684edo: Difference between revisions

Subsets and supersets
m Theory: link
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== Theory ==
== Theory ==
684edo divides the steps of [[171edo]] into four. It is [[consistent]] to the 17-odd-limit, tempering out [[2401/2400]], [[3025/3024]], [[4225/4224]], [[4375/4374]], and [[32805/32768]] in the 13-limit; [[1089/1088]], [[1225/1224]], [[1701/1700]], [[2025/2023]], 2058/2057, 2500/2499, 8624/8619, and 14875/14872 in the 17-limit.
684edo divides the steps of [[171edo]] into four. It is [[consistent]] to the 17-odd-limit, tempering out [[2401/2400]], [[3025/3024]], [[4225/4224]], [[4375/4374]], and [[32805/32768]] in the 13-limit; [[1089/1088]], [[1225/1224]], [[1701/1700]], [[2025/2023]], [[2058/2057]], [[2500/2499]], 8624/8619, and 14875/14872 in the 17-limit.


=== Prime harmonics ===
=== Prime harmonics ===
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=== Subsets and supersets ===
=== Subsets and supersets ===
Since 684 factors as 2<sup>2</sup> × 3<sup>2</sup> × 19, 684edo has subset edos {{EDOs| 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, and 342 }}.  
Since 684 factors as 2<sup>2</sup> × 3<sup>2</sup> × 19, 684edo has subset edos {{EDOs| 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, and 342 }}.


== Regular temperament properties ==
== Regular temperament properties ==