Stravinsky's Topology is an innovative explanation of the music of the great composer Igor Stravinsky (1882-1971). Specifically, this book examines Stravinsky's implementation of certain twelve-tone row forms for particular formal events and to enhance the poetry in his later works with poetic texts. This book, reprinted from a doctoral dissertation, presents a new analytical method called Object-Oriented analysis to study Stravinsky's smaller works Epitaphium, Anthem, Elegy for J. F. K., Fanfare for a New Theater, and The Owl and the Pussy-Cat. The remainder of this book is devoted to a detailed examination of Stravinsky's expanded Object-Oriented compositional technique in The Flood and in his largest late work, Threni. This investigation concludes with remarks about how a conductor can apply Object-Oriented analysis in performance. 216 pages.

This ground-breaking study of Stravinsky’s spirituality presents a new view of his music as unified, challenging the current view which describes it as often discontinuous and static. Stravinsky’s spirituality is the origin of his radical restoration of time in music.

This book introduces path-breaking applications of concepts from mathematical topology to music-theory topics including harmony, chord progressions, rhythm, and music classification. Contributions address topics of voice leading, Tonnetze (maps of notes and chords), and automatic music classification. Focusing on some geometrical and topological aspects of the representation and formalisation of musical structures and processes, the book covers topological features of voice-leading geometries in the most recent advances in this mathematical approach to representing how chords are connected through the motion of voices, leading to analytically useful simplified models of high-dimensional spaces; It generalizes the idea of a Tonnetz, a geometrical map of tones or chords, and shows how topological aspects of these maps can correspond to many concepts from music theory. The resulting framework embeds the chord maps of neo-Riemannian theory in continuous spaces that relate chords of different sizes and includes extensions of this approach to rhythm theory. It further introduces an application of topology to automatic music classification, drawing upon both static topological representations and time-series evolution, showing how static and dynamic features of music interact as features of musical style. This volume will be a key resource for academics, researchers, and advanced students of music, music analyses, music composition, mathematical music theory, computational musicology, and music informatics. It was originally published as a special issue of the Journal of Mathematics and Music.

The most celebrated of Western composers in the twentieth century, Igor Stravinsky may have been the greatest as well. Stretching across forty or so years, the essays in this volume address the dynamics of Igor Stravinsky’s music from a variety of analytical, critical, and aesthetic angles. Underscored are the features of melody, harmony, rhythm, and form that would remain consistently a part of Stravinsky’s oeuvre regardless of the changes in orientation from the Russian period to the neoclassical and the early serial. The Rite of Spring (1913), Les Noces (1917–23), the Symphony of Psalms (1930), and the Symphony in Three Movements (1945) are discussed in detail, as are many of the circumstances attending their conception. Other concerns include the composer’s "formalist" aesthetics and the strict performing style he pursued as an interpreter and conductor of his music.