The Geometry Of Musical Rhythm

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

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.

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.

With contributions by numerous experts

What is musical time? Where is it manifested? How does it enter into our experience, and how do we capture it in our analyses? A compelling approach among works on temporality, phenomenology, and the ecologies of the new sound worlds, Enacting Musical Time argues that musical time is itself the site of the interaction between musical sounds and a situated, embodied listener, created by the moving bodies of participants engaged in musical activities. Author Mariusz Kozak describes musical time as something that emerges when the listener enacts her implicit knowledge about "how music goes," from deliberate inactivity, to such simple actions as tapping her foot in time with the beat, to dancing in a way that engages her entire body. Kozak explores this idea in the context of modernist and postmodernist musical styles, where composers create unfamiliar and idiosyncratic temporal experiences, blur the line between spectatorship and participation, and challenge conventional notions of form. Basing his discussion on the phenomenology of Merleau-Ponty and on the ecological psychology of J. J. Gibson, Kozak examines different aspects of musical structure through the lens of embodied cognition and what phenomenologists call "lived time." A bold new theory derived from an unprecedented fusion of research perspectives, Enacting Musical Time will engage scholars across a range of disciplines, from music theory, music cognition, cognitive science, continental philosophy, and social anthropology.

This is the first volume of the second edition of the now classic book “The Topos of Music”. The author explains the theory's conceptual framework of denotators and forms, the classification of local and global musical objects, the mathematical models of harmony and counterpoint, and topologies for rhythm and motives.

Organized Time is the first attempt to unite theories of harmony, rhythm and meter, and form under a common idea of structured time. Building off of recent advances in music theory in essential subfields-rhythmic theory, tonal structure, and the theory of musical form--author Jason Yust demonstrates that tonal music exhibits similar hierarchical organization in each of these dimensions. Yust develops a network model for temporal structure with an application of mathematical graph theory, which leads ultimately to musical applications of a multi-dimensional polytope called the associahedron. A wealth of analytical examples includes not only the familiar tonal canon-J.S. Bach, Mozart, Schumann--but also lesser known masters of the musical Enlightenment such as C.P.E. and J.C. Bach, Boccherini, and Johann Gottlieb Graun. Yust's approach has wide-ranging ramifications across music theory, enabling new approaches to musical closure, hypermeter, formal function, syncopation, and rhythmic dissonance, as well as historical observations about the development of sonata form and the innovations of Haydn and Beethoven. Making a forceful argument for the independence of musical modalities and for a multivalent approach to music analysis, Organized Time establishes the aesthetic importance of structural disjunction, the conflict of structure in different modalities, in numerous analytical contexts.

Why did Pythagoras pause outside a Blacksmith's workshop? Can the nature of Harmony really be understood visually? Why do harmonies leave gaps or 'commas' when added together? In this charming little book Anthony Ashton uses a Victorian device called a Harmonograph to tell the story of Harmony and the intervals in the scale. With useful appendices and exquisite line drawings this is a unique and original introduction to this timeless subject. WOODEN BOOKS are small but packed with information. "e;Fascinating"e; FINANCIAL TIMES. "e;Beautiful"e; LONDON REVIEW OF BOOKS. "e;Rich and Artful"e; THE LANCET. "e;Genuinely mind-expanding"e; FORTEAN TIMES. "e;Excellent"e; NEW SCIENTIST. "e;Stunning"e; NEW YORK TIMES. Small books, big ideas.