Physical modeling of Tibetan bowls

Abstract

Tibetan bowls produce rich penetrating sounds, used in musical contexts and to induce a state of relaxation for meditation or therapy purposes. To understand the dynamics of these instruments under impact and rubbing excitation, we developed a simulation method based on the modal approach, following our previous papers on physical modeling of plucked/bowed strings and impacted/bowed bars. This technique is based on a compact representation of the system dynamics, in terms of the unconstrained bowl modes. Nonlinear contact/friction interaction forces, between the exciter (puja) and the bowl, are computed at each time step and projected on the bowl modal basis, followed by step integration of the modal equations. We explore the behavior of two different-sized bowls, for extensive ranges of excitation conditions (contact/friction parameters, normal force, and tangential puja velocity). Numerical results and experiments show that various self-excited motions may arise depending on the playing conditions and, mainly, on the contact/friction interaction parameters. Indeed, triggering of a given bowl modal frequency mainly depends on the puja material. Computed animations and experiments demonstrate that self-excited modes spin, following the puja motion. Accordingly, the sensed pressure field pulsates, with frequency controlled by the puja spinning velocity and the spatial pattern of the singing mode.