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.

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 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."

"Embark on a captivating journey through the intricate landscape of human emotions with 'Two-Factor Theory of Emotion: Heart and Mind in Harmony.' This insightful exploration delves into the profound interconnectedness of physiological arousal and cognitive interpretation, unraveling the threads that weave our emotional experiences. From the historical roots to contemporary applications, each chapter unveils the theory's significance, offering a comprehensive understanding of how our hearts and minds harmonize in the intricate dance of emotions. With engaging insights into identifying, labeling, and regulating emotions, this book is a guide to navigating the rich tapestry of our emotional world. Whether you're a student of psychology, a professional seeking practical applications, or simply curious about the depths of human emotion, this book provides a thought-provoking and accessible journey into the core of our shared emotional experience."

Volume I is the first part of the 3-volume book Mathematics of Harmony as a New Interdisciplinary Direction and 'Golden' Paradigm of Modern Science. 'Mathematics of Harmony' rises in its origin to the 'harmonic ideas' of Pythagoras, Plato and Euclid, this 3-volume book aims to promote more deep understanding of ancient conception of the 'Universe Harmony,' the main conception of ancient Greek science, and implementation of this conception to modern science and education.This 3-volume book is a result of the authors' 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 'Mathematics of Harmony,' a new interdisciplinary direction of modern science. This direction 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 generalized Binet's formulas), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational bases, Fibonacci computers, ternary mirror-symmetrical arithmetic).The books are 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.

Justice and harmony have long been two of the world’s most treasured ideals, but much of modern moral and political philosophy puts them on opposite sides of the divide between liberal theories of the right and communitarian theories of the good. Joshua Mason argues that the encounter with their Chinese counterparts, zhengyi and hexie, can overcome this opposition, revealing a pattern that reframes justice and harmony as mutually interdependent concepts in a three-part framework of root harmony (benhe), harmonic justice (heyi), and just harmony (zhenghe). Broadly surveying the histories of western and Chinese moral and political philosophies, Justice and Harmony: Cross-Cultural Ideals in Conflict and Cooperation explores our cross-cultural conceptual inventories and develops a comparative framework that can overcome entrenched binary oppositions and reconcile these grand global values.