Musimathics

Author: Gareth Loy
Publisher: MIT Press
ISBN: 0262516551
Format: PDF
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"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 this volume, 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. Musimathics is carefully structured so that new topics depend strictly on topics already presented, carrying the reader progressively from basic subjects to more advanced ones. Cross-references point to related topics and an extensive glossary defines commonly used terms. The book explains the mathematics and physics of music for the reader whose mathematics may not have gone beyond the early undergraduate level. Calling himself "a composer seduced into mathematics," Loy provides answers to foundational questions about the mathematics of music accessibly yet rigorously. The topics are all subjects that contemporary composers, musicians, and musical engineers have found to be important. The examples given are all practical problems in music and audio. The level of scholarship and the pedagogical approach also make Musimathics ideal for classroom use. Additional material can be found at a companion web site.

Musimathics

Author: Gareth Loy
Publisher: MIT Press
ISBN: 0262292769
Format: PDF, ePub
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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.

Mathematics and Music

Author: James S. Walker
Publisher: CRC Press
ISBN: 1439867097
Format: PDF, Mobi
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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.

Mathematics and Music

Author: David Wright
Publisher: American Mathematical Soc.
ISBN: 0821848739
Format: PDF, ePub, Docs
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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.

Foundations of Diatonic Theory

Author: Timothy A. Johnson
Publisher: Scarecrow Press
ISBN: 0810862336
Format: PDF
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Foundations of Diatonic Theory: A Mathematically Based Approach to Music Fundamentals is an introductory, undergraduate-level textbook that provides an easy entry point into the challenging field of diatonic set theory, a division of music theory that applies the techniques of discrete mathematics to the properties of diatonic scales. After introducing mathematical concepts that relate directly to music theory, the text concentrates on these mathematical relationships, firmly establishing a link between introductory pedagogy and recent scholarship in music theory. It then relates concepts in diatonic set theory directly to the study of music fundamentals through pedagogical exercises and instructions. Ideal for introductory music majors, the book requires only a general knowledge of mathematics, and the exercises are provided with solutions and detailed explanations. With its basic description of musical elements, this textbook is suitable for courses in music fundamentals, music theory for non-music majors, music and mathematics, and other similar courses that allow students to improve their mathematics skills while pursuing the study of music.

Harmonograph

Author: Anthony Ashton
Publisher: Wooden Books
ISBN: 1912706059
Format: PDF, Mobi
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Why did Pythagoras pause outside a Blacksmith's workshop? Can the nature of Harmony really be understood visually? Why do harmonies leave gaps or 'commas' when added together? In this charming little book Anthony Ashton uses a Victorian device called a Harmonograph to tell the story of Harmony and the intervals in the scale. With useful appendices and exquisite line drawings this is a unique and original introduction to this timeless subject. WOODEN BOOKS are small but packed with information. "Fascinating" FINANCIAL TIMES. "Beautiful" LONDON REVIEW OF BOOKS. "Rich and Artful" THE LANCET. "Genuinely mind-expanding" FORTEAN TIMES. "Excellent" NEW SCIENTIST. "Stunning" NEW YORK TIMES. Small books, big ideas.

The Audio Programming Book

Author: Richard Boulanger
Publisher: MIT Press
ISBN: 0262288605
Format: PDF, ePub, Mobi
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This comprehensive handbook of mathematical and programming techniques for audio signal processing will be an essential reference for all computer musicians, computer scientists, engineers, and anyone interested in audio. Designed to be used by readers with varying levels of programming expertise, it not only provides the foundations for music and audio development but also tackles issues that sometimes remain mysterious even to experienced software designers. Exercises and copious examples (all cross-platform and based on free or open source software) make the book ideal for classroom use. Fifteen chapters and eight appendixes cover such topics as programming basics for C and C++ (with music-oriented examples), audio programming basics and more advanced topics, spectral audio programming; programming Csound opcodes, and algorithmic synthesis and music programming. Appendixes cover topics in compiling, audio and MIDI, computing, and math. An accompanying DVD provides an additional 40 chapters, covering musical and audio programs with micro-controllers, alternate MIDI controllers, video controllers, developing Apple Audio Unit plug-ins from Csound opcodes, and audio programming for the iPhone.The sections and chapters of the book are arranged progressively and topics can be followed from chapter to chapter and from section to section. At the same time, each section can stand alone as a self-contained unit. Readers will find The Audio Programming Book a trustworthy companion on their journey through making music and programming audio on modern computers.

Musical Mathematics

Author: Cris Forster
Publisher: Chronicle Books
ISBN: 9780811874076
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.

Germany in the Loud Twentieth Century

Author: Florence Feiereisen
Publisher: Oxford University Press
ISBN: 0199759383
Format: PDF, Kindle
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This book introduces German Sound Studies using a transdisciplinary approach. It invites readers to auralize space by describing characteristically German soundscapes in the long twentieth century, including the noisy city of the early 1900s, the sounds of East and West Germany, and hip-hop soundscapes of the millennium.

The Physics of Music and Color

Author: Leon Gunther
Publisher: Springer Science & Business Media
ISBN: 9781461405573
Format: PDF, Kindle
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The Physics of Music and Color deals with two subjects, music and color - sound and light in the physically objective sense - in a single volume. The basic underlying physical principles of the two subjects overlap greatly: both music and color are manifestations of wave phenomena, and commonalities exist as to the production, transmission, and detection of sound and light. This book aids readers in studying both subjects, which involve nearly the entire gamut of the fundamental laws of classical as well as modern physics. Where traditional introductory physics and courses are styled so that the basic principles are introduced first and are then applied wherever possible, this book is based on a motivational approach: it introduces a subject by demonstrating a set of related phenomena, challenging readers by calling for a physical basis for what is observed. The Physics of Music and Color is written at level suitable for college students without any scientific background, requiring only simple algebra and a passing familiarity with trigonometry. It contains numerous problems at the end of each chapter that help the reader to fully grasp the subject.