32afdo: Difference between revisions

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 {{Infobox AFDO|steps=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. 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.
+'''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]].
 == Intervals ==
-# 33/32
+# [[33/32]]
-# 17/16
+# [[17/16]]
-# 35/32
+# [[35/32]]
-# 9/8
+# [[9/8]]
-# 37/32
+# [[37/32]]
-# 19/16
+# [[19/16]]
-# 39/32
+# [[39/32]]
-# 5/4
+# [[5/4]]
-# 41/32
+# [[41/32]]
-# 21/16
+# [[21/16]]
-# 43/32
+# [[43/32]]
-# 11/8
+# [[11/8]]
-# 45/32
+# [[45/32]]
-# 23/16
+# [[23/16]]
-# 47/32
+# [[47/32]]
-# 3/2
+# [[3/2]]
-# 49/32
+# [[49/32]]
-# 25/16
+# [[25/16]]
-# 51/32
+# [[51/32]]
-# 13/8
+# [[13/8]]
-# 53/32
+# [[53/32]]
-# 27/16
+# [[27/16]]
-# 55/32
+# [[55/32]]
-# 7/4
+# [[7/4]]
-# 57/32
+# [[57/32]]
-# 29/16
+# [[29/16]]
-# 59/32
+# [[59/32]]
-# 15/8
+# [[15/8]]
-# 61/32
+# [[61/32]]
-# 31/16
+# [[31/16]]
-# 61/31
+# [[63/32]]
-# 2/1
+# [[2/1]]
 == 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: 40/32-43/32-48/32-57/32-64/32
+* 32:34:36:38:40:43:44:48:52:54:56:58:60:64 ''loose approximation of [[fluid just intonation]]''
-* Cosmic: 43/32-48/32-51/32-57/32-64/32
+* 32:40:43:48:57:64 Arcade
+* 32:43:48:51:57:64 Cosmic
+* ''[[User:BudjarnLambeth/Some tunings for Japanese scales#Over-2]]'' (most of these are in 32afdo)
 == Music ==
-* [https://www.youtube.com/watch?v=tMSXdCWbRHw How to See Ghosts (demonstration piece)] by Adam Neely (2018) - the piece starts at 10:17
+; [[Adam Neely]]
+* [https://www.youtube.com/watch?v=tMSXdCWbRHw ''How to See Ghosts'' (demonstration piece)] (2018) – The piece starts at 10:17
+== See also ==
+* [[8afdo]]
+* [[16afdo]]