We studied the spectral evolution of plasmon modes associated with silver nanotriangles as a function of dielectric overlayer thickness in the range of 5-300 nm. A substantial red-shift of the resonance is observed that oscillates with increasing over-layer thickness. We explain this previously unreported oscillation through the cavity quantum electrodynamical effect of the array of triangles combined with the dielectric overlayer. The red-shift, though substantial, is less than expected. Comparison with numerical models indicates that this discrepancy is due to very tight field confinement around the tips of the triangles.