834edo
| ← 833edo | 834edo | 835edo → |
834 equal divisions of the octave (abbreviated 834edo or 834ed2), also called 834-tone equal temperament (834tet) or 834 equal temperament (834et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 834 equal parts of about 1.44 ¢ each. Each step represents a frequency ratio of 21/834, or the 834th root of 2.
Theory
834edo is enfactored in the 3-limit with the same tuning as 417edo and is inconsistent to the 5-odd-limit, with three mappings possible for the 7-limit:
- ⟨834 1322 1936 2341] (patent val),
- ⟨834 1322 1937 2341] (834c),
- ⟨834 1322 1937 2342] (834cd).
Using the patent val, it is enfactored in the 5-limit, tempering out 1600000/1594323 and [-71 -5 34⟩ in the 5-limit. It further tempers out 2401/2400, 4802000/4782969 and [-28 -1 20 -6⟩ in the 7-limit.
Using the 834c val, it tempers out [40 7 -22⟩ and [-31 43 -16⟩ in the 5-limit; 823543/820125, 1959552/1953125 and 1640558367/1638400000 in the 7-limit.
Using the 834cd val, it tempers out [40 7 -22⟩ and [-31 43 -16⟩ in the 5-limit; 250047/250000, 283435200/282475249 and 102760448/102515625 in the 7-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.203 | -0.702 | -0.481 | -0.239 | -0.240 | +0.081 | +0.329 | +0.503 | +0.639 | +0.288 |
| Relative (%) | +0.0 | +14.1 | -48.8 | -33.4 | -16.6 | -16.7 | +5.6 | +22.8 | +34.9 | +44.4 | +20.0 | |
| Steps (reduced) |
834 (0) |
1322 (488) |
1936 (268) |
2341 (673) |
2885 (383) |
3086 (584) |
3409 (73) |
3543 (207) |
3773 (437) |
4052 (716) |
4132 (796) | |
Subsets and supersets
Since 834 factors into 2 × 3 × 139, 834edo has subset edos 2, 3, 6, 139, 278, and 417. 1668edo, which doubles it, gives a good correction to the harmonic 5.
Music
- Lullaby For A Dead Planet (2024)