Principles of Musical Acoustics

Transcription

1 William M. Hartmann Principles of Musical Acoustics ^Spr inger

2 Contents 1 Sound, Music, and Science The Source Transmission Receiver 3 2 Vibrations Mass and Spring Definitions How It Works Mathematical Representation Audible Frequencies 14 3 Vibrations Damping Natural Modes of Vibration Multimode Systems The Tuning Fork The Spectrum Resonance A Wet Example Breaking Glassware Sympathetic Strings 24 4 Instrumentation Transducers The Oscilloscope Analog'Scope and CRT Display Digital'Scopes and Liquid Crystal Displays Beyond the Basic Oscilloscope The Spectrum Analyzer The Frequency Counter The Function Generator Virtual Instrumentation 36 ix

3 x Contents 5 Sound Waves Polarization The Speed of Sound Supersonic Things Sound vs Light Sound Waves in Space and Time Sound Waves in More Than One Dimension of Space 47 6 Wave Properties Wave Addition Interference Beats Audio Analogies Generalization Reflection Refraction Diffraction Segregation 63 7 Standing Waves Standing Waves in General Standing Waves on a String The Guitar Player's Equation The Stretched String: Some Observations 72 8 Standing Waves in Pipes Pipe with Both Ends Open Pipe with One End Open and One End Closed Playing a Pipe Thinking Critically Open-End Corrections 80 9 Fourier Analysis and Synthesis The Sine Wave Complex Waves Periodicity The Sawtooth The Sounds Harmonic and Inharmonic Spectra, Periodic and Aperiodic Tones Continuous Spectra Sound Intensity Pressure, Power, and Intensity The Inverse Square Law Decibels Absolute vs Relative db 104

4 Contents xi 11 The Auditory System Auditory Anatomy The Outer Ear The Middle Ear The Inner Ear Ill The Semicircular Canals Auditory Function Outer Ear Function Middle Ear Function Inner Ear Function Beyond the Cochlea Hearing Impairments Loudness Perception Loudness Level Loudness Psychophysics Neural Firing Rate Excitation Patterns Complex Sounds Critical Band Pitch Pitch of Sine Tones: Place Theory Pitch: Timing Theory Pitch of a Complex Tone The Template Theory Pitch as an Interpretative Percept Absolute Pitch Localization of Sound Horizontal Plane Interaural Level Differences Interaural Time Differences Localization in the Vertical Median Plane The Precedence Effect Perceived Auditory Space Sound Environments Reflections from a Surface Transmission Loss Room Acoustics Early Reflections in a Room Focused Sound Reverberation Gaining Control of Acoustical Spaces 164

5 xii Contents 16 Audio Transducers Basic Definitions The Current and Magnetism Principle Application of the Current-Magnetism Principle The Analog Concept The Generator Principle The Motor Principle Electrostatic Devices Electro-Optical Transducers Distortion and Noise Noise Distortion Distortion Not Linear Distortion Nonlinear Distortion Dynamic Range Audio Systems Sound Recording Public Address System Preamplifier Power Amplifier Mixer Tone Controls and Equalizers Dynamic Range Compressor Integrated Amplifiers Receiver More Integration Multichannel Audio Loudspeakers Loudspeakers: What We Want The Two-Way Speaker Enclosures More About Loudspeaker Diffusion Powered Speakers Subwoofers Digital Audio Digital vs Analog Digital Noise Sampling Contemporary Digital Audio Broadcasting Continuous Wave Amplitude Modulation 221

6 Contents xiii 21.3 Frequency Modulation Bandwidth Carrier Frequencies Speech Vocal Anatomy Voiced Sounds Speech Sounds Spectrograms Brass Musical Instruments Sustained-Tone Instruments Evolution of the Resonances of a Trumpet Tone Production: Feedback and Nonhnearities Woodwind Instruments Single-Reed Instruments Double Reeds Reeds in General Edge Tone Instruments Boatswain's Pipe The Flute String Instruments Percussive Strings The Guitar The Electric Guitar The Piano Bowed Strings Tone Generation in the Bowed Strings The Violin Body Percussion Instruments Bars, Rods, and Tubes Useful Bars Useful Tubes Membranes Chladni Patterns Timpani Plates: Cymbals, Gongs, and Bells Nonlinear Mode Coupling Bells Electronic Music Analog Synthesizers Digital Synthesizers Musical Instrument Device Interface 284

7 xiv Contents Appendix A: Composers 287 Appendix B: Trigonometric Functions 289 Appendix C: Traditional Musical Instruments 291 Appendix D: Keyboard Tuning 293 Appendix E: Standard Musical Frequencies 297 Appendix F: Power Law Dependences 299 Appendix G: Telephone Tones 303 Appendix H: Greek Alphabet 305 Answers to Exercises 307 Index 345 i