469edo
| ← 468edo | 469edo | 470edo → |
469 equal divisions of the octave (abbreviated 469edo or 469ed2), also called 469-tone equal temperament (469tet) or 469 equal temperament (469et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 469 equal parts of about 2.56 ¢ each. Each step represents a frequency ratio of 21/469, or the 469th root of 2.
Theory
469et is only consistent to the 5-odd-limit and the error of the harmonic 3 is quite large. It can be considered for the 2.9.5.7.13.17 subgroup, tempering out 2601/2600, 7616/7605, 5832/5831, 60112/60025 and 265625/264992. It supports gravity and french decimal.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.89 | +0.04 | +0.90 | +0.78 | -1.21 | +1.26 | -0.85 | -0.05 | -0.71 | +0.01 | +1.15 |
| Relative (%) | -34.7 | +1.6 | +35.1 | +30.5 | -47.3 | +49.4 | -33.2 | -2.0 | -27.8 | +0.3 | +44.9 | |
| Steps (reduced) |
743 (274) |
1089 (151) |
1317 (379) |
1487 (80) |
1622 (215) |
1736 (329) |
1832 (425) |
1917 (41) |
1992 (116) |
2060 (184) |
2122 (246) | |
Subsets and supersets
Since 469 factors into 7 × 67, 469edo has 7edo and 67edo as its subset edos. 938edo, which doubles it, gives a good correction to the harmonics 3 and 5.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.9 | [1487 -469⟩ | [⟨469 1487]] | -0.1232 | 0.1232 | 4.82 |
| 2.9.5 | [38 -1 -15⟩, [13 -29 34⟩ | [⟨469 1487 1089]] | -0.0879 | 0.1122 | 4.39 |