An acoustically dampened gas turbine engine having a gas turbine engine combustor with an acoustic damping resonator system is disclosed. The acoustic damping resonator system may be formed from one or more resonators positioned within the gas turbine engine combustor at an outer housing forming a combustor basket and extending circumferentially within the combustor. The resonator may be positioned in a head region of the combustor basket. In one embodiment, the resonator may be positioned in close proximity to an intersection between the outer housing and an upstream wall defining at least a portion of the combustor. The acoustic damping resonator system may mitigate longitudinal mode dynamics thereby increasing an engine operating envelope and decreasing emissions.