5edt: Difference between revisions

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-'''5edt''' (5 Equal Divisions of the Tritave) subdivides the interval of the [[tritave]], frequency ratio 3:1, into 5 equal-sized parts, each 380.391 [[Cent]]s in size.
+{{Infobox ET}}
+{{ED intro}}
-== Steps ==
+== Theory ==
+edt has steps too large to be used melodically, though it has some notable harmonic properties shared by other 5''n''-edts (such as [[10edt]], [[15edt]], etc.). It has a surprisingly accurate [[5/4]] major third (only 5.92{{cent}} flat), five of them making a tritave. (This phenomenon cannot be seen in single-digit [[edo]]s, and it is not until [[19edo]] that an approximation of 5/4 to within 10{{c}} can be seen.) 5edt therefore tempers out [[3125/3072]], the magic comma. Two of these major thirds give a septimal minor sixth, meaning that it also tempers out the marvel comma [[225/224]].
-{| class="wikitable"
+edt is the first edt to encompass elements of [[5-limit]] harmony. The available chords are 4:5:12 and 5:12:15; being inversions of each other, they essentially act as "major" and "minor" chords. This is similar to [[6edt]], which contains the same chords but with the major thirds transposed an octave higher, and vice versa. Also available is the chord 9:14:27, which can express the single [[7-limit]] consonance found in 5edt.
+=== Harmonics ===
+{{Harmonics in equal|5|3|1|columns=15}}
+=== Subsets and supersets ===
+edt is the 3rd [[prime equal division|prime edt]], after [[3edt]] and before [[7edt]].
+== Intervals ==
+{| class="wikitable right-all left-4"
 |-
-! Degrees
+! #
 ! Cents
-!hekts
+! Hekts
-! Approximate Ratios
+! Approximate ratios
 |-
-| colspan="3" | 0
+| 0
+| 0
+| 0
 | [[1/1]]
 |-
 | 1
-| 380.391
+| 380
-|260
+| 260
 | [[5/4]]
 |-
 | 2
-| 760.782
+| 761
-|520
+| 520
 | [[14/9]]
 |-
 | 3
-| 1141.173
+| 1141
-|780
+| 780
 | [[27/14]]
 |-
 | 4
-| 1521.564
+| 1522
-|1040
+| 1040
-| [[12/5]] ([[6/5|6/5]] plus an octave)
+| [[12/5]]
 |-
 | 5
-| 1901.955
+| 1902
-|1300
+| 1300
 | [[3/1]]
 |}
-edt isn't very useful melodically, though it has many notable harmonic properties shared by other 5n-edts (EDTs with 5 as a prime factor). It has a surprisingly accurate major third, five of them making a tritave. It therefore tempers out [[3125/3072]], the magic comma. Two of these major thirds give a septimal minor sixth, meaning that it also tempers out the 7-limit comma [[225/224]].
-edt is the lowest equal division of the tritave to encompass [[5-limit]] harmony. The available chords are 4:5:12 and 5:12:15; essentially major and minor chords. This is similar to [[6edt]], which contains the same chords but with the major thirds transposed an octave higher, and vice versa.
-== Other 5n-EDTs ==
-* [[10edt]]
-* [[15edt]]
-* [[20edt]]
-* [[25edt]]
-* [[30edt]]
-[[Category:Edt]]
-[[Category:Nonoctave]]
-[[Category:Macrotonal]]
 [[Category:Todo:add sound example]]