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