0.191 | +0.025 | -0.043 | -0.198 | +0.027 | +0.015 | +0.207 | +0.003 | -0.116 |
| Relative (%) | +0.0 | -6.9 | +40.5 | +5.2 | -9.1 | -42.1 | +5.7 | +3.3 | +44.1 | +0.6 | -24.6 | |
| Steps (reduced) |
2549 (0) |
4040 (1491) |
5919 (821) |
7156 (2058) |
8818 (1171) |
9432 (1785) |
10419 (223) |
10828 (632) |
11531 (1335) |
12383 (2187) |
12628 (2432) | |
Subsets and supersets
2549edo is the 373rd prime edo. 5098edo, which doubles it, gives a good correction to the harmonic 5.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-4040 2549⟩ | [⟨2549 4040]] | 0.0103 | 0.0103 | 2.19 |