Introduction

If we tried to begin this investigation of Pythagorean harmonics with Pythagoras himself (c. 500 BC), we would find ourselves floundering through a swamp in darkness, guided by little except Will-o’-the-Wisps, “false deluding lights,” as Dryden put it. We shall tiptoe towards this perilous territory in due course, but let us begin in clearer light and on rather more solid ground, with a remark by Ptolemaïs of Cyrene, a scholar writing several hundred years after Pythagoras died:

Ptolemaïs is the only Greek woman on record as a musical theorist. Her work is known through quotations by Porphyry, all of which are concerned with the epistemological commitments and methodologies of the various “schools” or traditions of harmonic theory. She divides them into two broad groups, distinguished by the “criteria” on which they principally rely, sense-perception in the case of one group (here called mousikoi but in other passages “Aristoxenians”), and reason, logos, in the case of the other (kanonikoi or “Pythagoreans”).