CHARTING BOETHIUS: MUSIC AND THE DIAGRAMMATIC TREE IN THE CAMBRIDGE UNIVERSITY LIBRARY’S DE INSTITUTIONE ARITHMETICA, MS II.3.12

Abstract This article discusses a full-page schematic diagram contained in a twelfth-century manuscript of Boethius’ De institutione arithmetica and De institutione musica from Christ Church Cathedral, Canterbury (Cambridge University Library MS Ii.3.12), which has not yet been the subject of any significant musicological study despite its remarkable scope and comprehensiveness. This diagrammatic tree, or arbor, maps the precepts of the first book of De institutione arithmetica into a unified whole, depicting the ways music and arithmetic are interrelated as sub-branches of the quadrivium. I suggest that this schematic diagram served not only as a conceptual and interpretative device for the scribe working through Boethius’ complex theoretical material, but also as a mnemonic guide to assist the medieval pedagogue wishing to instruct students in the mathematics of musica speculativa. The diagram constitutes a fully developed theoretical exercise in its own right, while also demonstrating the roles Boethian philosophy and mathematics played in twelfth-century musical scholarship.