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This is the fourth volume of the second edition of the now classic book “The Topos of Music”. The author presents appendices with background material on sound and auditory physiology; mathematical basics such as sets, relations, transformations, algebraic geometry, and categories; complements in physics, including a discussion on string theory; and tables with chord classes and modulation steps.
This book presents a new semiotic theory based upon category theory and applying to a classification of creativity in music and mathematics. It is the first functorial approach to mathematical semiotics that can be applied to AI implementations for creativity by using topos theory and its applications to music theory. Of particular interest is the generalized Yoneda embedding in the bidual of the category of categories (Lawvere) - parametrizing semiotic units - enabling a Čech cohomology of manifolds of semiotic entities. It opens up a conceptual mathematics as initiated by Grothendieck and Galois and allows a precise description of musical and mathematical creativity, including a classification thereof in three types. This approach is new, as it connects topos theory, semiotics, creativity theory, and AI objectives for a missing link to HI (Human Intelligence). The reader can apply creativity research using our classification, cohomology theory, generalized Yoneda embedding, and Java implementation of the presented functorial display of semiotics, especially generalizing the Hjelmslev architecture. The intended audience are academic, industrial, and artistic researchers in creativity.
This book fills a gap between theory and creativity in musicianship. This frequently observed gap fixes theory as a rigidified level of thought, where creativity is excluded from a canonized corpus of ideas. Creativity, on the other hand, is preconceived as a theory-less, wild activity that blossoms while performing pre-composed musical structures. This book provides a discussion of the creative drive in theory and theory-inspired thoughts while understanding how these ideas shape performance. The future of music is only as limited as one’s imagination, and, to this end, the text illuminates examples of creative musicianship.
This book presents and discusses the fundamental topic of classification of musical objects, such as chords, motifs, and gestures. Their classification deals with the exhibition of isomorphism classes. Our structure types include local and global constructions, the latter being similar to global structures in geometry, such as differentiable manifolds. The discussion extends to the role, which classification plays for the creative construction of musical compositions. Our examples include references to classical compositions, such as Beethoven’s sonatas, and some of the author’s own compositions of classical and jazz styles. We also discuss software that enables the application of classification to musical creativity. The volume is addressed to an audience that would apply classification to programming and creative musical construction.
This is the third volume of the second edition of the now classic book “The Topos of Music”. The authors present gesture theory, including a gesture philosophy for music, the mathematics of gestures, concept architectures and software for musical gesture theory, the multiverse perspective which reveals the relationship between gesture theory and the string theory in theoretical physics, and applications of gesture theory to a number of musical themes, including counterpoint, modulation theory, free jazz, Hindustani music, and vocal gestures.
This is the first volume of the second edition of the now classic book “The Topos of Music”. The author explains the theory's conceptual framework of denotators and forms, the classification of local and global musical objects, the mathematical models of harmony and counterpoint, and topologies for rhythm and motives.
The aim of this book is to stimulate debate by offering a critique of discourse about African music. Who writes about African music, how, and why? What assumptions and prejudices influence the presentation of ethnographic data? Even the term "African music" suggests there is an agreed-upon meaning, but African music signifies differently to different people. This book also poses the question then, "What is African music?" Agawu offers a new and provocative look at the history of African music scholarship that will resonate with students of ethnomusicology and post-colonial studies. He offers an alternative "Afro-centric" means of understanding African music, and in doing so, illuminates a different mode of creativity beyond the usual provenance of Western criticism. This book will undoubtedly inspire heated debate--and new thinking--among musicologists, cultural theorists, and post-colonial thinkers. Also includes 15 musical examples.
The idea of this monograph is to present an overview of decisive theoretical, computational, technological, aesthetical, artistic, economical, and sociological directions to create future music. It features a unique insight into dominant scientific and artistic new directions, which are guaranteed by the authors' prominent publications in books, software, musical, and dance productions. Applying recent research results from mathematical and computational music theory and software as well as new ideas of embodiment approaches and non-Western music cultures, this book presents new composition methods and technologies. Mathematical, computational, and semiotic models of artistic presence (imaginary time, gestural creativity) as well as strategies are also covered. This book will be of interest to composers, music technicians, and organizers in the internet-based music industry, who are offered concrete conceptual architectures and tools for their future strategies in musical creativity and production.
Expanded, updated, and fully revised—the definitive introduction to electronic music is ready for new generations of students. Essential and state-of-the-art, The Computer Music Tutorial, second edition is a singular text that introduces computer and electronic music, explains its motivations, and puts topics into context. Curtis Roads’s step-by-step presentation orients musicians, engineers, scientists, and anyone else new to computer and electronic music. The new edition continues to be the definitive tutorial on all aspects of computer music, including digital audio, signal processing, musical input devices, performance software, editing systems, algorithmic composition, MIDI, and psychoacoustics, but the second edition also reflects the enormous growth of the field since the book’s original publication in 1996. New chapters cover up-to-date topics like virtual analog, pulsar synthesis, concatenative synthesis, spectrum analysis by atomic decomposition, Open Sound Control, spectrum editors, and instrument and patch editors. Exhaustively referenced and cross-referenced, the second edition adds hundreds of new figures and references to the original charts, diagrams, screen images, and photographs in order to explain basic concepts and terms. Features New chapters: virtual analog, pulsar synthesis, concatenative synthesis, spectrum analysis by atomic decomposition, Open Sound Control, spectrum editors, instrument and patch editors, and an appendix on machine learning Two thousand references support the book’s descriptions and point readers to further study Mathematical notation and program code examples used only when necessary Twenty-five years of classroom, seminar, and workshop use inform the pace and level of the material