By using a sample of DNA-wrapped single-wall carbon nanotubes strongly enriched in the (6,5) nanotube, photoluminescence emissions observed at special excitation energy values were identified with specific mechanisms of phonon-assisted excitonic absorption and recombination processes associated with (6,5) nanotubes, including one-phonon, two-phonon, and some continuous-luminescence processes. Such detailed processes are not separately identified in three-dimensional semiconducting materials. A general theoretical framework is presented to interpret the experimentally observed phonon-assisted processes in terms of excitonic states.