Tonal Pitch Space by Fred Lerdahl

A Theory of Musical Hierarchy

This book develops a formal, cognitively grounded model of how listeners perceive tonal pitch relations by arranging pitch collections and keys in a hierarchical, multi-scale “pitch space” where proximity and stability encode perceived closeness, tension, and resolution; it specifies metrics for distances between pitch classes, chords, and keys, defines centers and regions of tonal attraction, and shows how voice-leading and harmonic progressions map onto paths through the space to explain cadences, modulations, and degrees of structural importance, offering a precise framework that extends earlier generative theories and makes testable predictions about musical perception and analysis.

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