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Musimathics, Volume 1

Author: Gareth Loy

Publisher: MIT Press

Published: 2011-08-19

Total Pages: 501

ISBN-13: 0262292750

A 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.

Musimathics

Author: D. Gareth Loy

Publisher: MIT Press (MA)

Published: 2006

Total Pages: 514

ISBN-13:

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A 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.

Musimathics, Volume 1

Author: Gareth Loy

Publisher: MIT Press

Published: 2011-08-19

Total Pages: 501

ISBN-13: 0262516551

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Musimathics, Volume 2

Author: Gareth Loy

Publisher: MIT Press

Published: 2011-08-19

Total Pages: 579

ISBN-13: 026251656X

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The second volume of a commonsense, self-contained introduction to the mathematics and physics of music, focusing on the digital and computational domain; essential reading for musicians, music engineers, and anyone interested in the intersection of art and science. 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.

Musimathics, Volume 2

Author: Gareth Loy

Publisher: MIT Press

Published: 2011-08-19

Total Pages: 579

ISBN-13: 0262292769

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The Audio Programming Book

Author: Richard Boulanger

Publisher: MIT Press

Published: 2010-10-22

Total Pages: 917

ISBN-13: 0262014467

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An encyclopedic handbook on audio programming for students and professionals, with many cross-platform open source examples and a DVD covering advanced topics. 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.

The Meaning of Proofs

Author: Gabriele Lolli

Publisher: MIT Press

Published: 2022-09-27

Total Pages: 177

ISBN-13: 0262371049

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Why mathematics is not merely formulaic: an argument that to write a mathematical proof is tantamount to inventing a story. In The Meaning of Proofs, mathematician Gabriele Lolli argues that to write a mathematical proof is tantamount to inventing a story. Lolli offers not instructions for how to write mathematical proofs, but a philosophical and poetic reflection on mathematical proofs as narrative. Mathematics, imprisoned within its symbols and images, Lolli writes, says nothing if its meaning is not narrated in a story. The minute mathematicians open their mouths to explain something—the meaning of x, how to find y—they are framing a narrative. Every proof is the story of an adventure, writes Lolli, a journey into an unknown land to open a new, connected route; once the road is open, we correct it, expand it. Just as fairy tales offer a narrative structure in which new characters can be inserted into recurring forms of the genre in original ways, in mathematics, each new abstract concept is the protagonist of a different theory supported by the general techniques of mathematical reasoning. In ancient Greece, there was more than an analogy between literature and mathematics, there was direct influence. Euclid’s proofs have roots in poetry and rhetoric. Mathematics, Lolli asserts, is not the mere manipulation of formulas.

Sleight of Mind

Author: Matt Cook

Publisher: MIT Press

Published: 2021-08-03

Total Pages: 369

ISBN-13: 0262542293

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This “fun, brain-twisting book . . . will make you think” as it explores more than 75 paradoxes in mathematics, philosophy, physics, and the social sciences (Sean Carroll, New York Times–bestselling author of Something Deeply Hidden). Paradox is a sophisticated kind of magic trick. A magician’s purpose is to create the appearance of impossibility, to pull a rabbit from an empty hat. Yet paradox doesn’t require tangibles, like rabbits or hats. Paradox works in the abstract, with words and concepts and symbols, to create the illusion of contradiction. There are no contradictions in reality, but there can appear to be. In Sleight of Mind, Matt Cook and a few collaborators dive deeply into more than 75 paradoxes in mathematics, physics, philosophy, and the social sciences. As each paradox is discussed and resolved, Cook helps readers discover the meaning of knowledge and the proper formation of concepts—and how reason can dispel the illusion of contradiction. The journey begins with “a most ingenious paradox” from Gilbert and Sullivan’s Pirates of Penzance. Readers will then travel from Ancient Greece to cutting-edge laboratories, encounter infinity and its different sizes, and discover mathematical impossibilities inherent in elections. They will tackle conundrums in probability, induction, geometry, and game theory; perform “supertasks”; build apparent perpetual motion machines; meet twins living in different millennia; explore the strange quantum world—and much more.

Reckonings

Author: Stephen Chrisomalis

Publisher: MIT Press

Published: 2020-12-15

Total Pages: 265

ISBN-13: 026236087X

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Insights from the history of numerical notation suggest that how humans write numbers is an active choice involving cognitive and social factors. Over the past 5,000 years, more than 100 methods of numerical notation--distinct ways of writing numbers--have been developed and used by specific communities. Most of these are barely known today; where they are known, they are often derided as cognitively cumbersome and outdated. In Reckonings, Stephen Chrisomalis considers how humans past and present use numerals, reinterpreting historical and archaeological representations of numerical notation and exploring the implications of why we write numbers with figures rather than words.

Lectures on the Philosophy of Mathematics

Author: Joel David Hamkins

Publisher: MIT Press

Published: 2021-03-09

Total Pages: 350

ISBN-13: 0262542234

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An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations.