The (2,2) Mode
The eighth mode of a circular membrane is the (2,2) mode which has two nodal diameters and two nodal circles. This mode does not contribute to the sustained harmonicity or pitch of a timpano.
But it is amazing how an exactly tuned pair of timpani faithfully maintain the intonation in the orchestra and also hold down those instrumentalists who, perhaps out of a need to accent their importance, like to raise the pitch level.