Harmonics 4–8: Difference between revisions

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[[File:4ado scale.wav|thumb]]

~~'''4afdo''' ([[AFDO~~|arithmetic division of the octave]]), or '''4odo''' ([[otonal division]] of the octave), divides the octave into four parts of 1/4 each. It is a superset of [[3afdo]] and a subset of [[5afdo]]. As a scale it may be known as [[Harmonic mode|mode 4 of the harmonic series]] or the [[Overtone scale #Over-n scales|Over-4]] scale. Because 4 ~~is a power of 2, 4afdo corresponds to the 4th to 8th harmonics octave-reduced.~~ The notes of ~~4afdo~~ create a [[4:5:6:7|harmonic seventh chord]].

{{Harmonics intro|4}} The notes of this scale create a [[4:5:6:7|harmonic seventh chord]].

The smallest [[edo]]s that maintain 25% or lower relative error on all intervals of ~~4afdo~~ are [[10edo]] and [[15edo]], though they are not very accurate. The next two edos, [[22edo]] and [[31edo]], are the smallest that approximate ~~4afdo~~ with appreciable accuracy.

The smallest [[edo]]s that maintain 25% or lower relative error on all intervals of this scale are [[10edo]] and [[15edo]], though they are not very accurate. The next two edos, [[22edo]] and [[31edo]], are the smallest that approximate this scale with appreciable accuracy.

== Intervals ==

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| 968.8

| [[7/4]]

| 1.~~7050~~

| 1.7500

| harmonic seventh

| [[File:Jid_7_4_pluck_adu_dr220.mp3]]

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| [[File:Jid_2_1_pluck_adu_dr220.mp3]]

|}

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-{{Infobox AFDO|steps=4}}
+{{Infobox harmonics|4}}
 [[File:4ado scale.wav|thumb]]
-'''4afdo''' ([[AFDO|arithmetic division of the octave]]), or '''4odo''' ([[otonal division]] of the octave), divides the octave into four parts of 1/4 each. It is a superset of [[3afdo]] and a subset of [[5afdo]]. As a scale it may be known as [[Harmonic mode|mode 4 of the harmonic series]] or the [[Overtone scale #Over-n scales|Over-4]] scale. Because 4 is a power of 2, 4afdo corresponds to the 4th to 8th harmonics octave-reduced. The notes of 4afdo create a [[4:5:6:7|harmonic seventh chord]].
+{{Harmonics intro|4}} The notes of this scale create a [[4:5:6:7|harmonic seventh chord]].
-The smallest [[edo]]s that maintain 25% or lower relative error on all intervals of 4afdo are [[10edo]] and [[15edo]], though they are not very accurate. The next two edos, [[22edo]] and [[31edo]], are the smallest that approximate 4afdo with appreciable accuracy.
+The smallest [[edo]]s that maintain 25% or lower relative error on all intervals of this scale are [[10edo]] and [[15edo]], though they are not very accurate. The next two edos, [[22edo]] and [[31edo]], are the smallest that approximate this scale with appreciable accuracy.
 == Intervals ==
@@ Line 40: / Line 40: @@
 | 968.8
 | [[7/4]]
-| 1.7050
+| 1.7500
 | harmonic seventh
 | [[File:Jid_7_4_pluck_adu_dr220.mp3]]
@@ Line 51: / Line 51: @@
 | [[File:Jid_2_1_pluck_adu_dr220.mp3]]
 |}
+{{Navbox harmonics}}