The *harmonic mean* of x_{1},...,x_{n} is

n / (1/x_{1} + ... + 1/x_{n})

As the name implies, it's a mean (between the smallest and largest values).

An extension to the AM-GM inequality relates the harmonic mean to its more famous cousins, the geometric mean and the arithmetic mean.

The word "harmonic" is often used when inverses are involved; doubtless the harmonic mean has (Pythagorean, and therefore mystical) connections to musical harmony and pleasing intervals.