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Musimathics The Mathematical Foundations of Music

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ISBN-10: 0262122820

ISBN-13: 9780262122825

Edition: 2006

Authors: Gareth Loy

List price: $55.00
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Description:

"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. Musimathicsis 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 Musimathicsideal for classroom use. Additional material can be found at a companion web site.
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Book details

List price: $55.00
Copyright year: 2006
Publisher: MIT Press
Publication date: 6/16/2006
Binding: Hardcover
Pages: 504
Size: 7.00" wide x 9.00" long x 1.00" tall
Weight: 2.090
Language: English

Foreword
Preface
About the Author
Acknowledgments
Music and Sound
Basic Properties of Sound
Waves
Summary
Representing Music
Notation
Tones, Notes, and Scores
Pitch
Scales
Interval Sonorities
Onset and Duration
Musical Loudness
Timbre
Summary
Musical Scales, Tuning, and Intonation
Equal-Tempered Intervals
Equal-Tempered Scale
Just Intervals and Scales
The Cent Scale
A Taxonomy of Scales
Do Scales Come from Timbre or Proportion?
Harmonic Proportion
Pythagorean Diatonic Scale
The Problem of Transposing Just Scales
Consonance of Intervals
The Powers of the Fifth and the Octave Do Not Form a Closed System
Designing Useful Scales Requires Compromise
Tempered Tuning Systems
Microtonality
Rule of 18
Deconstructing Tonal Harmony
Deconstructing the Octave
The Prospects for Alternative Tunings
Summary
Suggested Reading
Physical Basis of Sound
Distance
Dimension
Time
Mass
Density
Displacement
Speed
Velocity
Instantaneous Velocity
Acceleration
Relating Displacement, Velocity, Acceleration, and Time
Newton's Laws of Motion
Types of Force
Work and Energy
Internal and External Forces
The Work-Energy Theorem
Conservative and Nonconservative Forces
Power
Power of Vibrating Systems
Wave Propagation
Amplitude and Pressure
Intensity
Inverse Square Law
Measuring Sound Intensity
Summary
Geometrical Basis of Sound
Circular Motion and Simple Harmonic Motion
Rotational Motion
Projection of Circular Motion
Constructing a Sinusoid
Energy of Waveforms
Summary
Psychophysical Basis of Sound
Signaling Systems
The Ear
Psychoacoustics and Psychophysics
Pitch
Loudness
Frequency Domain Masking
Beats
Combination Tones
Critical Bands
Duration
Consonance and Dissonance
Localization
Externalization
Timbre
Summary
Suggested Reading
Introduction to Acoustics
Sound and Signal
A Simple Transmission Model
How Vibrations Travel in Air
Speed of Sound
Pressure Waves
Sound Radiation Models
Superposition and Interference
Reflection
Refraction
Absorption
Diffraction
Doppler Effect
Room Acoustics
Summary
Suggested Reading
Vibrating Systems
Simple Harmonic Motion Revisited
Frequency of Vibrating Systems
Some Simple Vibrating Systems
The Harmonic Oscilltor
Modes of Vibration
A Taxonomy of Vibrating Systems
One-Dimensional Vibrating Systems
Two-Dimensional Vibrating Elements
Resonance (Continued)
Transiently Driven Vibrating Systems
Summary
Suggested Reading
Composition and Methodology
Guido's Method
Methodology and Composition
Musimat: A Simple Programming Language for Music
Program for Guido's Method
Other Music Representation Systems
Delegating Choice
Randomness
Chaos and Determinism
Combinatorics
Atonality
Composing Functions
Traversing and Manipulating Musical Materials
Stochastic Techniques
Probability
Information Theory and the Mathematics of Expectation
Music, Information, and Expectation
Form in Unpredictability
Monte Carlo Methods
Markov Chains
Causality and Composition
Learning
Music and Connectionism
Representing Musical Knowledge
Next-Generation Musikalische Wurfelspiel
Calculating Beauty
Appendix A
Exponents
Logarithms
Series and Summations
About Trigonometry
Xeno's Paradox
Modulo Arithmetic and Congruence
Whence 0.161 in Sabine's Equation?
Excerpts from Pope John XXII's Bull Regarding Church Music
Greek Alphabet
Appendix B
Musimat
Music Datatypes in Musimat
Unicode (ASCII) Character Codes
Operator Associativity and Precedence in Musimat
Glossary
Notes
References
Equation Index
Subject Index