Triply periodic minimal surfaces (TPMS) lattice structures present outstanding properties such as lightweight, high strength, energy absorption, and wave propagation control, which are extensively investigated in recent years. However, one of the main challenges when designing TPMS is the proper selection of cell type and volume ratio in order to obtain the desired properties for specific applications. To this aim, this work provides a comprehensive numerical study of bandgap’s formation in the sub-2 kHz frequency range for the seven major cell type TPMS structures, including Primitive, Gyroid, Neovius, IWP, Diamond, Fischer–Koch S, and FRD, for a comprehensive range of volume ratios. Results show that these seven TPMS structures present a complete bandgap between the 3rd and 4th dispersion curves. The width of the bandgap is strongly dependent of the TPMS lattice and the widest bandgaps are seen on the Neovius and Primitive-based lattice (reaching a maximum width of 0.458 kHz and 0.483 kHz, respectively) for volume ratios over 0.3. Below this volume ratio, the bandgap of the Primitive structure becomes negligible, and the Neovius and IWP structures are the best candidates among the 7 tested TPMS cases. The central frequency of the bandgaps is less sensitive to the lattice and are predominantly tailored by the volume ratio. With this study, we demonstrate that the proper selection of the periodic cell type and volume ratio can tailor the bandwidth of complete bandgaps from a tens of Hz up to 0.48 kHz, while the central frequency can be selected from 0.72 to 1.81 kHz according to the volume ratio. The goal of this study is to serve as a database for the Primitive, Gyroid, Neovius, IWP, Diamond, Fischer–Koch S, and FRD TPMS structures for metamaterial designers.