Why You Hear What You Hear : An Experiential Approach to Sound, Music, and Psychoacoustics

This the first book on the physics of sound for the nonspecialist to empower readers with a hands-on, ears-open approach that includes production, analysis, and perception of sound. The book makes possible a deep intuitive understanding of many aspects of sound, as opposed to the usual approach of mere description. This goal is aided by hundreds of original illustrations and examples, many of which the reader can reproduce and adjust using the same tools used by the author. Readers are positioned to build intuition by participating in discovery. This introduction to sound engages and informs amateur and professional musicians, performers, teachers, sound engineers, students of many stripes, and indeed anyone interested in the auditory world. The book does not hesitate to follow entertaining and sometimes controversial side trips into the history and world of acoustics, reinforcing key concepts. You will discover how musical instruments really work, how pitch is perceived, and how sound can be amplified with no external power source.;I. Sound itself. How sound propagates -- Wave phenomenology -- II. Analyzing sound. Sound and sinusoids -- The power of autocorrelation -- Sonograms -- Capturing and re-creating sound -- III. Making sound. Sources of sound -- Making a stretched string -- Resonance rules -- Damped and driven oscillation -- Impulse response -- Impulse and power for complex systems -- Helmholtz resonators -- Sound generation by vortices and turbulence -- Membranes and shells -- IV. Musical instruments. Wind instruments -- Voice -- Violin -- Piano -- Hybrid musical instruments -- V. Psychoacoustics and music. Mechanisms of hearing -- Loudness -- Pitch perception -- Timbre -- Phantom tones -- Dissonance and temperament -- VI. Soundspaces. Modern architectural acoustics -- Sound outdoors. Cover 1 Contents 8 Preface 20 How to Use This Book 24 Acknowledgments 28 I: Sound Itself 32 1 How Sound Propagates 34 1.1 Push and Pushback: Impedance 37 What Is Impedance, Really? 39 Antireflection Strategies 40 Impedance and the Violin 41 Bullwhip—The High Art of Impedance Matching 42 Impedance Mismatches Are Not Always Bad 42 Impedance of Masses and Springs Together 43 Defining and Measuring Impedance 43 1.2 Impedance of Air 44 1.3 Propagation of Sound in Pipes 47 Reflection of Sound at a Closed End 48 Reflection of Sound at an Open End 48 Reflection of Sound at the Junction of Different-diameter Pipes 50 2 Wave Phenomenology 52 2.1 Relation between Speed, Frequency, and Wavelength 52 2.2 Falloff with Distance from the Source 54 Loudness Falloff with Distance 55 Ripple Simulation 56 2.3 Measuring the Speed of Sound 57 Box 2.1 Father Marin Mersenne 58 2.4 Interference and Superposition 58 Active Noise Cancellation— Deliberate Destructive Interference 60 2.5 Reflection 60 Shiny and Matte 61 2.6 Refraction 63 2.7 Diffraction 65 Diffraction at an Edge 66 Brush with the Law of Similarity 67 Active Noise Reduction of Diffracted Sound 68 2.8 Schlieren Photography 69 2.9 Ray Tracing 70 Corner (Retro-) Reflector 71 Box 2.2 The SOFAR Channel 74 2.10 Measures of Sound Power 75 Box 2.3 How Big? 78 II: Analyzing Sound 80 3 Sound and Sinusoids 82 3.1 The Atom of Sound 83 Building a Sine Wave 83 3.2 Sinusoidal Vibration 85 The Velocity 86 The Tuning Fork 87 The Sound of a Sinusoid 89 3.3 The Pendulum 89 3.4 The Double Tuning Fork 90 3.5 Microscopes for Vibration 93 3.6 Spying on Conversations 95 3.7 Fourier Decomposition 95 3.8 Power Spectra 97 3.9 Periodic Functions 99 3.10 Aperiodic Signals and Vibrations 100 4 The Power of Autocorrelation 102 4.1 Obtaining Autocorrelation Functions 105 Box 4.1 Autocorrelation Example: Temperature in Fairbanks 103 4.2 Autocorrelation and Power for a Sum of Sinusoids 105 Getting the Autocorrelation 105 Computing the Power Spectrum 107 4.3 Autocorrelation for Any Signal 107 Computing the Autocorrelation 108 Autocorrelation by Color 108 4.4 Power Spectrum from a General Autocorrelation 110 Power Spectrum by Color 112 The Wiener-Khinchin Theorem 113 4.5 The Uncertainty Principle 113 4.6 Autocorrelation and the Chorus Effect 116 4.7 Noise and Autocorrelation 118 Autocorrelation and Fast Echoes 118 Masking Signals with Noise 118 Box 4.2 Famous Fourier Transform Pairs 119 5 Sonograms 120 5.1 What Is a Sonogram? 120 5.2 Choosing Sonogram Parameters 122 6 Capturing and Re-creating Sound 124 6.1 Galileo—The First Recording? 124 6.2 Phonautograph—Sound Trace 126 6.3 Microphones and Loudspeakers 128 6.4 Sound Reproduction Fidelity 129 The Problem of Head Movement and Visual Concordance 130 The Edison Diamond Disc Phonograph 130 6.5 Digital Recording and Playback 131 6.6 Impulse Response and the Re-creation of a Soundspace 134 III Making Sound 136 8 Making a Stretched String 196 8.1 Single Bead 198 Tension and Force 198 The Motion of the Bead 199 8.2 Two Beads 200 Box 8.1 Working with Loaded String 200 The Sinusoid Reigns Supreme 201 8.3 Three Beads 202 8.4 Combining Modes 203 8.5 More Beads 203 The Sound and Spectrum of a Pluck 204 Box 8.2 Spectrum for a Large Number of Beads 207 8.6 Putting Shape and Time Together 209 8.7 Combining Modes 210 8.8 Traveling Waves on the String 211 Standing versus Traveling Waves 212 Fourier Again 212 Ends and Boundaries 212 Box 8.3 Experiment with Loaded String 213 Periodic or Not? 214 8.9 The Imperfect String 215 Weighted String 215 Real Strings 216 8.10 Membranes as Stretched Bead-filament Systems 216 8.11 A Metal Chair 218 8.12 Decomposing Complex Vibrations 218 Mersenne and Sauveur 219 9 Resonance Rules 222 9.1 Resonance and Constructive Interference 223 Proximity Resonance Revisited 223 Equivalent Viewpoints 223 Generalizing Proximity Resonance to Any Constructive Addition 224 Box 9.1 Echoes from Atoms 226 9.2 Definition of Driven Resonance 227 Remote versus Local Sources: Reciprocity 228 Multiple Sources 229 Autonomous Systems 229 Box 9.2 Resonance and the Divine Harmony 230 10 Damped and Driven Oscillation 233 10.1 Friction and Work 233 10.2 Friction and Decay 234 Kicked Damped Oscillator 235 10.3 Quality Factor Q 235 Equivalent Definitions of Q 235 10.4 Driving the Oscillator 238 Frequency of the Driven System 240 10.5 Resonance 240 Phase of the Drive: Reactive versus Resistive Force 240 Power near Resonance 242 10.6 Impedance and Forced Oscillation 243 Power, Impedance, and Admittance 244 Oscillator versus Wave Resonance 245 Driving a String 246 10.7 Coupling of Two or More Oscillators 247 Pure Modes 247 Two Coupled Pendula of Different Frequency 249 10.8 Tug-of-War: Resonance versus Damping 252 A Physical Model 254 11 Impulse Response 256 11.1 Impulse and Power 257 Five Easy Cases 257 Power and Echo 260 11.2 Average Power Theorem 262 Caveat for Proximity Resonance 263 11.3 Sculpting a Power Spectrum 263 Echo, Resonance, and Q 265 The Pop of a Cork and Its Echoes 266 Sculpting Principle for Any Signal 269 12 Impulse and Power for Complex Systems 270 12.1 Mode Density 270 12.2 Strength of Isolated Resonances 271 12.3 Impulse and Power Spectrum in an Open Wedge 272 12.4 High-Q Resonances: From Isolated to Densely Packed 276 12.5 Schroeder Frequency 277 Power Fluctuations above the Schroeder Frequency 278 Statistics of the Fluctuations 278 Statistics of the Wedge Spectrum 280 12.6 Is a Piano Soundboard Resonant? 281 Reverberant, Not Resonant 282 Foiling Short-circuiting 284 13 Helmholtz Resonators 286 13.1 How Helmholtz Resonators Work 286 Box 13.1 Deriving the Helmholtz Mode Frequency 288 The Ocarina: Size but Not Shape 288 13.2 Helmholtz Resonators and the Law of Similarity 289 Higher Modes 291 Ad Hominem Resonators 291 13.3 Phase and Power 292 Preresonance 293 Postresonance 293 On Resonance 294 13.4 Resonance and Short-circuiting of Pairs of Resonators 295 13.5 Helmholtz Resonance Amplification of Sound 297 Resonance and Reciprocity 297 13.6 Helmholtz Resonators at Work 297 Resonators as Transducers for Sound 298 Ported Loudspeakers 299 Box 13.2 Sound Enhancement in Ancient Greece? 299 Sound Attenuation 301 Helmholtz Bass Traps 302 Your Automobile as a Helmholtz Resonator 303 14 Sound Generation by Vortices and Turbulence 304 14.1 Vortex Streets 304 Föppl Vortices 305 Wagging, Shedding, and Sound Generation 305 14.2 Resonant Vortex Shedding 307 Entrainment 308 Aeolian Harps Big and Small 309 14.3 Reynolds Number 309 14.4 Edge Tones 310 14.5 Whistling—Ring and Slit Vortices 312 Instability and Sensitivity 312 14.6 What Is Happening in a Lip Whistle? 312 Box 14.1 Experiment: Second Formant Resonance 315 14.7 Sound from Turbulence 316 Jet Noise 316 Turbulence: Fricatives and Speech 317 Box 14.2 Experiment: Speech Turbulence 318 14.8 Other Sources of Noise 318 Noise from Tires 319 15 Membranes and Shells 320 15.1 Networks of Strings 320 15.2 Stretched Membranes 321 Box 15.1 Paul Falstad's Stretched Membrane Applets 321 15.3 Vibrations of Plates and Shells 323 15.4 Chladni and the Era of Modern Acoustics 323 Box 15.2 Chladni and Napoleon 326 15.5 Baffling and Acoustic Short-circuiting 327 15.6 Bowing a Metal Plate 328 15.7 Belleplates 329 15.8 Kettle Drums 330 7 Sources of Sound 138 7.1 Amplification without Active Amplifiers 139 Walls as Passive Amplifiers 140 Reactive versus Resistive Forces 141 7.2 The Method of Images 142 The 30-degree Wedge 143 7.3 The Horn 145 Ṣafī al-Dīn Gets It Right in the Thirteenth Century 145 Low-frequency Piston Source 147 Monopole Source in a Pipe 148 Horns as Impedance Control 148 The Mouth of the Horn 149 The Shape of the Horn 149 Box 7.1 The Exponential Horn 150 Speaking Trumpets and Ear Trumpets 151 Box 7.2 Horns through the Ages 152 7.4 The Siren 156 Software Siren 158 7.5 Reciprocity of Sound Propagation 159 7.6 Law of Similarity 161 7.7 Dipole Sources 162 Dipoles as Acoustical Short-circuiting 163 Dipoles as Destructive Interference 163 Example Dipole Sources 164 Relative Phase of Loudspeakers 165 Simulations of a Dipole Source 166 Baffling a Dipole 167 7.8 Tuning Fork—A Quadrupole Source 168 7.9 Supersonic Sources 169 Lightning and Thunder 173 7.10 Sound Launched by Surfaces 173 Sound Launched by a Baffled Piston 174 Building Up Larger Pistons from Small Ones 175 Force Goes in Phase with Velocity for Larger Pistons 176 7.11 Sound Launched by Surface-bending Waves 177 Supersonic versus Subsonic Surface Waves 179 The Critical Frequency 180 Sound Radiation Pattern from Surface Waves 181 Box 7.3 Seneca Guns and Cookie Cutters 184 7.12 Soundboards and Surface Sound Generation 189 Box 7.4 The SST That Never Was 190 7.13 Thermophones—Sound without Vibration 192 Box 7.5 Sound That Won't Leave 193 7.14 The ( Many) Other Sources of Sound 194 The 95 dB Sun Chips Bag 194 IV: Musical Instruments 334 16 Wind Instruments 336 16.1 Propagation of Sound in Pipes—Continued 336 Resonance in Tubes—Colored Echoes 337 Wall Losses 338 Box 16.1 Experiment: Resonance Frequencies and Wall Losses in a Tube 339 16.2 Frequencies of Tube Modes 340 Cylindrical Bore Tubes 340 The Conical Bore 343 The Inside-out Implosion 343 16.3 The Trumpet 346 Partials versus Resonances 346 Shaping the Trumpet's Timbre and Playing Qualities 347 The Mouthpiece Does Triple Duty 348 The Bell Does Triple Duty 351 Box 16.2 Gatekeeper Resonance Effect 351 The Trouble with Treble Boost 353 Box 16.3 The Horn Function 353 The Battle between Resonance and Wall Friction 356 Power in the Upper Partials—Up or Down When a Bell Is Added? 358 The Lip Reed 361 Understanding Nonlinearities: Benade's Water Trumpet 363 Playing the Resonances on a Trumpet 365 Other Factors: Vocal Tract 367 Valves and Intonation 367 The Natural Trumpet 367 16.4 The Transverse Flute 368 Impedance of a Flute 368 The Flute Cork 369 The Golden Flute 371 16.5 The Clarinet 372 Register Holes 373 Toneholes 374 16.6 The Saxophone 376 The Saxophone Mouthpiece 377 16.7 Blown Closed versus Blown Open 377 Blown Closed 378 Blown Open 379 16.8 The Importance of Vocal Tract Resonances to Wind Instruments 380 Tract Resonances and Payability 380 Bending Down 381 17 Voice 383 17.1 Tubes That Change Diameter or Shape 383 Constriction Yielding a Helmholtz Resonator 386 17.2 The Source: Vocal Folds 387 17.3 Formants 389 Getting Q for Your Vocal Tract 390 17.4 Sayonara Source-filter Model 391 17.5 Formants and Vowels 392 17.6 Formant Tuning in Singing 393 Singer's Formant 393 17.7 Multiphonics—Playing Two Notes at Once 396 17.8 The Speaking Trumpet (Megaphone) Revisited 398 17.9 Helium and SF6 Voice 400 17.10 Vocal Disguise, Mimicry, and Gender Switching 401 17.11 Fricatives and Other Sounds 403 17.12 Organ Pipe—VoxHumana 403 18 Violin 405 18.1 Bowing, Stick-slip, and the Helmholtz Wave 406 The Helmholtz Kink Wave 407 Nonlinear Cooperative Resonance 409 Inharmonic Strings 411 18.2 The Bridge and the Bridge Hill 411 Impulse on the Front Plate 414 18.3 Science and the Violin 415 18.4 Sound Radiation Patterns from a Violin 416 18.5 Strad or Bust? 417 18.6 The Helmholtz Air Mode 419 18.7 The Wolf 420 18.8 Summary of the Violin 421 18.9 Nondestructive Modifications 421 Breakdown of the Helmholtz Wave 422 19 Piano 423 19.1 The Railsback Curve 424 19.2 Three Strings per Key 426 19.3 The Hammer 427 Where Should the Hammer Hit the String? 428 Shape, Mass, and Texture 429 19.4 Digital Piano 429 20 Hybrid Musical Instruments 431 20.1 Stroh Violin 431 20.2 Aeolian Harp 432 20.3 Trornba Marina 434 20.4 Instruments Based on Near-field Capture (NFC) 434 The Marimba 435 20.5 Applying the NFC Mechanism 439 Savart's Cup and Resonator 440 Helmholtz Resonator Enhancement of a Tuning Fork 440 Wind Chimes and the Javanese Angklung 441 Other Hybrid and Unusual Musical Instruments 443 V: Psychoacoustics and Music 444 21 Mechanisms of Hearing 446 21.1 Anatomy of the Hearing System 447 21.2 Outer Ear: Direction Detection 448 Repetition Resonances and Antiresonances (Peaks and Notches) 449 21.3 Middle Ear: Masterpiece of Impedance Transduction 450 Lever Action 451 21.4 Inner Ear: Masterpiece of Detection 453 Initial Frequency Sorting 453 Transduction to Nerve ImpuIses 455 Amplification and Sharpening 455 Sending Data to the Auditory Cortex 456 21.5 The Bionic Ear 457 Box 21.1 Resonance and the Ear 459 22 Loudness 462 22.1 Fechner's (Weber's) Law 462 22.2 Equal Loudness Curves 463 22.3 Masking 465 22.4 Measuring Loudness 466 23 Pitch Perception 468 23.1 Overview 468 23.2 Pitch Is Not Partial 469 23.3 Pitch Is Not Periodicity 471 23.4 Pitched Battles 471 23.5 The Siren 473 23.6 Ohm's Law 474 23.7 Seebeck's Mistake 475 23.8 Ohm's Blunder 475 23.9 Helmholtz Falls Short 476 23.10 A Dramatic Residue Pitch Effect 478 Truth or Illusion? 480 23.11 Autocorrelation and Pitch 480 23.12 A Simple Formula for Pitch 481 23.13 Examples: Autocorrelation and Pitch 484 23.14 Seebeck's Pitch Experiments 487 The Marquee Effect 489 23.15 Shepard Tones 490 Shepard Tones and Autocorrelation 492 23.16 Chimes: Pitch without a Partial 494 The Hosanna Bell in Freiburg 495 Pitch of a Kettle Drum 496 23.17 Repetition Pitch 497 Huygens at Chantilly 498 Temple of Kukulkan, Chichén Itzá 499 Ground Reflections 500 23.18 Quantifying Frequency 503 Cents 503 Just Noticeable Difference (JND) 504 Time or Place? 504 23.19 Pitch Class, the Octave Ambiguity, and Perfect Pitch 506 23.20 Parsing and Persistence: Analytic versus Synthetic Hearing 507 23.21 Deutsch's Octave Illusion 508 Pitch and Loudness 509 23.22 An Extended Definition of Pitch 509 24 Timbre 480 511 24.1 Timbre and Phase 511 Shape Depends on Phase 511 Ohm-Helmholtz Phase Law 512 Rationale for Insensitivity to Relative Phase of Harmonic Partials 513 24.2 Amplitude and Timbre Beats 514 Generalizing the Concept of Beats 515 24.3 Waveform Beats and the Phase Law 515 24.4 The Perception of Waveform Beats 518 24.5 A Dramatic Phase Sensitivity 519 24.6 Timbre and Context 520 Box 24.1 Helmholtz'sand Koenig's Ingenious Tests of the Ohm-Helmholtz Phase Law 521 24.7 Timbre, Loudness, and Shock waves 523 25 Phantom Tones 524 25.1 Lies and Illusions 524 25.2 Sounds That Aren't There 526 Hearing Phantom Tones 526 25.3 How and Where Do Phantom Tones Arise? 527 Mechanical Causes 527 Neural Causes and the Auditory Cortex 528 25.4 Beat Tones 530 Phantom Loudness Beat Tones 530 Examples of Beat Tones 531 25.5 Nonlinear Harmonic Generation 532 Box 25.1 Experiment in Nonlinear Harmonic Generation 533 Box 25.2 Rudolph Koenig 534 26 Dissonance and Temperament 536 26.1 Critical Bands 538 Autodissonance 539 26.2 Figuring Dissonance 541 26.3 Helmholtz Theory of Consonance and Dissonance 543 Trouble with 7 and 11? 546 26.4 The Impossible Perfection of Pythagoras 547 The Perfect Fifth as the Basis for a Musical Scale 547 Another Path to a Musical Scale 549 Pythagorean Just Intonation 550 26.5 The Pythagorean Comma 551 26.6 The Circular Musical Scale and the Circle of Fifths 553 The Wolf Fifth 554 26.7 The Modern Solution: Equal Temperament 555 The Barbershop Seventh—Just versus Equal 557 26.8 Stretched Scales and Partials—Extreme Tests of Dissonance Theory 558 26.9 Downshifting Chopin 559 VI: Soundspaces 562 27 Modern Architectural Acoustics 564 27.1 Rooms as Resonant Spaces 564 Why Do Surfaces Absorb Sound? 567 Coloring Sound with Walls 568 27.2 W. C. Sabine and Architectural Acoustics 568 The Right Questions 569 Decay of Reverberations 570 Box 27.1 Sabine's Experiments 571 27.3 Understanding T60 571 Box 27.2 Deriving the Sabine Reverberation Formula 573 Rectangular Rooms and the Law of Similarity 576 Strength G 577 The Problem of Low Frequencies 579 27.4 Diffusion by Walls 579 27.5 Special Shapes 581 Box 27.3 Acoustics of the Mormon Tabernacle 582 27.6 Auditory Scene 582 27.7 The Precedence Effect 583 Electronic Enhancement in Concert Halls 584 27.8 Blind Navigation in Spaces 585 27.9 Frequency Response of Rooms and Concert Halls 586 Power Spectrum and Mode Density 586 Point-to-point Frequency-dependent Transmission 587 27.10 Reverberation Timeline 590 27.11 Best Hall Acoustics 591 27.12 Acoustical Triumphs and Disasters 591 Boston Symphony Hall 592 Philharmonic Hall, New York 592 Munich Philharmonic 594 28 Sound Outdoors 595 28.1 The Battle of Gaines Farm 595 28.2 Long-range Sound Propagation in the Atmosphere 596 Upwind versus Downwind 598 28.3 Scintillating Sound 600 28.4 Echoes 602 The Mystery of the Harmonic Echo 603 Flaws in Rayleigh's Arguments 605 Sir William Henry Bragg Gets into the Act 606 Bibliography 610 Index 614 A 614 B 614 C 615 D 615 E 615 F 615 G 616 H 616 I 616 J 616 K 616 L 616 M 617 N 617 O 617 P 617 Q 618 R 618 S 618 T 620 U 620 V 620 W 620 X 621 Y 621 Z 621 A groundbreaking textbook that explores the phenomena and physics of music and sound Why You Hear What You Hear is the first book on the physics of sound for the nonspecialist to empower readers with a hands-on, ears-open approach that includes production, analysis, and perception of sound. The book makes possible a deep intuitive understanding of many aspects of sound, as opposed to the usual approach of mere description. This goal is aided by hundreds of original illustrations and examples, many of which the reader can reproduce and adjust using the same tools used by the author (e.g., very accessible applets for PC and Mac, and interactive web-based examples, simulations, and analysis tools that can be found on the book's website: whyyouhearwhatyouhear.com). Readers are positioned to build intuition by participating in discovery. This truly progressive introduction to sound engages and informs amateur and professional musicians, performers, teachers, sound engineers, students of many stripes, and indeed anyone interested in the auditory world. The book does not hesitate to follow entertaining and sometimes controversial side trips into the history and world of acoustics, reinforcing key concepts. You will discover how musical instruments really work, how pitch is perceived, and how sound can be amplified with no external power source. Sound is key to our lives, and is the most accessible portal to the vibratory universe. This book takes you there. The first book on sound to offer interactive tools, building conceptual understanding via an experiential approach Supplementary website (http: //(http://www.whyyouhearwhatyouhear.com) www.whyyouhearwhatyouhear.com ) provides Java, MAX, and other free, multiplatform, interactive graphical and sound applets Extensive selection of original exercises available on the web with solutions Nearly 400 full-color illustrations, many of simulations that students can do

Why You Hear What You Hear is the first book on the physics of sound for the nonspecialist to empower readers with a hands-on, ears-open approach that includes production, analysis, and perception of sound. The book makes possible a deep intuitive understanding of many aspects of sound, as opposed to the usual approach of mere description. This goal is aided by hundreds of original illustrations and examples, many of which the reader can reproduce and adjust using the same tools used by the author (e.g., very accessible applets for PC and Mac, and interactive web-based examples, simulations, and analysis tools will be found on the book's website: whyyouhearwhatyouhear.com. Readers are positioned to build intuition by participating in discovery.

This truly progressive introduction to sound engages and informs amateur and professional musicians, performers, teachers, sound engineers, students of many stripes, and indeed anyone interested in the auditory world. The book does not hesitate to follow entertaining and sometimes controversial side trips into the history and world of acoustics, reinforcing key concepts. You will discover how musical instruments really work, how pitch is perceived, and how sound can be amplified with no external power source.

Sound is key to our lives, and is the most accessible portal to the vibratory universe. This book takes you there.

• The first book on sound to offer interactive tools, building conceptual understanding via an experiential approach
• Supplementary website (http://www.whyyouhearwhatyouhear.com) will provide Java, MAX, and other free, multiplatform, interactive graphical and sound applets
• Extensive selection of original exercises available on the web with solutions
• Nearly 400 full-color illustrations, many of simulations that students can do