834edo

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← 833edo834edo835edo →
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 834-tone equal temperament (834tet), 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 of 834edo 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 +14 -49 -33 -17 -17 +6 +23 +35 +44 +20
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

JUMBLE