The story of this book really begins in early 2001, when I was finishing up my first book, The Cognition of Basic Musical Structures (CBMS), and looking around for something new to work on. While satisfied with CBMS in many ways, I had certain nagging doubts about the project. CBMS—a computational study of basic aspects of music perception— employed the approach of preference rules, in which many possible anal- yses are considered and evaluated using a set of criteria. Although it has many virtues, the preference rule approach seemed to have few adherents beyond myself and a few others in music theory and linguistics. This troubled me; if so many aspects of music cognition (meter, harmony, and the like) reflected ‘‘preference-rule-like’’ mechanisms, why were such mechanisms not widely found in other domains of cognition, such as lan- guage and vision? I was also troubled by the seemingly ad hoc and arbi- trary nature of the preference-rule approach. One could develop a model by adding rules and tweaking their parameters in a trial-and-error fash- ion, but there didn’t seem to be any principled basis for making these decisions.