27edf: Difference between revisions

Line 1:

'''[[EDF|Division of the just perfect fifth]] into 27 equal parts''' (27EDF) is related to [[46edo|46 edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 4.0767 cents compressed and the step size is about 25.9983 cents. Unlike 46edo, it is only consistent up to the [[~~5-odd-limit|6-~~integer-limit]], with discrepancy for the 7th harmonic. It is related to the regular temperament which tempers out 4375/4374 and 2199023255552/2188322577315 in the 7-limit, which is supported by 46, [[323edo|323]], [[369edo|369]], [[415edo|415]], and [[692edo|692]] EDOs.

'''[[EDF|Division of the just perfect fifth]] into 27 equal parts''' (27EDF) is related to [[46edo|46 edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 4.0767 cents compressed and the step size is about 25.9983 cents. Unlike 46edo, it is only consistent up to the 6-[[integer-limit]], with discrepancy for the 7th harmonic.

It is related to the regular temperament which tempers out 4375/4374 and 2199023255552/2188322577315 in the 7-limit, which is supported by 46, [[323edo|323]], [[369edo|369]], [[415edo|415]], and [[692edo|692]] EDOs.

Lookalikes: [[46edo]], [[73edt]]

==Harmonics==

==Intervals==

{| class="wikitable"

{| class="wikitable mw-collapsible"

|+ Intervals of 27edf

|-

! | degree

Line 152:

Line 159:

|}

[[Category:Edf]]

[[Category:Edonoi]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-'''[[EDF|Division of the just perfect fifth]] into 27 equal parts''' (27EDF) is related to [[46edo|46 edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 4.0767 cents compressed and the step size is about 25.9983 cents. Unlike 46edo, it is only consistent up to  the [[5-odd-limit|6-integer-limit]], with discrepancy for the 7th harmonic. It is related to the regular temperament which tempers out 4375/4374 and 2199023255552/2188322577315 in the 7-limit, which is supported by 46, [[323edo|323]], [[369edo|369]], [[415edo|415]], and [[692edo|692]] EDOs.
+'''[[EDF|Division of the just perfect fifth]] into 27 equal parts''' (27EDF) is related to [[46edo|46 edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 4.0767 cents compressed and the step size is about 25.9983 cents. Unlike 46edo, it is only consistent up to the 6-[[integer-limit]], with discrepancy for the 7th harmonic.
+It is related to the regular temperament which tempers out 4375/4374 and 2199023255552/2188322577315 in the 7-limit, which is supported by 46, [[323edo|323]], [[369edo|369]], [[415edo|415]], and [[692edo|692]] EDOs.
 Lookalikes: [[46edo]], [[73edt]]
+==Harmonics==
+{{Harmonics in equal|27|3|2|intervals=prime|columns=8}}
+{{Harmonics in equal|27|3|2|intervals=prime|columns=8|start=9}}
 ==Intervals==
-{| class="wikitable"
+{| class="wikitable mw-collapsible"
+|+ Intervals of 27edf
 |-
 ! | degree
@@ Line 152: / Line 159: @@
 |}
+{{todo|expand}}
 [[Category:Edf]]
 [[Category:Edonoi]]