Greek Reflections on the Nature of Music (review)
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The focus of this book is Aristoxenus and his achievement in recognizing the universal laws governing the structure of music. Levin has spent several decades pondering the major issues raised in the book, and although I cannot anticipate how Pythagorean advocates might react to the book, I would suggest that she has resolved some of these Aristoxenian issues quite conclusively.
Levin's method of examining the nature of music is a focused study of the incommensurability of the whole-tone. As Levin explains, because the predominance of ancient Greek music theoreticians were Pythagoreans, they developed a preference for those intervals which mirrored the mathematical proportions of the measured cosmos, e.g. the octave (2:1), fifth (3:2), and fourth (4:3). But the whole-tone (9:8) stubbornly resisted rational analysis. Aristoxenus offered a completely different approach dependent not on precise mathematical ratios but on the inherent logic of music: within this context the incommensurability of the whole-tone is not relevant. Indeed, Aristoxenus defined a unit of twelve equal parts along the melodic time continuum, thereby establishing for the first time the well-tempered system of tuning, "an intellectual feat of no less brilliance" (9).
Levin sets the problem within wider theoretical and chronological contexts. The Introduction (xiii-xvii) associates the ancient Greeks' sensitivity to their musical pitch-accent and their production of prodigious amounts of musical poetry with their compulsion to analyze it thoroughly. It was therefore their particular predilections for musical sound and rational analysis that converged into this one vexing problem of musical irrationality.
Chapter 1 ("All Deep Things Are Song" [1-47]) offers a graceful essay on the nature of melody. Ranging from Bacchius to Wittgenstein, the essay follows the tradition of Pythagoras from his encounter with the anvils to his influence on Kepler and Leibniz. At times Levin's tendency to examine a single short quotation frustrates the reader, but her quotations prove her points and swiftly move the discussion along to demonstrate how music is physically, psychologically, and philosophically unique and all-inclusive. Her frequent use of dated citations renders the chapter, whether intentionally or not, a study in early- and mid-twentieth-century Rezeptionsgeschichte. [End Page 378]
Chapter 2 ("We Are All Aristoxenians" [48-87]) examines Aristoxenus' pivotal assumption that music is an organic phenomenon with its own logic. Despite the insistence of his Pythagorean predecessors and teachers, Aristoxenus claimed that musical space was homogeneous and that the nature of music was dissimilar to the spatio-temporal existence of the rest of nature.
Chapter 3 ("The Discrete and the Continuous" [88-120]) analyzes the concept of the continuum as the topology of melody and infinity. In the process Levin chronicles the Tarentine Aristoxenus, his encounters in Mantinea with Pythagoreans, and ultimate study with Aristotle in Athens, and then creates an interesting—albeit nonhistorical—debate with Theophrastus.
Chapter 4 ("Magnitudes and Multitudes" [121-53]) looks at Euclid and the Sectio Canonis, which is important for understanding the Pythagorean approach to the main issue, although the chapter is marred by the inclusion of graphics apparently rendered by a dot-matrix printer. Chapter 5 ("The Topology of Melody" [154-203]) offers an analysis of the harmony of the spheres, which "was in no sense understood as metaphorical; on the contrary, it was perceived to be as real as the movements of the planets themselves" (154). Here Levin brings in Jocelyn Godwin's superstring theory to connect musical intellect with not just the ancient planetary proportions but time itself. She does this to establish the importance of the topos of melody, which is a continuum. It was to perfect this study that Aristoxenus therefore avoided not only Pythagorean geometry but also the properties of musical instruments and musical notation.
Chapters 6 ("Aristoxenus of Tarentum and Ptolemaïs of Cyrene [204-40]) and 7 ("Aisthesis and Logos: A Single Continent" [241-95]) expand upon the points that Aristoxenus had few advocates and that the loss of most of his...
