834edo: Difference between revisions

834edo is [[enfactoring|enfactored]] in the [[3-limit]] with the same tuning as [[417edo]] and is in[[consistent]] to the [[5-odd-limit]], with three mappings possible for the [[7-limit]]:

* {{val| 834 1322 1936 2341 }} ([[patent val]]),

* {{val| 834 1322 '''1937''' 2341 }} (834c),

* {{val| 834 1322 '''1937''' '''2342''' }} (834cd).

Using the patent val, it is enfactored in the 5-limit, tempering out [[1600000/1594323]] and {{monzo| -71 -5 34 }} in the 5-limit. It further tempers out [[2401/2400]], [[4802000/4782969]] and {{monzo| -28 -1 20 -6 }} in the 7-limit.

Using the 834c val, it tempers out {{monzo| 40 7 -22 }} and {{monzo| -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 {{monzo| 40 7 -22 }} and {{monzo| -31 43 -16 }} in the 5-limit; [[250047/250000]], 283435200/282475249 and 102760448/102515625 in the 7-limit.

Since 834 factors into 2 × 3 × 139, 834edo has subset edos {{EDOs| 2, 3, 6, 139, 278, and 417 }}. [[1668edo]], which doubles it, gives a good correction to the harmonic 5.

! rowspan="2" | [[Subgroup]]

! rowspan="2" | [[Comma list|Comma List]]

! rowspan="2" | [[Mapping]]

! rowspan="2" | Optimal<br>8ve Stretch (¢)

! colspan="2" | Tuning Error

! [[TE error|Absolute]] (¢)

! [[TE simple badness|Relative]] (%)