«La Grandezza Del Numero Sonoro»: Canonic Techniques, Combinatorics, and Early Scientific Thought in Seventeenth-Century Rome

Abstract

<p>SOME MUSICAL ACHIEVEMENTS in early seventeenth-century Rome are less well known in today's music histories. Not without justification, historians have concentrated on the development of musical genres like the late madrigal, the monody, the opera, the oratorio, and the new instrumental genres. In part, this situation has arisen out of more recent historiographic biases like the search for the origins of modern music or the quest for musical innovation. This chapter focuses instead on the early seventeenth-century Roman school of contrapuntists who cultivated <i>artificioso</i> compositions. Although this learned style originated in the previous century, this generation of composers extended it, principally though the techniques of canon. Here, we speak of canon in the sense of a set of compositional techniques for combining a melodic subject with itself either unaltered or transformed systematically by devices like transposition, contrary motion, retrograde, augmentation and diminution.</p><p> The seventeenth-century resurgence of canon at centres like Rome shares some of its motivating forces with Early Modern scientific thought. Without too much difficulty, ingenious canonic techniques can be connected to a renewed interest in combinatorics as a tool for the analysis of the natural world. Canon echoes significant changes in European intellectual society, a musical manifestation of the mathematicization of knowledge of the natural world in writings of new astronomers like Johannes Kepler and Galileo Galilei, wherein natural laws of the sensible world are modelled mathematically, and natural phenomena explored through rational induction. Motivated by an interest in combinatorics, early seventeenth-century composers sought to extend traditional modes of contrapuntal composition as far as possible within the 'laws' of music. Visual representation also plays a part in this playful experimentation, although this element will only be explored here in terms of the 'analytical' use of musical scores.</p><p> At the epistemological heart of innovative experimentation by early seventeenth-century Roman contrapuntists in musical composition is mechanism, that knowledge system which conceptualizes material structures or objects in terms of their interrelation or interconnection of component parts, and the increased use of mathematics to model chose structures in nature. Through the lens of mechanism, historians can begin to understand firstly a renewed emphasis upon combinatorics in the early seventeenth century. Secondly, mechanism, when actualised by artificial machines that crowd seventeenth-century discourse, provides a pervasive thought paradigm that unifies an understanding of the mutually beneficial relationship between arc and science in this period.</p>