Partial groups in the bell sound
André Lehr · The Journal of the Acoustical Society of America · 1986
The flexural vibrations of a bell can be classified into different groups, each group consisting of partials with an equal number of nodal circles in about the same position on the bell wall. A bell also shows extensional vibrations which seldom occur at frequencies below the nominal, except in carillon bells with a thick wall. These vibrations are sometimes important for the timbre of the bell in spite of the fact that their amplitudes are usually small because extensional vibrations have an antinode at the head of the bell. Research into the dependence of partial frequencies on wall thickness did not support the linear function predicted by the elementary bending theory. Measurements on especially designed bells that differed only in wall thickness were more consistent with an extensive theory of, e.g., a ring. Partials were found to shift in groups, not individually, as a function of increasing wall thickness. From a musical viewpoint, the group of flexural partials with a nodal circle at the waist of the bell is important in forming the bell’s primary and secondary strike notes. The bell’s timbre will depend on relative partial amplitudes, the partial intervals within groups, and the position of partial groups with respect to one another.