"Bach's Art of Fugue and Musical Offering is the first comprehensive study of two closely related masterworks of the late Baroque fugal style. The initial volume in a series of American Bach Society Guides produced in collaboration with Oxford University Press, it unpacks these famously cerebral collections as endlessly fascinating material for study and play. Intended for a general readership, this compact guide also summarizes for practitioners a considerable body of knowledge about these singular works. Bach scholar and keyboard player Matthew Dirst explains their idiosyncratic musical language in initial chapters while reviewing how both projects took shape during Bach's final decade, as he reoriented his creative energies around capstone works of various kinds. The most systematic of these, the Art of Fugue and Musical Offering reflect his lifelong fascination with learned counterpoint, as demonstrated in elaborate series of fugues and canons in both and in an unusually intricate trio sonata in the latter. Later chapters provide commentary on individual movements and groups of pieces and on the historical reception of this music, including its impact on other disciplines. Recurring themes include Bach's diligent exploration of contrapuntal types and techniques, his embrace of musical games of various sorts, and his creative assimilation of diverse musical styles"--

J.S. Bach’s Musical Offering is a broadly known and extensively studied collection of musical pieces, written in 1747 shortly after his visit to the Potsdam court of Frederick the Great. The composition, however, survived in separated sheets of different formats, and finding the logic of its organization into a cycle became a great challenge for scholars of the following centuries. Based on ground-breaking findings by Christoph Wolff, who revealed the main principles of the Musical Offering’s structure, as well as those promulgated by Hans Theodor David, and more recently by G. Butler, W. Wiemer, R. Tatlow, and many other scholars, this book develops and revises their ideas, arriving at a unique conception of the possible original structure of the Musical Offering. While the rods of the collection do not provoke disagreements among scholars, the ordering of the ten canons (including the Fuga canonica) remains mysterious in many aspects, and this text gives them a close examination. It considers their kinds (thematic and contrapuntal); textual inscriptions; the canons’ function within the cycle (as vignettes to the main pieces); and their location, among other aspects. The volume includes profuse references to historical and cultural context; court etiquette; contrapuntal techniques; the history of the ricercar; expertise in Bach’s handwriting and habits of music layout in his manuscripts; and the Baroque principles of organization in arts.

This volume is a guide to the resources and materials of Bach scholarship, both for the non specialist wondering where to begin in the enormous literature on J. S. Bach, and for the Bach specialist looking for a convenient and up to date survey of the field. It describes the tools of Bach research and how to use them, and suggests how to get started in Bach research by describing the principal areas of research and citing the essential literature on each piece and topic. The authors emphasize the issues that have engaged Bach scholars for generations, focusing on particularly important writings; on recent literature; on overviews, collections of essays and handbooks; and on writings in English. Subjects covered include bibliographic tools of Bach research and sources of literature; Bach's family; Bach biographies; places Bach lived and worked; Bach's teaching; the liturgy; Bach source studies and the transmission of his music; repertory and editions; genres and individual vocal and instrumental works; performance practice; the reception and analysis of Bach's music; and many others. The book also offers explanations of important and potentially confusing topics in Bach research, such as the organization of the annual cantata cycles, pitch standards, the history of the Berlin libraries, the structure of the critical commentary volumes in the Neue Bach Ausgabe, and so on. This book opens up the rich world of Bach scholarship to students, teachers, performers, and listeners.

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.