Energy based synthesis of tension modulation in membranes

Above a certain amplitude, membrane vibration becomes nonlinear due to the variation of surface tension. This leads to audible pitch glides, that greatly contribute to the characteristic timbre of tom-tom drums of the classical drum set, and many other percussion instruments. Therefore, there is a strong motivation to take the tension modulation effect into account in drum synthesis. Some models do already exist that model this phenomenon, however, their computational complexity is significantly higher compared to linear membrane models. This paper applies an efficient methodology previously developed for the string to model the quasistatic part (short-time average) of the surface tension. The efficient modeling is based on the linear relationship between the quasistatic tension and membrane energy, since the energy can be computed at a relatively low computational cost. When this energy-based tension modulation is added to linear membrane models, the perceptually most relevant pitch glides are perfectly synthesized, while the increase in computational complexity is negligible.