A Sense of Proportion

Boethian arithmetic formed the basis of music theory for the medieval encyclopedist, Jacobus. His monumental Speculum musicae shows us how people around 1300, and particularly in the University of Paris, were slowly accommodating themselves to the newly rediscovered works of Aristotle, while the long-known works of Euclid and Boethius still gave a definitive theoretical basis to music. Not without effort Jacobus reworked Boethius and went further, though still using Boethian techniques. One difficulty he encountered was the problem of dividing the tone into two equal parts.