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.
-== Scales ==
+The smallest [[edo]] that maintains 25% or lower relative error on all intervals of 32afdo is [[3159811edo]].
-''see also: [[5- to 10-tone scales from the modes of the harmonic series]]''
-=== Irreducible ===
+== Intervals ==
+# [[33/32]]
+# [[17/16]]
+# [[35/32]]
+# [[9/8]]
+# [[37/32]]
+# [[19/16]]
+# [[39/32]]
+# [[5/4]]
+# [[41/32]]
+# [[21/16]]
+# [[43/32]]
+# [[11/8]]
+# [[45/32]]
+# [[23/16]]
+# [[47/32]]
+# [[3/2]]
+# [[49/32]]
+# [[25/16]]
+# [[51/32]]
+# [[13/8]]
+# [[53/32]]
+# [[27/16]]
+# [[55/32]]
+# [[7/4]]
+# [[57/32]]
+# [[29/16]]
+# [[59/32]]
+# [[15/8]]
+# [[61/32]]
+# [[31/16]]
+# [[63/32]]
+# [[2/1]]
-Arcade
+== Scales ==
-* 40/32
+{{See also| 5- to 10-tone scales from the modes of the harmonic series }}
-* 43/32
-* 48/32
-* 57/32
-* 64/32
-=== From 4, 8, 16afdo ===
-Mechanical
-* 38/32
-* 40/32
-* 48/32
-* 56/32
-* 64/32
-Moonbeam
-* 36/32
-* 38/32
-* 48/32
-* 60/32
-* 64/32
-Springwater
-* 36/32
-* 40/32
-* 48/32
-* 56/32
-* 64/32
+* Arcade: {{dash|40/32, 43/32, 48/32, 57/32, 64/32|med}}
+* Cosmic: {{dash|43/32, 48/32, 51/32, 57/32, 64/32|med}}
+* ''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
-Volcanic
+== Music ==
-* 34/32
+; [[Adam Neely]]
-* 40/32
+* [https://www.youtube.com/watch?v=tMSXdCWbRHw ''How to See Ghosts'' (demonstration piece)] (2018) – The piece starts at 10:17
-* 48/32
-* 56/32
-* 64/32