The acoustics of timpani

Abstract

The frequencies of the vibrational modes of kettledrum heads have long been known to differ from those of an ideal unloaded membrane [Lord Rayleigh (J. W. Strutt), The Theory of Sound (Macmillan, 1894), 2nd ed., Vol. 1]. The three principal modes, under normal playing and tuning conditions, have frequencies nearly in the ratio of 4:3:2, thus giving timpani a musical pitch which is easily discernible. This favorable relationship of modal frequencies is brought about by membrane stiffness and air loading; our experiments indicate that air loading is the more important factor. We have measured the frequencies of ten or more modes of vibration under various conditions: high and low tension, with and without the kettle, in air and helium atmospheres. The kettle raises the frequency of the lowest symmetric mode, and also fine tunes some of the higher modes; its most important role is that of a baffle, however.