In the Harmonics, Ptolemy reveals that the heavens and human souls share the same formal structure. They are characterized by the same set of ratios, the ones studied by harmonics, the mathematical science that investigates the relations among musical pitches. In other words, harmonic ratios describe the relations among not only musical pitches but also the parts of the human soul and the movements and configurations of heavenly bodies. Moreover, Ptolemy explains why it is that these various objects are characterized by these same ratios. It is because of harmonia. This chapter argues that concept of harmonia is the crux of Ptolemy's ethical theory. It is because harmonia operates most fully in human souls, the heavens, and musical scale systems that human beings' mathematical study of the latter two sets of phenomena has the power to shape and transform their souls.
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