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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.

Computer science. --- Music. --- Computer science --- Artificial intelligence. --- Application software. --- Mathematics. --- Computer Science. --- Computer Appl. in Arts and Humanities. --- Mathematics in Music. --- Mathematics of Computing. --- Artificial Intelligence (incl. Robotics). --- Math --- Application computer programs --- Application computer software --- Applications software --- Apps (Computer software) --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Art music --- Art music, Western --- Classical music --- Musical compositions --- Musical works --- Serious music --- Western art music --- Western music (Western countries) --- Informatics --- Mathematics --- Science --- Computer software --- Bionics --- Cognitive science --- Digital computer simulation --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Information systems. --- Artificial Intelligence. --- Computer science—Mathematics. --- Music

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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.

Mathematics. --- Music. --- User interfaces (Computer systems). --- Application software. --- Performing arts. --- Mathematics in Music. --- User Interfaces and Human Computer Interaction. --- Computer Appl. in Arts and Humanities. --- Performing Arts. --- Show business --- Arts --- Performance art --- Application computer programs --- Application computer software --- Applications software --- Apps (Computer software) --- Computer software --- Interfaces, User (Computer systems) --- Human-machine systems --- Human-computer interaction --- Art music --- Art music, Western --- Classical music --- Musical compositions --- Musical works --- Serious music --- Western art music --- Western music (Western countries) --- Math --- Science --- Music theory. --- Music --- Musical theory --- Theory of music --- Theory --- User interfaces (Computer systems)