Group theory and the bell

Abstract

It is shown that the modes of vibration of the bell can be classified into families according to their behaviour under the symmetry operations of the undistorted bell. These families are characterized by the number of nodal meridians rather than the number of nodal circles used in the usual ad hoc classification scheme. The phenomenon of bell warble is shown to be a direct consequence of the approximate nature of the symmetries of real bells and a new practical method for removing warble is suggested. It is argued that certain misshapen medieval bells were eccentrically cast not because of poor technique but deliberately in order to reduce warble.