Highly composite EDO: Difference between revisions

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Superabundant EDO is the equal division scale with a [[Wikipedia:Superabundant number|superabundant number]] of pitches in an octave. They can be seen as the opposite of [[Prime EDO]]<nowiki/>s.
#REDIRECT [[Highly composite equal division#Highly composite edo]]
 
== Superabundant numbers in EDOs ==
The defining feature is that the EDO has the largest number of sub-EDOs that it contains, in proportion to the EDO's number. This means that:
 
* The EDO contains the largest amount of symmetrical chords, and correspondingly, uniform octave-repeating scales, relative to its size.
* The EDO has the largest amount of [[Wikipedia:Mode of limited transposition|modes of limited transposition]] relative to its size.
* The EDO has the largest amount of rank-2 temperaments whose period is a fraction of the octave, relative to its size.
* By the virtue of point 1, the EDO has the largest amount of familiar scales relative to its size.

Latest revision as of 04:22, 21 October 2022