Jason Yust - Böcker

Organized Time is the first attempt to unites 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 multivalent a approach to music analysis, Organized Time establishes the aesthetic importance of structural disjunction, the conflict of structure in different modalities, in numerous analytical contexts.

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.

This book presents original research applying mathematics to musical rhythm, with a focus on computational methods, theoretical approaches, analysis of rhythm in folk and global music traditions, syncopation, and maximal evenness. It honours the legacy of computer scientist and music theorist Godfried Toussaint.In addition to addressing a topic pioneered by Toussaint, application of mathematics to representation of musical rhythms, the volume also builds upon his interest in analysis of music traditions outside the European classical canon and the use of computational methods. Empirical contributions include a study of timing in Scandinavian polska performance showing that timing interacts with rhythmic features and a study of vocal melody rhythm in pre- and post-millennial popular music, showing significant differences in tempo, rhythmic density, and repetition in the two corpora. Theoretical contributions include a survey of timeline rhythms of African and African diasporic musics showing the prevalence of rhythms of a special type related to maximal evenness, an application of matrix algebra to rhythm and syncopation with analysis of clave rhythms, a ragtime corpus, and Balinese gong cycles, and a mathematical development of a new classification of smooth rhythms using a “shadow rhythm” algorithm suggested by Toussaint. The volume also includes an original composition by Tom Johnson and a personal recollection of Toussaint by Francisco Gómez-Martín. This volume will be a key resource for academics, researchers, and advanced students of music, musicology, music analyses, mathematical music theory, computational musicology, and music informatics. It was originally published as a special issue of the Journal of Mathematics and 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.