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Author: Guerino Mazzola
Publisher: Springer
ISBN: 3319644955
Category : Mathematics
Languages : en
Pages : 353
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Book Description
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; complements in physics, including a discussion on string theory; and tables with chord classes and modulation steps.
Author: Guerino Mazzola
Publisher: Springer
ISBN: 3319644955
Category : Mathematics
Languages : en
Pages : 353
Get Book Here
Book Description
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; complements in physics, including a discussion on string theory; and tables with chord classes and modulation steps.
Author: Guerino Mazzola
Publisher: Springer
ISBN: 3319644815
Category : Mathematics
Languages : en
Pages : 626
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Book Description
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.
Author: Guerino Mazzola
Publisher: Springer
ISBN: 3319643649
Category : Mathematics
Languages : en
Pages : 675
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Book Description
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.
Author: Guerino Mazzola
Publisher: Birkhäuser
ISBN: 303488141X
Category : Mathematics
Languages : en
Pages : 1310
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Book Description
With contributions by numerous experts
Author: Linshujie Zheng
Publisher: Springer Nature
ISBN: 3031301838
Category : Mathematics
Languages : en
Pages : 156
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Book Description
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.
Author: Guerino Mazzola
Publisher: Springer Nature
ISBN: 3030851907
Category : Mathematics
Languages : en
Pages : 166
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Book Description
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.
Author: Guerino Mazzola
Publisher: Cambridge Scholars Publishing
ISBN: 1527501574
Category : Music
Languages : en
Pages : 149
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Book Description
This book fills a gap between theory and creativity in musicianship. This frequently observed gap fixes theory as a rigidified level of thought, where creativity is excluded from a canonized corpus of ideas. Creativity, on the other hand, is preconceived as a theory-less, wild activity that blossoms while performing pre-composed musical structures. This book provides a discussion of the creative drive in theory and theory-inspired thoughts while understanding how these ideas shape performance. The future of music is only as limited as one’s imagination, and, to this end, the text illuminates examples of creative musicianship.
Author: Jeffrey Kurtzman
Publisher: Clarendon Press
ISBN: 0191590711
Category :
Languages : en
Pages : 626
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Book Description
This is a thorough-going study of Monteverdi's Vespers, the single most significant and most widely known musical print from before the time of J.S. Bach. The author examines Monteverdi's Vespers from multiple perspectives, combining his own research with all that is known and thought of the Vespers by other scholars. The historical origin as well as the musical and liturgical context of the Vespers are surveyed; similarly the controversial historiography of the Vespers in the nineteenth and twentieth centuries is scrutinized and evaluated. A series of analytical chapters attempt to clarify Monteverdi's compositional process and the relationship between music and text in the light of recent research on modal and tonal aspects of early seventeenth century music. The final section is devoted to thirteen chapters investigating performance practice issues of the early seventeenth century and their application to the Vespers, including general and specific recommendations for performance where appropriate. The book concludes with a series of informational appendices, including the psalm cursus for Vespers of all major feasts in the liturgical calendar, texts, and structural outlines for the Vespers compositions based on a cantus firmus, an analytical discography, and bibliographies of seventeenth-century musical and theoretical sources.
Author: Emmanuel Amiot
Publisher: Springer
ISBN: 3319455818
Category : Computers
Languages : en
Pages : 214
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Book Description
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.
Author: Carlos Agon
Publisher: Springer Science & Business Media
ISBN: 3642215890
Category : Computers
Languages : en
Pages : 387
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Book Description
This book constitutes the refereed proceedings of the Third International Conference on Mathematics and Computation in Music, MCM 2011, held in Paris, France, in June 2011. The 24 revised full papers presented and the 12 short papers were carefully reviewed and selected from 62 submissions. The MCM conference is the flagship conference of the Society for Mathematics and Computation in Music. This year’s conference aimed to provide a multi-disciplinary platform dedicated to the communication and exchange of ideas amongst researchers involved in mathematics, computer science, music theory, composition, musicology, or other related disciplines. Areas covered were formalization and geometrical representation of musical structures and processes; mathematical models for music improvisation and gestures theory; set-theoretical and transformational approaches; computational analysis and cognitive musicology as well as more general discussions on history, philosophy and epistemology of music and mathematics.
