I understand that timpani normally have a tuning mechanism, usually involving a pedal that controls the tension on the drum surface, which allows the timpanist to play a range of melodies. However, it is not clear to me from the Wikipedia article whether this range of notes is continuous, or whether there are 'gaps' with notes that are not accessible inside the range for each size of drum. Additionally, it's not clear whether such tuning mechanisms are used throughout the performance to change the note played by the drum, or whether they're fixed at the start and function as single-note drums throughout each piece. How versatile, in practice, are these instruments, in this sense?
Tuning modern orchestral timpani is continuous. You can tune to any frequency. Also, in some compositions, the timpanist is required to re-tune the drums to different pitches while the orchestra is playing around them. Learning to do this, very quietly, while the orchestra is playing around you, is a skill required of professional timpanists.
This YouTube video is part of a series that explains tuning the timpani while playing.