4380edo: Difference between revisions

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4380edo is consistent in the 31-odd-limit and ~~has~~ the lowest relative error in the 47-limit, being only beaten by ~~the~~ [[7361edo|7361o ~~val~~]].

4380edo is [[consistent]] in the [[31-odd-limit]] and holds the record of lowest [[Tenney–Euclidean temperament measures #TE simple badness|relative error]] in the [[47-limit]], being only beaten by [[7361edo|7361o-edo]]. It is closely related to [[2190edo]], inheriting the same excellent tuning in the 2.3.5.7.11.13.19.29 subgroup while improving the mapping for many other primes.

In light of having 60 as a divisor, 4380edo is a tuning for the [[neodymium]] temperament in the 17-limit. It is worth noting that 4380edo tempers out the [[magnetisma]] on its 43-limit patent val, and therefore tunes the extension [[neodymium magnet]].

Some of the simpler [[comma]]s [[tempering out|tempered out]] include [[31213/31212]] in the [[17-limit]], [[23409/23408]] in the [[19-limit]], [[10625/10625]] in the [[23-limit]], [[7425/7424]] in the [[29-limit]], and [[6138/6137]] in the [[31-limit]].

In light of having 60 as a divisor, 4380edo is a tuning for the [[neodymium]] temperament in the 17-limit. It is worth noting that 4380edo tempers out the [[magnetisma]] on its [[43-limit]] patent val, and therefore tunes the extension [[neodymium magnet]].

=== Prime harmonics ===

{{Harmonics in equal|4380|columns=9|start=10|collapsed=true|title=Approximation of prime harmonics in 4380edo (continued)}}

=== Subsets and supersets ===

4380edo has subset edos {{EDOs|1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 73, 146, 219, 292, 365, 438, 730, 876, 1095, 1460, 2190}}. One step of 4380edo is one sixth of a [[Woolhouse unit]] (1\730).

4380edo has subset edos {{EDOs| 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 73, 146, 219, 292, 365, 438, 730, 876, 1095, 1460, 2190 }}. One step of 4380edo is one sixth of a [[Woolhouse unit]] (1\730).

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 {{ED intro}}
-edo is consistent in the 31-odd-limit and has the lowest relative error in the 47-limit, being only beaten by the [[7361edo|7361o val]].
+edo is [[consistent]] in the [[31-odd-limit]] and holds the record of lowest [[Tenney–Euclidean temperament measures #TE simple badness|relative error]] in the [[47-limit]], being only beaten by [[7361edo|7361o-edo]]. It is closely related to [[2190edo]], inheriting the same excellent tuning in the 2.3.5.7.11.13.19.29 subgroup while improving the mapping for many other primes.
-In light of having 60 as a divisor, 4380edo is a tuning for the [[neodymium]] temperament in the 17-limit. It is worth noting that 4380edo tempers out the [[magnetisma]] on its 43-limit patent val, and therefore tunes the extension [[neodymium magnet]].
+Some of the simpler [[comma]]s [[tempering out|tempered out]] include [[31213/31212]] in the [[17-limit]], [[23409/23408]] in the [[19-limit]], [[10625/10625]] in the [[23-limit]], [[7425/7424]] in the [[29-limit]], and [[6138/6137]] in the [[31-limit]].
+In light of having 60 as a divisor, 4380edo is a tuning for the [[neodymium]] temperament in the 17-limit. It is worth noting that 4380edo tempers out the [[magnetisma]] on its [[43-limit]] patent val, and therefore tunes the extension [[neodymium magnet]].
 === Prime harmonics ===
-{{Harmonics in equal|4380}}
+{{Harmonics in equal|4380|columns=9}}
+{{Harmonics in equal|4380|columns=9|start=10|collapsed=true|title=Approximation of prime harmonics in 4380edo (continued)}}
 === Subsets and supersets ===
-edo has subset edos {{EDOs|1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 73, 146, 219, 292, 365, 438, 730, 876, 1095, 1460, 2190}}. One step of 4380edo is one sixth of a [[Woolhouse unit]] (1\730).
+edo has subset edos {{EDOs| 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 73, 146, 219, 292, 365, 438, 730, 876, 1095, 1460, 2190 }}. One step of 4380edo is one sixth of a [[Woolhouse unit]] (1\730).