17ed4: Difference between revisions

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~~'''17ed4''' is the [[Ed4|equal division of the double octave]] into 17 parts of 141.18 [[cent|cents]] each, corresponding~~ to 8.5edo or every second step of [[17edo]].

{{ED intro}} It corresponds to 8.5edo or every second step of [[17edo]].

==Theory==

17ed4 is the smallest ED4 to contain a diatonic fifth, in this ~~cas~~ [[17edo]]'s sharp fifth, and it can be used to generate heptatonic (3L 4s<4/1>) and decatonic ([[7L 3s (4/1-equivalent)|7L 3s<4/1>]]) MOS scales with a period of [[4/1]]. The decatonic scale is the more usable of these two scales, corresponding to an octave-repeating pentatonic scale in terms of step sizes, while the heptatonic scale has too large step sizes, corresponding to an octave-repeating tritonic or tetratonic scale in terms of step sizes.

17ed4 is the smallest ED4 to contain a diatonic fifth, in this case [[17edo]]'s sharp fifth, and it can be used to generate heptatonic (3L 4s<4/1>) and decatonic ([[7L 3s (4/1-equivalent)|7L 3s<4/1>]]) MOS scales with a period of [[4/1]]. The decatonic scale is the more usable of these two scales, corresponding to an octave-repeating pentatonic scale in terms of step sizes, while the heptatonic scale has too large step sizes, corresponding to an octave-repeating tritonic or tetratonic scale in terms of step sizes.

==Intervals==

{|class="wikitable"

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!Approximate ratios

![[17edo]] notation

![[7L 3s (4/1-equivalent)|~~7L 3s<4/1>~~]] notation (J = 1/1)

![[7L 3s (4/1-equivalent)|Diaquadic]] notation (J = 1/1)

|-

|0

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|J

|}

== Harmonics ==

{{Harmonics in equal

| steps = 17

| num = 4

| denom = 1

}}

{{Harmonics in equal

| steps = 17

| num = 4

| denom = 1

| start = 12

| collapsed = 1

}}

[[Category:Macrotonal]]

[[Category:Nonoctave]]

~~[[Category:Ed4]]~~

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-'''17ed4''' is the [[Ed4|equal division of the double octave]] into 17 parts of 141.18 [[cent|cents]] each, corresponding to 8.5edo or every second step of [[17edo]].
+{{ED intro}} It corresponds to 8.5edo or every second step of [[17edo]].
 ==Theory==
-ed4 is the smallest ED4 to contain a diatonic fifth, in this cas [[17edo]]'s sharp fifth, and it can be used to generate heptatonic (3L 4s<4/1>) and decatonic ([[7L 3s (4/1-equivalent)|7L 3s<4/1>]]) MOS scales with a period of [[4/1]]. The decatonic scale is the more usable of these two scales, corresponding to an octave-repeating pentatonic scale in terms of step sizes, while the heptatonic scale has too large step sizes, corresponding to an octave-repeating tritonic or tetratonic scale in terms of step sizes.
+ed4 is the smallest ED4 to contain a diatonic fifth, in this case [[17edo]]'s sharp fifth, and it can be used to generate heptatonic (3L 4s<4/1>) and decatonic ([[7L 3s (4/1-equivalent)|7L 3s<4/1>]]) MOS scales with a period of [[4/1]]. The decatonic scale is the more usable of these two scales, corresponding to an octave-repeating pentatonic scale in terms of step sizes, while the heptatonic scale has too large step sizes, corresponding to an octave-repeating tritonic or tetratonic scale in terms of step sizes.
 ==Intervals==
 {|class="wikitable"
@@ Line 10: / Line 12: @@
 !Approximate ratios
 ![[17edo]] notation
-![[7L 3s (4/1-equivalent)|7L 3s<4/1>]] notation (J = 1/1)
+![[7L 3s (4/1-equivalent)|Diaquadic]] notation (J = 1/1)
 |-
 |0
@@ Line 120: / Line 122: @@
 |J
 |}
+== Harmonics ==
+{{Harmonics in equal
+| steps = 17
+| num = 4
+| denom = 1
+}}
+{{Harmonics in equal
+| steps = 17
+| num = 4
+| denom = 1
+| start = 12
+| collapsed = 1
+}}
 [[Category:Macrotonal]]
 [[Category:Nonoctave]]
-[[Category:Ed4]]
+{{todo|expand}}