In his well-known essay “The Americanization of Heinrich Schenker,” William Rothstein claims that, however they choose to regard their work, Schenkerians must eventually meet “the challenge posed by the ‘scientific’ theorists.” During the course of this book, we have seen one way in which this challenge might be met. We have seen that Schenkerian theory is explanatory insofar as it explains why certain notes appear in particular tonal contexts, why these notes behave in some ways and not in others, and how we can actually generate specific tonal relationships. It does so by invoking an appropriate set of concepts and covering laws, which it represents in procedural form as a system of prototypes, transformations, and levels. When picking one analysis over another, Schenkerians are guided by some of the same criteria as scholars working in the natural and social sciences, namely, they are motivated by a desire for accuracy, scope, consistency, simplicity, fruitfulness, and coherence.

Besides accepting Rothstein's challenge, this book has responded to some of the other issues outlined in the Preface. We have avoided the “cabalistic image of Schenker” abhorred by Dunsby by showing how Schenkerian theory is based on explicit laws of tonal voice leading and harmony. Since these laws are testable intersubjectively, we can not only reject Schenker's appeal to “magic numbers” or other mystical forces, but we can also counter the charge of circularity as leveled by Narmour. As mentioned earlier, the explanatory laws underpinning Schenkerian theory were actually discovered empirically in the Harmonielehre and Kontrapunkt I, long before Schenker formulated his concept of a single tonal prototype. By the same token, we have eliminated some of the inconsistencies discussed by Benjamin. What is most remarkable is that we did so by using some of Schenker's own ideas. This does not mean that we have necessarily resolved every anomaly in Schenker's work, but it does mean that we have overcome one particularly pressing problem.

In addition to shoring up the methodological foundations of Schenkerian theory, we have also clarified several other areas of debate. For one thing, we have responded to Laufer's claim about the completeness of Schenker's concepts.