Music that sounds despairing and sad usually has what kind of tempo?

Answer 1

It can have a number of tempos, depending on the melodic/motivic content, though they are usually marked with slower tempos (largo, adagio, etc.).

The second movement of Beethoven's Piano Sonata, op. 10 no. 3 is a beautiful example music that is generally thought of as sounding despairing and sad, and it is marked "largo e mesto".

Answer 2

Vigorous