c. 108 c.e.–c. 165 c.e.
Critiqued Current Theories.
The Harmonika of Claudius Ptolemy is considered to be second only to Aristoxenus in importance to the understanding of Greek music theory. A well-respected geographer, astronomer, and mathematician, Ptolemy was born at Pelusium, Egypt, around 108 c.e., and died near Alexandria around 165 c.e. The lexicographer Suda says that he lived during the reign of the emperor Marcus Aurelius (161–180 c.e.); he worked in the cities Canopus and Alexandria, writing many scientific books; he is one of the founders of the field of astronomy. In the three books of the Harmonika, Ptolemy employed Pythagorean mathematical concepts in his explanation of tuning systems, sound, pitch, and consonance, but he carefully critiqued both the Pythagorean and Aristoxenian definitions, noting the strengths and weaknesses of each approach. He agreed with the Aristoxenian principle that the purpose of keys is to bring the different segments of the "Greater Perfect System" (different species of octave, each with its own particular character) into the most comfortable vocal register. He regarded the pitches forming the interval of an octave as homophones, and therefore functionally identical.
Developed Own Theories.
In Book II, Ptolemy developed his own theory of the tonoi (keys or scales), restructuring them to demonstrate his belief that the only perfect scale was one that contained all the species of the basic consonances. Thus, for Ptolemy, the octave was not a perfect scale, as "previous scholars" had asserted. Ptolemy's book is full of impressive theoretical details (he must have had access to the great library at Alexandria); yet, the metaphysical view of music, expounded by both the Pythagoreans and the followers of Aristotle, is evident; the book's overall design treats music as a model for higher universal order and understanding.
Andrew Barker, ed., Greek Musical Writings (Cambridge: Cambridge University Press, 1984–1989).
Thomas J. Mathiesen, Apollo's Lyre: Greek Music and Music Theory in Antiquity and the Middle Ages (Lincoln: University of Nebraska Press, 1999).
Martin West, Ancient Greek Music (Oxford: Clarendon Press, 1994).