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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.

Human sciences (algemeen) --- Mathematics --- Computer science --- Programming --- Computer architecture. Operating systems --- Artificial intelligence. Robotics. Simulation. Graphics --- Computer. Automation --- Music --- applicatiebeheer --- apps --- computers --- informatica --- muziek --- sociale wetenschappen --- externe fixatie (geneeskunde --- wiskunde --- KI (kunstmatige intelligentie) --- computerkunde --- architectuur (informatica) --- robots --- AI (artificiële intelligentie)

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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.

Semiotics --- Didactics of the arts --- Mathematics --- Artificial intelligence. Robotics. Simulation. Graphics --- Computer. Automation --- Music --- informatica --- muziek --- semiotiek --- kunstonderwijs --- creativiteit --- wiskunde --- KI (kunstmatige intelligentie) --- AI (artificiële intelligentie)

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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)

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This book is a comprehensive examination of the conception, perception, performance, and composition of time in music across time and culture. It surveys the literature of time in mathematics, philosophy, psychology, music theory, and somatic studies (medicine and disability studies) and looks ahead through original research in performance, composition, psychology, and education. It is the first monograph solely devoted to the theory of construction of musical time since Kramer in 1988, with new insights, mathematical precision, and an expansive global and historical context. The mathematical methods applied for the construction of musical time are totally new. They relate to category theory (projective limits) and the mathematical theory of gestures. These methods and results extend the music theory of time but also apply to the applied performative understanding of making music. In addition, it is the very first approach to a constructive theory of time, deduced from the recent theory of musical gestures and their categories. Making Musical Time is intended for a wide audience of scholars with interest in music. These include mathematicians, music theorists, (ethno)musicologists, music psychologists / educators / therapists, music performers, philosophers of music, audiologists, and acousticians.

Didactics of mathematics --- Category theory. Homological algebra --- algebra --- didactiek --- wiskunde --- Time in rabbinical literature. --- Mathematics --- Study and teaching --- Activity programs. --- Rabbinical literature

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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 --- Programming --- Computer architecture. Operating systems --- Music --- Theatrical science --- performances (kunst) --- applicatiebeheer --- apps --- theater --- muziek --- wiskunde --- architectuur (informatica) --- interfaces