Can the MUSIC algorithm be used for period estimation? Prior works in this direction were based on modifying the search over the conventional complex-exponentials based pseudospectrum to look for harmonically spaced peaks. For applications where the period of the discrete signal can be well approximated by integers, this paper proposes much simpler integer valued basis functions. It is shown that this new re-formulation of MUSIC not only makes the pseudo-spectrum computation much simpler, but also offers significantly higher accuracy than the conventional techniques, especially for mixtures of periodic signals1.