Musimathics, Volume 1

Author: Gareth Loy
Publisher: MIT Press
ISBN: 0262516551
Category : Music
Languages : en
Pages : 501

Book Description
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, Volume 1

Author: Gareth Loy
Publisher: MIT Press
ISBN: 0262292750
Category : Music
Languages : en
Pages : 501

Musimathics, Volume 2

Author: Gareth Loy
Publisher: MIT Press
ISBN: 0262292769
Category : Music
Languages : en
Pages : 579

Book Description
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.

Music by the Numbers

Author: Eli Maor
Publisher: Princeton University Press
ISBN: 0691202966
Category : Mathematics
Languages : en
Pages : 176

Book Description
How music has influenced mathematics, physics, and astronomy from ancient Greece to the twentieth century.

The Topos of Music

Author: Guerino Mazzola
Publisher: Birkhäuser
ISBN: 303488141X
Category : Mathematics
Languages : en
Pages : 1310

Book Description
With contributions by numerous experts

On the Brink of Paradox

Author: Agustin Rayo
Publisher: MIT Press
ISBN: 0262039419
Category : Mathematics
Languages : en
Pages : 321

Book Description
An introduction to awe-inspiring ideas at the brink of paradox: infinities of different sizes, time travel, probability and measure theory, and computability theory. This book introduces the reader to awe-inspiring issues at the intersection of philosophy and mathematics. It explores ideas at the brink of paradox: infinities of different sizes, time travel, probability and measure theory, computability theory, the Grandfather Paradox, Newcomb's Problem, the Principle of Countable Additivity. The goal is to present some exceptionally beautiful ideas in enough detail to enable readers to understand the ideas themselves (rather than watered-down approximations), but without supplying so much detail that they abandon the effort. The philosophical content requires a mind attuned to subtlety; the most demanding of the mathematical ideas require familiarity with college-level mathematics or mathematical proof. The book covers Cantor's revolutionary thinking about infinity, which leads to the result that some infinities are bigger than others; time travel and free will, decision theory, probability, and the Banach-Tarski Theorem, which states that it is possible to decompose a ball into a finite number of pieces and reassemble the pieces so as to get two balls that are each the same size as the original. Its investigation of computability theory leads to a proof of Gödel's Incompleteness Theorem, which yields the amazing result that arithmetic is so complex that no computer could be programmed to output every arithmetical truth and no falsehood. Each chapter is followed by an appendix with answers to exercises. A list of recommended reading points readers to more advanced discussions. The book is based on a popular course (and MOOC) taught by the author at MIT.

A Geometry of Music

Author: Dmitri Tymoczko
Publisher: OUP USA
ISBN: 0195336674
Category : Mathematics
Languages : en
Pages : 469

Book Description
In 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.

A DSP Primer

Author: Kenneth Steiglitz
Publisher: Prentice Hall
ISBN:
Category : Computer music
Languages : en
Pages : 330

Book Description
This new book by Ken Steigliz offers an informal and easy-to-understand introduction to digital signal processing, emphasizing digital audio and applications to computer music. A DSP Primer covers important topics such as phasors and tuning forks; the wave equation; sampling and quantizing; feedforward and feedback filters; comb and string filters; periodic sounds; transform methods; and filter design. Steiglitz uses an intuitive and qualitative approach to develop the mathematics critical to understanding DSP. A DSP Primer is written for a broad audience including: Students of DSP in Engineering and Computer Science courses. Composers of computer music and those who work with digital sound. WWW and Internet developers who work with multimedia. General readers interested in science that want an introduction to DSP. Features: Offers a simple and uncluttered step-by-step approach to DSP for first-time users, especially beginners in computer music. Designed to provide a working knowledge and understanding of frequency domain methods, including FFT and digital filtering. Contains thought-provoking questions and suggested experiments that help the reader to understand and apply DSP theory and techniques.

The Raven's Hat

Author: Jonas Peters
Publisher: MIT Press
ISBN: 026204451X
Category : Mathematics
Languages : en
Pages : 193

Book Description
Games that show how mathematics can solve the apparently unsolvable. This book presents a series of engaging games that seem unsolvable--but can be solved when they are translated into mathematical terms. How can players find their ID cards when the cards are distributed randomly among twenty boxes? By applying the theory of permutations. How can a player guess the color of her own hat when she can only see other players' hats? Hamming codes, which are used in communication technologies. Like magic, mathematics solves the apparently unsolvable. The games allow readers, including university students or anyone with high school-level math, to experience the joy of mathematical discovery.

The Cognition of Basic Musical Structures

Author: David Temperley
Publisher: MIT Press
ISBN: 9780262701051
Category : Music
Languages : en
Pages : 432

Book Description
In this book, David Temperley addresses a fundamental question about music cognition: how do we extract basic kinds of musical information, such as meter, phrase structure, counterpoint, pitch spelling, harmony, and key from music as we hear it? Taking a computational approach, Temperley develops models for generating these aspects of musical structure. The models he proposes are based on preference rules, which are criteria for evaluating a possible structural analysis of a piece of music. A preference rule system evaluates many possible interpretations and chooses the one that best satisfies the rules. After an introductory chapter, Temperley presents preference rule systems for generating six basic kinds of musical structure: meter, phrase structure, contrapuntal structure, harmony, and key, as well as pitch spelling (the labeling of pitch events with spellings such as A flat or G sharp). He suggests that preference rule systems not only show how musical structures are inferred, but also shed light on other aspects of music. He substantiates this claim with discussions of musical ambiguity, retrospective revision, expectation, and music outside the Western canon (rock and traditional African music). He proposes a framework for the description of musical styles based on preference rule systems and explores the relevance of preference rule systems to higher-level aspects of music, such as musical schemata, narrative and drama, and musical tension.