We have demonstrated the application of many-body expansions to calculations of the anharmonic, local-mode, OH-stretching vibrational frequencies of water clusters. We focused on five low-lying isomers of the water hexamer and the DD*(20,1) isomer of (H2O)21. Our approach provides accurate OH-stretching vibrational frequencies when treating one- and two-body interactions with the CCSD(T)-F12 level of theory and the three- and four-body interactions with the DF-MP2-F12 level. Additionally, we have investigated the physical origin of the large contribution that two- and three-body interactions make to the shifts of vibrational frequencies using symmetry-adapted perturbation theory (SAPT). We conclude that while two-body vibrational frequency shifts can be correlated linearly with electrostatic energies, all strongly shifted three-body interactions can be correlated to the induction energy with a single regression coefficient of approximately 70 cm-1 (kcal·mol-1)-1.