3498edo
| ← 3497edo | 3498edo | 3499edo → |
3498 equal divisions of the octave (abbreviated 3498edo or 3498ed2), also called 3498-tone equal temperament (3498tet) or 3498 equal temperament (3498et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 3498 equal parts of about 0.343 ¢ each. Each step represents a frequency ratio of 21/3498, or the 3498th root of 2.
3498edo is consistent in the 25-odd-limit, and it is a good 19-limit tuning. Except for harmonic 17, it is a mostly flat system. In the 7-limit, it is enfactored, with the same tuning as 1749edo, and corrects its mappings for 11 and 19.
3498edo notably contains 53edo, tempering out the Mercator's comma, and also 106edo and 159edo.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.000 | -0.068 | -0.036 | -0.044 | -0.031 | -0.047 | +0.019 | -0.086 | -0.144 | -0.075 | +0.076 |
| relative (%) | +0 | -20 | -10 | -13 | -9 | -14 | +5 | -25 | -42 | -22 | +22 | |
| Steps (reduced) |
3498 (0) |
5544 (2046) |
8122 (1126) |
9820 (2824) |
12101 (1607) |
12944 (2450) |
14298 (306) |
14859 (867) |
15823 (1831) |
16993 (3001) |
17330 (3338) | |
Subsets and supersets
Since 3498edo factors as 2 × 3 × 11 × 53, it has subset edos 1, 2, 3, 6, 11, 22, 33, 53, 66, 106, 159, 318, 583, 1166, 1749.