5edt: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
'''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.
{{EDO intro}}
 
== Theory ==
 
5edt has steps too large to be used melodically, though it has some notable harmonic properties shared by other 5n-edts (such as [[10edt]], [[15edt]], etc.). It has a surprisingly accurate [[5/4]] major third (only 5.92 [[cents]] 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 cents 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]].
 
5edt is the lowest equal division of the tritave 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}}


== Steps ==
== Steps ==
Line 34: Line 43:
| 1521.564
| 1521.564
| 1040
| 1040
| [[12/5]] ([[6/5|6/5]] plus an octave)
| [[12/5]] ([[6/5]] plus an octave)
|-
|-
| 5
| 5
Line 41: Line 50:
| [[3/1]]
| [[3/1]]
|}
|}
5edt 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]].
5edt 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:Edt]]