We constructed a widely and continuously tunable terahertz frequency synthesizer traceable to a hydrogen maser linked to coordinated universal time. Photomixing of two optical frequency synthesizers, linked to the hydrogen maser via dual optical frequency combs, gave this THz synthesizer frequency uncertainty of 10⁻¹². To demonstrate the potential of wide and continuous tunability in the THz synthesizer, we tuned its output frequency up to 50 GHz discretely and 1.26 GHz continuously in the F-band while maintaining the unprecedented frequency uncertainty by using a uni-traveling-carrier photodiode as a photomixer. This THz synthesizer will be a powerful tool for broadband, high-precision THz spectroscopy and THz frequency metrology.