4ed5: Difference between revisions

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~~'''4 equal divisons of the fifth harmonic''' is a nonoctave tuning with the step size of 696.5784 cents.~~

== Theory ==

~~By definition, one step of this tuning~~ is ~~equal~~ to quarter-comma meantone, therefore it's just a ~~circle~~ of meantone fifths.

4ed5 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.

[[~~Category:Ed5~~]]

=== Harmonics ===

~~[[Category:Edonoi]]~~

{{Harmonics in equal|4|5|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 4ed5 (continued)}}

=== Subsets and supersets ===

4ed5 is the first composite ed5, containing [[2ed5]] as the only nontrivial subset ed5.

== Interval table ==

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-'''4 equal divisons of the fifth harmonic''' is a nonoctave tuning with the step size of 696.5784 cents.
+{{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.
+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.
-[[Category:Ed5]]
+=== Harmonics ===
-[[Category:Edonoi]]
+{{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}}