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 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.

~~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 ===

== ~~Steps~~ ==

=== Subsets and supersets ===

5edt is the 3rd [[prime equal division|prime edt]], after [[3edt]] and before [[7edt]].

== Intervals ==

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

|-

! ~~Degrees~~

! #

! Cents

! Hekts

! Approximate ~~Ratios~~

! Approximate ratios

|-

| 0

| 0.000

| 0

| [[1/1]]

|-

| 1

| 380~~.391~~

| 380

| 260

| [[5/4]]

|-

| 2

| ~~760.782~~

| 761

| 520

| [[14/9]]

|-

| 3

| 1141~~.173~~

| 1141

| 780

| [[27/14]]

|-

| 4

| ~~1521.564~~

| 1522

| 1040

| [[12/5]] ~~([[6/5]] plus an octave)~~

| [[12/5]]

|-

| 5

| ~~1901.955~~

| 1902

| 1300

| [[3/1]]

|}

~~[[Category:Edt]]~~

~~[[Category:Nonoctave]]~~

~~[[Category:Macrotonal]]~~

[[Category:Todo:add sound example]]

@@ Line 1: / Line 1: @@
 {{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 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.
-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.
 === Harmonics ===
-{{Harmonics in equal|5|3|1}}
+{{Harmonics in equal|5|3|1|columns=15}}
-== Steps ==
+=== 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
-! Approximate Ratios
+! Approximate ratios
 |-
 | 0
-| 0.000
+| 0
 | 0
 | [[1/1]]
 |-
 | 1
-| 380.391
+| 380
 | 260
 | [[5/4]]
 |-
 | 2
-| 760.782
+| 761
 | 520
 | [[14/9]]
 |-
 | 3
-| 1141.173
+| 1141
 | 780
 | [[27/14]]
 |-
 | 4
-| 1521.564
+| 1522
 | 1040
-| [[12/5]] ([[6/5]] plus an octave)
+| [[12/5]]
 |-
 | 5
-| 1901.955
+| 1902
 | 1300
 | [[3/1]]
 |}
-[[Category:Edt]]
-[[Category:Nonoctave]]
-[[Category:Macrotonal]]
 [[Category:Todo:add sound example]]