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This first book on this topic is a comprehensive reference on the state of the art. The topics addressed include counterpoint, the first-species model, quasipolarities and interval dichotomies, graphs and transformations, and hypergesture homology. The theory presented also develops counterpoint models for new consonance-dissonance dichotomies. The book is suitable for graduate courses, the authors have a supporting Java implementation available online.

The authors include recent theoretical results on counterpoint worlds, the extension of counterpoint to microtonal pitch systems, the singular homology of counterpoint models, and the software implementation of contrapuntal models. The book is suitable for graduates and researchers.