Efficient voice leading, in which melodic lines move by short distances from chord to chord, is a hallmark of many different Western musical styles. Although musicians can often find maximally efficient voice leadings with relative ease, theorists have not adequately described general principles or procedures for doing so. This article formalises the notion of voice leading, shows how to classify voice leadings according to transpositional and inversional equivalence and supplies algorithms for identifying maximally efficient voice leadings between arbitrarily chosen chords. (...) The article also includes analytical and theoretical discussions of neo-Riemannian theory, the 'tritone substitution' in contemporary jazz, the music of Wagner and Debussy, the relation between harmony and counterpoint and the connections between scale theory and serial theory. (shrink)