Harmonics 16–32: Difference between revisions

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~~'''16afdo''' ([[AFDO~~|~~arithmetic frequency division of the octave]]), or '''~~16-ODO''' ([[otonal division]] of the octave), divides the octave into 16 parts of 1/16 each. It is a superset of [[15afdo]] and a subset of [[17afdo]]. As a scale it may be known as [[Harmonic mode|mode 16 of the harmonic series]] or the [[Overtone scale #Over-n scales|Over-16]] scale. Because 16 is a power of 2, 16afdo corresponds to the 16th to 32nd harmonics octave-reduced.

The smallest [[edo]] that maintains 25% or lower relative error on all intervals of ~~16afdo~~ is [[311edo]].

The smallest [[edo]] that maintains 25% or lower relative error on all intervals of this scale is [[311edo]].

== Intervals ==

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| 1.8125

| octave-reduced 29th harmonic

| ~~[[File:Jid_7_4_pluck_adu_dr220.mp3]]~~

|

|-

| 14

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== Scales ==

{{See also| 5- to 10-tone scales from the modes of the harmonic series }}

{{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}}

* Deister Tune 216: 17~~/16–5/4–11/8–3/2–7/4–15/8–32/16~~

* 16:17:20:22:24:28:15:32 [[Bryan Deister|Deister]] Tune 216

* ~~Mechanical~~: 19~~/16–20/16–24/16–28/16–32/16~~

* 16:17:20:24:28:32 Volcanic

* ~~Moonbeam~~: 18~~/16–19/16–24/16–30/16–32/16~~

* 16:18:19:24:28:32 Moonbeam

* ~~Volcanic~~: ~~17/16–20/16–24/16–28/16–32/16~~

* 16:18:21:24:26:28:32 Canopy

* 16:19:20:24:28:32 Mechanical

== Music ==

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; [[Bryan Deister]]

* [https://www.youtube.com/watch?v=fdmunv0F9WA ''my tune 216 played on 2/16 at 216hz in 17-limit JI'']

== See also ==

* [[Harmonics 8–16]]

* [[Harmonics 32–64]]

@@ Line 1: / Line 1: @@
-{{Infobox AFDO|steps=16}}
+{{Infobox harmonics|16}}
-'''16afdo''' ([[AFDO|arithmetic frequency division of the octave]]), or '''16-ODO''' ([[otonal division]] of the octave), divides the octave into 16 parts of 1/16 each. It is a superset of [[15afdo]] and a subset of [[17afdo]]. As a scale it may be known as [[Harmonic mode|mode 16 of the harmonic series]] or the [[Overtone scale #Over-n scales|Over-16]] scale. Because 16 is a power of 2, 16afdo corresponds to the 16th to 32nd harmonics octave-reduced.
+{{Harmonics intro|16}}
-The smallest [[edo]] that maintains 25% or lower relative error on all intervals of 16afdo is [[311edo]].
+The smallest [[edo]] that maintains 25% or lower relative error on all intervals of this scale is [[311edo]].
 == Intervals ==
@@ Line 111: / Line 111: @@
 | 1.8125
 | octave-reduced 29th harmonic
-| [[File:Jid_7_4_pluck_adu_dr220.mp3]]
+|
 |-
 | 14
@@ Line 137: / Line 137: @@
 == Scales ==
 {{See also| 5- to 10-tone scales from the modes of the harmonic series }}
+{{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}}
-* Deister Tune 216: 17/16–5/4–11/8–3/2–7/4–15/8–32/16
+* 16:17:20:22:24:28:15:32 [[Bryan Deister|Deister]] Tune 216
-* Mechanical: 19/16–20/16–24/16–28/16–32/16
+* 16:17:20:24:28:32 Volcanic
-* Moonbeam: 18/16–19/16–24/16–30/16–32/16
+* 16:18:19:24:28:32 Moonbeam
-* Volcanic: 17/16–20/16–24/16–28/16–32/16
+* 16:18:21:24:26:28:32 Canopy
+* 16:19:20:24:28:32 Mechanical
 == Music ==
@@ Line 149: / Line 151: @@
 ; [[Bryan Deister]]
 * [https://www.youtube.com/watch?v=fdmunv0F9WA ''my tune 216 played on 2/16 at 216hz in 17-limit JI'']
+== See also ==
+* [[Harmonics 8–16]]
+* [[Harmonics 32–64]]
+{{Navbox harmonics}}