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The height-height correlation function for a fluctuating interface betweentwo coexisting bulk phases is derived by means of general equilibriumproperties of the corresponding density-density correlation function. Awavelength-dependent surface tension $\gamma(\mathbf{q})$ can be defined andexpressed in terms of the direct correlation function$c(\mathbf{r},\mathbf{r}')$, the equilibrium density profile$\rho_{\circ}(\mathbf{r})$ and an operator which relates density to surfaceconfigurations. Neither the concept of an effective interface Hamiltonian northe difference in pressure is needed to determine the general structure of theheight-height correlations or $\gamma(\mathbf{q})$, respectively. This resultgeneralizes the Mecke/Dietrich surface tension $\gmd$ (Phys. Rev. E {\bf 59},p. 6766 (1999)) and modifies recently published criticism concerning $\gmd$ (P.Tarazona, R. Checa and, E.Chac\'{o}n: Phys. Rev. Lett. {\bf 99}, p. 196101(2007)).

From density to interface fluctuations: the origin of wavelength dependence in surface tensions