# 834edo

 ← 833edo 834edo 835edo →
Prime factorization 2 × 3 × 139
Step size 1.43885¢
Fifth 488\834 (702.158¢) (→244\417)
Semitones (A1:m2) 80:62 (115.1¢ : 89.21¢)
Consistency limit 3
Distinct consistency limit 3

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

Approximation of prime harmonics in 834edo
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.

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