Harmony And Counterpoint

A Geometry of Music

How is the Beatles' "Help!" similar to Stravinsky's "Dance of the Adolescents?" How does Radiohead's "Just" relate to the improvisations of Bill Evans? And how do Chopin's works exploit the non-Euclidean geometry of musical chords? In this groundbreaking work, author Dmitri Tymoczko describes a new framework for thinking about music that emphasizes the commonalities among styles from medieval polyphony to contemporary rock. Tymoczko identifies five basic musical features that jointly contribute to the sense of tonality, and shows how these features recur throughout the history of Western music. In the process he sheds new light on an age-old question: what makes music sound good? A Geometry of Music provides an accessible introduction to Tymoczko's revolutionary geometrical approach to music theory. The book shows how to construct simple diagrams representing relationships among familiar chords and scales, giving readers the tools to translate between the musical and visual realms and revealing surprising degrees of structure in otherwise hard-to-understand pieces. Tymoczko uses this theoretical foundation to retell the history of Western music from the eleventh century to the present day. Arguing that traditional histories focus too narrowly on the "common practice" period from 1680-1850, he proposes instead that Western music comprises an extended common practice stretching from the late middle ages to the present. He discusses a host of familiar pieces by a wide range of composers, from Bach to the Beatles, Mozart to Miles Davis, and many in between. A Geometry of Music is accessible to a range of readers, from undergraduate music majors to scientists and mathematicians with an interest in music. Defining its terms along the way, it presupposes no special mathematical background and only a basic familiarity with Western music theory. The book also contains exercises designed to reinforce and extend readers' understanding, along with a series of appendices that explore the technical details of this exciting new theory.

Harmony Through Melody

Harmony Through Melody:The Interaction of Melody, Counterpoint, and Harmony in Western Music, Second Editionoffers a robust, composition-based approach to tonal music theory, ranging from early modality to recent film and popular music. Charles Horton, David A. Byrne, and Lawrence Ritchey develop techniques and strategies for exploring the fundamental interaction of melody and counterpoint with harmony, and provide students with opportunities to creatively express what they have learned in the writing and analysis of short passages and complete pieces in historical styles. This second edition contains additional examples from the standard literature, film music, and popular song, and features new assignments involving late nineteenth-century chromatic practice. The textbook present a step-by-step method for the composition and analysis of short passages and complete pieces, with more than 1400 musical examples drawn from a variety of styles and genres, plus classroom-tested examples for study and suggested assignments at the end of each chapter. The second edition has an online companion website (textbooks.rowman.com/horton2e) featuring: A student workbook with more than 260 assignments for individual work and classroom useAudio links to 315 newly-recorded live performances of model compositions and fully realized settingsAn instructor’s manual with guidelines for evaluation of assignments, additional repertoire for in-class analysis and assignments, sample syllabi, and other useful information is also available. Please email [email protected] for more information.

A Student's Guide to Harmony and Counterpoint