|
Musimathics, Volume 1: The Mathematical Foundations of Music | 
 enlarge | Author: Gareth Loy
Publisher: The MIT Press
Category: Book
List Price: $52.00
Buy New: $37.99
You Save: $14.01 (27%)
New (22) Used (6) from $37.99
Avg. Customer Rating:  2 reviews
Sales Rank: 59058
Media: Hardcover
Number Of Items: 1
Pages: 500
Shipping Weight (lbs): 2.1
Dimensions (in): 9.1 x 7.2 x 1.2
ISBN: 0262122820
Dewey Decimal Number: 781.2
EAN: 9780262122825
ASIN: 0262122820
Publication Date: June 23, 2006
Availability: Usually ships in 1-2 business days
Shipping: International shipping available
Condition: Brand new item. Over 3.5 million customers served. Order now. Selling online since 1995. Few left in stock - order soon. Code: M20080813113714T
|
| Similar Items:
|
| Editorial Reviews:
Product 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. 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.
|
| Customer Reviews:
Excellent March 25, 2008
The book is simply useful. Musicians and teachers can review their knowledge base. Novices have the possibility to learn the math-based laws of music by means of a non-academic language. Above all, the book is extended into a second volume for an in-depth learning.
Excellent book combines music, math, and programming January 10, 2007
25 out of 26 found this review helpful
After about a ten year hiatus on books of this type being published, this is one of several new books combining mathematics, music, and programming aimed at musicians who want to know more about the math behind their musical compositions and are not content to just know what drop-down windows to click on using the latest musical software. The book starts with the basics of music and sound and works up to basic music theory, physics and sound, and acoustics and psychoacoustics. The final chapter of the book is the most interesting, since it concerns mathematics and composition techniques using the author's C++ based library "Musimat". Both this book and Musimat have companion websites, although the Musimat site is the most interesting with plenty of downloads in case you are interested in how to use this compositional library. There is a volume two scheduled for release in Spring 2007 that gets into signal processing, the role of digital signals, and the wave equation, so together they are a very complete treatise on math, music, and programming aimed at the musical composer. I highly recommend it. Of course, if you want to dig deep into individual subjects such as acoustics and psychoacoustics, you are going to need additional references. But this text is clear enough to get you started. The following is the table of contents:
1 Music and Sound 1
1.1 Basic Properties of Sound 1
1.2 Waves 3
1.3 Summary 9
2 Representing Music 11
2.1 Notation 11
2.2 Tones, Notes, and Scores 12
2.3 Pitch 13
2.4 Scales 16
2.5 Interval Sonorities 18
2.6 Onset and Duration 26
2.7 Musical Loudness 27
2.8 Timbre 28
2.9 Summary 37
3 Musical Scales, Tuning, and Intonation 39
3.1 Equal-Tempered Intervals 39
3.2 Equal-Tempered Scale 40
3.3 Just Intervals and Scales 43
3.4 The Cent Scale 45
3.5 A Taxonomy of Scales 46
3.6 Do Scales Come from Timbre or Proportion? 47
3.7 Harmonic Proportion 48
3.8 Pythagorean Diatonic Scale 49
3.9 The Problem of Transposing Just Scales 51
3.10 Consonance of Intervals 56
3.11 The Powers of the Fifth and the Octave Do Not Form a Closed System 66
3.12 Designing Useful Scales Requires Compromise 67
3.13 Tempered Tuning Systems 68
3.14 Microtonality 72
3.15 Rule of 18 82
3.16 Deconstructing Tonal Harmony 85
3.17 Deconstructing the Octave 86
3.18 The Prospects for Alternative Tunings 93
3.19 Summary 93
3.20 Suggested Reading 95
4 Physical Basis of Sound 97
4.1 Distance 97
4.2 Dimension 97
4.3 Time 98
4.4 Mass 99
4.5 Density 100
4.6 Displacement 100
4.7 Speed 101
4.8 Velocity 102
4.9 Instantaneous Velocity 102
4.10 Acceleration 104
4.11 Relating Displacement,Velocity, Acceleration, and Time 106
4.12 Newton's Laws of Motion 108
4.13 Types of Force 109
4.14 Work and Energy 110
4.15 Internal and External Forces 112
4.16 The Work-Energy Theorem 112
4.17 Conservative and Nonconservative Forces 113
4.18 Power 114
4.19 Power of Vibrating Systems 114
4.20 Wave Propagation 116
4.21 Amplitude and Pressure 117
4.22 Intensity 118
4.23 Inverse Square Law 118
4.24 Measuring Sound Intensity 119
4.25 Summary 125
5 Geometrical Basis of Sound 129
5.1 Circular Motion and Simple Harmonic Motion 129
5.2 Rotational Motion 129
5.3 Projection of Circular Motion 136
5.4 Constructing a Sinusoid 139
5.5 Energy of Waveforms 143
5.6 Summary 147
6 Psychophysical Basis of Sound 149
6.1 Signaling Systems 149
6.2 The Ear 150
6.3 Psychoacoustics and Psychophysics 154
6.4 Pitch 156
6.5 Loudness 166
6.6 Frequency Domain Masking 171
6.7 Beats 173
6.8 Combination Tones 175
6.9 Critical Bands 176
6.10 Duration 182
6.11 Consonance and Dissonance 184
6.12 Localization 187
6.13 Externalization 191
6.14 Timbre 195
6.15 Summary 198
6.16 Suggested Reading 198
7 Introduction to Acoustics 199
7.1 Sound and Signal 199
7.2 A Simple Transmission Model 199
7.3 How Vibrations Travel in Air 200
7.4 Speed of Sound 202
7.5 Pressure Waves 207
7.6 Sound Radiation Models 208
7.7 Superposition and Interference 210
7.8 Reflection 210
7.9 Refraction 218
7.10 Absorption 221
7.11 Diffraction 222
7.12 Doppler Effect 228
7.13 Room Acoustics 233
7.14 Summary 238
7.15 Suggested Reading 238
8 Vibrating Systems 239
8.1 Simple Harmonic Motion Revisited 239
8.2 Frequency of Vibrating Systems 241
8.3 Some Simple Vibrating Systems 243
8.4 The Harmonic Oscillator 247
8.5 Modes of Vibration 249
8.6 A Taxonomy of Vibrating Systems 251
8.7 One-Dimensional Vibrating Systems 252
8.8 Two-Dimensional Vibrating Elements 266
8.9 Resonance (Continued) 270
8.10 Transiently Driven Vibrating Systems 278
8.11 Summary 282
8.12 Suggested Reading 283
9 Composition and Methodology 285
9.1 Guido's Method 285
9.2 Methodology and Composition 288
9.3 Musimat: A Simple Programming Language for Music 290
9.4 Program for Guido's Method 291
9.5 Other Music Representation Systems 292
9.6 Delegating Choice 293
9.7 Randomness 299
9.8 Chaos and Determinism 304
9.9 Combinatorics 306
9.10 Atonality 311
9.11 Composing Functions 317
9.12 Traversing and Manipulating Musical Materials 319
9.13 Stochastic Techniques 332
9.14 Probability 333
9.15 Information Theory and the Mathematics of Expectation 343
9.16 Music, Information, and Expectation 347
9.17 Form in Unpredictability 350
9.18 Monte Carlo Methods 360
9.19 Markov Chains 363
9.20 Causality and Composition 371
9.21 Learning 372
9.22 Music and Connectionism 376
9.23 Representing Musical Knowledge 390
9.24 Next-Generation Musikalische Wuerfelspiel 400
9.25 Calculating Beauty 406
Appendix A 409
A.1 Exponents 409
A.2 Logarithms 409
A.3 Series and Summations 410
A.4 About Trigonometry 411
A.5 Xeno's Paradox 414
A.6 Modulo Arithmetic and Congruence 414
A.7 Whence 0.161 in Sabine's Equation? 416
A.8 Excerpts from Pope John XXII's Bull Regarding Church Music 418
A.9 Greek Alphabet 419
Appendix B 421
B.1 Musimat 421
B.2 Music Datatypes in Musimat 439
B.3 Unicode (ASCII) Character Codes 450
B.4 Operator Associativity and Precedence in Musimat 450
|
|
|
Powered by Associate-O-Matic
| |
