The origin of the charge density wave in ${\mathrm{TaTe}}_4$ is discussed on the basis of a first-principles density functional theory analysis of the Fermi surface, electron-hole response function, phonon band structure of the average structure, and structural optimization of the modulated phase. Analysis of the band structure and Fermi surface of the average structure clearly proves that despite the presence of $\mathrm{Ta}{\mathrm{Te}}_4$ chains in the crystal structure, $\mathrm{Ta}{\mathrm{Te}}_4$ is in fact a 3D material as far as the electronic structure near the Fermi level is concerned.