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We study the effect of cubic and tidal interactions on the spectrum ofgravitational waves emitted in the inspiral phase of the merger of twonon-spinning objects. There are two independent parity-even cubic interactionterms, which we take to be $I_1 = {R^{\alpha \beta}}_{\mu \nu} {R^{\mu\nu}}_{\rho \sigma} {R^{\rho \sigma}}_{\alpha \beta}$ and $G_3 = I_1-2R^{\alpha}\,_{\mu}\,^{\beta}\,_{\nu} R^{\mu}\,_{\rho}\,^{\nu}\,_{\sigma}R^{\rho}\,_{\alpha}\,^{\sigma}\,_{\beta}$. The latter has vanishing puregraviton amplitudes but modifies mixed scalar/graviton amplitudes which arecrucial for our study. Working in an effective field theory set-up, we computethe modifications to the quadrupole moment due to $I_1$, $G_3$ and tidalinteractions, from which we obtain the power of gravitational waves radiated inthe process to first order in the perturbations and leading order in thepost-Minkowskian expansion. The $I_1$ predictions are novel, and we find thatour results for $G_3$ are related to the known quadrupole corrections arisingfrom tidal perturbations, although the physical origin of the $G_3$ coupling isunrelated to the finite-size effects underlying tidal interactions. We showthis by recomputing such tidal corrections and by presenting an explicit fieldredefinition. In the post-Newtonian expansion our results are complete atleading order, which for the gravitational-wave flux is 5PN for $G_3$ and tidalinteractions, and 6PN for $I_1$. Finally, we compute the correspondingmodifications to the waveforms.

From amplitudes to gravitational radiation with cubic interactions and tidal effects