Membrane Modes
The (1,2) mode
The sixth mode (1,2) has one nodal diameter and two nodal circles. The frequency of the (1,2) mode (ideal membrane only – one not affected by air loading) is 2.917 times the frequency of the (0,1) mode. As you might expect after looking at the first several modes of the circular membrane, the (1,2) mode does not radiate energy very effectively. It has somewhat of a quadrupole type behavior. Thus, the (1,2) mode takes a relatively long time to decay. However, this mode doesn’t play a dominant role in the sustained harmonicity of modern timpani, but it is believed to have played a significant role in the sound production of early timpani, due to the manner in which the early timpani were played, and because of the thickness of the membrane (head).
