Mathematical Music Theory: Algebraic, Geometric, Combinatorial, Topological And Applied Approaches To Understanding Musical Phenomena

Mathematical Music Theory: Algebraic, Geometric, Combinatorial, Topological And Applied Approaches To Understanding Musical Phenomena
Author :
Publisher : World Scientific Publishing
Total Pages : 371
Release :
ISBN-10 : 9789813235328
ISBN-13 : 9813235322
Rating : 4/5 (28 Downloads)

Synopsis Mathematical Music Theory: Algebraic, Geometric, Combinatorial, Topological And Applied Approaches To Understanding Musical Phenomena by : Mariana Montiel

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

Mathematics and Computation in Music
Author :
Publisher : Springer
Total Pages : 403
Release :
ISBN-10 : 9783030213923
ISBN-13 : 3030213927
Rating : 4/5 (23 Downloads)

Synopsis Mathematics and Computation in Music by : Mariana Montiel

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

Geometry and Topology in Music
Author :
Publisher : CRC Press
Total Pages : 130
Release :
ISBN-10 : 9781040156704
ISBN-13 : 1040156703
Rating : 4/5 (04 Downloads)

Synopsis Geometry and Topology in Music by : Moreno Andreatta

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

Quantum Mechanics and Avant-Garde Music
Author :
Publisher : Springer Nature
Total Pages : 287
Release :
ISBN-10 : 9783031631610
ISBN-13 : 3031631617
Rating : 4/5 (10 Downloads)

Synopsis Quantum Mechanics and Avant-Garde Music by : Rakhat-Bi Abdyssagin

Transformational analysis in practice: Music-analytical studies on composers and musicians from around the world

Transformational analysis in practice: Music-analytical studies on composers and musicians from around the world
Author :
Publisher : Vernon Press
Total Pages : 368
Release :
ISBN-10 : 9781648898136
ISBN-13 : 1648898130
Rating : 4/5 (36 Downloads)

Synopsis Transformational analysis in practice: Music-analytical studies on composers and musicians from around the world by : Bozhidar Chapkanov

'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

Music and Fuzzy Logic
Author :
Publisher : Springer Nature
Total Pages : 724
Release :
ISBN-10 : 9783662629079
ISBN-13 : 3662629070
Rating : 4/5 (79 Downloads)

Synopsis Music and Fuzzy Logic by : Hanns-Werner Heister

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.

Mathematical Music Theory

Mathematical Music Theory
Author :
Publisher :
Total Pages :
Release :
ISBN-10 : 9813235306
ISBN-13 : 9789813235304
Rating : 4/5 (06 Downloads)

Synopsis Mathematical Music Theory by :

Mathematics and Computation

Mathematics and Computation
Author :
Publisher : Princeton University Press
Total Pages : 434
Release :
ISBN-10 : 9780691189130
ISBN-13 : 0691189137
Rating : 4/5 (30 Downloads)

Synopsis Mathematics and Computation by : Avi Wigderson

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

The Mathematician's Brain

The Mathematician's Brain
Author :
Publisher : Princeton University Press
Total Pages : 180
Release :
ISBN-10 : 0691129827
ISBN-13 : 9780691129822
Rating : 4/5 (27 Downloads)

Synopsis The Mathematician's Brain by : David Ruelle

Examines mathematical ideas and the visionary minds behind them. This book provides an account of celebrated mathematicians and their quirks, oddities, personal tragedies, bad behavior, descents into madness, tragic ends, and the beauty of their mathematical discoveries.

Formalized Music

Formalized Music
Author :
Publisher : Pendragon Press
Total Pages : 410
Release :
ISBN-10 : 1576470792
ISBN-13 : 9781576470794
Rating : 4/5 (92 Downloads)

Synopsis Formalized Music by : Iannis Xenakis

Pendragon Press is proud to offer this new, revised, and expanded edition of Formalized Music, Iannis Xenakis's landmark book of 1971. In addition to three totally new chapters examining recent breakthroughs in music theory, two original computer programs illustrating the actual realization of newly proposed methods of composition, and an appendix of the very latest developments of stochastic synthesis as an invitation to future exploration, Xenakis offers a very critical self-examination of his theoretical propositions and artistic output of the past thirty-five years. This edition of Formalized Music is an essential tool for understanding the man and the thought processes of one of this century's most important and revolutionary musical figures.