The eigenspectra of Indian musical drums

Abstract

In a family of drums used in the Indian subcontinent, the circular drum head is made of material of non-uniform density. Remarkably, and in contrast to a circular membrane of uniform density, the low eigenmodes of the non-uniform membrane are harmonic. In this work we model the drum head by a non-uniform membrane whose density varies smoothly between two prescribed values. Using a Fourier-Chebyshev spectral collocation method we obtain the eigenmodes and eigenvalues of the drum head. For a suitable choice of parameters, which we find by optimising a cost function, the eigenspectra obtained from our model are in excellent agreement with experimental values. Our model and the numerical method should find application in numerical sound synthesis.

Vibration analysis of a musical drum head under nonuniform density and tension using a spectral method

“…The drum head is modeled as a nonuniform membrane with a density that varies smoothly, and its eigenmodes and eigenfrequencies are calculated using the proposed numerical method. The numerical method used in this section is the same as that applied in previous work [5]. However, in the previous work, the parametric study of the number of grid points was insufficient, and therefore we explore the relation between the number of grid points and the accuracy of the proposed numerical method in more detail, particularly by making an aspect of comparison with experimental data.…”

“…As referred to in the Introduction, it is acknowledged that using spectral collocation methods offers the greatest accuracy for the least computational expense in this class of problem [5]. Thus, we adopt a Fourier-Chebyshev spectral collocation technique [8] to numerically analyze the wave equation for a nonuniform membrane.…”

“…Furthermore, Sathej and Adhikari used a spectral collocation method in eigenfrequency analysis to numerically analyze the vibration of a circular membrane under nonuniform density [5]. Their study demonstrated that the spectral collocation method can offer greater accuracy for this class of problem than the finite element method.…”

Finite-Difference model of mode shape changes of the Myanmar pat wain drum circle using tuning paste

“…Indian drums, especially tablas are very well studied in terms of the additional paste applied to their drum head [8] [7] called sihai which is placed concentric for the dayan and off-centric for the bayan drum. Varying the width, position, smoothness and strength of the sihai it was found that the harmonic overtone relations of the drum modes change and can meet values very close to harmonic ratios.…”

“…Physical models of the drum have been performed for Indian drum heads [8], the snare drum [2], or the bass drum [1]. Basic models of viscoelastic damping have mainly been discussed with Finite-Element Methods [13].…”