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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 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.
The Geometry of Musical Rhythm: What Makes a "Good" Rhythm Good? is the first book to provide a systematic and accessible computational geometric analysis of the musical rhythms of the world. It explains how the study of the mathematical properties of musical rhythm generates common mathematical problems that arise in a variety of seemingly dispara
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 systematic definition. Charting this alternative triadic syntax, Cohn reconceives what consonant triads are, and how they relate to one another. In doing so, he shows that major and minor triads have two distinct natures: one based on their acoustic properties, and the other on their ability to voice-lead smoothly to each other in the chromatic universe. Whereas their acoustic nature underlies the diatonic tonality of the classical tradition, their voice-leading properties are optimized by the pan-triadic progressions characteristic of the 19th century. Audacious Euphony develops a set of inter-related maps that organize intuitions about triadic proximity as seen through the lens of voice-leading proximity, using various geometries related to the 19th-century Tonnetz. This model leads to cogent analyses both of particular compositions and of historical trends across the long nineteenth century. Essential reading for music theorists, Audacious Euphony is also a valuable resource for music historians, performers and composers.
The Quadrivium consists of the four Liberal Arts of Number, Geometry, Music, and Cosmology, studied from antiquity to the Renaissance as a way of glimpsing the nature of reality. They synthesize number, space, and time. Geometry is number in space, music is number in time, and the cosmos expresses number in space and time. Number, music, and geometry are metaphysical truths, good and beautiful everywhere at all times. Life across the universe investigates them. They foreshadow the physical sciences. This is the first volume to bring together the Quadrivium for many hundreds of years
An accessible scientific explanation for the traditional rules of voice leading, including an account of why listeners find some musical textures more pleasing than others. Voice leading is the musical art of combining sounds over time. In this book, David Huron offers an accessible account of the cognitive and perceptual foundations for this practice. Drawing on decades of scientific research, including his own award-winning work, Huron offers explanations for many practices and phenomena, including the perceptual dominance of the highest voice, chordal-tone doubling, direct octaves, embellishing tones, and the musical feeling of sounds “leading” somewhere. Huron shows how traditional rules of voice leading align almost perfectly with modern scientific accounts of auditory perception. He also reviews pertinent research establishing the role of learning and enculturation in auditory and musical perception. Voice leading has long been taught with reference to Baroque chorale-style part-writing, yet there exist many more musical styles and practices. The traditional emphasis on Baroque part-writing understandably leaves many musicians wondering why they are taught such an archaic and narrow practice in an age of stylistic diversity. Huron explains how and why Baroque voice leading continues to warrant its central pedagogical status. Expanding beyond choral-style writing, Huron shows how established perceptual principles can be used to compose, analyze, and critically understand any kind of acoustical texture from tune-and-accompaniment songs and symphonic orchestration to jazz combo arranging and abstract electroacoustic music. Finally, he offers a psychological explanation for why certain kinds of musical textures are more likely to be experienced by listeners as pleasing.
