"His reports of encounters with such composers as Taneyev, Glazunov, Scriabin, Stravinsky, Hindemith, Frommel, and David, and his thorough discussion of tonal systems and compositional methods reflect the approach and critical response to many procedures typical of music of the era.

A History of Twentieth-Century Music in a Theoretic-Analytical Context is an integrated account of the genres and concepts of twentieth-century art music, organized topically according to aesthetic, stylistic, technical, and geographic categories, and set within the larger political, social, economic, and cultural framework. While the organization is topical, it is historical within that framework. Musical issues interwoven with political, cultural, and social conditions have had a significant impact on the course of twentieth-century musical tendencies and styles. The goal of this book is to provide a theoretic-analytical basis that will appeal to those instructors who want to incorporate into student learning an analysis of the musical works that have reflected cultural influences on the major musical phenomena of the twentieth century. Focusing on the wide variety of theoretical issues spawned by twentieth-century music, A History of Twentieth-Century Music in a Theoretic-Analytical Context reflects the theoretical/analytical essence of musical structure and design.

Compositional Process in Elliott Carter’s String Quartets is an interdisciplinary study examining the evolution and compositional process in Elliott Carter’s five string quartets. Offering a systematic and logical way of unpacking concepts and processes in these quartets that would otherwise remain opaque, the book’s narrative reveals new aspects of understanding these works and draws novel conclusions on their collective meaning and Carter’s place as the leading American modernist. Each of Carter’s five string quartets is driven by a new idea that Carter was exploring during a particular period, which allows for each quartet to be examined under a unique lens and a deeper understanding of his oeuvre at large. Drawing on key ideas from a variety of subjects including performance studies, philosophy, music cognition, musical meaning and semantics, literary criticism, and critical theory, this is an informative volume for scholars and researchers in the areas of music theory and musicology. Analyses are supplemented with sketch study, correspondence, text manuscripts, and other archival sources from the Paul Sacher Stiftung, the Library of Congress, and the New York Public Library.

Paul Hindemith never accepted the complete engagement with social issues suggested in the writings of Brecht, but he developed many of his ideas regarding the place of an artist in the thirties and forties, his music eventually gaining official disapproval. His strong opinions about musical composition make him a particularly interesting subject and this research guide will provide a complete bibliography of works to guide the scholar and student.

Anton Webern: A Research and Information Guide offers carefully selected and annotated sources regarding Webern from 1975 to present day, including sources on Webern’s life, his music, and the interpretation and reception of his music. Along with this comprehensive annotated listing of print and online sources, the book discusses the history of research on Webern and includes a brief chronology of his life. It is a major reference tool for those interested in Webern and his music and valuable for researchers of 20th century music and the Second Viennese School.

A guided tour of the mathematical principles inherent in music. Taking a "music first" approach, Gareth E. Roberts's From Music to Mathematics will inspire students to learn important, interesting, and at times advanced mathematics. Ranging from a discussion of the geometric sequences and series found in the rhythmic structure of music to the phase-shifting techniques of composer Steve Reich, the musical concepts and examples in the book motivate a deeper study of mathematics. Comprehensive and clearly written, From Music to Mathematics is designed to appeal to readers without specialized knowledge of mathematics or music. Students are taught the relevant concepts from music theory (notation, scales, intervals, the circle of fifths, tonality, etc.), with the pertinent mathematics developed alongside the related musical topic. The mathematics advances in level of difficulty from calculating with fractions, to manipulating trigonometric formulas, to constructing group multiplication tables and proving a number is irrational. Topics discussed in the book include • Rhythm • Introductory music theory • The science of sound • Tuning and temperament • Symmetry in music • The Bartók controversy • Change ringing • Twelve-tone music • Mathematical modern music • The Hemachandra–Fibonacci numbers and the golden ratio • Magic squares • Phase shifting Featuring numerous musical excerpts, including several from jazz and popular music, each topic is presented in a clear and in-depth fashion. Sample problems are included as part of the exposition, with carefully written solutions provided to assist the reader. The book also contains more than 200 exercises designed to help develop students' analytical skills and reinforce the material in the text. From the first chapter through the last, readers eager to learn more about the connections between mathematics and music will find a comprehensive textbook designed to satisfy their natural curiosity.