It will be shown how the non-relativistic quark model, with both flavor dependent and flavor independent effective quark-quark interactions, matches to the $1/N_c$ quark operator basis. Analytic expressions in terms of radial integrals are obtained for the $1/N_c$ operator coefficients. Several new, parameter free relations between the masses and the two mixing angles of the negative parity $L=1$ excited baryons will be presented. They can discriminate between quark-quark interactions with different spin-flavor structures. Within the present experimental uncertainties, consistency with the best values of the mixing angles, as determined by a recent global fit to masses and decays, does not exclude any of the two most extreme possibilities of flavor dependent (independent) quark-quark interactions, as generated by pion (gluon) exchange models.