This book is a music-theoretical and critical-theoretical study of late tonal music, and, in particular, of the music of Wagner’s Götterdämmerung. First, in terms of music theory, it proposes a new theory of tonal function that returns to the theories of Hugo Riemann to rediscover a development of his thought that has been covered over by the recent project of neo-Riemannian theory. Second, in terms of its philosophical approach, it reawakens the critical-theoretical examination of the relation between music and the late capitalist society that is sedimented in the musical materials themselves, and which the music, in turn, subjects to aesthetically embodied critique. The music, the theory, and the listeners and critics who respond to them are all radically reimagined. This book will be of interest to professional music theorists, undergraduates, and technically inclined musicians and listeners, that is, anyone who is fascinated by the chromatic magic of late-nineteenth-century music.

This book is a music-theoretical and critical-theoretical study of late tonal music, and, in particular, of the music of Wagner's Götterdämmerung. First, in terms of music theory, it proposes a new theory of tonal function, which returns to the theories of Hugo Riemann to rediscover a development of his thought that has been covered over by the recent project of neo-Riemannian theory. Second, in terms of its philosophical approach, it reawakens the critical-theoretical examination of the relation between music and the late capitalist society which is sedimented in the musical materials themselves, and which the music in turn subjects to aesthetically embodied critique. The music, the theory, and the listeners and critics who respond to them, are all radically reimagined. This book will be of interest to professional music theorists, undergraduates, and technically inclined musicians and listeners: anyone, that is, who is fascinated by the chromatic magic of late-nineteenth-century music

Generally acknowledged as the most important German musicologist of his age, Hugo Riemann (1849–1919) shaped the ideas of generations of music scholars, not least because his work coincided with the institutionalisation of academic musicology around the turn of the last century. This influence, however, belies the contentious idea at the heart of his musical thought, an idea he defended for most of his career - harmonic dualism. By situating Riemann's musical thought within turn-of-the-century discourses about the natural sciences, German nationhood and modern technology, this book reconstructs the cultural context in which Riemann's ideas not only 'made sense' but advanced an understanding of the tonal tradition as both natural and German. Riemann's musical thought - from his considerations of acoustical properties to his aesthetic and music-historical views - thus regains the coherence and cultural urgency that it once possessed.

In recent years neo-Riemannian theory has established itself as the leading approach of our time, and has proven particularly adept at explaining features of chromatic music. The Oxford Handbook of Neo-Riemannian Music Theories assembles an international group of leading music theory scholars in an exploration of the music-analytical, theoretical, and historical aspects of this new field.

This book explores the origins of mathematical analysis in an accessible, clear, and precise manner. Concepts such as function, continuity, and convergence are presented with a unique historical point of view. In part, this is accomplished by investigating the impact of and connections between famous figures, like Newton, Leibniz, Johann Bernoulli, Euler, and more. Of particular note is the treatment of Karl Weierstraß, whose concept of real numbers has been frequently overlooked until now. By providing such a broad yet detailed survey, this book examines how analysis was formed, how it has changed over time, and how it continues to evolve today. A Brief History of Analysis will appeal to a wide audience of students, instructors, and researchers who are interested in discovering new historical perspectives on otherwise familiar mathematical ideas.

R for College Mathematics and Statistics encourages the use of R in mathematics and statistics courses. Instructors are no longer limited to ``nice'' functions in calculus classes. They can require reports and homework with graphs. They can do simulations and experiments. R can be useful for student projects, for creating graphics for teaching, as well as for scholarly work. This book presents ways R, which is freely available, can enhance the teaching of mathematics and statistics. R has the potential to help students learn mathematics due to the need for precision, understanding of symbols and functions, and the logical nature of code. Moreover, the text provides students the opportunity for experimenting with concepts in any mathematics course. Features: Does not require previous experience with R Promotes the use of R in typical mathematics and statistics course work Organized by mathematics topics Utilizes an example-based approach Chapters are largely independent of each other

Brings musicology to the cutting edge of debates in the postmodern philosophy of history.