Type Ia supernovae (SNe Ia) span a range of luminosities and timescales, from rapidly evolving subluminous to slowly evolving overluminous subtypes. Previous theoretical work has, for the most part, been unable to match the entire breadth of observed SNe Ia with one progenitor scenario. Here, for the first time, we apply non-local thermodynamic equilibrium radiative transfer calculations to a range of accurate explosion models of sub-Chandrasekhar-mass white dwarf detonations. The resulting photometry and spectra are in excellent agreement with the range of observed nonpeculiar SNe Ia through 15 days after the time of B-band maximum, yielding one of the first examples of a quantitative match to the entire Phillips relation. The intermediate-mass element velocities inferred from theoretical spectra at maximum light for the more massive white dwarf explosions are higher than those of bright observed SNe Ia, but these and other discrepancies likely stem from the one-dimensional nature of our explosion models and will be improved upon by future non-local thermodynamic equilibrium radiation transport calculations of multidimensional sub-Chandrasekhar-mass white dwarf detonations.