We present a scaling theory for the vibrational properties of tenuous fractal objects and a numerical calculation of the density of states for percolation clusters and diffusion-limited aggregates. A microscopic elastic Hamiltonian is used, which contains bending energy terms and properly describes the elasticity of such structures. We find that the density of states is weakly divergent at low frequencies implying that fractal aggregates relax to a new configuration beyond a critical size.