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

Cover
Contents
Preface
How to Use This Book
Acknowledgments
I: Sound Itself
	1 How Sound Propagates
		1.1 Push and Pushback: Impedance
			What Is Impedance, Really?
			Antireflection Strategies
			Impedance and the Violin
			Bullwhip—The High Art of Impedance Matching
			Impedance Mismatches Are Not Always Bad
			Impedance of Masses and Springs Together
			Defining and Measuring Impedance
		1.2 Impedance of Air
		1.3 Propagation of Sound in Pipes
			Reflection of Sound at a Closed End
			Reflection of Sound at an Open End
			Reflection of Sound at the Junction of Different-diameter Pipes
	2 Wave Phenomenology
		2.1 Relation between Speed, Frequency, and Wavelength
		2.2 Falloff with Distance from the Source
			Loudness Falloff with Distance
			Ripple Simulation
		2.3 Measuring the Speed of Sound
			Box 2.1 Father Marin Mersenne
		2.4 Interference and Superposition
			Active Noise Cancellation— Deliberate Destructive Interference
		2.5 Reflection
			Shiny and Matte
		2.6 Refraction
		2.7 Diffraction
			Diffraction at an Edge
			Brush with the Law of Similarity
			Active Noise Reduction of Diffracted Sound
		2.8 Schlieren Photography
		2.9 Ray Tracing
			Corner (Retro-) Reflector
			Box 2.2 The SOFAR Channel
		2.10 Measures of Sound Power
			Box 2.3 How Big?
	II: Analyzing Sound	#80,582,-5	3 Sound and Sinusoids
		3.1 The Atom of Sound
			Building a Sine Wave
		3.2 Sinusoidal Vibration
			The Velocity
			The Tuning Fork
			The Sound of a Sinusoid
		3.3 The Pendulum
		3.4 The Double Tuning Fork
		3.5 Microscopes for Vibration
		3.6 Spying on Conversations
		3.7 Fourier Decomposition
		3.8 Power Spectra
		3.9 Periodic Functions
		3.10 Aperiodic Signals and Vibrations
	4 The Power of Autocorrelation
		4.1 Obtaining Autocorrelation Functions
			Box 4.1 Autocorrelation Example: Temperature in Fairbanks
		4.2 Autocorrelation and Power for a Sum of Sinusoids
			Getting the Autocorrelation
			Computing the Power Spectrum
		4.3 Autocorrelation for Any Signal
			Computing the Autocorrelation
			Autocorrelation by Color
		4.4 Power Spectrum from a General Autocorrelation
			Power Spectrum by Color
			The Wiener-Khinchin Theorem
		4.5 The Uncertainty Principle
		4.6 Autocorrelation and the Chorus Effect
		4.7 Noise and Autocorrelation
			Autocorrelation and Fast Echoes
			Masking Signals with Noise
			Box 4.2 Famous Fourier Transform Pairs
	5 Sonograms
		5.1 What Is a Sonogram?
		5.2 Choosing Sonogram Parameters
	6 Capturing and Re-creating Sound
		6.1 Galileo—The First Recording?
		6.2 Phonautograph—Sound Trace
		6.3 Microphones and Loudspeakers
		6.4 Sound Reproduction Fidelity
			The Problem of Head Movement and Visual Concordance
			The Edison Diamond Disc Phonograph
		6.5 Digital Recording and Playback
		6.6 Impulse Response and the Re-creation of a Soundspace
III Making Sound
	8 Making a Stretched String
		8.1 Single Bead
			Tension and Force
			The Motion of the Bead
		8.2 Two Beads
			Box 8.1 Working with Loaded String
			The Sinusoid Reigns Supreme
		8.3 Three Beads
		8.4 Combining Modes
		8.5 More Beads
			The Sound and Spectrum of a Pluck
			Box 8.2 Spectrum for a Large Number of Beads
		8.6 Putting Shape and Time Together
		8.7 Combining Modes
		8.8 Traveling Waves on the String
			Standing versus Traveling Waves
			Fourier Again
			Ends and Boundaries
			Box 8.3 Experiment with Loaded String
			Periodic or Not?
		8.9 The Imperfect String
			Weighted String
			Real Strings
		8.10 Membranes as Stretched Bead-filament Systems
		8.11 A Metal Chair
		8.12 Decomposing Complex Vibrations
			Mersenne and Sauveur
	9 Resonance Rules
		9.1 Resonance and Constructive Interference
			Proximity Resonance Revisited
			Equivalent Viewpoints
			Generalizing Proximity Resonance to Any Constructive Addition
			Box 9.1 Echoes from Atoms
		9.2 Definition of Driven Resonance
			Remote versus Local Sources: Reciprocity
			Multiple Sources
			Autonomous Systems
			Box 9.2 Resonance and the Divine Harmony
	10 Damped and Driven Oscillation
		10.1 Friction and Work
		10.2 Friction and Decay
			Kicked Damped Oscillator
		10.3 Quality Factor Q
			Equivalent Definitions of Q
		10.4 Driving the Oscillator
			Frequency of the Driven System
		10.5 Resonance
			Phase of the Drive: Reactive versus Resistive Force
			Power near Resonance
		10.6 Impedance and Forced Oscillation
			Power, Impedance, and Admittance
			Oscillator versus Wave Resonance
			Driving a String
		10.7 Coupling of Two or More Oscillators
			Pure Modes
			Two Coupled Pendula of Different Frequency
		10.8 Tug-of-War: Resonance versus Damping
			A Physical Model
	11 Impulse Response
		11.1 Impulse and Power
			Five Easy Cases
			Power and Echo
		11.2 Average Power Theorem
			Caveat for Proximity Resonance
		11.3 Sculpting a Power Spectrum
			Echo, Resonance, and Q
			The Pop of a Cork and Its Echoes
			Sculpting Principle for Any Signal
	12 Impulse and Power for Complex Systems
		12.1 Mode Density
		12.2 Strength of Isolated Resonances
		12.3 Impulse and Power Spectrum in an Open Wedge
		12.4 High-Q Resonances: From Isolated to Densely Packed
		12.5 Schroeder Frequency
			Power Fluctuations above the Schroeder Frequency
			Statistics of the Fluctuations
			Statistics of the Wedge Spectrum
		12.6 Is a Piano Soundboard Resonant?
			Reverberant, Not Resonant
			Foiling Short-circuiting
	13 Helmholtz Resonators
		13.1 How Helmholtz Resonators Work
			Box 13.1 Deriving the Helmholtz Mode Frequency
			The Ocarina: Size but Not Shape
		13.2 Helmholtz Resonators and the Law of Similarity
			Higher Modes
			Ad Hominem Resonators
		13.3 Phase and Power
			Preresonance
			Postresonance
			On Resonance
		13.4 Resonance and Short-circuiting of Pairs of Resonators
		13.5 Helmholtz Resonance Amplification of Sound
			Resonance and Reciprocity
		13.6 Helmholtz Resonators at Work
			Resonators as Transducers for Sound
			Ported Loudspeakers
			Box 13.2 Sound Enhancement in Ancient Greece?
			Sound Attenuation
			Helmholtz Bass Traps
			Your Automobile as a Helmholtz Resonator
	14 Sound Generation by Vortices and Turbulence
		14.1 Vortex Streets
			Föppl Vortices
			Wagging, Shedding, and Sound Generation
		14.2 Resonant Vortex Shedding
			Entrainment
			Aeolian Harps Big and Small
		14.3 Reynolds Number
		14.4 Edge Tones
		14.5 Whistling—Ring and Slit Vortices
			Instability and Sensitivity
		14.6 What Is Happening in a Lip Whistle?
			Box 14.1 Experiment: Second Formant Resonance
		14.7 Sound from Turbulence
			Jet Noise
			Turbulence: Fricatives and Speech
			Box 14.2 Experiment: Speech Turbulence
		14.8 Other Sources of Noise
			Noise from Tires
	15 Membranes and Shells
		15.1 Networks of Strings
		15.2 Stretched Membranes
			Box 15.1 Paul Falstad\'s Stretched Membrane Applets
		15.3 Vibrations of Plates and Shells
		15.4 Chladni and the Era of Modern Acoustics
			Box 15.2 Chladni and Napoleon
		15.5 Baffling and Acoustic Short-circuiting
		15.6 Bowing a Metal Plate
		15.7 Belleplates
		15.8 Kettle Drums
	7 Sources of Sound
		7.1 Amplification without Active Amplifiers
			Walls as Passive Amplifiers
			Reactive versus Resistive Forces
		7.2 The Method of Images
			The 30-degree Wedge
		7.3 The Horn
			Ṣafī al-Dīn Gets It Right in the Thirteenth Century
			Low-frequency Piston Source
			Monopole Source in a Pipe
			Horns as Impedance Control
			The Mouth of the Horn
			The Shape of the Horn
			Box 7.1 The Exponential Horn
			Speaking Trumpets and Ear Trumpets
			Box 7.2 Horns through the Ages
		7.4 The Siren
			Software Siren
		7.5 Reciprocity of Sound Propagation
		7.6 Law of Similarity
		7.7 Dipole Sources
			Dipoles as Acoustical Short-circuiting
			Dipoles as Destructive Interference
			Example Dipole Sources
			Relative Phase of Loudspeakers
			Simulations of a Dipole Source
			Baffling a Dipole
		7.8 Tuning Fork—A Quadrupole Source
		7.9 Supersonic Sources
			Lightning and Thunder
		7.10 Sound Launched by Surfaces
			Sound Launched by a Baffled Piston
			Building Up Larger Pistons from Small Ones
			Force Goes in Phase with Velocity for Larger Pistons
		7.11 Sound Launched by Surface-bending Waves
			Supersonic versus Subsonic Surface Waves
			The Critical Frequency
			Sound Radiation Pattern from Surface Waves
			Box 7.3 Seneca Guns and Cookie Cutters
		7.12 Soundboards and Surface Sound Generation
			Box 7.4 The SST That Never Was
		7.13 Thermophones—Sound without Vibration
			Box 7.5 Sound That Won\'t Leave
		7.14 The ( Many) Other Sources of Sound
			The 95 dB Sun Chips Bag
IV: Musical Instruments
	16 Wind Instruments
		16.1 Propagation of Sound in Pipes—Continued
			Resonance in Tubes—Colored Echoes
			Wall Losses
			Box 16.1 Experiment: Resonance Frequencies and Wall Losses in a Tube
		16.2 Frequencies of Tube Modes
			Cylindrical Bore Tubes
			The Conical Bore
			The Inside-out Implosion
		16.3 The Trumpet
			Partials versus Resonances
			Shaping the Trumpet\'s Timbre and Playing Qualities
			The Mouthpiece Does Triple Duty
			The Bell Does Triple Duty
			Box 16.2 Gatekeeper Resonance Effect
			The Trouble with Treble Boost
			Box 16.3 The Horn Function
			The Battle between Resonance and Wall Friction
			Power in the Upper Partials—Up or Down When a Bell Is Added?
			The Lip Reed
			Understanding Nonlinearities: Benade\'s Water Trumpet
			Playing the Resonances on a Trumpet
			Other Factors: Vocal Tract
			Valves and Intonation
			The Natural Trumpet
		16.4 The Transverse Flute
			Impedance of a Flute
			The Flute Cork
			The Golden Flute
		16.5 The Clarinet
			Register Holes
			Toneholes
		16.6 The Saxophone
			The Saxophone Mouthpiece
		16.7 Blown Closed versus Blown Open
			Blown Closed
			Blown Open
		16.8 The Importance of Vocal Tract Resonances to Wind Instruments
			Tract Resonances and Payability
			Bending Down
	17 Voice
		17.1 Tubes That Change Diameter or Shape
			Constriction Yielding a Helmholtz Resonator
		17.2 The Source: Vocal Folds
		17.3 Formants
			Getting Q for Your Vocal Tract
		17.4 Sayonara Source-filter Model
		17.5 Formants and Vowels
		17.6 Formant Tuning in Singing
			Singer\'s Formant
		17.7 Multiphonics—Playing Two Notes at Once
		17.8 The Speaking Trumpet (Megaphone) Revisited
		17.9 Helium and SF6 Voice
		17.10 Vocal Disguise, Mimicry, and Gender Switching
		17.11 Fricatives and Other Sounds
		17.12 Organ Pipe—VoxHumana
	18 Violin
		18.1 Bowing, Stick-slip, and the Helmholtz Wave
			The Helmholtz Kink Wave
			Nonlinear Cooperative Resonance
			Inharmonic Strings
		18.2 The Bridge and the Bridge Hill
			Impulse on the Front Plate
		18.3 Science and the Violin
		18.4 Sound Radiation Patterns from a Violin
		18.5 Strad or Bust?
		18.6 The Helmholtz Air Mode
		18.7 The Wolf
		18.8 Summary of the Violin
		18.9 Nondestructive Modifications
			Breakdown of the Helmholtz Wave
	19 Piano
		19.1 The Railsback Curve
		19.2 Three Strings per Key
		19.3 The Hammer
			Where Should the Hammer Hit the String?
			Shape, Mass, and Texture
		19.4 Digital Piano
	20 Hybrid Musical Instruments
		20.1 Stroh Violin
		20.2 Aeolian Harp
		20.3 Trornba Marina
		20.4 Instruments Based on Near-field Capture (NFC)
			The Marimba
		20.5 Applying the NFC Mechanism
			Savart\'s Cup and Resonator
			Helmholtz Resonator Enhancement of a Tuning Fork
			Wind Chimes and the Javanese Angklung
			Other Hybrid and Unusual Musical Instruments
V: Psychoacoustics and Music
	21 Mechanisms of Hearing
		21.1 Anatomy of the Hearing System
		21.2 Outer Ear: Direction Detection
			Repetition Resonances and Antiresonances (Peaks and Notches)
		21.3 Middle Ear: Masterpiece of Impedance Transduction
			Lever Action
		21.4 Inner Ear: Masterpiece of Detection
			Initial Frequency Sorting
			Transduction to Nerve ImpuIses
			Amplification and Sharpening
			Sending Data to the Auditory Cortex
		21.5 The Bionic Ear
			Box 21.1 Resonance and the Ear
	22 Loudness
		22.1 Fechner\'s (Weber\'s) Law
		22.2 Equal Loudness Curves
		22.3 Masking
		22.4 Measuring Loudness
	23 Pitch Perception
		23.1 Overview
		23.2 Pitch Is Not Partial
		23.3 Pitch Is Not Periodicity
		23.4 Pitched Battles
		23.5 The Siren
		23.6 Ohm\'s Law
		23.7 Seebeck\'s Mistake
		23.8 Ohm\'s Blunder
		23.9 Helmholtz Falls Short
		23.10 A Dramatic Residue Pitch Effect
			Truth or Illusion?
		23.11 Autocorrelation and Pitch
		23.12 A Simple Formula for Pitch
		23.13 Examples: Autocorrelation and Pitch
		23.14 Seebeck\'s Pitch Experiments
			The Marquee Effect
		23.15 Shepard Tones
			Shepard Tones and Autocorrelation
		23.16 Chimes: Pitch without a Partial
			The Hosanna Bell in Freiburg
			Pitch of a Kettle Drum
		23.17 Repetition Pitch
			Huygens at Chantilly
			Temple of Kukulkan, Chichén Itzá
			Ground Reflections
		23.18 Quantifying Frequency
			Cents
			Just Noticeable Difference (JND)
			Time or Place?
		23.19 Pitch Class, the Octave Ambiguity, and Perfect Pitch
		23.20 Parsing and Persistence: Analytic versus Synthetic Hearing
		23.21 Deutsch\'s Octave Illusion
			Pitch and Loudness
		23.22 An Extended Definition of Pitch
	24 Timbre 480
		24.1 Timbre and Phase
			Shape Depends on Phase
			Ohm-Helmholtz Phase Law
			Rationale for Insensitivity to Relative Phase of Harmonic Partials
		24.2 Amplitude and Timbre Beats
			Generalizing the Concept of Beats
		24.3 Waveform Beats and the Phase Law
		24.4 The Perception of Waveform Beats
		24.5 A Dramatic Phase Sensitivity
		24.6 Timbre and Context
			Box 24.1 Helmholtz\'sand Koenig\'s Ingenious Tests of the Ohm-Helmholtz Phase Law
		24.7 Timbre, Loudness, and Shock waves
	25 Phantom Tones
		25.1 Lies and Illusions
		25.2 Sounds That Aren\'t There
			Hearing Phantom Tones
		25.3 How and Where Do Phantom Tones Arise?
			Mechanical Causes
			Neural Causes and the Auditory Cortex
		25.4 Beat Tones
			Phantom Loudness Beat Tones
			Examples of Beat Tones
		25.5 Nonlinear Harmonic Generation
			Box 25.1 Experiment in Nonlinear Harmonic Generation
			Box 25.2 Rudolph Koenig
	26 Dissonance and Temperament
		26.1 Critical Bands
			Autodissonance
		26.2 Figuring Dissonance
		26.3 Helmholtz Theory of Consonance and Dissonance
			Trouble with 7 and 11?
		26.4 The Impossible Perfection of Pythagoras
			The Perfect Fifth as the Basis for a Musical Scale
			Another Path to a Musical Scale
			Pythagorean Just Intonation
		26.5 The Pythagorean Comma
		26.6 The Circular Musical Scale and the Circle of Fifths
			The Wolf Fifth
		26.7 The Modern Solution: Equal Temperament
			The Barbershop Seventh—Just versus Equal
		26.8 Stretched Scales and Partials—Extreme Tests of Dissonance Theory
		26.9 Downshifting Chopin
VI: Soundspaces
	27 Modern Architectural Acoustics
		27.1 Rooms as Resonant Spaces
			Why Do Surfaces Absorb Sound?
			Coloring Sound with Walls
		27.2 W. C. Sabine and Architectural Acoustics
			The Right Questions
			Decay of Reverberations
			Box 27.1 Sabine\'s Experiments
		27.3 Understanding T60
			Box 27.2 Deriving the Sabine Reverberation Formula
			Rectangular Rooms and the Law of Similarity
			Strength G
			The Problem of Low Frequencies
		27.4 Diffusion by Walls
		27.5 Special Shapes
			Box 27.3 Acoustics of the Mormon Tabernacle
		27.6 Auditory Scene
		27.7 The Precedence Effect
			Electronic Enhancement in Concert Halls
		27.8 Blind Navigation in Spaces
		27.9 Frequency Response of Rooms and Concert Halls
			Power Spectrum and Mode Density
			Point-to-point Frequency-dependent Transmission
		27.10 Reverberation Timeline
		27.11 Best Hall Acoustics
		27.12 Acoustical Triumphs and Disasters
			Boston Symphony Hall
			Philharmonic Hall, New York
			Munich Philharmonic
	28 Sound Outdoors
		28.1 The Battle of Gaines Farm
		28.2 Long-range Sound Propagation in the Atmosphere
			Upwind versus Downwind
		28.3 Scintillating Sound
		28.4 Echoes
			The Mystery of the Harmonic Echo
			Flaws in Rayleigh\'s Arguments
			Sir William Henry Bragg Gets into the Act
Bibliography
Index
	A
	B
	C
	D
	E
	F
	G
	H
	I
	J
	K
	L
	M
	N
	O
	P
	Q
	R
	S
	T
	U
	V
	W
	X
	Y
	Z