Well-quantified directivity patterns of sound sources provide greater insights into their acoustical properties and the potential to simulate the propagation of their sounds in various settings. Moreover, clear descriptions of detailed spherically sampled directivities of highly complex and dynamic sound sources such as musical instruments have broad applications. Because spherical harmonics are a suitable basis set for representing functions on the sphere, this work reviews and compares methods for computing spherical harmonic expansion coefficients. It further presents distinct quadrature methods applicable to the five-degree polar and azimuthal sampling distribution commonly used in directivity measurements, and analysis regarding convergence and accuracy of the expansions. Finally, it presents selected results of spherical harmonic expansions of musical instruments.

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