The Math Behind the Music
Author: Leon Harkleroad
Publisher: Cambridge University Press
Published: 2006-08-14
Total Pages: 7
ISBN-13: 0521810957
DOWNLOAD EBOOKAccompanying CD-ROM includes musical selections.
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From Music to Mathematics
Author: Gareth E. Roberts
Publisher: JHU Press
Published: 2016-02-15
Total Pages: 320
ISBN-13: 1421419181
DOWNLOAD EBOOKA 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.
The Topos of Music
Author: Guerino Mazzola
Publisher: Birkhäuser
Published: 2012-12-06
Total Pages: 1310
ISBN-13: 303488141X
DOWNLOAD EBOOKWith contributions by numerous experts
Music: A Mathematical Offering
Author: Dave Benson
Publisher: Cambridge University Press
Published: 2007
Total Pages: 426
ISBN-13: 0521853877
DOWNLOAD EBOOKThis book explores the interaction between music and mathematics including harmony, symmetry, digital music and perception of sound.
Mathematics and Music
Author: David Wright
Publisher: American Mathematical Soc.
Published: 2009
Total Pages: 178
ISBN-13: 0821848739
DOWNLOAD EBOOKMany 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.
Harmonograph
Author: Anthony Ashton
Publisher: Bloomsbury Publishing USA
Published: 2003-04-01
Total Pages: 68
ISBN-13: 0802714099
DOWNLOAD EBOOKAshton presents a short, illustrated introduction to the evolution of simple harmonic theory. Illustrations.
Cool Math for Hot Music
Author: Guerino Mazzola
Publisher: Springer
Published: 2016-10-26
Total Pages: 314
ISBN-13: 331942937X
DOWNLOAD EBOOKThis textbook is a first introduction to mathematics for music theorists, covering basic topics such as sets and functions, universal properties, numbers and recursion, graphs, groups, rings, matrices and modules, continuity, calculus, and gestures. It approaches these abstract themes in a new way: Every concept or theorem is motivated and illustrated by examples from music theory (such as harmony, counterpoint, tuning), composition (e.g., classical combinatorics, dodecaphonic composition), and gestural performance. The book includes many illustrations, and exercises with solutions.
Math and Music
Author: Trudi Hammel Garland
Publisher: Dale Seymour Publications Secondary
Published: 1995
Total Pages: 0
ISBN-13: 9780866518291
DOWNLOAD EBOOKFrom 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.
Musimathics, Volume 1
Author: Gareth Loy
Publisher: MIT Press
Published: 2011-08-19
Total Pages: 501
ISBN-13: 0262516551
DOWNLOAD EBOOKA commonsense, self-contained introduction to the mathematics and physics of music; essential reading for musicians, music engineers, and anyone interested in the intersection of art and science. “Mathematics can be as effortless as humming a tune, if you know the tune,” writes Gareth Loy. In Musimathics, Loy teaches us the tune, providing a friendly and spirited tour of the mathematics of music—a commonsense, self-contained introduction for the nonspecialist reader. It is designed for musicians who find their art increasingly mediated by technology, and for anyone who is interested in the intersection of art and science. In Volume 1, Loy presents the materials of music (notes, intervals, and scales); the physical properties of music (frequency, amplitude, duration, and timbre); the perception of music and sound (how we hear); and music composition. Calling himself “a composer seduced into mathematics,” Loy provides answers to foundational questions about the mathematics of music accessibly yet rigorously. The examples given are all practical problems in music and audio. Additional material can be found at http://www.musimathics.com.
A Geometry of Music
Author: Dmitri Tymoczko
Publisher: OUP USA
Published: 2011-03-21
Total Pages: 469
ISBN-13: 0195336674
DOWNLOAD EBOOKIn this groundbreaking book, Tymoczko uses contemporary geometry to provide a new framework for thinking about music, one that emphasizes the commonalities among styles from Medieval polyphony to contemporary jazz.
