Characteristics of digital waveguide meshes with more than three physical dimensions are studied. Especially, the properties of a 4-D mesh are analyzed and compared to waveguide structures of lower dimensionalities. The hypermesh produces a response with a dense and irregular modal pattern at high frequencies, which is beneficial in modeling the reverberation of rooms or musical instrument bodies. In addition, it offers a high degree of decorrelation between output points selected at different locations, which is advantageous for multi-channel reverberation. The frequencydependent decay of the hypermesh response can be controlled using boundary filters introduced recently by one of the authors. Several hypermeshes can be effectively combined in a multirate system, in which each mesh produces reverberation on a finite frequency band. The paper presents two hypermesh application examples: the modeling of the impulse response of a lecture hall and the simulation of the response of a clavichord soundbox.

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