We report results from a study with the numerical spectral model (NSM), which produces significant interannual variations in the diurnal tide. Applying Hines's Doppler spread parameterization, small-scale gravity waves (GWs) drive the quasi-biennial oscillation (QBO) and semiannual oscillation. With a GW source that peaks at the equator and is taken to be isotropic and independent of season, the NSM generates a QBO with variable periods around 26 months and zonal wind amplitudes close to 25 m s-1 at 30 km. As reported earlier, the NSM reproduces the observed equinoctial maxima in the diurnal tide at altitudes around 95 km. In the present paper it is shown that the QBO also modulates the tide such that the seasonal amplitude maxima can vary from one year to another by as much as 30%. To shed light on the underlying mechanisms, the relative importance of the linearized advection terms is discussed, which involve the meridional and vertical winds of the diurnal tide. These interactions generate pronounced QBO modulations of the tide at altitudes below 50 km. In the mesosphere between 50 and 80 km the signature is not well defined because of interference from the seasonal variations. At altitudes above 80 km, however, the QBO-related interannual variations of the tide are again relatively large, but they are generated primarily by GW momentum deposition. Since the period of the QBO is variable and its phase is relative to the seasonal cycle changes, the magnitude of the QBO modulation of the tide in the upper mesosphere varies considerably as our long-term model simulation shows. This intermittency must be attributed to nonlinear interactions, and GW drag (momentum deposition) is discussed as a potential candidate.