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Music A Mathematical Offering

Author: Dave Benson
Publisher: Cambridge University Press
ISBN: 0521853877
Size: 13.63 MB
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Explores interaction between music and mathematics including harmony, symmetry, digital music and perception of sound.

Musical Mathematics

Author: Cris Forster
Publisher: Chronicle Books
ISBN: 9780811874076
Size: 14.22 MB
Format: PDF, Docs
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Musical Mathematics is the definitive tome for the adventurous musician. Integrating mathematics, music history, and hands-on experience, this volume serves as a comprehensive guide to the tunings and scales of acoustic instruments from around the world. Author, composer, and builder Cris Forster illuminates the mathematical principles of acoustic music, offering practical information and new discoveries about both traditional and innovative instruments.With this knowledge readers can improve, or begin to build, their own instruments inspired by Forster's creationsshown in 16 color plates. For those ready to step outside musical conventions and those whose curiosity about the science of sound is never satisfied, Musical Mathematics is the map to a new musical world.

Music

Author: David J. Benson
Publisher:
ISBN: 9781139641630
Size: 79.25 MB
Format: PDF, Kindle
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Explores interaction between music and mathematics including harmony, symmetry, digital music and perception of sound.

The Math Behind The Music

Author: Leon Harkleroad
Publisher: Cambridge University Press
ISBN: 0521810957
Size: 49.95 MB
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Looks at the mathematical aspects of music, covering such topics as compositional techniques, scales, tuning systems, and music criticism.

Mathematics And Music

Author: David Wright
Publisher: American Mathematical Soc.
ISBN: 0821848739
Size: 70.68 MB
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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.

Music And Mathematics

Author: John Fauvel
Publisher: Oxford University Press on Demand
ISBN: 9780199298938
Size: 43.22 MB
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From Ancient Greek times, music has been seen as a mathematical art, and the relationship between mathematics and music has fascinated generations. This collection of wide ranging, comprehensive and fully-illustrated papers, authorized by leading scholars, presents the link between these two subjects in a lucid manner that is suitable for students of both subjects, as well as the general reader with an interest in music. Physical, theoretical, physiological, acoustic, compositional and analytical relationships between mathematics and music are unfolded and explored with focus on tuning and temperament, the mathematics of sound, bell-ringing and modern compositional techniques.

From Music To Mathematics

Author: Gareth E. Roberts
Publisher: JHU Press
ISBN: 1421419181
Size: 43.98 MB
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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.

Emblems Of The Mind

Author: Edward Rothstein
Publisher: Harper Perennial
ISBN: 9780380727476
Size: 50.86 MB
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Unravels the mystery of the relationship between music and mathematics, discussing their differences and their surprising similarities--including their origins and historical links

Musimathics

Author: Gareth Loy
Publisher: MIT Press
ISBN: 0262292769
Size: 34.84 MB
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Volume 2 of Musimathics continues the story of music engineering begun in Volume 1, focusing on the digital and computational domain. Loy goes deeper into the mathematics of music and sound, beginning with digital audio, sampling, and binary numbers, as well as complex numbers and how they simplify representation of musical signals. Chapters cover the Fourier transform, convolution, filtering, resonance, the wave equation, acoustical systems, sound synthesis, the short-time Fourier transform, and the wavelet transform. These subjects provide the theoretical underpinnings of today's music technology. The examples given are all practical problems in music and audio. Additional material can be found at http://www.musimathics.com.

Mathematical Analysis Of Physical Problems

Author: Philip Russell Wallace
Publisher: Courier Corporation
ISBN: 0486646769
Size: 10.20 MB
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This mathematical reference for theoretical physics employs common techniques and concepts to link classical and modern physics. It provides the necessary mathematics to solve most of the problems. Topics include the vibrating string, linear vector spaces, the potential equation, problems of diffusion and attenuation, probability and stochastic processes, and much more. 1972 edition.