Guerino Mazzola Livres

Man kann einen jeden BegrifJ, einen jeden Titel, darunter viele Erkenntnisse gehoren, einen logischen Ort nennen. Immanuel Kant [258, p. B 324] This book's title subject, The Topos of Music, has been chosen to communicate a double First, the Greek word "topos" (r01rex; = location, site) alludes to the logical and transcendental location of the concept of music in the sense of Aristotle's [20, 592] and Kant's [258, p. B 324] topic. This view deals with the question of where music is situated as a concept­ and hence with the underlying ontological What is the type of being and existence of music? The second message is a more technical understanding insofar as the system of musical signs can be associated with the mathematical theory of topoi, which realizes a powerful synthesis of geometric and logical theories. It laid the foundation of a thorough geometrization of logic and has been successful in central issues of algebraic geometry (Grothendieck, Deligne), independence proofs and intuitionistic logic (Cohen, Lawvere, Kripke). But this second message is intimately entwined with the first since the present concept framework of the musical sign system is technically based on topos theory, so the topos of music receives its top os-theoretic foundation. In this perspective, the double message of the book's title in fact condenses to a unified to unite philosophical insight with mathematical explicitness.

Exploring the landscape of modern performance, this book presents a foundational framework for understanding the discipline's evolution and potential. It delves into various forms of performance, emphasizing their cultural significance and the interplay between tradition and innovation. By examining key themes and practices, the author invites readers to consider the future of performance art in contemporary society, making it a thought-provoking resource for artists, scholars, and enthusiasts alike.

The two-volume textbook Comprehensive Mathematics for the Working Computer Scientist, of which this is the second volume, is a self-contained comprehensive presentation of mathematics including sets, numbers, graphs, algebra, logic, grammars, machines, linear geometry, calculus, ODEs, and special themes such as neural networks, Fourier theory, wavelets, numerical issues, statistics, categories, and manifolds. The concept framework is streamlined but defining and proving virtually everything. The style implicitly follows the spirit of recent topos-oriented theoretical computer science. Despite the theoretical soundness, the material stresses a large number of core computer science subjects, such as, for example, a discussion of floating point arithmetic, Backus-Naur normal forms, L-systems, Chomsky hierarchies, algorithms for data encoding, e.g., the Reed-Solomon code. The numerous course examples are motivated by computer science and bear a generic scientific meaning. This text is complemented by an online university course which covers the same theoretical content, albeit in a totally different presentation. The student or working scientist who gets involved in this text may at any time consult the online interface which comprises applets and other interactive tools.

The two-volume textbook, of which this is the first volume, is a self-contained yet comprehensive presentation of mathematics. The numerous course examples are motivated by computer science and bear a generic scientific meaning. For the second edition the entire text has been carefully re-written. Many examples and illustrations have been added, and explanations have been clarified. This makes the book more accessible to both instructors and students.

This book introduces a novel approach to musical creativity, exploring semiotics, mathematical principles, and software involved in creative processes. It begins with a comprehensive introduction, followed by a practical tutorial designed for students in composition and improvisation, utilizing musical instruments and software. The theoretical section examines historical and contemporary principles of creative processes in music, drawing on insights from the author’s previous work and referencing semiotics, predicative objects, topos theory, and object-oriented architectures. The book also includes four case studies in musical creativity, such as an analysis of Beethoven's sonata op. 109, a discussion on a 2011 CD co-produced by the authors, a recomposition of Boulez’s "Structures pour deux pianos" using the BigBang software module, and the application of the Escher theorem from mathematical gesture theory in music. This work serves as both a textbook for undergraduate and graduate students of music composition and improvisation and a comprehensive survey for researchers in creativity studies and music technology. It features summaries and end-of-chapter questions, and has been utilized as a key resource in teaching creativity studies and composition, supported by musical score examples throughout.

This book explores free jazz as a collaborative art form, highlighting artists like John Coltrane and Archie Shepp. It develops geometric theories of gestures and swarm intelligence, integrating insights from psychology, physics, and computer science to analyze the creative processes within free jazz.

Focusing on the theory of musical performance, this volume explores concepts through differential geometry, introducing performance vector fields that enhance understanding of tempo and intonation. It highlights the innovative Rubato software platform, which facilitates composition, analysis, and performance, allowing for experimental evaluation of expressive performance theories. This work aims to bridge theoretical concepts with practical applications in music.

The fourth volume of the second edition delves into the intricate relationship between music and mathematics, offering appendices that cover sound and auditory physiology. It includes foundational mathematical concepts like sets, relations, and algebraic geometry, alongside insights from physics, particularly string theory. Additionally, the book provides valuable tables detailing chord classes and modulation steps, making it a comprehensive resource for understanding the theoretical aspects of music.

The book delves into the conceptual framework of musical theory, focusing on denotators and forms. It classifies both local and global musical objects while exploring mathematical models related to harmony and counterpoint. Additionally, it examines topologies concerning rhythm and motives, making it a foundational text for understanding the intricate relationships within music theory. This first volume of the second edition enhances the classic work's insights into the mathematical underpinnings of music.

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. The acoustical theory is applied to its implementation in analogue and digital technology, including a detailed discussion of Fast Fourier Transform and MP3 compression. Beyond acoustics, the book discusses important symbolic sound event representation and software as typically realized by MIDI and denotator formalisms. The concluding chapters deal with globalization of music on the Internet, referring to iTunes, Spotify and similar environments. The book will be valuable for students of music, music informatics, and sound engineering.