Composers on Mathematical Music
Subtext 207544


Historically, of course, music is no poor relation of the arts and sciences. In the golden age of Greece it occupied a post of honor. The Platonic dialogues show music to be never very far from the thoughts of Socrates and his fellow Athenians. Besides offering witty, elegant, and often profound comment on the subject, the dialogues give music an important philosophical role. In the Timaeus, Plato tells a “likely story” of a creator who imposed on originally irreconcilable elements the mathematical pattern of the ratios of a musical scale, in order to fashion the soul of the universe. Elsewhere, as in The Republic (Book III), Plato finds that music imposes order on the motions of the body and the soul, teaching gracious and harmonious conduct and giving the young student a knowledge of good and evil. Three years, says Plato in the Laws, should be devoted to learning how to play the lyre and to kindred musical subjects. Philosophical discussions must be included so that the student will never be deceived by “appearances” and forget the true music of which this earthly music is only a shadow. For a music lover only interested in sounds, the kind that conservatories then as now produced, Plato had contempt. They are “the last persons who would come to anything like a philosophical discussion, if they could help, while they run about at the Dionysiac festivals as if they had let out their ears to hear every chorus; whether the performance is in town or country—that makes no difference—they are there.”

The moral benefits to be derived from the study of music as Plato saw it gave music great importance in the Academy of Athens, where its relation to geometry and astronomy was endlessly discussed. This early association of subjects later played an important part in the plan of the Medieval university. Here music, one of the “seven liberal arts,” now systematized as a discipline, became a branch of mathematics. As the art of measurement, it was an object of major study for several centuries. Under this alliance with what we today call mathematical physics, our aural art, though occupying a lesser position, was widely cultivated. And in the Renaissance, so long as Medieval thinking continued to dominate education, no education, according to Thomas Morley, was complete without some actual musical training in playing or singing.

That the practice of musicians was deeply influenced by the liberal arts discipline is written on the pages of every treatise of the period. In turn, the practice of music itself influenced thinking in many different fields, as witness the treatises on architecture by Palladio and on astronomy by Kepler. Kepler in the early seventeenth century drew extended analogies between Copernican heliocentric theory and the art of polyphony of his day, contrasting it to Ptolemy’s analogy between Greek music and the geocentric theory. His method enabled him to describe the orbit of the planet Mars, a mathematical mystery before his time.

Elliott Carter



Composers on Mathematical Music: A Subtext Poem

Other Work by John Greschak

Public Domain