14618edo: Difference between revisions

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14618edo is an extremely strong 13-limit system, with a lower [[relative error]] than any previous equal temperaments, beating [[6079edo|6079]] and not until 73591 do we find a better equal temperament in the same subgroup. A [[comma basis]] is {[[123201/123200]], 1990656/1990625, 3294225/3294172, 4084223/4084101, 781258401/781250000}. It is much less impressive beyond that limit, though it does well in the 2.3.5.7.11.13.19.29 subgroup.

14618edo is an extremely strong [[13-limit]] system, with a lower [[relative error]] than any previous equal temperaments, beating [[6079edo|6079]] and not until 73591 do we find a better equal temperament in the same subgroup. A [[comma basis]] is {[[123201/123200]], [[1990656/1990625]], 3294225/3294172, 4084223/4084101, 781258401/781250000}. It is much less impressive beyond that limit, though it does well in the 2.3.5.7.11.13.19.29 subgroup, holding the record of lowest relative error until [[16808edo|16808]].

=== Prime harmonics ===

{{Harmonics in equal|14618|columns=9|start=10|collapsed=true|title=Approximation of prime harmonics in 14618edo (continued)}}

=== Subsets and supersets ===

29236edo, which doubles 14618edo, provides a good correction to the harmonics 17 and 23.

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 {{Infobox ET}}
-{{EDO intro|14618}}
+{{ED intro}}
-edo is an extremely strong 13-limit system, with a lower [[relative error]] than any previous equal temperaments, beating [[6079edo|6079]] and not until 73591 do we find a better equal temperament in the same subgroup. A [[comma basis]] is {[[123201/123200]], 1990656/1990625, 3294225/3294172, 4084223/4084101, 781258401/781250000}. It is much less impressive beyond that limit, though it does well in the 2.3.5.7.11.13.19.29 subgroup.
+edo is an extremely strong [[13-limit]] system, with a lower [[relative error]] than any previous equal temperaments, beating [[6079edo|6079]] and not until 73591 do we find a better equal temperament in the same subgroup. A [[comma basis]] is {[[123201/123200]], [[1990656/1990625]], 3294225/3294172, 4084223/4084101, 781258401/781250000}. It is much less impressive beyond that limit, though it does well in the 2.3.5.7.11.13.19.29 subgroup, holding the record of lowest relative error until [[16808edo|16808]].
 === Prime harmonics ===
-{{Harmonics in equal|14618}}
+{{Harmonics in equal|14618|columns=9}}
+{{Harmonics in equal|14618|columns=9|start=10|collapsed=true|title=Approximation of prime harmonics in 14618edo (continued)}}
 === Subsets and supersets ===
 edo, which doubles 14618edo, provides a good correction to the harmonics 17 and 23.