The Math Behind the Music
Author: Leon Harkleroad
Publisher: Cambridge University Press
Published: 2006-08-14
Total Pages: 7
ISBN-13: 0521810957
DOWNLOAD EBOOK →Accompanying CD-ROM includes musical selections.
Author: Leon Harkleroad
Publisher: Cambridge University Press
Published: 2006-08-14
Total Pages: 7
ISBN-13: 0521810957
DOWNLOAD EBOOK →Accompanying CD-ROM includes musical selections.
Author: Gareth E. Roberts
Publisher: JHU Press
Published: 2016-02-15
Total Pages: 320
ISBN-13: 1421419181
DOWNLOAD EBOOK →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.
Author: David Wright
Publisher: American Mathematical Soc.
Published: 2009
Total Pages: 178
ISBN-13: 0821848739
DOWNLOAD EBOOK →Many people intuitively sense that there is a connection between mathematics and music. If nothing else, both involve counting. There is, of course, much more to the association. David Wright's book is an investigation of the interrelationships between mathematics and music, reviewing the needed background concepts in each subject as they are encountered. Along the way, readers will augment their understanding of both mathematics and music. The text explores the common foundations of the two subjects, which are developed side by side. Musical and mathematical notions are brought together, such as scales and modular arithmetic, intervals and logarithms, tone and trigonometry, and timbre and harmonic analysis. When possible, discussions of musical and mathematical notions are directly interwoven. Occasionally the discourse dwells for a while on one subject and not the other, but eventually the connection is established, making this an integrative treatment of the two subjects. The book is a text for a freshman level college course suitable for musically inclined or mathematically inclined students, with the intent of breaking down any apprehension that either group might have for the other subject. Exercises are given at the end of each chapter. The mathematical prerequisites are a high-school level familiarity with algebra, trigonometry, functions, and graphs. Musically, the student should have had some exposure to musical staffs, standard clefs, and key signatures, though all of these are explained in the text.
Author: David Sulzer
Publisher:
Published: 2021-03-23
Total Pages: 240
ISBN-13: 9780231193788
DOWNLOAD EBOOK →This book offers a lively exploration of the mathematics, physics, and neuroscience that underlie music. Written for musicians and music lovers with any level of science and math proficiency, including none, Music, Math, and Mind demystifies how music works while testifying to its beauty and wonder.
Author: Leon Harkleroad
Publisher: Cambridge University Press
Published: 2006-08-07
Total Pages: 158
ISBN-13: 9780521009355
DOWNLOAD EBOOK →Mathematics has been used for centuries to describe, analyze, and create music. In this book, Leon Harkleroad explores the math related aspects of music from its acoustical bases to compositional techniques to music criticism, touching on - overtones, scales, and tuning systems - the musical dice game attributed to Mozart and Haydn - the several-hundred-year-old style of bell-playing known as ringing the changes - the twelve-tone school of composition that strongly influenced music throughout the 20th century and many other topics involving mathematical ideas from probability theory to Fourier series to group theory. He also relates some cautionary tales of misguided attempts to mix music and mathematics. Both the mathematical and the musical concepts are described in an elementary way, making the book accessible to general readers as well as to mathematicians and musicians of all levels. The book is accompanied by an audio CD of musical examples.
Author: Dave Benson
Publisher: Cambridge University Press
Published: 2007
Total Pages: 426
ISBN-13: 0521853877
DOWNLOAD EBOOK →This book explores the interaction between music and mathematics including harmony, symmetry, digital music and perception of sound.
Author: Anthony Ashton
Publisher: Bloomsbury Publishing USA
Published: 2003-04-01
Total Pages: 68
ISBN-13: 0802714099
DOWNLOAD EBOOK →Ashton presents a short, illustrated introduction to the evolution of simple harmonic theory. Illustrations.
Author: Nikita Braguinski
Publisher: CRC Press
Published: 2022-03-13
Total Pages: 127
ISBN-13: 1000545504
DOWNLOAD EBOOK →Mathematical Music offers a concise and easily accessible history of how mathematics was used to create music. The story presented in this short, engaging volume ranges from ratios in antiquity to random combinations in the 17th century, 20th-century statistics, and contemporary artificial intelligence. This book provides a fascinating panorama of the gradual mechanization of thought processes involved in the creation of music. How did Baroque authors envision a composition system based on combinatorics? What was it like to create musical algorithms at the beginning of the 20th century, before the computer became a reality? And how does this all explain today’s use of artificial intelligence and machine learning in music? In addition to discussing the history and the present state of mathematical music, Braguinski also takes a look at what possibilities the near future of music AI might hold for listeners, musicians, and the society. Grounded in research findings from musicology and the history of technology, and written for the non-specialist general audience, this book helps both student and professional readers to make sense of today’s music AI by situating it in a continuous historical context.
Author: Trudi Hammel Garland
Publisher: Dale Seymour Publications Secondary
Published: 1995
Total Pages: 0
ISBN-13: 9780866518291
DOWNLOAD EBOOK →From the beat of a tribal drum to a choir of crickets--music is everywhere. Math and Music explores the music of various cultures and the sounds heard in nature while highlighting the mathematical concepts, such as proportion, patterns, Fibonacci numbers, geometric transformations, and trigonometry, found in music. The companion poster explores mysterious connections between seemingly different entities, such as music and animals! A four-page guide explains the connections students may discover.
Author: Guerino Mazzola
Publisher: Birkhäuser
Published: 2012-12-06
Total Pages: 1310
ISBN-13: 303488141X
DOWNLOAD EBOOK →With contributions by numerous experts