Efficient synthesis of tension modulation in strings and membranes based on energy estimation

String and membrane vibrations cannot be considered as linear above a certain amplitude due to the variation in string or membrane tension. A relevant special case is when the tension is spatially constant and varies in time only in dependence of the overall string length or membrane surface. The most apparent perceptual effect of this tension modulation phenomenon is the exponential decay of pitch in time. Pitch glides due to tension modulation are an important timbral characteristic of several musical instruments, including the electric guitar and tom-tom drum, and many ethnic instruments. This paper presents a unified formulation to the tension modulation problem for one-dimensional (1-D) (string) and two-dimensional (2-D) (membrane) cases. In addition, it shows that the short-time average of the tension variation, which is responsible for pitch glides, is approximately proportional to the system energy. This proportionality allows the efficient physics-based sound synthesis of pitch glides. The proposed models require only slightly more computational resources than linear models as opposed to earlier tension-modulated models of higher complexity.