The Well Tempered Timpani

The Well Tempered Timpani gives a technical, but really interesting overview of the acoustic properties of timpani.

Contrary to wind and string instruments (and the voice), resonating membranes do not have a harmonic overtone series. In addition, the fundamental is not very resonant or pleasant-sounding. This is caused by the acoustic properties of a membrane: rather than vibrating in just one direction, a membrane can vibrate in various modes simultaneously. Most of these modes are non-harmonic.

Still, it's possible to get pitch and near-harmonic overtones from a timpano. This is possible mainly due to air loading: columns of air above and below the air that make the membrane act almost as if it's a single vibrating system. This has been the subject of various studies, some of which are discussed in this article.