Download or read book Functorial Semiotics for Creativity in Music and Mathematics written by Guerino Mazzola and published by Springer Nature. This book was released on 2022-04-23 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Musical Creativity written by Guerino Mazzola and published by Springer Science & Business Media. This book was released on 2011-11-03 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book represents a new approach to musical creativity, dealing with the semiotics, mathematical principles, and software for creativity processes. After a thorough introduction, the book offers a first practical part with a detailed tutorial for students in composition and improvisation, using musical instruments and music software. The second, theoretical part deals with historical, actual, and new principles of creative processes in music, based on the results and methods developed in the first author’s book Topos of Music and referring to semiotics, predicative objects, topos theory, and object-oriented concept architectures. The third part of the book details four case studies in musical creativity, including an analysis of the six variations of Beethoven's sonata op. 109, a discussion of the creative process in a CD coproduced in 2011 by the first and second authors, a recomposition of Boulez’s "Structures pour deux pianos" using the Rubato software module BigBang developed by the third author, and the Escher theorem from mathematical gesture theory in music. This is both a textbook addressed to undergraduate and graduate students of music composition and improvisation, and also a state-of-the-art survey addressed to researchers in creativity studies and music technology. The book contains summaries and end-of-chapter questions, and the authors have used the book as the main reference to teach an undergraduate creativity studies program and also to teach composition. The text is supported throughout with musical score examples.
Download or read book The Topos of Music III Gestures written by Guerino Mazzola and published by Springer. This book was released on 2018-03-28 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Semiotics in Mathematics Education written by Norma Presmeg and published by Springer. This book was released on 2016-04-11 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume discusses semiotics in mathematics education as an activity with a formal sign system, in which each sign represents something else. Theories presented by Saussure, Peirce, Vygotsky and other writers on semiotics are summarized in their relevance to the teaching and learning of mathematics. The significance of signs for mathematics education lies in their ubiquitous use in every branch of mathematics. Such use involves seeing the general in the particular, a process that is not always clear to learners. Therefore, in several traditional frameworks, semiotics has the potential to serve as a powerful conceptual lens in investigating diverse topics in mathematics education research. Topics that are implicated include (but are not limited to): the birth of signs; embodiment, gestures and artifacts; segmentation and communicative fields; cultural mediation; social semiotics; linguistic theories; chains of signification; semiotic bundles; relationships among various sign systems; intersubjectivity; diagrammatic and inferential reasoning; and semiotics as the focus of innovative learning and teaching materials.
Download or read book All About Music written by Guerino Mazzola and published by Springer. This book was released on 2016-11-23 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. The book unfolds in a basic discourse in everyday language that is accessible to everybody who wants to understand what this topic is about. Musical ontology is delayed in its fundamental dimensions: its realities, its meaningful communication, and its embodied utterance from musical creators to an interested audience. The authors' approach is applicable to every musical genre and is scientific, the book is suitable for non-musicians and non-scientists alike.
Download or read book The Topos of Music written by Guerino Mazzola and published by Birkhäuser. This book was released on 2012-12-06 with total page 1310 pages. Available in PDF, EPUB and Kindle. Book excerpt: With contributions by numerous experts
Download or read book Mathematics and Computation in Music written by Jason Yust and published by Springer. This book was released on 2013-06-05 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed proceedings of the Fourth International Conference on Mathematics and Computation in Music, MCM 2013, held in Montreal, Canada, in June 2013. The 18 papers presented were carefully reviewed and selected from numerous submissions. They are promoting the collaboration and exchange of ideas among researchers in music theory, mathematics, computer science, musicology, cognition and other related fields.
Download or read book Classification of Musical Objects for Analysis and Composition written by Linshujie Zheng and published by Springer Nature. This book was released on 2023-07-01 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Musical Mathematical Mind written by Gabriel Pareyon and published by Springer. This book was released on 2018-08-23 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a deep spectrum of musical, mathematical, physical, and philosophical perspectives that have emerged in this field at the intersection of music and mathematics. In particular the contributed chapters introduce advanced techniques and concepts from modern mathematics and physics, deriving from successes in domains such as Topos theory and physical string theory. The authors include many of the leading researchers in this domain, and the book will be of value to researchers working in computational music, particularly in the areas of counterpoint, gesture, and Topos theory.
Download or read book Mathematical Music Theory written by and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathemusical Conversations written by Jordan B. L. Smith and published by . This book was released on 2016 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Musica Mathematica written by Rima Povilionienė and published by PL Academic Research. This book was released on 2016 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author displays versatile cases of the intersection of music and mathematics, moving from philosophical and aesthetic considerations about «mathesis» to practical studies, discussing the interaction between music and other arts, and providing a practical research of contemporary music compositions.
Download or read book Patterns of Intuition written by Gerhard Nierhaus and published by Springer. This book was released on 2015-01-22 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book is the result of a three year research project which investigated the creative act of composing by means of algorithmic composition. Central to the investigation are the compositional strategies of 12 composers, which were documented through a dialogic and cyclic process of modelling and evaluating musical materials. The aesthetic premises and compositional approaches configure a rich spectrum of diverse positions, which is reflected also in the kinds of approaches and methods used. These approaches and methods include the generation and evaluation of chord sequences using genetic algorithms, the application of morphing strategies to research harmonic transformations, an automatic classification of personal preferences via machine learning, and an application of mathematical music theory to the analysis and resynthesis of musical material. The second part of the book features contributions by Sandeep Bhagwati, William Brooks, David Cope, Darla Crispin, Nicolas Donin, and Guerino Mazzola. These authors variously consider the project from different perspectives, offer independent approaches, or provide more general reflections from their respective research fields.
Download or read book Music Via Math written by Dirk Schlingmann and published by . This book was released on 2019-07-31 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This book demonstrates how mathematics can be useful to better understand and explore music and how to increase appreciation of the relationship between mathematics and music. An understanding of mathematics is important to having a greater appreciation of music. Mathematics can be useful to analyze, manipulate, and create music. The book discusses topics that are fundamentally related to music such as pleasing and unpleasing sounds, digital sound files, mathematical modeling of sound, pitch, timbre, dynamics, rhythm, consonance and dissonance, musical tone systems, musical notation, instrument design, MIDI (Musical Instrument Digital Interface), statistical analysis of musical compositions, and artistic creation of new styles of music using computing. Computer code has been included whenever possible to highlight the importance of computer programming.
Download or read book The Topos of Music I Theory written by Guerino Mazzola and published by Springer. This book was released on 2018-04-11 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Mathematics of Music and Art written by Arturo Portnoy and published by Springer. This book was released on 2023-07-28 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the relationships between music, the sciences, and mathematics, both ancient and modern, with a focus on the big picture for a general audience as opposed to delving into very technical details. The language of music is deciphered through the language of mathematics. Readers are shown how apparently unrelated areas of knowledge complement each other and in fact propel each other’s advancement. The presentation as well as the collection of topics covered throughout is unique and serves to encourage exploration and also, very concretely, illustrates the cross- and multidisciplinary nature of knowledge. Inspired by an introductory, multidisciplinary course, the author explores the relationships between the arts, sciences, and mathematics in the realm of music. The book has no prerequisites; rather it aims to give a broad overview and achieve the integration of the three presented themes. Mathematical tools are introduced and used to explain various aspects of music theory, and the author illustrates how, without mathematics, music could not have been developed.
Download or read book The Rubato Composer Music Software written by Gérard Milmeister and published by Springer. This book was released on 2009-08-29 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: Both modern mathematical music theory and computer science are strongly influenced by the theory of categories and functors. One outcome of this research is the data format of denotators, which is based on set-valued presheaves over the category of modules and diaffine homomorphisms. The functorial approach of denotators deals with generalized points in the form of arrows and allows the construction of a universal concept architecture. This architecture is ideal for handling all aspects of music, especially for the analysis and composition of highly abstract musical works. This book presents an introduction to the theory of module categories and the theory of denotators, as well as the design of a software system, called Rubato Composer, which is an implementation of the category-theoretic concept framework. The application is written in portable Java and relies on plug-in components, so-called rubettes, which may be combined in data flow networks for the generation and manipulation of denotators. The Rubato Composer system is open to arbitrary extension and is freely available under the GPL license. It allows the developer to build specialized rubettes for tasks that are of interest to composers, who in turn combine them to create music. It equally serves music theorists, who use them to extract information from and manipulate musical structures. They may even develop new theories by experimenting with the many parameters that are at their disposal thanks to the increased flexibility of the functorial concept architecture. Two contributed chapters by Guerino Mazzola and Florian Thalmann illustrate the application of the theory as well as the software in the development of compositional tools and the creation of a musical work with the help of the Rubato framework.
