In calculating the F-measure with precision and recall, why is the harmonic mean used?

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?

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

• From wikipedia: Typically, it is appropriate for situations when the average of rates is desired. This thread might also be of interest: "Which “mean” to use and when?" – user10525 Sep 19 '12 at 15:59
• In fact it is more that F is defined as a harmonic mean of precision and recall rather that F is defined as a mean of precision and recall and for some reason we are using harmonic mean. – user88 Sep 19 '12 at 18:54