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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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This book explains the state of the art in the use of the discrete Fourier transform (DFT) of musical structures such as rhythms or scales. In particular the author explains the DFT of pitch-class distributions, homometry and the phase retrieval problem, nil Fourier coefficients and tilings, saliency, extrapolation to the continuous Fourier transform and continuous spaces, and the meaning of the phases of Fourier coefficients. This is the first textbook dedicated to this subject, and with supporting examples and exercises this is suitable for researchers and advanced undergraduate and graduate students of music, computer science and engineering. The author has made online supplementary material available, and the book is also suitable for practitioners who want to learn about techniques for understanding musical notions and who want to gain musical insights into mathematical problems.

Computer science. --- Music. --- Computer science --- User interfaces (Computer systems). --- Application software. --- Mathematics. --- Computer Science. --- Computer Appl. in Arts and Humanities. --- Mathematics in Music. --- Mathematics of Computing. --- User Interfaces and Human Computer Interaction. --- Signal, Image and Speech Processing. --- Math --- Application computer programs --- Application computer software --- Applications software --- Apps (Computer software) --- Interfaces, User (Computer systems) --- 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 --- Human-machine systems --- Human-computer interaction --- Information systems. --- Music --- Computer science—Mathematics. --- Signal processing. --- Image processing. --- Speech processing systems. --- Computational linguistics --- Electronic systems --- Information theory --- Modulation theory --- Oral communication --- Speech --- Telecommunication --- Singing voice synthesizers --- Pictorial data processing --- Picture processing --- Processing, Image --- Imaging systems --- Optical data processing --- Processing, Signal --- Information measurement --- Signal theory (Telecommunication)