Descartes: A Biography

c CUNYB/Clarke     December, :

In Search of a Career (–) 

involved. One of these was a familiar problem about the acceleration of

falling bodies.The other problem resulted from their joint discussion of

an equally commonplace issue in theories of music. This resulted in one

of Descartes’ first essays, theCompendium of Music, which he completed

in manuscript form and dated at Breda onDecember.

This apparent deviation from scientific investigations into music is easy

to understand. Music had been taught as part of mathematics for gener-

ations, and was recognized as one of the four subjects in the medieval

quadrivium(arithmetic, geometry, music, and astronomy). Philosophers

since the time of Pythagoras had dreamed of discovering a natural har-

mony in the universe that would be expressed in mathematical terms.

This suggested that, if one could crack that cosmological code and then

express it in musical notation, one could use music to help bring the

human soul into harmony with the universe. This Pythagorean and faintly

mathematical-mystical inspiration was expressed, in rigorous form, in

attempts to find an ideal mathematical division of a monochord to pro-

duce notes that would resonate, in some sense, with the harmony of the

universe. One sees remnants of that tradition in some of Descartes’ con-

temporaries, such as Kepler’sHarmony of the World() and Mersenne’s

Universal Harmony(). There was nothing novel, therefore, in the

Cartesian attempt to match musical notes with lengths of a monochord;

it had long been established that the pitch of a sound is related to the

length of a vibrating string. Descartes’ contribution, though minor, lay

elsewhere.

The Pythagorean tradition assumed that the objective of musical studies

was to express the natural harmony of the universe, even if only feebly,

in musical harmonies. The tradition of tuning stringed instruments that

resulted from this tradition limited the acceptable ratios of lengths of a

monochord to:(the octave) and:(pure fifth), on the assumption

that the simplest mathematical ratios could best capture the relations

between different sounds. The problems associated with these limitations

forkeyboard instruments had been recognized as early asbyGioseffo

Zarlino. One of Descartes’ Dutch contemporaries, Simon Stevin (–

), also made a modest contribution, in a posthumously published

short treatise, to the production of a tempered intonation.Thus the

issues associated with devising an equal temperament were familiar to

almost anyone working in this field in. Descartes joined this debate

as evidence of his mathematical skills, but primarily as an expression of his