De Gruyter (2016) h/b 326 pp £89.99 (ISBN 9783110419672)
Imagine that we lived in a world in which sound-recording technology did not exist, and we wanted to provide information to posterity about exactly how a stringed instrument, say an 8-stringed lyre, was tuned—that is, to which precise pitches. In the 2nd C AD, a mathematical genius with considerable practical skills, the polymath Claudius Ptolemy, achieved that goal. The modern investigator who sets out to reconstruct the sounds of ancient music—a project that I am currently engaged on together with specialist colleagues across the world—is hugely indebted to Ptolemy for the measurements preserved in his Harmonics. In that book Ptolemy gives precise measurements that he made on a purpose-built apparatus, the so-called kanōn, constructed with strings and moveable bridges to replicate the tension of strings of an ancient lyre. As a result, we can recreate with minute accuracy the different tunings of lyre-strings that were actually used in Ptolemy’s day.
While the value of the Harmonics’ painstaking mathematisation of musical intervals is indisputable, Ptolemy inherited a lively tradition of scholarly debate going back to Aristotle and Plato about the nature of musical sound. Ptolemy himself was therefore concerned to justify his mathematical approach to musical intervals, and to relate it to the qualitative approach promoted by the school of Aristoxenus. About a hundred years after Ptolemy’s death, the Neoplatonic philosopher Porphyry (late 3rd C AD) sought to comment on and elucidate Ptolemy’s views and arguments; his Commentarius here reviewed is the only surviving ancient commentary on a technical text.
One central issue had long been debated by the competing schools named after Pythagoras and Aristoxenus: how far should the intervals of music be judged by sense criteria, and how far by mathematical measurement? On this matter Porphyry respectfully diverges from Ptolemy, concluding that differences in pitch are in practice differences of quality rather than quantity. A practising musician can only agree: while Ptolemy’s mathematical approach provides a firm theoretical basis for relations between notes, in pitching a note or an interval ‘correctness’ cannot be established by mathematical means.
Porphyry’s work is far from easy to read and understand in the original Greek. To tackle the Commentarius, superbly edited and presented by Massimo Raffa in this volume, is a forbidding task. Fortunately, a recent publication by Andrew Barker (CUP 2015) gives a text of the Commentarius with an excellent English translation, together with a lucid introduction and notes to help students engage with this difficult but rewarding treatise. Massimo Raffa would be happy to acknowledge that his own consummate scholarship may best be enjoyed by readers who can simultaneously consult his mentor’s excellent book.
Armand D’Angour—Jesus College, Oxford