The paper outlines the Pythagorean science of harmonics in its historical and theoretical aspects. It is intended to be a chapter in the history of ancient mathematical studies of nature, although the author occasionally touches upon such related areas as the history of philosophy and the history of music, and hopes that his work will be interesting to scholars working in these fields. After a short introduction the author first turns to the phenomenology of harmony and then analyses in considerable (...) details the harmony as a structure of numerical relations and – alleged or real – acoustic experiments designed to establish the qualities of sound, as well as consonant and dissonant intervals. (shrink)