Building on ideas first advanced by Arnold Schoenberg and later developed by Erwin Ratz, this book introduces a new theory of form for instrumental music in the classical style. The theory provides a broad set of principles and a comprehensive methodology for the analysis of classical form, from individual ideas, phrases, and themes to the large-scale organization of complete movements. It emphasizes the notion of formal function, that is, the specific role a given formal unit plays in the structural organization of a classical work.

Analyzing Classical Form offers an approach to the analysis of musical form that is especially suited for classroom use at both undergraduate and graduate levels. Students will learn how to make complete harmonic and formal analyses of music drawn from the instrumental works of Haydn, Mozart, and Beethoven.

Introducing a new theory of musical form for the analysis of instrumental music of the classical style. The book provides a broad set of principles and a comprehensive methodology for analysing phrases and themes to complete movements. Illustrated with over 250 annotated musical examples by Haydn, Mozart and Beethoven.

The theory of modular forms is a fundamental tool used in many areas of mathematics and physics. It is also a very concrete and “fun” subject in itself and abounds with an amazing number of surprising identities. This comprehensive textbook, which includes numerous exercises, aims to give a complete picture of the classical aspects of the subject, with an emphasis on explicit formulas. After a number of motivating examples such as elliptic functions and theta functions, the modular group, its subgroups, and general aspects of holomorphic and nonholomorphic modular forms are explained, with an emphasis on explicit examples. The heart of the book is the classical theory developed by Hecke and continued up to the Atkin–Lehner–Li theory of newforms and including the theory of Eisenstein series, Rankin–Selberg theory, and a more general theory of theta series including the Weil representation. The final chapter explores in some detail more general types of modular forms such as half-integral weight, Hilbert, Jacobi, Maass, and Siegel modular forms. Some “gems” of the book are an immediately implementable trace formula for Hecke operators, generalizations of Haberland's formulas for the computation of Petersson inner products, W. Li's little-known theorem on the diagonalization of the full space of modular forms, and explicit algorithms due to the second author for computing Maass forms. This book is essentially self-contained, the necessary tools such as gamma and Bessel functions, Bernoulli numbers, and so on being given in a separate chapter.

Analyzing Classical Form builds upon the foundations of the author's critically acclaimed Classical Form by offering an approach to the analysis of musical form that is especially suited for classroom use. Providing ample material for study in both undergraduate and graduate courses, Analyzing Classical Form presents the most up-to-date version of the author's "theory of formal functions." Students will learn how to make complete harmonic and formal analyses of music drawn from the instrumental works of Haydn, Mozart, and Beethoven. Part 1 introduces the principal theme-types of classical instrumental music; part 2 provides a methodology for analyzing sonata form, the most important formal type in this style period; and part 3 considers other full-movement forms found in this repertory (such as minuet, rondo, and concerto). The chapters are organized in a way that presents the most basic materials upfront and then leads the student through more details and finer points of theory. Every topic is illustrated with annotated musical examples; as well, the book contains many unannotated examples that can be used for in-class discussion and for out-of-class analytical exercises. A complete glossary of terms and questions for reviewing the theory will help students assimilate the many theoretical concepts employed in the book. A companion website hosted by the author at music.mcgill.ca/acf/ provides audio and musical scores for all of the examples in the book as well as additional examples for the analysis of the simple theme-types presented in part 1.

This Companion to Schubert examines the career, music, and reception of one of the most popular yet misunderstood and elusive composers. Sixteen chapters by leading Schubert scholars make up three parts. The first seeks to situate the social, cultural, and musical climate in which Schubert lived and worked, the second surveys the scope of his musical achievement, and the third charts the course of his reception from the perceptions of his contemporaries to the assessments of posterity. Myths and legends about Schubert the man are explored critically and the full range of his musical accomplishment is examined.

This volume discusses various perspectives of the theory of automorphic forms drawn from the author's notes from a Rutgers University graduate course. In addition to detailed and often nonstandard treatment of familiar theoretical topics, the author also gives special attention to such subjects as theta- functions and representatives by quadratic forms. Annotation copyrighted by Book News, Inc., Portland, OR