The making of the harmonic drum
Brian L. Ball · Digital WPI · 2000
It has been shown that two Indian drums, the Mridanga and the Tabla, have a most desirable musical quality of harmonic overtones. It was first observed by C.V. Raman that not only do the drums have overtones in a harmonic ratio, but also that the higher overtones are degenerate. This degeneracy gives the Indian drums a more pronounced musical tone. The cause of this remarkable quality is the symmetrical weighting of the drumhead. The Finite Element Method (FEM) was used to numerically explore how a changing density profile affects the eigenvalues of the drum. The use of the Newton-Raphson multi-dimensional root finding technique was explored to find an optimal density profile that will yield the desired harmonic ratios of the frequencies of the drum.