The Preferred Timpani Modes
Information and charts courtesy of Georgia State University
Assuming that these selected modes are excited, the relative frequencies and intervals in cents are given compared to the 1,1-mode. The preferred vibrational modes for timpani are a subset of the modes of a theoretical vibrating circular membrane.
The interval values in cents here are calculated from the mode frequencies given by Berg & Stork. They can be compared to equal tempered intervals. N.B The actual sounding frequencies of these modes for timpani are affected by air loading.
f0 = mode (1,1) which is the ideal membrane’s principal tone as if it were a timpano. It is also assumed the the membrane is vibrating as well as circular so it will be referred to as an ideal membrane. Figure 3c shows the mode shapes, the ratios and the number of cents for each of the preferred modes of an ideal membrane as calculated by Berg & Stork. It is important to note that the ratios indicated by Berg & Stork reflect preferred modes, which have not been affected by air loading and without the actual dampened fundamental.
Animation of the First Five Preferred Modes
(courtesy of Dr. Dan Russell, Grad. Prog. Acoustics, Penn State)