Look guys, the Coptic euponium back there has no bearing on the issue.
What you have here is an ancient north Lancashire counting mnemonic dating back to the viking invasions. The DUM element is a softening device used to minimise the impact of the more penetrating latin UNO which carries much further in a resonant fog.

Thus DUM - one
    DUM-DE- two
    DUM-DE-DUM- One plus two. I/e three
Since in those days the next word beyond three was "Many" it was necessary to repeat the exercise thus getting a base three mathemetical model.

This accounts for the great number of threes in the Anglo Celtic folk tradition; The three great heroes of Ireland. The idea of the trinity in its various forms and of course the three stooges, The epitomy of DUM-if I may say so.

                         Jack Halyard.