5edt: Difference between revisions

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== Theory ==

5edt 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]].

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.

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== Steps ==

{| class="wikitable right-all left-4"

|-

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 {{Infobox ET}}
-{{EDO intro}}
+{{ED intro}}
 == 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]].
-edt 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]].
 edt 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.
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 == Steps ==
 {| class="wikitable right-all left-4"
 |-