Bücher von Guerino Mazzola

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 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 ¿ech 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.

Dieses Lehrbuch stellt eine Einführung in die noch junge Disziplin der Musikinformatik dar. Es beginnt mit einer Übersicht über die gegenwärtige Entwicklung der Musik aus der Wechselwirkung zwischen Technologie und Komposition. Darauf aufbauend werden Kodierung und Programmierung musikalischer Objekte für Komposition, Analyse und Interpretation besprochen, sowie Standards und Darstellungsmethoden, wie: MIDI, Musik-N, Fourier, FM, Wavelets, Physical Modeling und Denotatoren. Eine vertiefte Diskussion erfährt dabei der FFT-Algorithmus und natürlich das Kompressionsverfahren MP3.Anschließend werden Plattformen für die computergestützte Analyse, Komposition und Interpretation vorgestellt, darunter RUBATO, MAX und Presto. Darauf folgt eine Einführung in Methoden der Navigation im Begriffsraum der Musik. Abschließend wird die Perspektive einer verteilten globalen Musikkultur diskutiert, wie sie sich etwa durch den iPod, sowie Internet-basierte Musikdistribution, -produktion und -komposition abzeichnet.

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.

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; and tables with chord classes and modulation steps.

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.

The author explains his theory of musical performance, developed in the language of differential geometry, introducing performance vector fields that generalize tempo and intonation.

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.

This is an introduction to basic music technology, including acoustics for sound production and analysis, Fourier, frequency modulation, wavelets, and physical modeling and a classification of musical instruments and sound spaces for tuning and counterpoint.

This book offers a new approach to musical creativity, dealing with software and the semiotics and mathematical principles of creativity. The text is supported with musical score examples, and the authors' sound and video examples are freely available online.

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; and tables with chord classes and modulation steps.

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.

The author explains his theory of musical performance, developed in the language of differential geometry, introducing performance vector fields that generalize tempo and intonation.

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.

This book explains music's comprehensive ontology, its way of existence and processing, as specified in its compact characterization: music embodies meaningful communication and mediates physically between its emotional and mental layers.

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.

The authors include recent theoretical results on counterpoint worlds, the extension of counterpoint to microtonal pitch systems, the singular homology of counterpoint models, and the software implementation of contrapuntal models. The book is suitable for graduates and researchers.

This book is a first sketch of what the overall field of performance could look like as a modern scientific field but not its stylistically differentiated practice, pedagogy, and history.

Free jazz, as performed by such artists as John Coltrone and Archie Shepp, is a creative, collaborative art form. This book examines free jazz and develops geometric theories of gestures and distributed identities, also known as swarm intelligence.

This second volume of a comprehensive tour through mathematical core subjects for computer scientists completes the ?rst volume in two - gards: Part III ?rst adds topology, di?erential, and integral calculus to the t- ics of sets, graphs, algebra, formal logic, machines, and linear geometry, of volume 1.

Contains all the mathematics that computer scientists need to know in one place.