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 (%) | +0.0 | -19.9 | -10.4 | -12.8 | -9.2 | -13.8 | +5.5 | -25.0 | -42.0 | -21.8 | +22.1 | |
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.