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Methods and aims in the Euclidean Sectio Canonis

For the writers of the imperial period, music theory presented a sharp dichotomy. One might be an Aristoxenus, or one might be a follower of the mathematikoi or Pythagoreans. The methods and doctrines of the two schools were thought of as radically incompatible with one another; and it is true that from the fourth century B.C., when their respective doctrines were first formally articulated, members of each tradition held views which their opposite numbers denied. But their disagreements are easily misunderstood. I have argued elsewhere that Aristoxenus' attitude to the Pythagoreans has sometimes been distorted. Here, in discussing the Sectio, which appears to be the earliest continuous treatise surviving from the other side of the fence, I shall try to show some of the ways in which its objectives differ from Aristoxenus', and thus the sense in which certain major disagreements between them reflect an oblique rather than a direct confrontation. I hope also to show that further study of this rather arid looking work for its own sake would repay both musicologists and philosophers.