Harmonics 8–16: Difference between revisions

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'''8afdo''' ([[AFDO|arithmetic frequency division of the octave]]), or '''8odo''' ([[otonal division]] of the octave), divides the octave into eight parts of 1/8 each. It is a superset of [[7afdo]] and a subset of [[9afdo]]. As a scale it may be known as [[Harmonic mode|mode 8 of the harmonic series]] or the [[Overtone scale #Over-n scales|~~Over-8]] scale. [[Dante Rosati]] calls this the "Diatonic harmonic series scale". Because~~ 8 ~~is a power of 2, 8afdo corresponds to the 8th to 16th harmonics octave-reduced. 8afdo is a highly effective scale.~~ Above its root it contains many commonly-used intervals such as [[9/8]], [[5/4]], [[3/2]], [[7/4]], [[15/8]], and [[2/1]].

{{Harmonics intro|8}} Above its root it contains many commonly-used intervals such as [[9/8]], [[5/4]], [[3/2]], [[7/4]], [[15/8]], and [[2/1]].

The [[otonal heptad]] can be obtained by removing harmonic 15.

The smallest [[edo]] that maintains 25% or lower relative error on all intervals of ~~8afdo~~ is [[87edo]].

The smallest [[edo]] that maintains 25% or lower relative error on all intervals of this scale is [[87edo]].

== Intervals ==

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{{Idiosyncratic terms|Most of these names were coined, and are solely used, by [[Budjarn Lambeth]] - however he was only the first to ''name'' many of these scales, others have probably already ''used'' them before him.}}

* 8:9:10:12:13:16 Metamorphic

* 8:9:10:12:14:16 [[Otonalpentad]] (aka "rotated [[~~5afdo~~]]", aka "springwater"~~; a similar scale * is used by [[African music|traditional Wagogo musicians in Tanzania]] such as Hukwe Zawose~~)

* 8:9:10:12:14:16 [[Otonalpentad]] (aka "rotated [[Harmonics 5–10]]", aka "springwater")

* 8:9:10:12:15:16 Ionosphere

* 8:9:11:12:13:16 Upwelling (clashes with some timbres, be careful with instrumentation)

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* [https://www.youtube.com/watch?v=FlwN7qSGz9U ''Paracelsus for Diatonic Harmonic Guitar'']

* [https://www.youtube.com/watch?v=U6ElPRoIZak ''No Snow for Diatonic Harmonic Guitar'']

== See also ==

* [[Harmonics 16–32]]

* [[Harmonics 32–64]]

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-{{Infobox AFDO|steps=8}}
+{{Infobox harmonics|8}}
-'''8afdo''' ([[AFDO|arithmetic frequency division of the octave]]), or '''8odo''' ([[otonal division]] of the octave), divides the octave into eight parts of 1/8 each. It is a superset of [[7afdo]] and a subset of [[9afdo]]. As a scale it may be known as [[Harmonic mode|mode 8 of the harmonic series]] or the [[Overtone scale #Over-n scales|Over-8]] scale. [[Dante Rosati]] calls this the "Diatonic harmonic series scale". Because 8 is a power of 2, 8afdo corresponds to the 8th to 16th harmonics octave-reduced. 8afdo is a highly effective scale. Above its root it contains many commonly-used intervals such as [[9/8]], [[5/4]], [[3/2]], [[7/4]], [[15/8]], and [[2/1]].
+{{Harmonics intro|8}} Above its root it contains many commonly-used intervals such as [[9/8]], [[5/4]], [[3/2]], [[7/4]], [[15/8]], and [[2/1]].
+The [[otonal heptad]] can be obtained by removing harmonic 15.
-The smallest [[edo]] that maintains 25% or lower relative error on all intervals of 8afdo is [[87edo]].
+The smallest [[edo]] that maintains 25% or lower relative error on all intervals of this scale is [[87edo]].
 == Intervals ==
@@ Line 81: / Line 82: @@
 {{Idiosyncratic terms|Most of these names were coined, and are solely used, by [[Budjarn Lambeth]] - however he was only the first to ''name'' many of these scales, others have probably already ''used'' them before him.}}
 * 8:9:10:12:13:16 Metamorphic
-* 8:9:10:12:14:16 [[Otonalpentad]] (aka "rotated [[5afdo]]", aka "springwater"; a similar scale * is used by [[African music|traditional Wagogo musicians in Tanzania]] such as Hukwe Zawose)
+* 8:9:10:12:14:16 [[Otonalpentad]] (aka "rotated [[Harmonics 5–10]]", aka "springwater")
 * 8:9:10:12:15:16 Ionosphere
 * 8:9:11:12:13:16 Upwelling (clashes with some timbres, be careful with instrumentation)
@@ Line 91: / Line 92: @@
 * [https://www.youtube.com/watch?v=FlwN7qSGz9U ''Paracelsus for Diatonic Harmonic Guitar'']
 * [https://www.youtube.com/watch?v=U6ElPRoIZak ''No Snow for Diatonic Harmonic Guitar'']
+== See also ==
+* [[Harmonics 16–32]]
+* [[Harmonics 32–64]]
+{{Navbox harmonics}}