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.

The essays in Sound Judgment span the full career of Richard Leppert, from his earliest to work that appears here for the first time, on subjects drawn from early modernity to the present concerning music both popular and classical, European and North American. Noted for his path-breaking interdisciplinary scholarship on music and visual culture, the collection includes key essays on music's visualization in art practices in virtually all visual media, including film. The fourteen essays comprising this volume demonstrate Leppert's many contributions to critical musicology, particularly in the areas of aesthetics as well as social and intellectual history, all of it grounded in a heterodox body of critical and cultural theory, with the work of Theodor W. Adorno particularly noteworthy. The collection is preceded by an introduction in which Leppert traces his intellectual development, defined in large part by the social, cultural, and political upheavals of the 1960s and their aftermath both in the academy and in society at large.

As one of the salient forces in the ritual life of those who worship the pre-Christian and Muslim deities called orishas, the Yoruba god of drumming, known as Ayan in Africa and Ana in Cuba, is variously described as the orisha of drumming, the spirit of the wood, or the more obscure Yoruba praise name AsoroIgi (Wood That Talks). With the growing global importance of orisha religion and music, the consequence of this deity's power for devotees continually reveals itself in new constellations of meaning as a sacred drum of Nigeria and Cuba finds new diasporas. Despite the growing volume of literature about the orishas, surprisingly little has been published about the ubiquitous Yoruba music spirit. Yet wherever one hears drumming for the orishas, Ayan or Ana is nearby. This groundbreaking collection addresses the gap in the research with contributions from a cross-section of prestigious musicians, scholars, and priests from Nigeria, the Americas, and Europe who have dedicated themselves to studying Yoruba sacred drums and the god sealed within. As well as offering multidisciplinary scholarly insights from transatlantic researchers, the volume includes compelling first-hand accounts from drummer-priests who were themselves history-makers in Nigerian and Cuban diasporas in the United States, Venezuela, and Brazil. This collaboration between diverse scholars and practitioners constitutes an innovative approach, where differing registers of knowledge converge to portray the many faces and voices of a single god.

An iconic symbol and sound of the Lucumi/Santeria religion, Afro-Cuban bata are talking drums that express the epic mythological narratives of the West African Yoruba deities known as "orisha." By imitating aspects of speech and song, and by metaphorically referencing salient attributes of the deities, bata drummers facilitate the communal praising of "orisha" in a music ritual known as a "toque de santo."

In "The Artistry of Afro-Cuban Bata Drumming," Kenneth Schweitzer blends musical transcription, musical analysis, interviews, ethnographic descriptions, and observations from his own experience as a ritual drummer to highlight the complex variables at work during a live Lucumi performance.

Integral in enabling trance possessions by the "orisha," by far the most dramatic expressions of Lucumi faith, bata drummers are also entrusted with controlling the overall ebb and flow of the four- to six-hour "toque de santo." During these events, bata drummers combine their knowledge of ritual with an extensive repertoire of rhythms and songs. Musicians focus on the many thematic acts that unfold both concurrently and in quick succession. In addition to creating an emotionally charged environment, playing salute rhythms for the "orisha," and supporting the playful song competitions that erupt between singers, bata drummers are equally dedicated to nurturing their own drumming community by creating a variety of opportunities for the musicians to grow artistically and creatively."

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.

In Crossing Paths, John Daverio explores the connections between art and life in the works of three giants of musical romanticism. Drawing on contemporary critical theory and a wide variety of nineteenth-century sources, he considers topics including Schubert and Schumann's uncanny ability to evoke memory in music, the supposed cryptographic practices of Schumann and Brahms, and the allure of the Hungarian Gypsy style for Brahms and others in the Schumann circle. Daverio portrays the book's three key players as musical storytellers, each in his own way simulating the structure of lived experience in works of art.

Discordant Democracy: Noise, Affect, Populism, and the Presidential Campaign paints a portrait of the political experience at a pivotal time in American political and social history. The modern political campaign is aestheticized and assimilated into mass culture, divorced from fact and policy, and nakedly tethered to emotional appeal. Through a multi-modal comparative examination of the sonic and emotional cultures of the 2008 and 2016 campaigns, Justin Patch raises critical queries about our affective relationship to modern politics and the impact of emotional campaigning on democracy. Discordant Democracy asks: how do campaign sounds affect us; what role do we the electorate play in creating and sustaining these sounds and affects; and what actions do they generate? Theories from anthropology, cognitive science, sound studies and philosophy are engaged to grapple with these questions and connect bombastic mass-mediated political events, campaign media and individual sonic experience. The analyses complicate notions of top-down campaigning, political spin, and enthusiastic millennial populism by examining our role in producing and animating political sounds through conversation, applause, laughter, media, and music.

Site and Sound: Understanding Independent Music Scenes examines how independent pop and rock music scenes of the 1980s and 1990s were constituted within social and geographical spaces. Those active in the production and consumption of « indie pop and rock music thought of their practices as largely independent of the music mainstream - even though some acts recorded for major labels. This book explores the web of personal, social, historical, geographical, cultural, and economic practices and relationships involved in the production and consumption of « indie music.

In his third volume on musical expressive meaning, Robert S. Hatten examines virtual agency in music from the perspectives of movement, gesture, embodiment, topics, tropes, emotion, narrativity, and performance. Distinguished from the actual agency of composers and performers, whose intentional actions either create music as notated or manifest music as significant sound, virtual agency is inferred from the implied actions of those sounds, as they move and reveal tendencies within music-stylistic contexts. From our most basic attributions of sources for perceived energies in music, to the highest realm of our engagement with musical subjectivity, Hatten explains how virtual agents arose as distinct from actual ones, how unspecified actants can take on characteristics of (virtual) human agents, and how virtual agents assume various actorial roles. Along the way, Hatten demonstrates some of the musical means by which composers and performers from different historical eras have staged and projected various levels of virtual agency, engaging listeners imaginatively and interactively within the expressive realms of their virtual and fictional musical worlds.

Music Theory: the essential guide offers musicians of all ages and levels a practical and relevant guide to music theory today. Written and structured to make content as easily digestible as possible, this indispensable guide: introduces key musical concepts such as pitch, tempo, rhythm, harmony, scales, instruments, musical forms and structure outlines the conventions governing music notation, demonstrating their relevance to the musical language of the twenty-first century provides interesting facts and real music examples to contextualise music theory offers practical tips on how to identify intervals, make up melodies and rhythms, set words to music and much more supports all aspects of the ABRSM Theory examinations (grades 1 to 5) includes an introduction and 'theory in practice' notes by renowned educationalist Paul Harris contains quick-reference tools including an appendix, list of further repertoire examples, table of instruments, periods of music history, table of scales and modes and summary keys and time signatures. Music Theory: the essential guide is a joint publication, published by Faber Music and Edition Peters.

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.

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.

"Taken as a trilogy, consent not to be a single being is a monumental accomplishment: a brilliant theoretical intervention that might be best described as a powerful case for blackness as a category of analysis."-Brent Hayes Edwards, author of Epistrophies: Jazz and the Literary Imagination In Black and Blur-the first volume in his sublime and compelling trilogy consent not to be a single being-Fred Moten engages in a capacious consideration of the place and force of blackness in African diaspora arts, politics, and life. In these interrelated essays, Moten attends to entanglement, the blurring of borders, and other practices that trouble notions of self-determination and sovereignty within political and aesthetic realms. Black and Blur is marked by unlikely juxtapositions: Althusser informs analyses of rappers Pras and Ol' Dirty Bastard; Shakespeare encounters Stokely Carmichael; thinkers like Kant, Adorno, and Jose Esteban Munoz and artists and musicians including Thornton Dial and Cecil Taylor play off each other. Moten holds that blackness encompasses a range of social, aesthetic, and theoretical insurgencies that respond to a shared modernity founded upon the sociological catastrophe of the transatlantic slave trade and settler colonialism. In so doing, he unsettles normative ways of reading, hearing, and seeing, thereby reordering the senses to create new means of knowing.

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.

German music critic and opera producer Paul Bekker (1882-1937) is a rare example of a critic granted the opportunity to turn his ideas into practice. In this first full-length study of Bekker in English, Nanette Nielsen investigates Bekker's theory and practice in light of ethics and aesthetics, in order to uncover the ways in which these intersect in his work and contributed to the cultural and political landscape of the Weimar Republic. By linking Beethoven's music to issues of freedom and individuality, as he argues for its potential to unify the masses, Bekker had already in 1911 begun to construct the ethical framework for his musical sociology and opera aesthetics. Nielsen discusses some of the complex (and conflicting) layers of modernism and conservatism in Bekker that would have a continued presence in his work and its reception throughout his career. Bekker's demands for a 'practical ethics' led to his criticisms of metaphysically grounded approaches to aesthetics, and his ethical views are put into further relief in a sketch of the development of his music phenomenology in the 1920s. Nielsen unravels the complex intersections between Bekker's ethics and his opera aesthetics in connection with his practice as an Intendant at the Wiesbaden State Theatre (1927-1932), offering a critical reading of an opera staged during his tenure: Hugo Herrmann's Vasantasena (1930). Further works are considered in light of the theoretical framework underpinning the book, inspired by several intersections between ethics and aesthetics encountered in Bekker's work.

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.

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.

What is the place of ethnic minorities in the identity and culture of the majority? What happens when the colonizer appropriates the culture of the colonized? Throughout Russia's nineteenth-century expansion into the Caucasus and Central Asia, Russian intellectuals struggled with these questions that cut to the core of imperial identity. Representing Russia's Orient draws on political, cultural, and social history to tell the story of how Russia's imperial advancements and encounters with its southern and eastern neighbors influenced the development of Russian musical identity. While Russia's ethnic minorities, or inorodtsy, were located at the geographical and cultural periphery, they loomed large in composers' musical imagination and became central to the definition of Russianness itself. Drawing from previously untapped archival and published materials, including music scores, visual art, and ethnographies, author Adalyat Issiyeva offers an in-depth study of Russian musical engagement with oriental subjects. Within a complex matrix of politics, competing ideological currents, and social and cultural transformations, some Russian composers and writers developed multidimensional representations of oriental "others" and sometimes even embraced elements of Asian musical identity. Mapping the vast repertoire of bylinas, military and children songs, music ethnographies, rare collections of Asian folk songs, art songs inspired by Decembrist literature, and the art music of famous composers from the Mighty Five and their followers - all set against the development of oriental studies in Russia - the book sheds new light on how and why Russians sometimes rejected, sometimes absorbed and transformed elements of Asian history and culture in forging their own national identity.

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.

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.

What does it mean to talk about musical coherence at the end of a century characterised by fragmentation and discontinuity? How can the diverse influences which stand behind the works of many late twentieth-century composers be reconciled with the singular immediacy of the experiences that they can create? How might an awareness of the distinctive ways in which these experiences are generated and controlled affect the way we listen to, reflect upon and write about this music? Mark Hutchinson outlines a novel concept of coherence within Western art music from the 1980s to the turn of the millennium as a means of understanding the work of a number of contemporary composers, including Thomas Ades, Kaija Saariaho, Toru Takemitsu and Gyoergy Kurtag, whose music cannot be fitted easily into a particular compositional school or analytical framework. Coherence is understood as a multi-layered phenomenon experienced, above all, in the act of listening, but reliant upon a variety of other aspects of musical experience, including compositional statements, analysis, and connections of aesthetic, as well as listeners' own, imaginative conceptualisations. Accordingly, the approach taken here is similarly multi-faceted: close analytical readings of a number of specific works are combined with insights drawn from philosophy and aesthetics, music perception, and critical theory, with a particular openness to novel metaphorical presentations of basic musical ideas about form, language and time.

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.

Byron Almen proposes an original synthesis of approaches to musical narrative from literary criticism, semiotics, historiography, musicology, and music theory, resulting in a significant critical reorientation of the field. This volume includes an extensive survey of traditional approaches to musical narrative illustrated by a wide variety of musical examples that highlight the range and applicability of the theoretical apparatus. Almen provides a careful delineation of the essential elements and preconditions of musical narrative organization, an eclectic analytical model applicable to a wide range of musical styles and repertoires, a classification scheme of narrative types and subtypes reflecting conceptually distinct narrative strategies, a wide array of interpretive categories, and a sensitivity to the dependence of narrative interpretation on the cultural milieu of the work, its various audiences, and the analyst. A Theory of Musical Narrative provides both an excellent introduction to an increasingly important conceptual domain and a complex reassessment of its possibilities and characteristics.