4ed5: Difference between revisions

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-{{niche}}
+{{Mathematical interest}}
 {{Infobox ET}}
 {{ED intro}}
 == Theory ==
-By definition, one step of this tuning is equal to [[quarter-comma meantone]], therefore it's just a circle of meantone fifths without octave equivalence if treated as a 3/2.5 temperament. By adding an independent dimension for 2, the tuning of quarter-comma meantone is attained.
+ed5 is equivalent to the [[generator]] chain of [[quarter-comma meantone]], and therefore, treated as a 3/2.5-subgroup temperament, it is just a chain of meantone fifths without octaves. By adding an independent dimension for 2, the tuning of quarter-comma meantone is attained.
-{{todo|clarify|inline=1}}
+=== Harmonics ===
+{{Harmonics in equal|4|5|1|intervals=integer|columns=11}}
+{{Harmonics in equal|4|5|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 4ed5 (continued)}}
+=== Subsets and supersets ===
+ed5 is the first composite ed5, containing [[2ed5]] as the only nontrivial subset ed5.
 == Interval table ==
 {{Interval table}}
-== Harmonics ==
-{{Harmonics in equal
-| steps = 4
-| num = 5
-| denom = 1
-}}
-{{Harmonics in equal
-| steps = 4
-| num = 5
-| denom = 1
-| start = 12
-| collapsed = 1
-}}