Music Through Fourier Space

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Publisher : Springer
ISBN 13 : 3319455818
Total Pages : 206 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Music Through Fourier Space by : Emmanuel Amiot

Download or read book Music Through Fourier Space written by Emmanuel Amiot and published by Springer. This book was released on 2016-10-26 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematics of the Discrete Fourier Transform (DFT)

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Author :
Publisher : Julius Smith
ISBN 13 : 097456074X
Total Pages : 323 pages
Book Rating : 4.9/5 (745 download)

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Book Synopsis Mathematics of the Discrete Fourier Transform (DFT) by : Julius O. Smith

Download or read book Mathematics of the Discrete Fourier Transform (DFT) written by Julius O. Smith and published by Julius Smith. This book was released on 2008 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The DFT can be understood as a numerical approximation to the Fourier transform. However, the DFT has its own exact Fourier theory, and that is the focus of this book. The DFT is normally encountered as the Fast Fourier Transform (FFT)--a high-speed algorithm for computing the DFT. The FFT is used extensively in a wide range of digital signal processing applications, including spectrum analysis, high-speed convolution (linear filtering), filter banks, signal detection and estimation, system identification, audio compression (such as MPEG-II AAC), spectral modeling sound synthesis, and many others. In this book, certain topics in digital audio signal processing are introduced as example applications of the DFT"--Back cover

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

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Publisher : Vernon Press
ISBN 13 : 1648898130
Total Pages : 368 pages
Book Rating : 4.6/5 (488 download)

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

Download or read book Transformational analysis in practice: Music-analytical studies on composers and musicians from around the world written by Bozhidar Chapkanov and published by Vernon Press. This book was released on 2023 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: '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.

Introduction to Fourier Analysis on Euclidean Spaces (PMS-32), Volume 32

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Publisher : Princeton University Press
ISBN 13 : 140088389X
Total Pages : 312 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Introduction to Fourier Analysis on Euclidean Spaces (PMS-32), Volume 32 by : Elias M. Stein

Download or read book Introduction to Fourier Analysis on Euclidean Spaces (PMS-32), Volume 32 written by Elias M. Stein and published by Princeton University Press. This book was released on 2016-06-02 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors present a unified treatment of basic topics that arise in Fourier analysis. Their intention is to illustrate the role played by the structure of Euclidean spaces, particularly the action of translations, dilatations, and rotations, and to motivate the study of harmonic analysis on more general spaces having an analogous structure, e.g., symmetric spaces.

Mathematics and Computation in Music

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Publisher : Springer Nature
ISBN 13 : 3031070151
Total Pages : 418 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Mathematics and Computation in Music by : Mariana Montiel

Download or read book Mathematics and Computation in Music written by Mariana Montiel and published by Springer Nature. This book was released on 2022-06-03 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed proceedings of the 8th International Conference on Mathematics and Computation in Music, MCM 2022, held in Atlanta, GA, USA, in June 2022. The 29 full papers and 8 short papers presented were carefully reviewed and selected from 45 submissions. The papers feature research that combines mathematics or computation with music theory, music analysis, composition, and performance. They are organized in Mathematical Scale and Rhythm Theory: Combinatorial, Graph Theoretic, Group Theoretic and Transformational Approaches; Categorical and Algebraic Approaches to Music; Algorithms and Modeling for Music and Music-Related Phenomena; Applications of Mathematics to Musical Analysis; Mathematical Techniques and Microtonality

Mathematics and Computation in Music

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Publisher : Springer
ISBN 13 : 3319718274
Total Pages : 373 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Mathematics and Computation in Music by : Octavio A. Agustín-Aquino

Download or read book Mathematics and Computation in Music written by Octavio A. Agustín-Aquino and published by Springer. This book was released on 2017-11-17 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed proceedings of the 6th International Conference on Mathematics and Computation in Music, MCM 2017, held in Mexico City, Mexico, in June 2017. The 26 full papers and 2 short papers presented were carefully reviewed and selected from 40 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 models, computer assisted performance, Fourier analysis, Gesture Theory, Graph Theory and Combinatorics, Machine Learning, and Probability and Statistics in Musical Analysis and Composition.

Fourier Transforms

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Publisher : John Wiley & Sons
ISBN 13 : 1118479149
Total Pages : 788 pages
Book Rating : 4.1/5 (184 download)

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Book Synopsis Fourier Transforms by : Eric W. Hansen

Download or read book Fourier Transforms written by Eric W. Hansen and published by John Wiley & Sons. This book was released on 2014-09-22 with total page 788 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fourier Transforms: Principles and Applications explains transform methods and their applications to electrical systems from circuits, antennas, and signal processors—ably guiding readers from vector space concepts through the Discrete Fourier Transform (DFT), Fourier series, and Fourier transform to other related transform methods. Featuring chapter end summaries of key results, over two hundred examples and four hundred homework problems, and a Solutions Manual this book is perfect for graduate students in signal processing and communications as well as practicing engineers. Class-tested at Dartmouth Provides the same solid background as classic texts in the field, but with an emphasis on digital and other contemporary applications to signal and image processing Modular coverage of material allows for topics to be covered by preference MATLAB files and Solutions Manual available to instructors Over 300 figures, 200 worked examples, and 432 homework problems

Music: A Mathematical Offering

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Publisher : Cambridge University Press
ISBN 13 : 0521853877
Total Pages : 426 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis Music: A Mathematical Offering by : Dave Benson

Download or read book Music: A Mathematical Offering written by Dave Benson and published by Cambridge University Press. This book was released on 2007 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the interaction between music and mathematics including harmony, symmetry, digital music and perception of sound.

Pattern in Music

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Publisher : CRC Press
ISBN 13 : 1003800831
Total Pages : 127 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Pattern in Music by : Darrell Conklin

Download or read book Pattern in Music written by Darrell Conklin and published by CRC Press. This book was released on 2023-11-14 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents analyses of pattern in music from different computational and mathematical perspectives. A central purpose of music analysis is to represent, discover, and evaluate repeated structures within single pieces or within larger corpora of related pieces. In the chapters of this book, music corpora are structured as monophonic melodies, polyphony, or chord sequences. Patterns are represented either extensionally as locations of pattern occurrences in the music, or intensionally as sequences of pitch or chord features, rhythmic profiles, geometric point sets, and logical expressions. The chapters cover both deductive analysis, where music is queried for occurrences of a known pattern, and inductive analysis, where patterns are found using pattern discovery algorithms. Results are evaluated using a variety of methods including visualization, contrasting corpus analysis, and reference to known and expected patterns. Pattern in Music will be a key resource for academics, researchers, and advanced students of music, musicology, music analyses, mathematical music theory, computational musicology, and music informatics. This book was originally published as a special issue of the Journal of Mathematics and Music.

Theoretical And Practical Pedagogy Of Mathematical Music Theory: Music For Mathematics And Mathematics For Music, From School To Postgraduate Levels

Download Theoretical And Practical Pedagogy Of Mathematical Music Theory: Music For Mathematics And Mathematics For Music, From School To Postgraduate Levels PDF Online Free

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Publisher : World Scientific
ISBN 13 : 9813228369
Total Pages : 324 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Theoretical And Practical Pedagogy Of Mathematical Music Theory: Music For Mathematics And Mathematics For Music, From School To Postgraduate Levels by : Mariana Montiel

Download or read book Theoretical And Practical Pedagogy Of Mathematical Music Theory: Music For Mathematics And Mathematics For Music, From School To Postgraduate Levels written by Mariana Montiel and published by World Scientific. This book was released on 2018-10-24 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the past 40 years, mathematical music theory has grown and developed in both the fields of music and mathematics. In music pedagogy, the need to analyze patterns of modern composition has produced Musical Set Theory, and the use of Group Theory and other modern mathematical structures have become almost as common as the application of mathematics in the fields of engineering or chemistry. Mathematicians have been developing stimulating ideas when exploring mathematical applications to established musical relations. Mathematics students have seen in Music in Mathematics courses, how their accumulated knowledge of abstract ideas can be applied to an important human activity while reinforcing their dexterity in Mathematics. Similarly, new general education courses in Music and Mathematics are being developed and are arising at the university level, as well as for high school and general audiences without requiring a sophisticated background in either music nor mathematics. Mathematical Music Theorists have also been developing exciting, creative courses for high school teachers and students of mathematics. These courses and projects have been implemented in the USA, in China, Ireland, France, Australia, and Spain.The objective of this volume is to share the motivation and content of some of these exciting, new Mathematical Theory and Music in Mathematics courses while contributing concrete materials to interested readers.

Fourier Transforms

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Publisher : Springer Science & Business Media
ISBN 13 : 1461523591
Total Pages : 374 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Fourier Transforms by : Robert M. Gray

Download or read book Fourier Transforms written by Robert M. Gray and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Fourier transform is one of the most important mathematical tools in a wide variety of fields in science and engineering. In the abstract it can be viewed as the transformation of a signal in one domain (typically time or space) into another domain, the frequency domain. Applications of Fourier transforms, often called Fourier analysis or harmonic analysis, provide useful decompositions of signals into fundamental or "primitive" components, provide shortcuts to the computation of complicated sums and integrals, and often reveal hidden structure in data. Fourier analysis lies at the base of many theories of science and plays a fundamental role in practical engineering design. The origins of Fourier analysis in science can be found in Ptolemy's decomposing celestial orbits into cycles and epicycles and Pythagorus' de composing music into consonances. Its modern history began with the eighteenth century work of Bernoulli, Euler, and Gauss on what later came to be known as Fourier series. J. Fourier in his 1822 Theorie analytique de la Chaleur [16] (still available as a Dover reprint) was the first to claim that arbitrary periodic functions could be expanded in a trigonometric (later called a Fourier) series, a claim that was eventually shown to be incorrect, although not too far from the truth. It is an amusing historical sidelight that this work won a prize from the French Academy, in spite of serious concerns expressed by the judges (Laplace, Lagrange, and Legendre) re garding Fourier's lack of rigor.

Mathematics and Computation in Music

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Publisher : Springer Nature
ISBN 13 : 3031606388
Total Pages : 474 pages
Book Rating : 4.0/5 (316 download)

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Book Synopsis Mathematics and Computation in Music by : Thomas Noll

Download or read book Mathematics and Computation in Music written by Thomas Noll and published by Springer Nature. This book was released on with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Compendium Of Musical Mathematics

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Publisher : World Scientific
ISBN 13 : 9811284385
Total Pages : 286 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis A Compendium Of Musical Mathematics by : Franck Jedrzejewski

Download or read book A Compendium Of Musical Mathematics written by Franck Jedrzejewski and published by World Scientific. This book was released on 2024-02-28 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to provide a concise introduction to the mathematical theory of music, opening each chapter to the most recent research. Despite the complexity of some sections, the book can be read by a large audience. Many examples illustrate the concepts introduced. The book is divided into 9 chapters.In the first chapter, we tackle the question of the classification of chords and scales. Chapter 2 is a mathematical presentation of David Lewin's Generalized Interval Systems. Chapter 3 offers a new theory of diatonicity in equal-tempered universes. Chapter 4 presents the Neo-Riemannian theories based on the work of David Lewin, Richard Cohn and Henry Klumpenhouwer. Chapter 5 is devoted to the application of word combinatorics to music. Chapter 6 studies the rhythmic canons and the tessellation of the line. Chapter 7 is devoted to serial knots. Chapter 8 presents combinatorial designs and their applications to music. The last chapter, chapter 9, is dedicated to the study of tuning systems.

The Musical-Mathematical Mind

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Publisher : Springer
ISBN 13 : 3319473379
Total Pages : 345 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis The Musical-Mathematical Mind by : Gabriel Pareyon

Download or read book The Musical-Mathematical Mind written by Gabriel Pareyon and published by Springer. This book was released on 2017-10-20 with total page 345 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.

Mathematics of Musical Rhythm

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Publisher : Taylor & Francis
ISBN 13 : 1040120989
Total Pages : 129 pages
Book Rating : 4.0/5 (41 download)

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Book Synopsis Mathematics of Musical Rhythm by : Jason Yust

Download or read book Mathematics of Musical Rhythm written by Jason Yust and published by Taylor & Francis. This book was released on 2024-09-06 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents original research applying mathematics to musical rhythm, with a focus on computational methods, theoretical approaches, analysis of rhythm in folk and global music traditions, syncopation, and maximal evenness. It honours the legacy of computer scientist and music theorist Godfried Toussaint. In addition to addressing a topic pioneered by Toussaint, application of mathematics to representation of musical rhythms, the volume also builds upon his interest in analysis of music traditions outside the European classical canon and the use of computational methods. Empirical contributions include a study of timing in Scandinavian polska performance showing that timing interacts with rhythmic features and a study of vocal melody rhythm in pre- and post-millennial popular music, showing significant differences in tempo, rhythmic density, and repetition in the two corpora. Theoretical contributions include a survey of timeline rhythms of African and African diasporic musics showing the prevalence of rhythms of a special type related to maximal evenness, an application of matrix algebra to rhythm and syncopation with analysis of clave rhythms, a ragtime corpus, and Balinese gong cycles, and a mathematical development of a new classification of smooth rhythms using a “shadow rhythm” algorithm suggested by Toussaint. The volume also includes an original composition by Tom Johnson and a personal recollection of Toussaint by Francisco Gómez-Martín. This volume will be a key resource for academics, researchers, and advanced students of music, musicology, music analyses, mathematical music theory, computational musicology, and music informatics. It was originally published as a special issue of the Journal of Mathematics and Music.

Imagine Math 6

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Publisher : Springer
ISBN 13 : 3319939491
Total Pages : 327 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Imagine Math 6 by : Michele Emmer

Download or read book Imagine Math 6 written by Michele Emmer and published by Springer. This book was released on 2018-11-06 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: Imagine mathematics, imagine with the help of mathematics, imagine new worlds, new geometries, new forms. Imagine building mathematical models that make it possible to manage our world better, imagine combining music, art, poetry, literature, architecture and cinema with mathematics. Imagine the unpredictable and sometimes counterintuitive applications of mathematics in all areas of human endeavour. Imagination and mathematics, imagination and culture, culture and mathematics. This sixth volume in the series begins with a homage to the architect Zaha Hadid, who died on March 31st, 2016, a few weeks before the opening of a large exhibition of her works in Palazzo Franchetti in Venice, where all the Mathematics and Culture conferences have taken place in the last years. A large section of the book is dedicated to literature, narrative and mathematics including a contribution from Simon Singh. It discusses the role of media in mathematics, including museums of science, journals and movies. Mathematics and applications, including blood circulation and preventing crimes using earthquakes, is also addressed, while a section on mathematics and art examines the role of math in design. A large selection presents photos of mathematicians and mathematical objects by Vincent Moncorge. Discussing all topics in a way that is rigorous but captivating, detailed but full of evocations, it offers an all-embracing look at the world of mathematics and culture.

The Fourier Transform and Its Applications

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Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (22 download)

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Book Synopsis The Fourier Transform and Its Applications by : Ronald Newbold Bracewell

Download or read book The Fourier Transform and Its Applications written by Ronald Newbold Bracewell and published by . This book was released on 1978 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: