  We describe a method for comparing the real analytic eigenbranches of two
families of quadratic forms that degenerate as t tends to zero. One of the
families is assumed to be amenable to `separation of variables' and the other
one not. With certain additional assumptions, we show that if the families are
asymptotic at first order as t tends to 0, then the generic spectral simplicity
of the separable family implies that the eigenbranches of the second family are
also generically one-dimensional. As an application, we prove that for the
generic triangle (simplex) in Euclidean space (constant curvature space form)
each eigenspace of the Laplacian is one-dimensional. We also show that for all
but countably many t, the geodesic triangle in the hyperbolic plane with
interior angles 0, t, and t, has simple spectrum.
