The Science of Harmonics in Classical Greece (review)

In 1562, the humanist author of De modis musicis antiquorum, Girolamo Mei, wrote to his mentor, Piero Vettori, on Greek harmonic theory, "I had to turn completely around more than twice before I could arrive at the truth. I swear to you that I have passed more than ten nights without sleeping because of these trifles" (Letters, ed. Palisca [1977] 181). By contrast with Mei, Andrew Barker's masterly volume on empirical harmonikoi and music mathematikoi, the culmination of thirty years' work on harmonic science in the fifth and fourth centuries, demonstrates that the problems and controversies raised by those who measured musical intervals by hearing or by numbers (see Plato, Rep. 531) were no trifles. In Timaeus harmonics even conjures the structure of the universe. Yet both scholars would acknowledge the difficulties of their tasks.

After part I's "Preliminaries," in part II ("Empirical Harmonics") Barker first analyzes the complex, largely unstudied evidence for the harmonikoi, at once empirical analysts and practicing (perhaps even "anti-theoretical") musicians, who among other things diagrammed played music by quartertones quite possibly since the early fifth century (35–36, 78–88). Like other contemporary humanists, these men sought to order the phenomena of human culture. A Leitmotif of Barker's study is the active engagement by both harmonikoi and mathematikoi with actual music. In key discussions, Barker attributes to fifth-century harmonikoi the "strange and irregular scales" which Aristides presents as the harmoniai in Plato's Republic. He also explains—a new star?—Eratokles' apparently unique attempt to systematize music.

After presenting Aristotle's Posterior Analytics on what constitutes scientific knowledge, material essential for understanding the Peripatetic Aristoxenos' more rigorous and superior conception of his work, Barker undertakes a densely argued, 146-page analysis of Aristoxenos' Elementa Harmonica. He starts with a survey of Aristoxenos' life and the structure and composition of EH (deriving from lectures, book 2 revised book 1 which still remained useful; book 3 revised what followed book 1). Often critical of earlier harmonikoi, book 1 focuses on the proper scope and limits of harmonics: a complete study of the patterns of melodic structures and the principles that guide them, as determined by empirical perception. On book 2, Barker tackles various conceptual and methodological problems involved in Aristoxenos' concept of harmonic science, offering, e.g., eight pages on notes' dunamis, and arguing the importance of Aristotelian demonstrative reasoning starting from observation. He then explores book 3's twenty-three theorems about melodic sequences. A concluding chapter links Aristoxenos with some realities of musical practice: composition, music criticism, and music êthos.

Part III, "Mathematical Harmonics," gives a chapter each to five late fifth- and fourth-century giants: the Pythagoreans Philolaus and Archytas, Plato, Aristotle, and Theophrastus. Unlike the harmonikoi, these gentlemen are mostly well known, so with little ado Barker plunges into major problems. Thus, a famous fragment of Philolaus is a "hybrid," mixing mathematical and empirical calculations in cosmological analyses. Archytas' requirement that music conform to mathematical principles leads into dense mathematical discussions; yet Archytas based his work on the realities of musical practice. Even for Plato's more purely mathematical uses of music, Barker canvasses how far Republic (316) and even Timaeus (320–324), with its universal scale, reflect heard music. Relevant material in Aristotle, disiecta membra, is heavier going, because (Barker argues) Aristotle was not especially interested or competent in what he considered a specialist discipline. After a lengthy chapter on the complex mathematical harmonics of Sectio Canonis ("division of the monochord"), also "bridging" empirical and mathematical harmonics and "in tune with musical realities," Barker turns to Theophrastus' critique of the mathematikoi, for example for their quantification (instead of qualification) of pitch, and his own idea of music as a movement of the soul. A postscript indicates the less important work in harmonics of later centuries.

This is a lucid, nearly flawless, and polished performance, delightfully written—even the many technical discussions show clarity and good sense—and...