Introduction to Harmonics by Introduction to Harmonics

The Introduction to Harmonics is an anonymous ancient Greek treatise on music theory. Written in Koine Greek, it serves as a primer on harmonics, the mathematical study of musical scales and intervals. The work systematically defines basic terms like "note," "interval," and "scale." A central theme is its comparison of the two schools of ancient musical thought: the Pythagorean approach, based on mathematical ratios, and the Aristoxenian approach, which emphasized perceptual criteria and the judgement of the ear.

Only part of the text survives today, preserved as 24 fragments quoted within a much later commentary by the philosopher Porphyry (3rd century CE). Consequently, the original full length and structure of the work are unknown. The date of its composition is uncertain, but scholars place it in the Hellenistic or early Roman Imperial period. It is thought to have been written as a student guide or a doxographic survey cataloging the ideas of earlier theorists. Its survival within Porphyry's work indicates that it was considered a historical source for the discipline in late antiquity. While a later Byzantine source mentions a female theorist named Ptolemaïs of Cyrene, the attribution of this specific text to her remains speculative and unverified.