The Mathematics Of Harmony
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The Mathematics Of Harmony
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Author : Alekse? Petrovich Stakhov
language : en
Publisher: World Scientific
Release Date : 2009
The Mathematics Of Harmony written by Alekse? Petrovich Stakhov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
Assisted by Scott Olsen (Central Florida Community College, USA) This volume is a result of the author's four decades of research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the ?Mathematics of Harmony,? a new interdisciplinary direction of modern science. This direction has its origins in ?The Elements? of Euclid and has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the ?golden? algebraic equations, the generalized Binet formulas, Fibonacci and ?golden? matrices), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational radices, Fibonacci computers, ternary mirror-symmetrical arithmetic, a new theory of coding and cryptography based on the Fibonacci and ?golden? matrices).The book is intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science.
A Geometry Of Music
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Author : Dmitri Tymoczko
language : en
Publisher: Oxford University Press
Release Date : 2010-12-03
A Geometry Of Music written by Dmitri Tymoczko and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-03 with Music categories.
How is the Beatles' "Help!" similar to Stravinsky's "Dance of the Adolescents?" How does Radiohead's "Just" relate to the improvisations of Bill Evans? And how do Chopin's works exploit the non-Euclidean geometry of musical chords? In this groundbreaking work, author Dmitri Tymoczko describes a new framework for thinking about music that emphasizes the commonalities among styles from medieval polyphony to contemporary rock. Tymoczko identifies five basic musical features that jointly contribute to the sense of tonality, and shows how these features recur throughout the history of Western music. In the process he sheds new light on an age-old question: what makes music sound good? A Geometry of Music provides an accessible introduction to Tymoczko's revolutionary geometrical approach to music theory. The book shows how to construct simple diagrams representing relationships among familiar chords and scales, giving readers the tools to translate between the musical and visual realms and revealing surprising degrees of structure in otherwise hard-to-understand pieces. Tymoczko uses this theoretical foundation to retell the history of Western music from the eleventh century to the present day. Arguing that traditional histories focus too narrowly on the "common practice" period from 1680-1850, he proposes instead that Western music comprises an extended common practice stretching from the late middle ages to the present. He discusses a host of familiar pieces by a wide range of composers, from Bach to the Beatles, Mozart to Miles Davis, and many in between. A Geometry of Music is accessible to a range of readers, from undergraduate music majors to scientists and mathematicians with an interest in music. Defining its terms along the way, it presupposes no special mathematical background and only a basic familiarity with Western music theory. The book also contains exercises designed to reinforce and extend readers' understanding, along with a series of appendices that explore the technical details of this exciting new theory.
Mathematics Of Harmony From Euclid To Contemporary Mathematics And Computer Science
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Author : Alexey Stakhov
language : en
Publisher: World Scientific
Release Date : 2009-09-11
Mathematics Of Harmony From Euclid To Contemporary Mathematics And Computer Science written by Alexey Stakhov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-11 with Mathematics categories.
Assisted by Scott Olsen (Central Florida Community College, USA) This volume is a result of the author's four decades of research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the “Mathematics of Harmony,” a new interdisciplinary direction of modern science. This direction has its origins in “The Elements” of Euclid and has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the “golden” algebraic equations, the generalized Binet formulas, Fibonacci and “golden” matrices), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational radices, Fibonacci computers, ternary mirror-symmetrical arithmetic, a new theory of coding and cryptography based on the Fibonacci and “golden” matrices).The book is intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science.
Music A Mathematical Offering
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Author : Dave Benson
language : en
Publisher: Cambridge University Press
Release Date : 2007
Music A Mathematical Offering written by Dave Benson 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 2007 with Mathematics categories.
This book explores the interaction between music and mathematics including harmony, symmetry, digital music and perception of sound.
Mathematics And Music
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Author : James S. Walker
language : en
Publisher: CRC Press
Release Date : 2013-04-10
Mathematics And Music written by James S. Walker and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-10 with Mathematics categories.
At first glance, mathematics and music seem to be from separate worlds—one from science, one from art. But in fact, the connections between the two go back thousands of years, such as Pythagoras’s ideas about how to quantify changes of pitch for musical tones (musical intervals). Mathematics and Music: Composition, Perception, and Performance explores the many links between mathematics and different genres of music, deepening students’ understanding of music through mathematics. In an accessible way, the text teaches the basics of reading music and explains how various patterns in music can be described with mathematics. The authors extensively use the powerful time-frequency method of spectrograms to analyze the sounds created in musical performance. Numerous examples of music notation assist students in understanding basic musical scores. The text also provides mathematical explanations for musical scales, harmony, and rhythm and includes a concise introduction to digital audio synthesis. Along with helping students master some fundamental mathematics, this book gives them a deeper appreciation of music by showing how music is informed by both its mathematical and aesthetic structures. Web Resource On the book’s CRC Press web page, students can access videos of many of the spectrograms discussed in the text as well as musical scores playable with the free music software MuseScore. An online bibliography offers many links to free downloadable articles on math and music. The web page also provides links to other websites related to math and music, including all the sites mentioned in the book.
From Music To Mathematics
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Author : Gareth E. Roberts
language : en
Publisher: JHU Press
Release Date : 2016-02-15
From Music To Mathematics written by Gareth E. Roberts and has been published by JHU Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-15 with Mathematics categories.
A guided tour of the mathematical principles inherent in music. Taking a "music first" approach, Gareth E. Roberts's From Music to Mathematics will inspire students to learn important, interesting, and at times advanced mathematics. Ranging from a discussion of the geometric sequences and series found in the rhythmic structure of music to the phase-shifting techniques of composer Steve Reich, the musical concepts and examples in the book motivate a deeper study of mathematics. Comprehensive and clearly written, From Music to Mathematics is designed to appeal to readers without specialized knowledge of mathematics or music. Students are taught the relevant concepts from music theory (notation, scales, intervals, the circle of fifths, tonality, etc.), with the pertinent mathematics developed alongside the related musical topic. The mathematics advances in level of difficulty from calculating with fractions, to manipulating trigonometric formulas, to constructing group multiplication tables and proving a number is irrational. Topics discussed in the book include • Rhythm • Introductory music theory • The science of sound • Tuning and temperament • Symmetry in music • The Bartók controversy • Change ringing • Twelve-tone music • Mathematical modern music • The Hemachandra–Fibonacci numbers and the golden ratio • Magic squares • Phase shifting Featuring numerous musical excerpts, including several from jazz and popular music, each topic is presented in a clear and in-depth fashion. Sample problems are included as part of the exposition, with carefully written solutions provided to assist the reader. The book also contains more than 200 exercises designed to help develop students' analytical skills and reinforce the material in the text. From the first chapter through the last, readers eager to learn more about the connections between mathematics and music will find a comprehensive textbook designed to satisfy their natural curiosity.
Mathematics Of Harmony As A New Interdisciplinary Direction And Golden Paradigm Of Modern Science Volume 1 The Golden Section Fibonacci Numbers Pascal Triangle And Platonic Solids
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Author : Alekseĭ Petrovich Stakhov
language : en
Publisher:
Release Date : 2020
Mathematics Of Harmony As A New Interdisciplinary Direction And Golden Paradigm Of Modern Science Volume 1 The Golden Section Fibonacci Numbers Pascal Triangle And Platonic Solids written by Alekseĭ Petrovich Stakhov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Electronic books categories.
Golden Non Euclidean Geometry The Hilbert S Fourth Problem Golden Dynamical Systems And The Fine Structure Constant
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Author : Alexey Stakhov
language : en
Publisher: World Scientific
Release Date : 2016-07-14
Golden Non Euclidean Geometry The Hilbert S Fourth Problem Golden Dynamical Systems And The Fine Structure Constant written by Alexey Stakhov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-14 with Mathematics categories.
This unique book overturns our ideas about non-Euclidean geometry and the fine-structure constant, and attempts to solve long-standing mathematical problems. It describes a general theory of 'recursive' hyperbolic functions based on the 'Mathematics of Harmony,' and the 'golden,' 'silver,' and other 'metallic' proportions. Then, these theories are used to derive an original solution to Hilbert's Fourth Problem for hyperbolic and spherical geometries. On this journey, the book describes the 'golden' qualitative theory of dynamical systems based on 'metallic' proportions. Finally, it presents a solution to a Millennium Problem by developing the Fibonacci special theory of relativity as an original physical-mathematical solution for the fine-structure constant. It is intended for a wide audience who are interested in the history of mathematics, non-Euclidean geometry, Hilbert's mathematical problems, dynamical systems, and Millennium Problems.See Press Release: Application of the mathematics of harmony - Golden non-Euclidean geometry in modern math
Infinite Measure
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Author : Rachel Fletcher
language : en
Publisher: George F Thompson Publishing
Release Date : 2013
Infinite Measure written by Rachel Fletcher and has been published by George F Thompson Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Architectural design categories.
The desire for harmony is universal among all cultures. In Infinite Measure, we rediscover a fundamental starting point for designers of all ages: the simple act of drawing with a compass and a rule can sensitize the designer to the rich subtleties of spatial harmony, no matter how one ultimately chooses to express it.
Algebraic Serenity A Journey Through Mathematical Harmony
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Author : Pasquale De Marco
language : en
Publisher: Pasquale De Marco
Release Date : 2025-07-07
Algebraic Serenity A Journey Through Mathematical Harmony written by Pasquale De Marco and has been published by Pasquale De Marco this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-07 with Education categories.
"Algebraic Harmony: A Journey Through the Symphony of Equations" is an enchanting invitation to discover the beauty and elegance of algebra. This comprehensive guidebook unveils the mysteries of algebraic concepts, transforming them from abstract symbols into tangible tools for problem-solving and critical thinking. With clear explanations, engaging examples, and thought-provoking exercises, "Algebraic Harmony" guides readers through a harmonious journey of exploration, enlightenment, and discovery. Each chapter delves into a specific algebraic concept, revealing its significance and practical applications. From the fundamental building blocks of variables, expressions, and equations to the intricacies of functions, graphs, and systems of equations, this book provides a comprehensive understanding of algebra's fundamental principles. Readers will learn how to solve equations, graph functions, and analyze algebraic structures, gaining a deeper appreciation for the interconnectedness of mathematical ideas. "Algebraic Harmony" is not just a textbook; it is an experience that ignites a passion for mathematics. With its engaging narrative and accessible approach, this book transforms algebra from a daunting subject into an enthralling adventure, suitable for high school students seeking to conquer algebraic challenges and adult learners seeking to refresh their mathematical knowledge. Step into the world of "Algebraic Harmony" and embark on a journey of mathematical discovery. Let the symphony of equations serenade your mind as you unlock the secrets of algebra, transforming your perception of this fascinating subject and opening up a world of endless possibilities. If you like this book, write a review on google books!