The musical drums of the Indian subcontinent are known for their harmonic quality due to their non uniform membrane, requiring a precise distribution of mass. Extending the works of previous authors, the present work uses a non-parametric optimisation procedure to find an optimal density for a membrane loaded by air. The modes of the loaded membrane are computed using a Finite Element Method coupled with a Boundary Element Method, and a mimimum of inharmocity if found using a gradient algorithm with an explicitly computed gradient.