This textbook is a first introduction to mathematics for music theorists, covering basic topics such as sets and functions, universal properties, numbers and recursion, graphs, groups, rings, matrices and modules, continuity, calculus, and gestures. It approaches these abstract themes in a new way: Every concept or theorem is motivated and illustrated by examples from music theory (such as harmony, counterpoint, tuning), composition (e.g., classical combinatorics, dodecaphonic composition), and gestural performance. The book includes many illustrations, and exercises with solutions.

James McNeill Whistler and France: A Dialogue in Paint, Poetry, and Music is the first full-length and in-depth study to position this painter within the overall trajectory of French modernism during the second half of the nineteenth century and to view the artist as integral to the aesthetic projects of its most original contributors. Suzanne M. Singletary maintains that Whistler was in a unique situation as an insider within the emerging French avant-garde, thereby in an enviable position to both absorb and transform the innovations of others - and that until now, his widespread influence as a catalyst among his colleagues has been neither investigated nor appreciated. Singletary contends that Whistler's importance rivals that of Manet, whose multi-layered (and often unexpected) interconnections with Whistler are the focus of one chapter. In addition, Whistler's pivotal role in linking the legacies of Baudelaire, Delacroix, Gautier, Wagner, and other mid-century innovators to the later French Symbolists has previously been largely ignored. Courbet, Degas, Monet, and Seurat complete the roster of French artists whose dialogue with Whistler is highlighted.

Metal, Rap, and Electro in Tunisia is a trip into the music scenes of Tunisia after the Arab Springs. Based on extensive field research, the book explores the social life of heavy metal, rap, and electronic music in a North African country whose mass revolution of 2010/2011 led the way to a troubled and yet unique democracy. What is it like to be part of a music scene in a place affected by poverty and inequality? How do the many conflicted souls of Tunisian Islam shape local metal, rap, and electro? What are the social and cultural stakes for music in a nation constantly represented as a bridge between Europe and the Middle East? How do music scenes articulate the complex political scenario that followed the Tunisian revolution of 2011? Barone answers these questions by offering new theoretical reflections on youth cultures and popular music in a global perspective, and thus pushing the debate on "post-subcultures" and scenes forward. At the same time, the book offers a dense sociological analysis of youth and music in reality - the Tunisian one - whose society, culture, religion, and politics are at stake in a historical transformation.

George Harrison was one of the most prolific popular music composers of the late 20th century. During his tenure with the Beatles, he caught the wave of 1960s pop culture and began channeling its pervasive influence through his music. Often described as "The Invisible Singer," his solo recordings reveal him to be an elusive, yet essential, element in the Beatles' sound. The discussion of George Harrison's Beatle tracks featured in the text employs a Songscape approach that blends accessible music analysis with an exploration of the virtual space created on the sound recording. This approach is then used to explore Harrison's extensive catalog of solo works, which, due to their varied cultural sources, seem increasingly like early examples of Global Pop. In that sense, the music of George Harrison may ultimately be viewed as an important locus for pan-cultural influence in the 20th century, making this book essential reading for those interested in the history of songwriting and recording as well as the cultural study of popular music.

Boy Bands and the Performance of Pop Masculinity provides a history of the boy band from the Beatles to One Direction, placing the modern male pop group within the wider context of twentieth- and twenty-first-century popular music and culture. Offering the first extended look at pop masculinity as exhibited by boy bands, this volume links the evolving expressions of gender and sexuality in the boy band to wider economic and social changes that have resulted in new ways of representing what it is to be a man. The popularity of boy bands is unquestionable, and their contributions to popular music are significant, yet they have attracted relatively little study. This book fills that gap with chapters exploring the challenges of defining the boy band phenomenon, its origins and history from the 1940s to the present, the role of management and marketing, the performance of gender and sexuality, and the nature of fandom and fan agency. Throughout, the author illuminates the ways in which identity politics influence the production and consumption of pop music and shows how the mainstream pop of boy bands can both reinforce and subvert gender and class hierarchies.

Digital technology is transforming the musical score as a broad array of innovative score systems have become available to musicians. From attempts to mimic the print score, to animated and graphical scores, to artificial intelligence-based options, digital scoring affects the musical process by opening up new possibilities for dynamic interaction between the performer and the music, changing how we understand the boundaries between composition, score, improvisation and performance. The Digital Score: Musicianship, Creativity and Innovation offers a guide into this new landscape, reflecting on what these changes mean for music-making from both theoretical and applied perspectives. Drawing on findings from over a decade's worth of practice-based experimentation in the field, author Craig Vear builds a framework for understanding how digital scores create meaning. He considers the interactions between affect, embodiment and digital scores, offering the first comprehensive and critical consideration of an exciting field with no agreed-upon borders. Featuring insights from interviews with over fifty musicians and composers from across four continents, this book is a valuable resource for music researchers and practitioners alike.

Boy Bands and the Performance of Pop Masculinity provides a history of the boy band from the Beatles to One Direction, placing the modern male pop group within the wider context of twentieth- and twenty-first-century popular music and culture. Offering the first extended look at pop masculinity as exhibited by boy bands, this volume links the evolving expressions of gender and sexuality in the boy band to wider economic and social changes that have resulted in new ways of representing what it is to be a man. The popularity of boy bands is unquestionable, and their contributions to popular music are significant, yet they have attracted relatively little study. This book fills that gap with chapters exploring the challenges of defining the boy band phenomenon, its origins and history from the 1940s to the present, the role of management and marketing, the performance of gender and sexuality, and the nature of fandom and fan agency. Throughout, the author illuminates the ways in which identity politics influence the production and consumption of pop music and shows how the mainstream pop of boy bands can both reinforce and subvert gender and class hierarchies.

This book explains music's comprehensive ontology, its way of existence and processing, as specified in its compact characterization: music embodies meaningful communication and mediates physically between its emotional and mental layers. The book unfolds in a basic discourse in everyday language that is accessible to everybody who wants to understand what this topic is about. Musical ontology is delayed in its fundamental dimensions: its realities, its meaningful communication, and its embodied utterance from musical creators to an interested audience. The authors' approach is applicable to every musical genre and is scientific, the book is suitable for non-musicians and non-scientists alike.

"The Danger of Music" gathers some two decades of Richard Taruskin's writing on the arts and politics, ranging in approach from occasional pieces for major newspapers such as "The New York Times" to full-scale critical essays for leading intellectual journals. Hard-hitting, provocative, and incisive, these essays consider contemporary composition and performance, the role of critics and historians in the life of the arts, and the fraught terrain where ethics and aesthetics interact and at times conflict. Many of the works collected here have themselves excited wide debate, including the title essay, which considers the rights and obligations of artists in the aftermath of the 9/11 terrorist attacks. In a series of lively postscripts written especially for this volume, Taruskin, America's 'public' musicologist, addresses the debates he has stirred up by insisting that art is not a utopian escape and that artists inhabit the same world as the rest of society. Among the book's forty-two essays are two public addresses - one about the prospects for classical music at the end of the second millennium C. E., the other a revisiting of the performance issues previously discussed in the author's "Text and Act (1995)" - that appear in print for the first time.

Questions about variation, similarity, enumeration, and classification of musical structures have long intrigued both musicians and mathematicians. Mathematical models can be found from theoretical analysis to actual composition or sound production. Increasingly in the last few decades, musical scholarship has incorporated modern mathematical content. One example is the application of methods from Algebraic Combinatorics, or Topology and Graph Theory, to the classification of different musical objects. However, these applications of mathematics in the understanding of music have also led to interesting open problems in mathematics itself.The reach and depth of the contributions on mathematical music theory presented in this volume is significant. Each contribution is in a section within these subjects: (i) Algebraic and Combinatorial Approaches; (ii) Geometric, Topological, and Graph-Theoretical Approaches; and (iii) Distance and Similarity Measures in Music.

The Oxford Handbook of Sound and Image in Western Art is the first book to examine, under one umbrella, different kinds of analogies, mutual influences, integrations and collaborations of audio and visual in different art forms: painting, sculpture, installation, architecture, performance art, animation, film, video art, visual music, multimedia, experimental music, sound art, opera, theatre and dance. Sitting at the cutting edge of the field of music and visual arts, the book offers a unique, at times controversial view of this rapidly evolving area of study. The book is organized around three core thematic sections. The first, Sights & Sounds, concentrates on interaction between the experience of seeing and the experience of hearing. Sound, Space & Matter expands the idea of music to include environmental sounds, vibrating frequencies, homemade instruments, linguistic utterances, noise and silence. Architecture, likewise, faces a similar discourse that examines non-material spaces, environments, human habitats, performances, destruction and void. Enhanced by advanced digital technologies, this aesthetic shift opened the door for endless experiments, which give a new context to theoretical issues such as medium, matter and process in creating and perceiving art. In the third section, Performance, Performativity & Text, music as a performing art provides the point of departure. The new light shed by modernism and the avant-garde on the performative aspect of music have led it - together with sound and text - to become active in new ways in contemporary dance, theatre and the visual arts. The chapters in the handbook make and prove their arguments using case studies in contemporary art, music, and sound as illustrations, building upon exsiting thought as a foundation for discussion. Artists, curators, students and scholars will find here a panoramic view of cutting-edge discourse in the field, by an international roster of scholars and practitioners.

During the past 40 years, mathematical music theory has grown and developed in both the fields of music and mathematics. In music pedagogy, the need to analyze patterns of modern composition has produced Musical Set Theory, and the use of Group Theory and other modern mathematical structures have become almost as common as the application of mathematics in the fields of engineering or chemistry. Mathematicians have been developing stimulating ideas when exploring mathematical applications to established musical relations. Mathematics students have seen in Music in Mathematics courses, how their accumulated knowledge of abstract ideas can be applied to an important human activity while reinforcing their dexterity in Mathematics. Similarly, new general education courses in Music and Mathematics are being developed and are arising at the university level, as well as for high school and general audiences without requiring a sophisticated background in either music nor mathematics. Mathematical Music Theorists have also been developing exciting, creative courses for high school teachers and students of mathematics. These courses and projects have been implemented in the USA, in China, Ireland, France, Australia, and Spain.The objective of this volume is to share the motivation and content of some of these exciting, new Mathematical Theory and Music in Mathematics courses while contributing concrete materials to interested readers.

Thomas Ades (b. 1971) is an established international figure, both as composer and performer, with popular and critical acclaim and admiration from around the world. Edward Venn examines in depth one of Ades's most significant works so far, his orchestral Asyla (1997). Its blend of virtuosic orchestral writing, allusions to various idioms, including rave music, and a musical rhetoric encompassing both high modernism and lush romanticism is always compelling and utterly representative of Ades's distinctive compositional voice. The reception of Asyla since its premiere in 1997 by Sir Simon Rattle and the City of Birmingham Symphony Orchestra (CBSO) has been staggering. Instantly hailed as a classic, Asyla won the 1997 Royal Philharmonic Society Award for Large-Scale Composition. An internationally acclaimed recording made of the work was nominated for the 1999 Mercury Music Prize, and in 2000, Ades became the youngest composer (and only the third British composer) to win the Grawemeyer prize, for Asyla. Asyla is fast becoming a repertory item, rapidly gaining over one hundred performances: a rare distinction for a contemporary work.

An Anthology of Australian Albums offers an overview of Australian popular music through the lens of significant, yet sometimes overlooked, Australian albums. Chapters explore the unique qualities of each album within a broader history of Australian popular music. Artists covered range from the older and non-mainstream yet influential, such as the Missing Links, Wendy Saddington and the Coloured Balls, to those who have achieved very recent success (Courtney Barnett, Dami Im and Flume) and whose work contributes to international pop music (Sia), to the more exploratory or experimental (Curse ov Dialect and A.B. Original). Collectively the albums and artists covered contribute to a view of Australian popular music through the non-canonical, emphasizing albums by women, non-white artists and Indigenous artists, and expanding the focus to include genres outside of rock including hip hop, black metal and country.

Beethoven's seventy-two settings of traditional Irish airs constitute his most prolific output in any genre. The arrangements were commissioned in the early nineteenth century by the Scottish editor and publisher, George Thomson, who sent airs, but no texts, to Beethoven. Poetry, mostly by less well-known poets, was attached to the finished settings before publication by Thomson, and perhaps therein lies the reason why the songs never achieved the popularity which they deserve: many of the poems have been judged to be of inferior quality. In this edition, the first in which all Beethoven's Irish folksong settings are published together, the late baritone, broadcaster and musicologist, Tomas O Suilleabhain, selected texts, mostly by Burns and Moore, which he felt were more appropriate to the airs and to Beethoven's settings.

For students learning the principles of music theory, it can often seem as though the tradition of tonal harmony is governed by immutable rules that define which chords, tones, and intervals can be used where. Yet even within the classical canon, there are innumerable examples of composers diverging from these foundational "rules." Drawing on examples from composers including J.S. Bach, Mozart, Beethoven, Schubert, Mendelssohn, Chopin, Brahms, and more, Bending the Rules of Music Theory seeks to take readers beyond the basics of music theory and help them to understand the inherent flexibility in the system of tonal music. Chapters explore the use of different rule-breaking elements in practice and why they work, introducing students to a more nuanced understanding of music theory.

Morton Feldman viewed Piano and String Quartet as his capstone work-the culminating example of the aesthetic that Feldman spent his life seeking. Written in 1985, the year before Feldman's death, this single movement, roughly 80-minute composition was heralded by Steve Reich as "the most beautiful work [of Feldman's] I know." Ray Fields presents a detailed analysis of the complete piece and examines the elements that contribute to its formal and expressive design, including local and large-scale temporal architecture, pitch/interval formations, texture, timbre, and register. It discusses the aural experience of the music itself and provides insights into Feldman's aesthetic influences. Basic biographical information is provided, describing the music of his early, middle, and late periods and providing an overview of analyses of other Feldman works. By examining this beloved piece, the book addresses the question: what was everything Feldman wanted in his music? Also included are interviews with Kronos Quartet's David Harrington about the origins of Piano and String Quartet and Aki Takahashi providing crucial information about the work.

In recent years, scholars and musicians have become increasingly interested in the revival of musical improvisation as it was known in the Renaissance and Baroque periods. This historically informed practice is now supplanting the late Romantic view of improvised music as a rhapsodic endeavour-a musical blossoming out of the capricious genius of the player-that dominated throughout the twentieth century. In the Renaissance and Baroque eras, composing in the mind (alla mente) had an important didactic function. For several categories of musicians, the teaching of counterpoint happened almost entirely through practice on their own instruments. This volume offers the first systematic exploration of the close relationship among improvisation, music theory, and practical musicianship from late Renaissance into the Baroque era. It is not a historical survey per se, but rather aims to re-establish the importance of such a combination as a pedagogical tool for a better understanding of the musical idioms of these periods. The authors are concerned with the transferral of historical practices to the modern classroom, discussing new ways of revitalising the study and appreciation of early music. The relevance and utility of such an improvisation-based approach also changes our understanding of the balance between theoretical and practical sources in the primary literature, as well as the concept of music theory itself. Alongside a word-centred theoretical tradition, in which rules are described in verbiage and enriched by musical examples, we are rediscovering the importance of a music-centred tradition, especially in Spain and Italy, where the music stands alone and the learner must distil the rules by learning and playing the music. Throughout its various sections, the volume explores the path of improvisation from theory to practice and back again.

The flourishing of religious or spiritually-inspired music in the late twentieth and early twenty-first centuries remains largely unexplored. The engagement and tensions between modernism and tradition, and institutionalized religion and spirituality are inherent issues for many composers who have sought to invoke spirituality and Otherness through contemporary music. Contemporary Music and Spirituality provides a detailed exploration of the recent and current state of contemporary spiritual music in its religious, musical, cultural and conceptual-philosophical aspects. At the heart of the book are issues that consider the role of secularization, the claims of modernity concerning the status of art, and subjective responses such as faith and experience. The contributors provide a new critical lens through which it is possible to see the music and thought of Cage, Ligeti, Messiaen, Stockhausen as spiritual music. The book surrounds these composers with studies of and by other composers directly associated with the idea of spiritual music (Harvey, Gubaidulina, MacMillan, Part, Pott, and Tavener), and others (Adams, Birtwistle, Ton de Leeuw, Ferneyhough, Ustvolskaya, and Vivier) who have created original engagements with the idea of spirituality. Contemporary Music and Spirituality is essential reading for humanities scholars and students working in the areas of musicology, music theory, theology, religious studies, philosophy of culture, and the history of twentieth-century culture.

Alfred Schnittke (1934-1998) was arguably the most important Russian composer since Shostakovich, and his music has generated a great deal of academic interest in the years since his death. Schnittke Studies provides a variety of perspectives on the composer and his music. The field is currently diverse and vibrant, and this book demonstrates the range of academic approaches being applied to Schnittke's work and the insights they provide, covering: polystylism, for which Schnittke is best known, the significance of the composer's Christian faith, and detailed formal analyses of key works, with connections drawn between the apparently divergent periods of the composer's career. This book has been prepared as a memorial to Professor Alexander Ivashkin, a leading scholar in the field, who died in 2014, and will be of interest not only to those studying Schnittke's music, but also those with an interest in late Soviet-era music in general.

Since Gyoergy Ligeti's death in 2006, there has been a growing acknowledgement of how central he was to the late twentieth-century cultural landscape. This collection is the first book devoted to exploring the composer's life and music within the context of his East European roots, revealing his dual identities as both Hungarian national and cosmopolitan modernist. Contributors explore the artistic and socio-cultural contexts of Ligeti's early works, including composition and music theory, the influence of East European folk music, notions of home and identity, his ambivalent attitude to his Hungarian past and his references to his homeland in his later music. Many of the valuable insights offered profit from new research undertaken at the Paul Sacher Foundation, Basel, while also drawing on the knowledge of long-time associates such as the composer's assistant, Louise Duchesneau. The contributions as a whole reveal Ligeti's thoroughly cosmopolitan milieu and values, and illuminate why his music continues to inspire new generations of performers, composers and listeners.

Felix Mendelssohn is one of the most celebrated figures of the early Romantic period. As a composer of sacred texts, he is chiefly remembered today for the oratorios Paulus (1836) and Elijah (1846). In this groundbreaking study, Siegwart Reichwald offers a meticulous analysis of Paulus, beginning with a general overview of the oratorio traditions of the early nineteenth century. He details the phases of the compositional process of Paulus as well as principles governing its development. Numerous musical examples, figures, and tables accompany the text. This thorough treatment of Paulus, while shedding light on Mendelssohn's approach to the oratorio and to sacred music in general, will be of interest to students of musicology.

A fascinating aspect of the study of music in medieval Islamic and Judaic writings is the broad and interdisciplinary nature of the works and treatises in which it is covered. In addition, such works verbalize an art that was transmitted orally and took shape spontaneously, typically with improvisation during performance. As a result of this outlook the musical concept (or science) is often intertwined with practice (or history). This second collection by Amnon Shiloah brings together twenty-two studies exemplifying such multi-faceted viewpoints on the world of sounds and its virtue. The first studies concern the origin and originators of music and to how its essential constituents came into being; included here is the art of dance along with the controversial attitudes towards it. Next comes the symbolic, philosophical and metaphorical interpretation of music; one of the major ideas epitomizing this approach claimed that the pursuit of knowledge is the path to human perfection and happiness. There follow studies on the transmission of knowledge, along with some annotated key works dealing with therapeutic effects. The last articles focus on cultural traditions elaborated on European soil developing a particular style and musical practice, centred on the Iberian Peninsula, which was the scene of one of the most fascinating examples of cultural interchange.

This innovative study re-evaluates the philosophical significance of aesthetics in the context of contemporary debates on the nature of philosophy. Lewis's main argument is that contemporary conceptions of meaning and truth have been reified, and that aesthetics is able to articulate why this is the case, with important consequences for understanding the horizons and nature of philosophical inquiry. Reification and the Aesthetics of Music challenges the most emphatic and problematic conceptions of meaning and truth in both analytic philosophy and postmodern thought by acknowledging the ontological and logical primacy of our concrete, practice-based experiences with aesthetic phenomena. By engaging with a variety of aesthetic practices, including Beethoven's symphonies and string quartets, Wagner's music dramas, Richard Strauss's Elektra, the twentieth-century avant-garde, Jamaican soundsystem culture, and punk and contemporary noise, this book demonstrates the aesthetic relevance of reification as well as the concept's applicability to contemporary debates within philosophy.

"Everything But Bach, Beethoven and Brahms," comprises this multicultural repertoire guide for pianists, composers, music teachers and students, world music enthusiasts and scholars. It identifies pieces in the contemporary solo piano literature which show world music influences not traditionally associated with the standard repertoire of Western European art music. The resulting annotated bibliography therefore includes pieces which use or attempt to emulate non-Western scales, modes, folk tunes, rhythmic, percussive or harmonic devices and timbres. Axford highlights the music cultures of the Middle East and North Africa, Sub-Saharan Africa, India, the Far East, Indonesia, Oceania, ethnic North America, Latin America and Spain, and Eastern Europe, Russia, and Scandinavia. Separate bibliographies for each world music region show examples of contemporary solo piano pieces that demonstrate some of the traditional musical influences associated with the region.