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The search for Earth-like exoplanets with the Doppler radial velocity (RV) technique is an extremely challenging and multifaceted precision spectroscopy problem. Currently, one of the limiting instrumental factors in reaching the required long-term 10⁻¹⁰level of radial velocity precision is the defect-driven subpixel quantum efficiency (QE) variations in the large-format detector arrays used by precision echelle spectrographs. Tunable frequency comb calibration sources that can fully map the point spread function (PSF) across a spectrograph’s entire bandwidth are necessary for quantifying and correcting these detector artifacts. In this work, we demonstrate a combination of laser frequency and mode spacing control that allows full and deterministic tunability of a 30 GHz electro-optic comb together with its filter cavity. After supercontinuum generation, this gives access to any optical frequency across 700–1300 nm. Our specific implementation is intended for the comb deployed at the Habitable-Zone Planet Finder (HPF) spectrograph and its near-infrared Hawaii-2RG array, but the techniques apply to all laser frequency combs (LFCs) used for precision astronomical spectrograph calibration and other applications that require broadband tuning.