Highly composite EDO: Difference between revisions

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The first 19 superabundant and highly composite numbers are the same.

An example when they are not the same: [[50400edo|50400]] is the 27th highly composite number, that is not on the superabundant list. The count of divisors of 50400 is 108, which means it supports 106 symmetrical scales that aren't the chromatic and whole-octave scale. However, by the note count in all those scales, which is 102311 not counting 1 and 50400, the EDO lags slightly behind [[27720edo]], with it's coefficient being 4.~~05195~~ and 50400edo's coefficient being 4.03.

An example when they are not the same: [[50400edo|50400]] is the 27th highly composite number, that is not on the superabundant list. The count of divisors of 50400 is 108, which means it supports 106 symmetrical scales that aren't the chromatic and whole-octave scale. However, by the note count in all those scales, which is 102311 not counting 1 and 50400, the EDO lags slightly behind [[27720edo]], with it's coefficient being 4.05 and 50400edo's coefficient being 4.03. This means that while 27720 is less composite than 50400, it carries a more impressive task in providing notes to compose with, if the composer is interested in smaller EDOs as subscales.

And indeed it's somewhat obvious - 27720 is divisible by 11, therefore contains [[11edo]], while 50400 recycles EDOs from 1 to 10 multiple times.

== First superabundant EDOs ==

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 The first 19 superabundant and highly composite numbers are the same.
-An example when they are not the same: [[50400edo|50400]] is the 27th highly composite number, that is not on the superabundant list. The count of divisors of 50400 is 108, which means it supports 106 symmetrical scales that aren't the chromatic and whole-octave scale. However, by the note count in all those scales, which is 102311 not counting 1 and 50400, the EDO lags slightly behind [[27720edo]], with it's coefficient being 4.05195 and 50400edo's coefficient being 4.03.
+An example when they are not the same: [[50400edo|50400]] is the 27th highly composite number, that is not on the superabundant list. The count of divisors of 50400 is 108, which means it supports 106 symmetrical scales that aren't the chromatic and whole-octave scale. However, by the note count in all those scales, which is 102311 not counting 1 and 50400, the EDO lags slightly behind [[27720edo]], with it's coefficient being 4.05 and 50400edo's coefficient being 4.03. This means that while 27720 is less composite than 50400, it carries a more impressive task in providing notes to compose with, if the composer is interested in smaller EDOs as subscales.
+And indeed it's somewhat obvious - 27720 is divisible by 11, therefore contains [[11edo]], while 50400 recycles EDOs from 1 to 10 multiple times.
 == First superabundant EDOs ==