What are the three advantages of harmonic mean?

Efficiencies as High as 90% Measured on actual shaft-to-shaft losses rather than tooth losses (as with other gearing), standard Harmonic Drive gearing efficiencies are normally in the 80-90% range.
The harmonic mean has the following merits. It is rigidly defined. It is based on all the observations of a series i.e. it cannot be calculated ignoring any item of a series. It is capable of further algebraic treatment. It gives better result when the ends to be achieved are the same for the different means adopted.