The multidimensional modeling techniques presented in the previous section would seem to be an obvious choice for synthesizing a variety of percussion instrument sounds. For example, a circular membrane can be modeled with a two-dimensional waveguide system and then coupled to a drum cavity model. However, there are several drawbacks to this approach: 1. It requires significant computational power; and 2. The resulting sounds are often not significantly better than ones produced using efficient modal synthesis techniques. Cook (1997) proposed a series of simplified approaches to the modeling of percussion sounds that he generally refers to as ``physically informed sonic modeling (PhISM)'' Drawing on techniques from physical modeling, Fourier analysis/synthesis, and granular synthesis, a sonically convincing and computationally efficient synthesis method is developed that is founded on an understanding of the physical behavior of systems without actually attempting to accurately simulate their vibrational patterns and interactions.
Cook (1997) offers two PhISM approaches: Physically Informed Control of Modal Synthesis (PhISAM) and Physically Informed Stochastic Event Modeling (PhISEM). PhISAM provides augmented parametric control to modal synthesis models. The PhISEM algorithm is based on pseudorandom overlapping and adding of small grains of sound or pseudorandom modification of the parameters of a parametric synthesis model, according to rules and parameters derived from off-line physical simulations and heuristics. The PhISEM approach is suitable for synthesizing sounds characterized by random interactions of sound-producing component objects, such as a maraca, sleigh bell, bamboo wind chimes, and water drops.
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