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Published:
Dec 4, 2013DOI:
10.4314/just.v33i2.8Keywords:
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The Mathematics of Ghanaian circular musical drumheads: varying tension versus constant tension. The case of the ‘Donno’
Abstract
Most drums used in Africa and in other parts of the world have varied shapes and sizes in their design. The hourglass shaped talking drums in Ghana is a pressurized drum which alters the tension on the drumhead, and as a result the pitches of the sounds emanating from it due to the strings that hold the drumhead in place, both from its upper and lower circumference. Remarkably, and in contrast to the circular drum with constant tension on the drum head, this drum possesses both harmonic and rhythmic characteristics. In this work the drumhead is modeled, by making the tension in it to vary as a periodic function of time, using the two dimensional wave equation. The separated Ordinary Differential Equations (ODEs) are solved and the Fourier- Bessel coefficients are determined using the initial and boundary conditions imposed on the equation. For a suitable choice of radial functions, the normal modes from our model are in good agreement with experimental values for harmonic instruments which produce integral overtones.
Keywords: Talking drum, Fourier-Bessel , Eigenvalues, rhythmic, harmonic
