Connection between Chladni Plates and Projective Geometry?

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Does anybody know of a connection between Chladni Plates and Projective Geometry? Any published research on the subject? I am interested to know if Chladni Plates (or surfaces) can be explained/expressed in projective-geometric terms.

Chladni Plates http://en.wikipedia.org/wiki/Ernst_Chladni#Chladni_figures

Chladni plate interference surfaces http://paulbourke.net/geometry/chladni/