The robust and efficient computation of the macroscopic tangent moduli represents a challenging numerical task in the process of the determination of the effective macroscopic properties of heterogeneous media. The aim of the present contribution is to compare the performances of three numerical techniques for the computation of the tangent moduli via the periodic homogenization multiscale scheme: the condensation technique, the fluctuation technique and the perturbation technique. A total Lagrangian approach is adopted in the formulation of the equations governing the periodic homogenization scheme as well as in the derivation of the macroscopic tangent moduli. Through a comparative study, the condensation technique is shown to have better performance as compared to the two other techniques.