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.
The tympanist must be a musician, not a mere drummer. And by musician I mean a player in the possession of a developed ear to recognize the different tones, as well as a sense of rhythm and tempi.