THE WRITINGS of BOETHIUS and the COGITATIONS of JACOBUS de ISPANIA on MUSICAL PROPORTIONS

Thirteenth-century music theory, which followed the ideas of Boethius, was very largely concerned with the numerical proportions associated with musical intervals. Numbers provided an intellectual foundation that did not suffer from the vagaries of the senses. In general neither Boethius nor his greatest exponent, Jacobus (writing c. 1320), explained how they obtained the numbers they used. In this essay I attempt to reconstruct their methods and show how they developed ideas from the first-century Nicomachus to achieve their aims. Jacobus is explicit in saying that the use of the relatively newly introduced methods of algorism - calculating with Arabic numerals - made his cogitations easier. I shall argue that the manuscripts we have of his Speculum musicae show that Jacobus did indeed use algorism in his work.