Harmonics 32–64: Difference between revisions

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~~'''32afdo''' ([[AFDO~~|~~arithmetic frequency division of the octave]]), or '''32odo''' ([[otonal division]] of the octave), divides the octave into~~ 32 parts of 1/32 each. It is a superset of [[31afdo]] and a subset of [[33afdo]]. As a scale it may be known as [[Harmonic mode|mode 32 of the harmonic series]] or the [[Overtone scale #Over-n scales|Over-32]] scale.

The smallest [[edo]] that maintains 25% or lower relative error on all intervals of ~~32afdo~~ is [[3159811edo]].

The smallest [[edo]] that maintains 25% or lower relative error on all intervals of this scale is [[3159811edo]].

== Intervals ==

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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}}

* ~~Arcade{{idio}}~~: ~~{{dash|~~40/32, 43~~/32,~~ 48~~/32,~~ 57~~/32,~~ 64~~/32|med}}~~

* 32:34:36:38:40:43:44:48:52:54:56:58:60:64 ''loose approximation of [[fluid just intonation]]''

* ~~Cosmic{{idio}}~~: ~~{{dash|~~43~~/32,~~ 48~~/32,~~ 51~~/32,~~ 57~~/32,~~ 64~~/32|med}}~~

* 32:40:43:48:57:64 Arcade

* ''~~Loose approximation of~~ [[~~fluid just intonation~~]]''~~: 17/16—9/8—19/16—5/4—43/32—11/8—3/2—13/8—27/16—7/4—29/16—15/8—2/1~~

* 32:43:48:51:57:64 Cosmic

* ''[[User:BudjarnLambeth/Some tunings for Japanese scales#Over-2]]'' (most of these are in this scale)

== Music ==

; [[Adam Neely]]

* [https://www.youtube.com/watch?v=tMSXdCWbRHw ''How to See Ghosts'' (demonstration piece)] (2018) – The piece starts at 10:17

== See also ==

* [[Harmonics 8–16]]

* [[Harmonics 16–32]]

@@ Line 1: / Line 1: @@
-{{Infobox AFDO|steps=32}}
+{{Infobox harmonics|32}}
-'''32afdo''' ([[AFDO|arithmetic frequency division of the octave]]), or '''32odo''' ([[otonal division]] of the octave), divides the octave into 32 parts of 1/32 each. It is a superset of [[31afdo]] and a subset of [[33afdo]]. As a scale it may be known as [[Harmonic mode|mode 32 of the harmonic series]] or the [[Overtone scale #Over-n scales|Over-32]] scale.
+{{Harmonics intro|32}}
-The smallest [[edo]] that maintains 25% or lower relative error on all intervals of 32afdo is [[3159811edo]].
+The smallest [[edo]] that maintains 25% or lower relative error on all intervals of this scale is [[3159811edo]].
 == Intervals ==
@@ Line 41: / Line 41: @@
 == 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}}
-* Arcade{{idio}}: {{dash|40/32, 43/32, 48/32, 57/32, 64/32|med}}
+* 32:34:36:38:40:43:44:48:52:54:56:58:60:64 ''loose approximation of [[fluid just intonation]]''
-* Cosmic{{idio}}: {{dash|43/32, 48/32, 51/32, 57/32, 64/32|med}}
+* 32:40:43:48:57:64 Arcade
-* ''Loose approximation of [[fluid just intonation]]'': 17/16—9/8—19/16—5/4—43/32—11/8—3/2—13/8—27/16—7/4—29/16—15/8—2/1
+* 32:43:48:51:57:64 Cosmic
+* ''[[User:BudjarnLambeth/Some tunings for Japanese scales#Over-2]]'' (most of these are in this scale)
 == Music ==
 ; [[Adam Neely]]
 * [https://www.youtube.com/watch?v=tMSXdCWbRHw ''How to See Ghosts'' (demonstration piece)] (2018) – The piece starts at 10:17
+== See also ==
+* [[Harmonics 8–16]]
+* [[Harmonics 16–32]]
+{{Navbox harmonics}}