Abstract Musical Intervals


Book Description

This book is an introduction to GIS (Generalized Interval Systems) theory that includes the major results of pitch-class theory. It provides mathematicians with applications of group theory to music and music theorists with the essential connections between GIS theory and pitch-class theory. Many of the results in pitch-class theory are not addressed by David Lewin (such as power functions or the Common Tone Theorem for inversions). The book states those results and generalizes them to conform with GIS theory. Finally, it addresses recent criticisms leveled at pitch-class theory and suggests how they can be addressed in GIS theory.




Generalized Musical Intervals and Transformations


Book Description

Generalized Musical Intervals and Transformations is by far the most significant contribution to the field of systematic music theory in the last half-century, generating the framework for the "transformational theory" movement.




Musical Excellence


Book Description

Offers performers, teachers, and researchers, new perspectives and practical guidance for enhancing performance and managing the stress that typically accompanies performance situations. It draws together the findings of pioneering initiatives from across the arts and sciences.




Stravinsky


Book Description

Studie over het werk van de Russische componist (1882-1971).




A Geometry of Music


Book Description

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.




The Oxford Handbook of Critical Concepts in Music Theory


Book Description

Music Theory operates with a number of fundamental terms that are rarely explored in detail. This book offers in-depth reflections on key concepts from a range of philosophical and critical approaches that reflect the diversity of the contemporary music theory landscape.




Intervals, Scales, Tones and the Concert Pitch C


Book Description

Why is it that certain intervals, scales, and tones sound genuine, while others sound false? Is the modern person able to experience a qualitative difference in a tone's pitch? If so, what are the implications for modern concert pitch and how instruments of fixed tuning are tuned? Renold tackles these and many other questions and provides a wealth of scientific data. Her pioneering work is the result of a lifetime of research into the Classical Greek origin of Western music and the search for modern developments. She deepens our musical understanding by using Rudolf Steiner's spiritual science as a basis, and she elucidates many of his puzzling statements about music. The results of her work include the following discoveries: - The octave has two sizes (a 'genuine' sounding octave is bigger than the "perfect octave") - There are three sizes of "perfect fifths" - An underlying "form principle" for all scales can be found - Equal temperament is not the most satisfactory method of tuning a piano - She provides a basis for some of Steiner's statements, such as, "C is always prime" and "C = 128 Hz = Sun." Intervals, Scales, Tones is a valuable resource for those who wish to understand the deeper, spiritual aspects of music.




Mathematics and Computation in Music


Book Description

This book constitutes the refereed proceedings of the Second International Conference on Mathematics and Computation in Music, MCM 2009, held in New Haven, CT, USA, in June 2009. The 26 revised full papers presented were carefully reviewed and selected from 38 submissions. The MCM conference is the flagship conference of the Society for Mathematics and Computation in Music. The papers deal with topics within applied mathematics, computational models, mathematical modelling and various further aspects of the theory of music. This year’s conference is dedicated to the honor of John Clough whose research modeled the virtues of collaborative work across the disciplines.




Conceptualizing Music


Book Description

This book shows how recent work in cognitive science, especially that developed by cognitive linguists and cognitive psychologists, can be used to explain how we understand music. The book focuses on three cognitive processes--categorization, cross-domain mapping, and the use of conceptual models--and explores the part these play in theories of musical organization. The first part of the book provides a detailed overview of the relevant work in cognitive science, framed around specific musical examples. The second part brings this perspective to bear on a number of issues with which music scholarship has often been occupied, including the emergence of musical syntax and its relationship to musical semiosis, the problem of musical ontology, the relationship between words and music in songs, and conceptions of musical form and musical hierarchy. The book will be of interest to music theorists, musicologists, and ethnomusicologists, as well as those with a professional or avocational interest in the application of work in cognitive science to humanistic principles.







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