Scientific Method in Ptolemy's Harmonics (review)

Ptolemy's Harmonics is an important source not only for the history of music, but also for the history and philosophy of science. Two recent monographs, by J. Solomon, and A. Barker, now provide a basis for a more widespread discussion of this much neglected work. Barker focuses on the part that is concerned with musical science proper (I, 1-III, 3), and more specifically on the scientific method it displays.

Barker uses an analysis of Ptolemy's programmatic statements in I, 1/2, as a key to a reading of Ptolemy's treatise. His exposition has the format of a commentary, with special emphasis on the methodologically relevant passages. For the most part, he follows the order of Ptolemy's text closely, providing historical background information in excursus form. One needs to read a complete text of Ptolemy's treatise along with Barker's exposition in order to understand some of his arguments. It is preferable to also use Düring's edition of the Greek text. One is rewarded with a detailed and in-depth analysis of the passages that helps one understand Ptolemy's method in harmonics as it unfolds in his treatise. This is so even if one disagrees with Barker's claims concerning Ptolemy's methodology.

These claims are outlined in chapter 2, on the basis of I, 1/2 of the Harmonics. The methodological program Barker filters out of the text remains vague in a number of important respects. One misses, for example, a clear exposition on what will count as a sufficient integration of "empirical and theoretical phases," and on what will count as "empirical." This is a serious drawback, since Barker claims that Ptolemy instantiates a complex scientific methodology with a decisive, fully integrated empiricist trait. The drawback is aggravated by the fact that the already vague terms of the postulated methodology have to be watered down considerably in the subsequent chapters to make them fit with Ptolemy's actual procedures. Ptolemy does not seem to deliver even on the vague terms. One may very well remain unconvinced both by Barker's initial arguments concerning Ptolemy's methodology, and by his attempts to show that Ptolemy's procedure in the Harmonics can count as a satisfactory instantiation. Perhaps Ptolemy's intentions are less ambitious. When he states (5.13 ff. Düring, ed.) that "the aim of the student of harmonics must be to preserve the hupotheseis . . ., as never in any way conflicting with the perceptions that correspond to most people's estimation," he may just mean that he intends to vindicate an essentially Pythagorean (locally modified) account by showing it does not conflict with the phenomena. In my view, he certainly delivers on this less ambitious program. In fact, it seems to me that the understanding of Ptolemy's argumentative path is impeded by Barker's interpretation of Ptolemy's goal of "saving the hupotheseis" as a commitment to the integration of a genuine empiricist trait.

Chapters 7 and 8 give an exposition of Ptolemy's tetrachord divisions. For the reader interested in an evaluation of the theoretical aspect of Ptolemy's scientific method, these are the central chapters of Barker's book. Barker provides a detailed analysis, together with an exposition of the historical and technical information needed for a non-specialist to follow both his and Ptolemy's argument. Barker's analysis reveals inter alia that a considerable part of Ptolemy's theory has no counterpart in the realm of phenomena perceived as musical, and that another part, concerning the single most important division of musical practice, is not justified, and not justifiable, by derivation from the principles. It is difficult to see how Ptolemy's account can nevertheless be viewed as a genuine integration of empirical and theoretical aspects. It appears to be an attempt at showing that an essentially Pythagorean theory...