Music Theory

This book shows how recent work in cognitive science, especially that developed by cognitive linguists and cognitive psychologists, can be used to explain how we understand music. The book focuses on three cognitive processes--categorization, cross-domain mapping, and the use of conceptual models--and explores the part these play in theories of musical organization. The first part of the book provides a detailed overview of the relevant work in cognitive science, framed around specific musical examples. The second part brings this perspective to bear on a number of issues with which music scholarship has often been occupied, including the emergence of musical syntax and its relationship to musical semiosis, the problem of musical ontology, the relationship between words and music in songs, and conceptions of musical form and musical hierarchy. The book will be of interest to music theorists, musicologists, and ethnomusicologists, as well as those with a professional or avocational interest in the application of work in cognitive science to humanistic principles.

The discovery and application of abstract musical properties has had a prominent role in compositional and theoretical literature during the past 40 years, and an accumulation of source material has been produced that makes a single cross-referenced source essential for standard working procedures. Abstract musical properties most often associated with specific analytical or compositional systems, are presented here in an unbiased context that allows the reader freedom of association and interpretation. This type of reference is an important tool for anyone who uses set-class analysis in coursework, or independent thesis research.

An accessible exploration of an important and understudied music theory topic, Swain's book examines the dimensional technique of analyzing harmonic rhythm. Simply defined, harmonic rhythm is the relationship between changes in harmony and perceived changes in rhythm. This phenomenon plays a large role in shaping the texture and style of much of Western music, from Renaissance polyphonic pieces to the works of Debussy. Swain provides a clear and thorough discussion of how harmonic theory works, using a small core of repeated musical examples.

Hugo Riemann (1849-1919) is generally acknowledged as the most important musicologist of his age. By analyzing his musical thought within the turn-of-the-century context of interest in the natural sciences, German nationhood and modern technology, this book reconstructs how Riemann's ideas not only "made sense" but advanced a belief of the tonal tradition as both natural and German. Riemann influenced the ideas of generations of music scholars because his work coincided with the institutionalization of academic musicology around the turn of the last century.

This book examines, for the first time, the scientific procedures devised by Ptolemy (second century AD) for investigating the structures underlying musical melody, a project that he conceived as closely related to astronomy. Ptolemy's account of his methods is unusually explicit, and he pursues them faithfully. By providing an analysis of Ptolemy's sophisticated theoretical apparatus, his strategies for integrating theory with observation, and his meticulous instructions for the design and conduct of experimental tests, the book offers historians of science a new starting-point for wider studies of ancient scientific method.