Byzantine Musical Theory (Harmonics)

Harmonics was one of the four mathematical sciences in the Byzantine higher education curriculum, together with Arithmetic, Geometry, and Astronomy (what was called quadrivium in the Latin West). Our knowledge of Byzantine harmonics is rather limited, as only two or three of the relevant treatises have been published in new editions. In this paper a systematic approach is attempted, while, at the same time, keeping distances from the well-studied practical aspect of Byzantine music, i.e. ecclesiastical music. Furthermore, the tradition of Greek musical theory (both Pythagorean and Aristoxenian), which the Byzantines developed further from a dual, both textual and educational, interest, presenting us at the same time with some original contributions.