Ptolemaaїs is the only Greek woman on record as a musical theorist. Most writings in Pythagorean harmonics after the fourth century BC were heavily influenced by Plato's Republic, with its rejection of empirical considerations and its insistence on the authority of reason, and especially by the cosmological and psychological implications of his musical construction of the World-Soul in the Timaeus. One of the Pythagorean approaches that Ptolemaїs describes seems nevertheless to preserve a pre-Platonic character, privileging reason over perception but still focused at least in part on the analysis of audible music; and so too do the Pythagoreans discussed by Ptolemy and Porphyry. The principle that a concord's ratio must be either multiple or epimoric has a significant consequence: the interval of an octave plus a fourth (which sense-perception, according to Aristoxenus, Ptolemy and many others, unquestionably recognizes as a concord) cannot really be concordant.