Computational Models of Rhythm and Meter


Book Description

This book presents the latest computational models of rhythm and meter that are based on number theory, combinatorics and pattern matching. Two computational models of rhythm and meter are evaluated: The first one explores a relatively new field in Mathematics, namely Combinatorics on Words, specifically Christoffel Words and the Burrows-Wheeler Transform, together with integer partitions. The second model uses filtered Farey Sequences in combination with specific weights that are assigned to inter-onset ratios. This work is assessed within the context of the current state of the art of tempo tracking and computational music transcription. Furthermore, the author discusses various representations of musical rhythm, which lead to the development of a new shorthand notation that will be useful for musicologists and composers. Computational Models of Rhythm and Meter also contains numerous investigations into the timing structures of human rhythm and metre perception carried out within the last decade. Our solution to the transcription problem has been tested using a wide range of musical styles, and in particular using two recordings of J.S. Bach's Goldberg Variations by Glenn Gould. The technology is capable of modelling musical rhythm and meter by using Farey Sequences, and by detecting duration classes in a windowed analysis, which also detects the underlying tempo. The outcomes represent human performances of music as accurate as possible within Western score notation.




Mathematical and Computational Modeling


Book Description

Mathematical and Computational Modeling Illustrates the application of mathematical and computational modeling in a variety of disciplines With an emphasis on the interdisciplinary nature of mathematical and computational modeling, Mathematical and Computational Modeling: With Applications in the Natural and Social Sciences, Engineering, and the Arts features chapters written by well-known, international experts in these fields and presents readers with a host of state-of-theart achievements in the development of mathematical modeling and computational experiment methodology. The book is a valuable guide to the methods, ideas, and tools of applied and computational mathematics as they apply to other disciplines such as the natural and social sciences, engineering, and technology. The book also features: Rigorous mathematical procedures and applications as the driving force behind mathematical innovation and discovery Numerous examples from a wide range of disciplines to emphasize the multidisciplinary application and universality of applied mathematics and mathematical modeling Original results on both fundamental theoretical and applied developments in diverse areas of human knowledge Discussions that promote interdisciplinary interactions between mathematicians, scientists, and engineers Mathematical and Computational Modeling: With Applications in the Natural and Social Sciences, Engineering, and the Arts is an ideal resource for professionals in various areas of mathematical and statistical sciences, modeling and simulation, physics, computer science, engineering, biology and chemistry, and industrial and computational engineering. The book also serves as an excellent textbook for graduate courses in mathematical modeling, applied mathematics, numerical methods, operations research, and optimization.




Mathematics of Musical Rhythm


Book Description

This book presents original research applying mathematics to musical rhythm, with a focus on computational methods, theoretical approaches, analysis of rhythm in folk and global music traditions, syncopation, and maximal evenness. It honours the legacy of computer scientist and music theorist Godfried Toussaint. In addition to addressing a topic pioneered by Toussaint, application of mathematics to representation of musical rhythms, the volume also builds upon his interest in analysis of music traditions outside the European classical canon and the use of computational methods. Empirical contributions include a study of timing in Scandinavian polska performance showing that timing interacts with rhythmic features and a study of vocal melody rhythm in pre- and post-millennial popular music, showing significant differences in tempo, rhythmic density, and repetition in the two corpora. Theoretical contributions include a survey of timeline rhythms of African and African diasporic musics showing the prevalence of rhythms of a special type related to maximal evenness, an application of matrix algebra to rhythm and syncopation with analysis of clave rhythms, a ragtime corpus, and Balinese gong cycles, and a mathematical development of a new classification of smooth rhythms using a “shadow rhythm” algorithm suggested by Toussaint. The volume also includes an original composition by Tom Johnson and a personal recollection of Toussaint by Francisco Gómez-Martín. This volume will be a key resource for academics, researchers, and advanced students of music, musicology, music analyses, mathematical music theory, computational musicology, and music informatics. It was originally published as a special issue of the Journal of Mathematics and Music.




Bridging Music Informatics with Music Cognition


Book Description

Music informatics is an interdisciplinary research area that encompasses data driven approaches to the analysis, generation, and retrieval of music. In the era of big data, two goals weigh heavily on many research agendas in this area: (a) the identification of better features and (b) the acquisition of better training data. To this end, researchers have started to incorporate findings and methods from music cognition, a related but historically distinct research area that is concerned with elucidating the underlying mental processes involved in music-related behavior.




Foundations in Music Psychology


Book Description

A state-of-the-art overview of the latest theory and research in music psychology, written by leaders in the field. This authoritative, landmark volume offers a comprehensive state-of-the-art overview of the latest theory and research in music perception and cognition. Eminent scholars from a range of disciplines, employing a variety of methodologies, describe important findings from core areas of the field, including music cognition, the neuroscience of music, musical performance, and music therapy. The book can be used as a textbook for courses in music cognition, auditory perception, science of music, psychology of music, philosophy of music, and music therapy, and as a reference for researchers, teachers, and musicians. The book's sections cover music perception; music cognition; music, neurobiology, and evolution; musical training, ability, and performance; and musical experience in everyday life. Chapters treat such topics as pitch, rhythm, and timbre; musical expectancy, musicality, musical disorders, and absolute pitch; brain processes involved in music perception, cross-species studies of music cognition, and music across cultures; improvisation, the assessment of musical ability, and singing; and music and emotions, musical preferences, and music therapy. Contributors Fleur Bouwer, Peter Cariani, Laura K. Cirelli, Annabel J. Cohen, Lola L. Cuddy, Shannon de L'Etoile, Jessica A. Grahn, David M. Greenberg, Bruno Gingras, Henkjan Honing, Lorna S. Jakobson, Ji Chul Kim, Stefan Koelsch, Edward W. Large, Miriam Lense, Daniel Levitin, Charles J. Limb, Psyche Loui, Stephen McAdams, Lucy M. McGarry, Malinda J. McPherson, Andrew J. Oxenham, Caroline Palmer, Aniruddh Patel, Eve-Marie Quintin, Peter Jason Rentfrow, Edward Roth, Frank A. Russo, Rebecca Scheurich, Kai Siedenburg, Avital Sternin, Yanan Sun, William F. Thompson, Renee Timmers, Mark Jude Tramo, Sandra E. Trehub, Michael W. Weiss, Marcel Zentner




The Evolution of Rhythm Cognition: Timing in Music and Speech


Book Description

Human speech and music share a number of similarities and differences. One of the closest similarities is their temporal nature as both (i) develop over time, (ii) form sequences of temporal intervals, possibly differing in duration and acoustical marking by different spectral properties, which are perceived as a rhythm, and (iii) generate metrical expectations. Human brains are particularly efficient in perceiving, producing, and processing fine rhythmic information in music and speech. However a number of critical questions remain to be answered: Where does this human sensitivity for rhythm arise? How did rhythm cognition develop in human evolution? How did environmental rhythms affect the evolution of brain rhythms? Which rhythm-specific neural circuits are shared between speech and music, or even with other domains? Evolutionary processes’ long time scales often prevent direct observation: understanding the psychology of rhythm and its evolution requires a close-fitting integration of different perspectives. First, empirical observations of music and speech in the field are contrasted and generate testable hypotheses. Experiments exploring linguistic and musical rhythm are performed across sensory modalities, ages, and animal species to address questions about domain-specificity, development, and an evolutionary path of rhythm. Finally, experimental insights are integrated via synthetic modeling, generating testable predictions about brain oscillations underlying rhythm cognition and its evolution. Our understanding of the cognitive, neurobiological, and evolutionary bases of rhythm is rapidly increasing. However, researchers in different fields often work on parallel, potentially converging strands with little mutual awareness. This research topic builds a bridge across several disciplines, focusing on the cognitive neuroscience of rhythm as an evolutionary process. It includes contributions encompassing, although not limited to: (1) developmental and comparative studies of rhythm (e.g. critical acquisition periods, innateness); (2) evidence of rhythmic behavior in other species, both spontaneous and in controlled experiments; (3) comparisons of rhythm processing in music and speech (e.g. behavioral experiments, systems neuroscience perspectives on music-speech networks); (4) evidence on rhythm processing across modalities and domains; (5) studies on rhythm in interaction and context (social, affective, etc.); (6) mathematical and computational (e.g. connectionist, symbolic) models of “rhythmicity” as an evolved behavior.




The Geometry of Musical Rhythm


Book Description

The Geometry of Musical Rhythm: What Makes a "Good" Rhythm Good? is the first book to provide a systematic and accessible computational geometric analysis of the musical rhythms of the world. It explains how the study of the mathematical properties of musical rhythm generates common mathematical problems that arise in a variety of seemingly dispara




The Oxford Handbook of Time in Music


Book Description

"The work of this introductory chapter is twofold; first, to provide a brief historical overview of the changing nature and conception of musical time over the last two thousand years, and second, to set out the arc of the work through detailing the central points of each chapter. While the individual pieces of writing bring vital and varied perspectives from musicology, ethnomusicology, philosophy, psychology, and socio-cultural work, what unites them is their attention to music of the modern period, with a strong focus on the multiplicities of contemporary practice, while also pointing to their nineteenth-century antecedents. In introducing the main themes of the book, the introduction calls attention to the burgeoning scholarship on time in music ranging between the immediate feelings and socialities of being in time with others and the broader imaginings of the cultural politics of time in music"--




The Oxford Handbook of Computer Music


Book Description

This handbook provides a cross-section of the most field-defining topics and debates in the field of computer music today. From music cognition to pedagogy, it situates computer music in the broad context of its creation and performance across the full range of issues that crop up in discourse in the field.




The Psychology of Music


Book Description

The Psychology of Music serves as an introduction to an interdisciplinary field in psychology, which focuses on the interpretation of music through mental function. This interpretation leads to the characterization of music through perceiving, remembering, creating, performing, and responding to music. In particular, the book provides an overview of the perception of musical tones by discussing different sound characteristics, like loudness, pitch and timbre, together with interaction between these attributes. It also discusses the effect of computer resources on the psychological study of music through computational modeling. In this way, models of pitch perception, grouping and voice separation, and harmonic analysis were developed. The book further discusses musical development in social and emotional contexts, and it presents ways that music training can enhance the singing ability of an individual. The book can be used as a reference source for perceptual and cognitive psychologists, neuroscientists, and musicians. It can also serve as a textbook for advanced courses in the psychological study of music. - Encompasses the way the brain perceives, remembers, creates, and performs music - Contributions from the top international researchers in perception and cognition of music - Designed for use as a textbook for advanced courses in psychology of music