"The Hammers and the Bow: Western Polyphony, the Metaphysics of Unity, and the Concept of Harmony"

Heraclitus, invoking the tensed string of a bow, conceived harmony as the stasis and equilibrium of conflicting forces held in continuing tension. Plato in the Symposium rejects this view in favor of a concept of harmony in which all conflict must already have been resolved. At a higher level, so to speak, the famous legend of Pythagoras and the blacksmiths’ hammers offers an attempt to resolve the tension between these two conflicting visions of harmony itself. The fundamental, underlying question of harmony thereby becomes the nature of the relation between multiplicity and unity; that is, the relation between the concept of harmony and a metaphysics of unity derived from the late thought of Plato. This book analyzes the ways in which the foundational concept of harmony, and the inherently paradoxical nature it owes to this metaphysics of unity, have played themselves out in the theory and practice of western polyphony, from its earliest surviving documents in the ninth and tenth centuries to the theories of Schoenberg and Schenker.