The (0,3) Mode
The sixth mode (0,3), shown below has three circular nodes, but no diameter nodes. The frequency of the (0,3) mode is 3.598 times the frequency of the (0,1) mode. Like the (0,1) and (0,2) modes, the (0,3) mode is excited when the membrane is struck at the center. The sound radiation characteristics of the (0,3) mode are rather complicated. This mode is excited when the membrane is struck at the center, and it dies away fairly quickly. As a result, it contributes to the thump sound when a drum is hit at the center, but does not contribute much to the musical pitch of a drum when hit off-center.
Note that none of the modal frequencies above the fundamental (1.593, 2.135, 2.295, 2.917, 3.598) consist of multiples of the fundamental (i.e.1, 2, 3, 4 etc), and thus do not constitute a harmonic series. In theory, the sound of the timpani should not have any more pitch than that of any other drum if the partials are not harmonic.