The [article for F-measure in Wikipedia](http://en.wikipedia.org/wiki/F-score) says:

> The traditional F-measure or balanced F-score (F1 score) is the harmonic mean of precision and recall: 
$F_1=2\times\frac{precision \times recall}{precision+recall}$

Why is the *harmonic mean* used in particular, and not the arithmetic mean or geometric mean or any other type of [averages](http://en.wikipedia.org/wiki/Average)?

What exactly does it mean, to calculate an harmonic mean?