ON AN “OLD” CONCEPT OF QUANTITY

Abstract

Today music is just entertainment. Perhaps it is also a cultural fact, but in an aesthetic realm, foreign to science. Indeed this is the view that has prevailed in the last three centuries. Until the 17 th century however, music was regarded either as a practice or as a mathematical theory, that every good mathematician and every good musicologist knew. In ancient Greece music played an even greater role, in the platonic polis it was part of both basic education (with gymnastics and grammar) and higher education (with arithmetic, geometry and astronomy). In a previous paper I analyzed the crucial role played by musical mathematical theory in shaping ancient Greek mathematics. In this chapter my aim is to outline the role played by musical themes and musical mathematical theory between the Middle Ages and the early Modern Ages in the evolution of several ideas:. 1) Symbolic representation 2) Quantification of qualities: musical notation by neumes and tetragrams was the first example of the representation of a quality by a geometrical metaphor. 3) Opposition between the discrete and the continuous: time is continuous but music as a mathematical science is subordinated to arithmetic. 4) The correlation between arithmetic and geometric progressions: on the chord the sum of intervals tallies with the product of the corresponding ratios. 5) The numerical nature of ratios. In this way the evolution of musical mathematical theory in the 17 th century, from the arithmetic theory of harmonic consonances to the physical-mathematical theory of sound, can be interpreted as the emergence of a new view about the relation between mathematics and nature that shaped the Scientific Revolution: from mathematics as made up of immanent and immediately perceivable real attributes to mathematics as a representation language of a real, but concealed, structure of nature, attainable only by artificial experiment and measure. Such a dislocation explains the profound reasons for which the old connection between Muses and Science vanished in modern times, when musical harmony suddenly moved from the Scholastic Quadrivium to the Realm of Beauty, in perhaps the most astonishing turnaround in the history of human culture. This also hints at the role musical education could play in framing human cognition between the manipulation of signs and holistic perception.