Annual Meeting / Congrès annuel 
Université Laval, Québec, 24-26 mai / May, 2001

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Committee / Comité

Konoval, Brandon (University of British Columbia)
Music and the Book of Nature : 
Pythagorean Tradition and Empirical Mathematics in the Discourses of Vincenzo Galilei

The Discourses, 1589-91, of Vincenzo Galilei (c. 1530-91) have received considerable scholarly interest in recent decades. Vincenzo’s investigations of musical consonance and dissonance have been said to articulate developments that were likewise central to the practice and conceptual foundations of early modern science. In particular, Vincenzo’s work has been taken to represent an early model of empirical science and a radical reformulation of the ontology of number essential to the birth of mathematical empiricism. Vincenzo is thus portrayed as exorcising the numerological ghost of Pythagoras from both the musical and scientific thought of his era. 

I review Vincenzo’s confrontation with the traditional Pythagorean ratios of musical consonance and their Renaissance counterparts by considering the experimental, ontological and historical claims of the Discourses.  Furthermore, I examine the arena of this confrontation--the debate engaged by Vincenzo with the pre-eminent music theorist, Gioseffo Zarlino (1517-90)--so as to clarify the relevant issues of tuning and musical practice that motivated Vincenzo’s work, comparing Vincenzo’s concerns with claims made on his behalf more recently by musicologists or historians of science. I highlight the difficulties encountered by Vincenzo as he attempted to rationalize divergent experimental results, insofar as these reveal the fundamental ontological challenges that confronted mathematical empiricism.

Far from “liberating” musical or scientific thought from an alleged tyranny of Pythagorean numerology, Vincenzo Galilei developed his own “empirical numerology” in attempting to provide a coherent mathematical reading of phenomena that otherwise revealed no consistent mathematical identity to him. Thus Vincenzo’s Discourses posit a challenge, not a solution, to an empirical reading of the Book of Nature in mathematical terms.  The significance of this challenge is acknowledged by Vincenzo’s son Galileo in the Discourses on Two New Sciences (1638), where the problem is engaged in attempts to relate pendulum motion to the ratios of the musical consonances.  Vincenzo’s contribution to early modern science is therefore best understood as a failure to integrate mathematics with certain phenomena of sound in empirical terms, one consequence of which was a rededication by Galileo to pursue empirical mathematics in the realm of motion.