Voice Leadings as Generalized Key Signatures

Abstract

A key signature is a collection of paths in pitch-class space.As such, it provides a powerful tool for thinking about voice leading, one that can be used to answer familiar objections to the very notion of a voice leading between pitch-class sets.I begin by generalizing the traditional Western system of musical notation, defining paths in pitch-class space, and showing that key signatures are collections of such paths.I then show that it is always possible to find a minimal voice leading that has no voice crossings; however, it is not always possible to avoid voice crossings while maximizing common-tone retention.I describe a general method for identifying a minimal voice leading between arbitrary chords, and show that our familiar system of diatonic key signatures implements this method.I conclude by deriving a set of key signatures for the acoustic scale.These key signatures represent minimal voice leadings from the diatonic to the acoustic collection, and are interestingly related to the familiar diatonic key signatures.

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