Photon Dominated Regions (PDRs) are interfaces between the mainly ionized and mainly molecular material around young massive stars. Analysis of the physical and chemical structure of such regions traces the impact of far-ultraviolet radiation of young massive stars on their environment. We present results on the physical and chemical structure of the prototypical high UV-illumination edge-on Orion Bar PDR from an unbiased spectral line survey with a wide spectral coverage. A spectral scan from 480-1250 GHz and 1410-1910 GHz at 1.1 MHz resolution was obtained by the HIFI instrument onboard the Herschel Space Observatory. For molecules with multiple transitions we used rotational diagrams to obtain excitation temperatures and column densities. For species with a single detected transition we used an optically thin LTE approximation. In case of species with available collisional rates, we also performed a non-LTE analysis to obtain kinetic temperatures, H2 volume densities, and column densities. About 120 lines corresponding to 29 molecules (including isotopologues) have been detected in the Herschel/HIFI line survey, including 11 transitions of CO, 7 transitions of 13CO, 6 transitions of C18O, 10 transitions of H2CO, and 6 transitions of H2O. Most species trace kinetic temperatures in the range between 100 and 150 K and H2 volume densities in the range between 10^5 and 10^6 cm^-3. The species with temperatures and / or densities outside of this range include the H2CO transitions tracing a very high temperature (315 K) and density (1.4x10^6 cm^-3) component and SO corresponding to the lowest temperature (56 K) measured as a part of this line survey. The observed lines/species reveal a range of physical conditions (gas density /temperature) involving structures at high density / high pressure, obsoleting the traditional clump / interclump picture of the Orion Bar.