More than a Musician

We so often study famous people in isolation, forgetting that their lives and successes probably overlapped other well-known people. Imagine the possibilities when people of vision and ingenuity met with and influence each other?

Philippe de Vitry (1291-1361) is not a well-known name today, but in his lifetime he was acknowledged as the greatest musician of the age, and his own works and his connections with others are worth knowing. In his lifetime, he was a diplomat, a soldier, a poet, a composer and music theorist. Like most university-educated men of the Middle Ages, de Vitry was in Holy Orders and held several clerical positions, finally being appointed Bishop of Meaux by Pope Clement VI.

Some of the motets he composed have survived. His chief contribution to music, however, was in the evolving system of notation. In Ars nova notandi (Art of the new notation), de Vitry improved on Franconian musical notation that had been set out in Franco of Cologne's Ars Cantus Mensurabilis (The Art of Measurement of Songs); de Vitry recognized the existence and importance of duple and triple meter. For connoisseurs of music:

In the treatise Vitry recognizes the existence of five note values (duplex longa, longa, brevis, semibrevis, and minima), codifies a system of binary as well as ternary mensuration at four levels (maximodus, modus, tempus, prolatio), and introduces four time signatures. He also discusses the use of red notes to signal both changes of mensural meaning and deviations from an original cantus firmus. (source)

And of course he knew other accomplished figures of his age, such as Petrarch, Nicholas Oresme, and Gersonides. In fact, de Vitry's musical approach to mathematics (the two subjects were closely linked in medieval education) prompted him to request of Gersonides a work to prove a theory. This 1342 work, De harmonicis numeris (On the harmony of numbers), maintained that, "except for the pairs 1-2, 2-3, 3-4, and 8-9, it is impossible for two numbers that follow each other to be composed of the factors 2 and 3." (source) The result is known today as the Theorem of Gersonides.

The Oxford Calculators

The men before Galileo

In the first half of the 1300s, a handful of scholars at Oxford University, most of whom were at Merton College, applied observation and careful thought to what had been proposed by Aristotle and other Classical philosophers.

Their first innovation was to distinguish between kinematics (motion of bodies regardless of the forces acting upon them) and dynamics (the study of the forces that initiate or affect motion). Their use of observation, experimentation, and mathematics led them to understand that Aristotle was wrong when he said the motion/speed of a falling body was determined by its weight (which, to Aristotle, was affected by the proportions in the object of the four elements; water and earth tended to make it fall faster, while a greater amount of fire or air made it fall more slowly). They understood that two bodies of different weights accelerated similarly; they were able to prove this with math. This knowledge spread to universities on the continent. Nicholas Oresme, a bishop in France, and Giovanni di Casali, a Franciscan in Italy, were each inspired to produce graphs and diagrams to explain this motion.

Despite this dissemination of information, it is assumed that these works were not likely to have been known by Galileo (1564-1642), who gets the credit in physics texts for developing the theory of falling bodies.