Ernst Levy was a visionary Swiss pianist, composer, and teacher who developed an approach to music theory that has come to be known as "negative harmony." Levy's theories have had a wide influence, from young British performer/composer Jacob Collier to jazz musicians like Steve Coleman. His posthumous text, A Theory of Harmony, summarizes his innovative ideas. A Theory of Harmony is a highly original explanation of the harmonic language of the modern era, illuminating the approaches of diverse styles of music. By breaking through age-old conceptions, Levy was able to reorient the way we experience musical harmony. British composer/music pedagogue Paul Wilkinson has written a new introduction that offers multiple points of entry to Levy’s work to make this text more accessible for a new generation of students, performers, and theorists. He relates Levy's work to innovations in improvisation, jazz, twentieth-century classical music, and the theoretical writings of a wide range of musical mavericks, including Harry Partch, Hugo Riemann, and David Lewin. Wilkinson shows how A Theory of Harmony continues to inspire original musical expression across multiple musical genres.

Reprint of the original, first published in 1872. The publishing house Anatiposi publishes historical books as reprints. Due to their age, these books may have missing pages or inferior quality. Our aim is to preserve these books and make them available to the public so that they do not get lost.

This book will come as a joy, a revelation, a warm reassurance. From this one book one might well learn less about harmony than about form, about aesthetics, even about life. Some will accuse Schoenberg of not concentrating on the topic at hand, but such an accusation, though well-founded, would miss the point of Theory of Harmony, because the heart and soul of the book is to be found in his vivid and penetrating digressions. They are the fascinating reflections of a great and humane musician who was a born writer as well. - from the book.

Reprint of the original, first published in 1873.

Assisted by Scott Olsen ( Central Florida Community College, USA ). This volume is a result of the author's four decades of research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the OC Mathematics of Harmony, OCO a new interdisciplinary direction of modern science. This direction has its origins in OC The ElementsOCO of Euclid and has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the OC goldenOCO algebraic equations, the generalized Binet formulas, Fibonacci and OC goldenOCO matrices), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational radices, Fibonacci computers, ternary mirror-symmetrical arithmetic, a new theory of coding and cryptography based on the Fibonacci and OC goldenOCO matrices). The book is intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science. Sample Chapter(s). Introduction (503k). Chapter 1: The Golden Section (2,459k). Contents: Classical Golden Mean, Fibonacci Numbers, and Platonic Solids: The Golden Section; Fibonacci and Lucas Numbers; Regular Polyhedrons; Mathematics of Harmony: Generalizations of Fibonacci Numbers and the Golden Mean; Hyperbolic Fibonacci and Lucas Functions; Fibonacci and Golden Matrices; Application in Computer Science: Algorithmic Measurement Theory; Fibonacci Computers; Codes of the Golden Proportion; Ternary Mirror-Symmetrical Arithmetic; A New Coding Theory Based on a Matrix Approach. Readership: Researchers, teachers and students in mathematics (especially those interested in the Golden Section and Fibonacci numbers), theoretical physics and computer science."

In this introduction to natural-base music theory, Ernst Levy presents the essentials of a comprehensive, consistent theory of harmony developed from tone structure. A Theory of Harmony is a highly original explanation of the harmonic language of the last few centuries, showing the way toward an understanding of diverse styles of music. Basic harmony texts exist, but none supply help to students seeking threads of logic in the field. In a text abundantly illustrated with musical examples, Levy makes clear the few principles that illuminate the natural forces in harmony. He shows that general principles can be successfully extracted from the wealth of examples. This book actually provides a theory of harmony. One of the major musical minds of the twentieth century, Ernst Levy was born in Basel, Switzerland, in 1895. His musical career spanned more than seven decades, from his first public piano performance at age six. A naturalized U.S. citizen, he lived here from 1941 to 1966, teaching at the New England Conservatory, the University of Chicago, Bennington College, the Massachusetts institute of Technology, and Brooklyn College. After his retirement, Levy returned to Switzerland where he continued to compose until his death in 1981. He was an enormously productive composer, with hundreds of works to his credit including symphonies, string quartets, songs in English, French, and German, and music for solo instruments and small ensembles. His piano recordings, particularly of the last Beethoven sonatas and the Liszt sonata, have become collectors' items. He thought of himself as a successor to Reimann, immediately, and Rameau, more remotely.

In a time marked by profound polarisation, this volume draws our attention to a virtue that is of key importance in many non-Western cultures but is largely neglected in modern Western thought: the virtue of harmony. The book comprises 13 chapters that examine harmony from a particular cultural or disciplinary perspective. A broad variety of cultural traditions are represented, including the Confucian, Daoist, Buddhist, Judaist, Greek, Christian, Islamic, African, and Native American traditions, as well as different disciplinary approaches, such as philosophy, religious studies, linguistics, psychology, and political theory. This book is suitable for general readers, students, as well as researchers interested in this flourishing topic of research.