Ptolema"is of Kyrene. The Pythagorean elements of music

Extracts of the musical treatise of Ptolemaïs of Kyrene, the only female musical theorist in Antiquity, preserved by Porphyry in his Commentary to Ptolemy's Harmonics, are important, first of all, because, they belongs to those very scanty testimonies that witness continuous development of the musical science from the time of Aristoxenus to this of Nicomachus of Gerasa. In this respect the present study supplements two earlier our publications: the musical sections of The Mathematics Useful for Understanding Plato by Theon of Smyrna (the 2nd c. CE), which contain material taken from Thrasyllus (the beginning of the 1st c. CE) and Adrastus (the end of the 1st c. CE) [cf. Vol. 3.2 (2009) of the journal], and some passages from Heraclides the Younger (active in the time of Claudius and Nero), Didymus the Musician (active in the time of Nero), Panaetius the Younger (unknown date), and Aelianus (the end of the 2nd c.), preserved by Porphyry and translated as supplements to our study on Theophrastus [included in this volume]. Apparently Porphyry quotes Ptolemaïs on the basis of the work of Didymus and gives absolutely no information about her live. Most recently Levin (2009) speculated that this Ptolemaïs could be a woman of noble origin and live in Alexandria in the time of Eratosthenes (c. 275-194 BCE), which would be nice but cannot be proved. The extracts introduce the notion of the science of kanonike and contribute to the famous polemics between the mathematikoi and the mousikoi, which lead to 'reason-based' Pythagorean and 'perception-based' Aristoxenian approaches to musical theory, and Ptolemaïs apparently prefers the latter despite the title of her work, given by Porphyry.