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A Geometry of Music
In this groundbreaking book, Tymoczko uses contemporary geometry to provide a new framework for thinking about music, one that emphasizes the commonalities among styles from Medieval polyphony to contemporary jazz.
The Oxford Handbook of Neo-Riemannian Music Theories
In recent years neo-Riemannian theory has established itself as the leading approach of our time, and has proven particularly adept at explaining features of chromatic music. The Oxford Handbook of Neo-Riemannian Music Theories assembles an international group of leading music theory scholars in an exploration of the music-analytical, theoretical, and historical aspects of this new field.
Audacious Euphony
Music theorists have long believed that 19th-century triadic progressions idiomatically extend the diatonic syntax of 18th-century classical tonality, and have accordingly unified the two repertories under a single mode of representation. Post-structuralist musicologists have challenged this belief, advancing the view that many romantic triadic progressions exceed the reach of classical syntax and are mobilized as the result of a transgressive, anti-syntactic impulse. In Audacious Euphony, author Richard Cohn takes both of these views to task, arguing that romantic harmony operates under syntactic principles distinct from those that underlie classical tonality, but no less susceptible to sys...
Music Theory and Mathematics
Essays in diatonic set theory, transformation theory, and neo-Riemannian theory -- the newest and most exciting fields in music theory today. The essays in Music Theory and Mathematics: Chords, Collections, and Transformations define the state of mathematically oriented music theory at the beginning of the twenty-first century. The volume includes essays in diatonic set theory, transformation theory, and neo-Riemannian theory -- the newest and most exciting fields in music theory today. The essays constitute a close-knit body of work -- a family in the sense of tracing their descentfrom a few key breakthroughs by John Clough, David Lewin, and Richard Cohn in the 1980s and 1990s. They are int...
Composition and Cognition
In Composition and Cognition, renowned composer and theorist Fred Lerdahl builds on his careerlong work of developing a comprehensive model of music cognition. Bringing together his dual expertise in composition and music theory, he reveals the way in which his research has served as a foundation for his compositional style and how his intuitions as a composer have guided his cognitively oriented theories. At times personal and reflective, this book offers an overall picture of the musical mind that has implications for central issues in contemporary composition, including the recurrent gap between method and result, and the tension between cognitive constraints and utopian aesthetic views of musical progress. Lerdahl’s succinct volume provides invaluable insights for students and instructors, composers and music scholars, and anyone engaged with contemporary music.
The Geometry of Musical Rhythm
The original edition of The Geometry of Musical Rhythm was the first book to provide a systematic and accessible computational geometric analysis of the musical rhythms of the world. It explained how the study of the mathematical properties of musical rhythm generates common mathematical problems that arise in a variety of seemingly disparate fields. The book also introduced the distance approach to phylogenetic analysis and illustrated its application to the study of musical rhythm. The new edition retains all of this, while also adding 100 pages, 93 figures, 225 new references, and six new chapters covering topics such as meter and metric complexity, rhythmic grouping, expressive timbre and timing in rhythmic performance, and evolution phylogenetic analysis of ancient Greek paeonic rhythms. In addition, further context is provided to give the reader a fuller and richer insight into the historical connections between music and mathematics.
Generalized Musical Intervals and Transformations
Generalized Musical Intervals and Transformations is by far the most significant contribution to the field of systematic music theory in the last half-century, generating the framework for the "transformational theory" movement.
Tonality
This encyclopaedic book proposes a sweeping reformulation of the basic concepts of Western music theory, revealing simple structures underlying a wide range of practices from the Renaissance to contemporary pop. Its core innovation is a collection of simple geometrical models describing the implicit knowledge governing a broad range of music-making, much as the theory of grammar describes principles that tacitly guide our speaking and writing. Each of its central chapters re-examines a basic music-theoretical concept such as voice leading, repetition, nonharmonic tones, the origins of tonal harmony, the grammar of tonal harmony, modulation, and melody. These are flanked by two largely analytical chapters on rock harmony and Beethoven. Wide-ranging in scope, and with almost 700 musical examples from the Middle Ages to the present day, Tonality: An Owner's Manual weaves philosophy, mathematics, statistics, and computational analysis into a new and truly twenty-first century theory of music.
