We consider the implications of the most general two-body quark-quark interaction Hamiltonian for the spin-flavor structure of the negative parity L = 1 excited baryons. Assuming the most general two-body quark interaction Hamiltonian, we derive two correlations among the masses and mixing angles of these states, which constrain the mixing angles, and can be used to test for the presence of three-body quark interactions. We find that the pure gluon-exchange model is disfavored by data, independently of any assumptions about hadronic wave functions.