Approximate two-fermion interactions and Bethe-Salpeter equations for hadron spectra are obtained by making a Fock space expansion of the quantum chromodynamics (QCD) mass eigenstate. Following a partial wave decomposition, we perform an average over quartic gluon vertices and a root mean square (rms) average over cubic vertices. The expansions in terms of quark and gluon configurations are truncated. Equations for the gluon eigenvalues and eigenvectors are derived and approximate solutions are obtained analytically. Using values for the QCD coupling constant and the quark rest masses obtained from a relativistic two- and three-constituent quark model as starting values, the resulting algebraic eigenvalue equations for the mesons and the light baryons are then solved using a multiscale expansion in harmonic oscillator eigenfunctions. Through an approximate but analytic treatment we demonstrate that, at large distances our formalism gives rise to an effective two fermion potential exhibiting linear confinement. That is, we do not introduce any phenomenological confinement interaction. With minor adjustments of the quark rest masses, our results compare favorably with the results of the phenomenological two- and three-constituent quark models and with experiment.