Building on the foundation of Lerdahl and Jackendoff's influential A Generative Theory of Tonal Music, this volume presents a multidimensional model of diatonic and chromatic spaces that quantifies listeners' intuitions of the relative distances of pitches, chords, and keys from a given tonic. The model is employed to assign prolongational structure, represent paths through the space, and compute patterns of tension and attraction as musical events unfold, thereby providing a partial basis for understanding musical narration, expectation, and expression. Conceived as both a music-theoretic treatise and a contribution to the cognitive science of music, this book will be of interest to music theorists, musicologists, composers, computer musicians, and cognitive psychologists.
Exploring Musical Spaces is a comprehensive synthesis of mathematical techniques in music theory, written with the aim of making these techniques accessible to music scholars without extensive prior training in mathematics. The book adopts a visual orientation, introducing from the outset a number of simple geometric models--the first examples of the musical spaces of the book's title--depicting relationships among musical entities of various kinds such as notes, chords, scales, or rhythmic values. These spaces take many forms and become a unifying thread in initiating readers into several areas of active recent scholarship, including transformation theory, neo-Riemannian theory, geometric music theory, diatonic theory, and scale theory. Concepts and techniques from mathematical set theory, graph theory, group theory, geometry, and topology are introduced as needed to address musical questions. Musical examples ranging from Bach to the late twentieth century keep the underlying musical motivations close at hand. The book includes hundreds of figures to aid in visualizing the structure of the spaces, as well as exercises offering readers hands-on practice with a diverse assortment of concepts and techniques.
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 integrated by the ongoing dialogue they conduct with one another. The editors are Jack Douthett, a mathematician and music theorist who collaborated extensively with Clough; Martha M. Hyde, a distinguished scholar of twentieth-century music; and Charles J. Smith, a specialist in tonal theory. The contributors are all prominent scholars, teaching at institutions such as Harvard, Yale, Indiana University, and the University at Buffalo. Six of them (Clampitt, Clough, Cohn, Douthett, Hook, and Smith) have received the Society for Music Theory's prestigious PublicationAward, and one (Hyde) has received the ASCAP Deems Taylor Award. The collection includes the last paper written by Clough before his death, as well as the last paper written by David Lewin, an important music theorist also recently deceased. Contributors: David Clampitt, John Clough, Richard Cohn, Jack Douthett, Nora Engebretsen, Julian Hook, Martha Hyde, Timothy Johnson, Jon Kochavi, David Lewin, Charles J. Smith, and Stephen Soderberg.
Reconstructing historical conceptions of harmonic distance, Audacious Euphony advances a geometric model appropriate to understanding triadic progressions characteristic of 19th-century music. Author Rick Cohn uncovers the source of the indeterminacy and uncanniness of romantic music, as he focuses on the slippage between chromatic and diatonic progressions and the systematic principles under which each operate.
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.
Film music often tells us how to feel, but it also guides us how to hear. Filmgoing is an intensely musical experience, one in which the soundtrack structures our interpretations and steers our emotions. Hollywood Harmony explores the inner workings of film music, bringing together tools from music theory, musicology, and music psychology in this first ever book-length analytical study of this culturally central repertoire. Harmony, and especially chromaticism, is emblematic of the "film music sound," and it is often used to evoke that most cinematic of feelings-wonder. To help parse this familiar but complex musical style, Hollywood Harmony offers a first-of-its kind introduction to neo-Riemannian theory, a recently developed and versatile method of understanding music as a dynamic and transformational process, rather than a series of inert notes on a page. This application of neo-Riemannian theory to film music is perfect way in for curious newcomers, while also constituting significant scholarly contribution to the larger discipline of music theory. Author Frank Lehman draws from his extensive knowledge of cinematic history with case-studies that range from classics of Golden Age Hollywood to massive contemporary franchises to obscure cult-films. Special emphasis is placed on scores for major blockbusters such as Lord of the Rings, Star Wars, and Inception. With over a hundred meticulously transcribed music examples and more than two hundred individual movies discussed, Hollywood Harmony will fascinate any fan of film and music.
What goes on in human beings when they make or listen to music? What is it about music, what gives it such peculiar power over us, power delectable and beneficent for the most part, but also capable of uncontrollable and sometimes destructive force? Music has no concepts, it lacks images; it has no power of representation, it has no relation to the world. And yet it is evident in all of us–we tap our feet, we keep time, hum, sing, conduct music, mirror the melodic contours and feelings of what we hear in our movements and expressions. In this book, Oliver Sacks explores the power music wields over us–a power that sometimes we control and at other times don’t. He explores, in his inimitable fashion, how it can provide access to otherwise unreachable emotional states, how it can revivify neurological avenues that have been frozen, evoke memories of earlier, lost events or states or bring those with neurological disorders back to a time when the world was much richer. This is a book that explores, like no other, the myriad dimensions of our experience of and with 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.
