Additive manufacturing has expanded greatly in recent years with the promise of being able to create complex and custom structures at will. Enhanced control over the microstructure properties, such as percent porosity, is valuable to the acoustic design of materials. In this work, aluminum foams are fabricated using a modified powder bed fusion method, which enables voxel-by-voxel printing of structures ranging from fully dense to approximately 50% porosity. To understand the acoustic response, samples are measured in an acoustic impedance tube and characterized with the Johnson-Champoux-Allard-Lafarge model for rigid-frame foams. Bayesian statistical inversion of the model parameters is performed to assess the applicability of commonly employed measurement and modeling methods for traditional foams to the additively manufactured, low porosity aluminum foams. This preliminary characterization provides insights into how emerging voxel-by-voxel additive manufacturing approaches could be used to fabricate acoustic metal foams and what could be learned about the microstructure using traditional measurement and analysis techniques.