Mathematical Music Theory Algebraic Geometric Combinatorial Topological And Applied Approaches To Understanding Musical Phenomena
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Mathematical Music Theory
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Author : Mariana Montiel
language : en
Publisher:
Release Date : 2020-04-28
Mathematical Music Theory written by Mariana Montiel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-28 with Music categories.
Questions about variation, similarity, enumeration, and classification of musical structures have long intrigued both musicians and mathematicians. Mathematical models can be found from theoretical analysis to actual composition or sound production. Increasingly in the last few decades, musical scholarship has incorporated modern mathematical content. One example is the application of methods from Algebraic Combinatorics, or Topology and Graph Theory, to the classification of different musical objects. However, these applications of mathematics in the understanding of music have also led to interesting open problems in mathematics itself. The reach and depth of the contributions on mathematical music theory presented in this volume is significant. Each contribution is in a section within these subjects: (i) Algebraic and Combinatorial Approaches; (ii) Geometric, Topological, and Graph-Theoretical Approaches; and (iii) Distance and Similarity Measures in Music.
Mathematical Music Theory Algebraic Geometric Combinatorial Topological And Applied Approaches To Understanding Musical Phenomena
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Author : Mariana Montiel
language : en
Publisher: World Scientific Publishing
Release Date : 2018-11-08
Mathematical Music Theory Algebraic Geometric Combinatorial Topological And Applied Approaches To Understanding Musical Phenomena written by Mariana Montiel and has been published by World Scientific Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-08 with Technology & Engineering categories.
Questions about variation, similarity, enumeration, and classification of musical structures have long intrigued both musicians and mathematicians. Mathematical models can be found from theoretical analysis to actual composition or sound production. Increasingly in the last few decades, musical scholarship has incorporated modern mathematical content. One example is the application of methods from Algebraic Combinatorics, or Topology and Graph Theory, to the classification of different musical objects. However, these applications of mathematics in the understanding of music have also led to interesting open problems in mathematics itself.The reach and depth of the contributions on mathematical music theory presented in this volume is significant. Each contribution is in a section within these subjects: (i) Algebraic and Combinatorial Approaches; (ii) Geometric, Topological, and Graph-Theoretical Approaches; and (iii) Distance and Similarity Measures in Music.
Mathematics And Computation In Music
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Author : Mariana Montiel
language : en
Publisher: Springer
Release Date : 2019-06-11
Mathematics And Computation In Music written by Mariana Montiel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-11 with Language Arts & Disciplines categories.
This book constitutes the thoroughly refereed proceedings of the 7th International Conference on Mathematics and Computation in Music, MCM 2019, held in Madrid, Spain, in June 2019. The 22 full papers and 10 short papers presented were carefully reviewed and selected from 48 submissions. The papers feature research that combines mathematics or computation with music theory, music analysis, composition, and performance. They are organized in topical sections on algebraic and other abstract mathematical approaches to understanding musical objects; remanaging Riemann: mathematical music theory as “experimental philosophy”?; octave division; computer-based approaches to composition and score structuring; models for music cognition and beat tracking; pedagogy of mathematical music theory. The chapter “Distant Neighbors and Interscalar Contiguities” is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
Geometry And Topology In Music
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Author : Moreno Andreatta
language : en
Publisher: CRC Press
Release Date : 2024-11-01
Geometry And Topology In Music written by Moreno Andreatta and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-01 with Mathematics categories.
This book introduces path-breaking applications of concepts from mathematical topology to music-theory topics including harmony, chord progressions, rhythm, and music classification. Contributions address topics of voice leading, Tonnetze (maps of notes and chords), and automatic music classification. Focusing on some geometrical and topological aspects of the representation and formalisation of musical structures and processes, the book covers topological features of voice-leading geometries in the most recent advances in this mathematical approach to representing how chords are connected through the motion of voices, leading to analytically useful simplified models of high-dimensional spaces; It generalizes the idea of a Tonnetz, a geometrical map of tones or chords, and shows how topological aspects of these maps can correspond to many concepts from music theory. The resulting framework embeds the chord maps of neo-Riemannian theory in continuous spaces that relate chords of different sizes and includes extensions of this approach to rhythm theory. It further introduces an application of topology to automatic music classification, drawing upon both static topological representations and time-series evolution, showing how static and dynamic features of music interact as features of musical style. This volume will be a key resource for academics, researchers, and advanced students of music, music analyses, music composition, mathematical music theory, computational musicology, and music informatics. It was originally published as a special issue of the Journal of Mathematics and Music.
Quantum Mechanics And Avant Garde Music
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Author : Rakhat-Bi Abdyssagin
language : en
Publisher: Springer Nature
Release Date : 2024-09-23
Quantum Mechanics And Avant Garde Music written by Rakhat-Bi Abdyssagin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-23 with Music categories.
"Fascinating details and anecdotes accompany this engaging account of the emergence of dramatic new ideas and forms in music over the centuries..." David Politzer, winner of the 2004 Nobel Prize in Physics. "A thought-provoking, stimulating, and highly original exploration of deep metaphorical links between music and physics...Highly recommended." Prof. Ian Stewart FRS, author, What’s the Use? "An astonishing book!" Tristan Murail, composer and co-creator of the "spectral" technique. Have you ever wondered about the connection between Pauli's exclusion principle and Schoenberg's dodecaphony? Or the symphonic echoes of Heisenberg's uncertainty principle in the compositions of Stockhausen and Cage? This book not only poses these questions but skillfully uncovers the artistic answers, exploring interdisciplinary connections that bridge the gap between modern physics and contemporary music. Dive into philosophical discourses on time, witness the metamorphosis of Boolean algebra, bits, and qubits into musical notation, and discover the limitations of the 12-tone scale mirrored in the speed of light. The author's unique methodology offers a fresh perspective, linking the language of mathematics and physics to the creation of musical scores. This book transcends the boundaries of physics and music, revealing the inevitable fusion of modern physics and avant-garde music in the twentieth century. Through meticulous research, the author showcases the profound impact of revolutionary ideas such as quantum physics and relativity on all aspects of life and demonstrates that modern physics and contemporary music were born not out of chance—their emergence and development were inevitable events. Delving into the historical accounts, he explores the musical endeavors of great physicists like Max Planck and Albert Einstein, unraveling the quantum entanglement of physics mirrored in the extended techniques of contemporary music and unveiling the musical universe of Werner Heisenberg through captivating personal encounters with his descendants. Crafted for general readers and seasoned experts alike, the book maintains clarity and style, ensuring accessibility without sacrificing depth. This pioneering exploration not only draws connections between modern physics and music but also serves as a unique bridge for scientists, musicians, and the curious general audience. Requiring no formal background in physics or music, the book is a compelling read for those intrigued by the uncharted territories where science and art converge, offering a concise and illuminating journey into the shadows of the void.
Transformational Analysis In Practice Music Analytical Studies On Composers And Musicians From Around The World
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Author : Bozhidar Chapkanov
language : en
Publisher: Vernon Press
Release Date : 2024-01-16
Transformational Analysis In Practice Music Analytical Studies On Composers And Musicians From Around The World written by Bozhidar Chapkanov and has been published by Vernon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-16 with Music categories.
'Transformational analysis in practice' is a Must-Have for everyone working in the field or aspiring to develop their music-analytical and theoretical skills in transformational theory. This co-authored book puts together a plethora of analytical studies, diverse both in the repertoires covered and the methodologies employed. It is a much-needed anthology in this sub-field of music analysis, which has been developing and growing in recent years, reaching ever wider outlets in English-speaking countries and beyond, from dedicated conference panels to YouTube videos. The book is divided into four parts based on the repertoires under discussion. Part I encompasses four analytical studies on familiar composers from the European Romanticism of the nineteenth century. Part II analyzes the music of less familiar composers from Brazil and Turkey. Part III offers four contrasting ways to adapt the analytical capabilities of neo-Riemannian theory to the post-tonal music of the twentieth century. Catering to the interests of jazz performers and researchers, as well as those into popular music production, Part IV offers transformational analytical approaches to both notated and improvised jazz, emphasizing John Coltrane’s performance. Providing an invaluable synthesis of a wide range of analytical studies, this book will be an essential companion for many musicology students, as well as for performers and composers.
Music And Fuzzy Logic
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Author : Hanns-Werner Heister
language : en
Publisher: Springer Nature
Release Date : 2021-02-21
Music And Fuzzy Logic written by Hanns-Werner Heister and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-21 with Technology & Engineering categories.
This book unfolds the manifold, complex and intertwined relations between Fuzzy Logic and music in a first comprehensive overview on this topic: systematically as an outline, as completely as possible, in the aspects of Fuzzy Logic in this relation, and especially in music as a process with three main phases, five anthropological layers, and thirteen forms of existence of the art work (Classics, Jazz, Pop, Folklore). Being concerned with the ontological, gnoseological, psychological, and (music-) aesthetical status and the relative importance of different phenomena of relationship between music and Fuzzy Logic, the explication follows the four main principles (with five phenotypes) of Fuzzy Logic with respect to music: similarity, sharpening 1 as filtering, sharpening 2 as crystallization, blurring, and variation. The book reports on years of author’s research on topics that have been only little explored so far in the area of Music and Fuzzy Logic. It merges concepts of music analysis with fuzzy logical modes of thinking, in a unique way that is expected to attract both specialists of music and specialists of Fuzzy Logic, and also non-specialists in both fields. The book introduces the concept of dialectic between sharpening and – conscious – “blurring”. In turn, some important aspects of this dialectic are discussed, placing them in an historical dimension, and ending in the postulation of a 'musical turn' in the sciences, with some important reflections concerning a “Philosophy of Fuzzy Logic”. Moreover, a production-oriented thinking is borrowed from fuzzy logic to musicology in this book, opening new perspectives in music, and possibly also in other artistic fields.
Mathematics And Computation
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Author : Avi Wigderson
language : en
Publisher: Princeton University Press
Release Date : 2019-10-29
Mathematics And Computation written by Avi Wigderson and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-29 with Computers categories.
From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography
Foundations Of Computational Mathematics
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Author : Ronald A. DeVore
language : en
Publisher: Cambridge University Press
Release Date : 2001-05-17
Foundations Of Computational Mathematics written by Ronald A. DeVore and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-05-17 with Mathematics categories.
Collection of papers by leading researchers in computational mathematics, suitable for graduate students and researchers.
5000 Years Of Geometry
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Author : Christoph J. Scriba
language : en
Publisher: Birkhäuser
Release Date : 2015-04-22
5000 Years Of Geometry written by Christoph J. Scriba and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-22 with Mathematics categories.
The present volume provides a fascinating overview of geometrical ideas and perceptions from the earliest cultures to the mathematical and artistic concepts of the 20th century. It is the English translation of the 3rd edition of the well-received German book “5000 Jahre Geometrie,” in which geometry is presented as a chain of developments in cultural history and their interaction with architecture, the visual arts, philosophy, science and engineering. Geometry originated in the ancient cultures along the Indus and Nile Rivers and in Mesopotamia, experiencing its first “Golden Age” in Ancient Greece. Inspired by the Greek mathematics, a new germ of geometry blossomed in the Islamic civilizations. Through the Oriental influence on Spain, this knowledge later spread to Western Europe. Here, as part of the medieval Quadrivium, the understanding of geometry was deepened, leading to a revival during the Renaissance. Together with parallel achievements in India, China, Japan and the ancient American cultures, the European approaches formed the ideas and branches of geometry we know in the modern age: coordinate methods, analytical geometry, descriptive and projective geometry in the 17th an 18th centuries, axiom systems, geometry as a theory with multiple structures and geometry in computer sciences in the 19th and 20th centuries. Each chapter of the book starts with a table of key historical and cultural dates and ends with a summary of essential contents of geometr y in the respective era. Compelling examples invite the reader to further explore the problems of geometry in ancient and modern times. The book will appeal to mathematicians interested in Geometry and to all readers with an interest in cultural history. From letters to the authors for the German language edition I hope it gets a translation, as there is no comparable work. Prof. J. Grattan-Guinness (Middlesex University London) "Five Thousand Years of Geometry" - I think it is the most handsome book I have ever seen from Springer and the inclusion of so many color plates really improves its appearance dramatically! Prof. J.W. Dauben (City University of New York) An excellent book in every respect. The authors have successfully combined the history of geometry with the general development of culture and history. ... The graphic design is also excellent. Prof. Z. Nádenik (Czech Technical University in Prague)