The Science of Brass Instruments

Preface
Acknowledgements
Contents
Part I The Musician's Experience and the Scientific Perspective
	1 The Musician's Experience of Brass Instruments
		1.1 Creating Music from Lip Vibration: Labrosones Through the Ages
			1.1.1 Labrosones from Found Objects
			1.1.2 Early Metal Labrosones
			1.1.3 Labrosones in Renaissance and Baroque Music
			1.1.4 The Nineteenth-Century Labrosone Revolution
		1.2 The Musician's Interpretation of the Brass Playing Experience
			1.2.1 Musical Pitch Notation
			1.2.2 Natural Notes  and Harmonics:  The Musician's View
			1.2.3 Nominal Pitches of Brass Instruments
			1.2.4 Compass
			1.2.5 Intonation Control
			1.2.6 Dynamic Range
			1.2.7 Timbre
			1.2.8 Blowing Pressure and Air Flow
			1.2.9 Resistance and Playing Effort
			1.2.10 Responsiveness and Rapid Articulation
			1.2.11 Wrap, Directivity and Ergonomics
		1.3 Subjective and Objective Evaluation of Brass Instrument Quality
			1.3.1 Sound Quality and Playability
			1.3.2 Descriptive Terms Used by Musicians to Describe Brass Instrument Behaviour
			1.3.3 Biases in Quality Evaluation of Musical Instruments
	2 The Scientist's Perspective on Brass Instrument Behaviour
		2.1 Scientific Measurements of Brass Instrument Behaviour
			2.1.1 Sound Radiated from a Brass Instrument
			2.1.2 Sound Measured Inside a Trombone Mouthpiece
			2.1.3 Pressure Measured Inside a Brass Player's Mouth
			2.1.4 Lip Vibration and Air Flow: The Valve Effect Sound Source
			2.1.5 Is Air Flow Through the Instrument Tube Important?
			2.1.6 Is Sound Radiation from the Vibrating Bell Important?
			2.1.7 Warming Up a Brass Instrument
		2.2 An Approach to Modelling Brass Instruments
			2.2.1 The Scientific Case for Simplified Models
			2.2.2 Coupled Systems and Feedback Loops
			2.2.3 Natural Notes and Harmonics: The Scientific View
			2.2.4 Self-Sustained Oscillations
			2.2.5 The Wind Instrument Paradox
Part II Acoustical Modelling of Brasswinds
	3 Buzzing Lips: Sound Generation in Brass Instruments
		3.1 The Nature of Lip Vibration
			3.1.1 The Brass Player's Embouchure
			3.1.2 Experimental Studies of Vibrating Lips
			3.1.3 Time Dependence of the Lip Opening Area
			3.1.4 The Lip Opening Area-Height Function
			3.1.5 Two-Dimensional Motion of the Brass Player's Lips
			3.1.6 Experiments with Artificial Lips
		3.2 An Equation of Motion for the Lips
			3.2.1 A One-Mass Model of the Lips
			3.2.2 The Sliding Door Lip Model
			3.2.3 The Swinging Door Lip Model
			3.2.4 Inward-Striking and Outward-Striking Reeds
		3.3 The Mechanical Response of the Vibrating Lips
			3.3.1 Resonances of Artificial Lips
			3.3.2 Resonances of Human Lips
		3.4 Why Do the Lips Buzz?
		3.5 Volume Flow in Buzzing Lips
			3.5.1 Acoustic Volume Flow Through the Lip Aperture
			3.5.2 Acoustic Volume Flow Equation
	4 After the Lips: Acoustic Resonances and Radiation
		4.1 Internal Sounds in Brass Instruments
			4.1.1 Lumped and Distributed Resonators
			4.1.2 Travelling Waves
			4.1.3 Standing Waves
			4.1.4 Frequency Domain and Time Domain
			4.1.5 Impulse Response and Reflection Function
			4.1.6 Input Impedance
		4.2 Measuring Input Impedance
			4.2.1 Capillary-Based Methods
			4.2.2 Complementary Cavity Methods
			4.2.3 Wave Separation Methods
			4.2.4 Acoustic Pulse Reflectometry
		4.3 Bore Profiles of Brass Instruments
			4.3.1 Different Parts of the Bore
			4.3.2 Cylindrical Tubes
			4.3.3 Conical Tubes
			4.3.4 Equivalent Fundamental Pitch and Equivalent Cone Length
			4.3.5 The Mouthpiece as a Helmholtz Resonator
			4.3.6 Mouthpiece Effects on Intonation and Timbre
			4.3.7 Sound Waves in Flaring Bells
			4.3.8 A Theoretical Example: The Bessel Horn
			4.3.9 A Practical Example: The Complete Trombone
			4.3.10 Instruments with Predominantly Expanding Bore Profiles
		4.4 Toneholes
		4.5 Mutes
			4.5.1 Straight Mutes
			4.5.2 Effects of Internal Resonances in the Straight Mute
			4.5.3 Harmon Mute
			4.5.4 Plunger and Cup Mutes
			4.5.5 Transposing Mutes
			4.5.6 Hand Technique on the Horn
		4.6 Radiation of Sound from Brass Instruments
			4.6.1 Near Field and Far Field
			4.6.2 Monopole Radiation
			4.6.3 Transition from Internal to External Sound Fields
			4.6.4 Mapping the Radiation Fields of Brass Instruments
			4.6.5 Visualising Wavefronts with Schlieren Optics
			4.6.6 Far Field Directivity in Brass Instruments
		4.7 Going Further: Calculating Input Impedance
			4.7.1 Analytical Calculations
			4.7.2 Lossless Plane Wave TMM Calculations
			4.7.3 Including Losses in TMM Calculations
			4.7.4 TMM with Non-Cylindrical Elements
			4.7.5 Radiation Impedance
			4.7.6 Multimodal Calculations
			4.7.7 Bends in Brass Instruments
		4.8 Going Further: The Wogram Sum Function
	5 Blow That Horn: An Elementary Model of Brass Playing
		5.1 The Three Equations of the Brass Instrument Model
			5.1.1 The First Constituent Equation: Lip Dynamics
			5.1.2 The Second Constituent Equation: Flow Conditions
			5.1.3 The Third Constituent Equation: Instrument Acoustics
		5.2 Crossing the Threshold: Small Amplitude Oscillating Solutions
			5.2.1 Phase Relationships in the Lip Valve
			5.2.2 Silence or Sound? Stability Analysis of Brass Instruments
		5.3 Beyond Pianissimo: Modelling Realistic Playing Amplitudes
			5.3.1 Analysis of Brass Performance Using Simulations
			5.3.2 Bifurcation Diagrams
		5.4 Going Further: From Linear Stability Analysis to Oscillation Regimes
			5.4.1 Introduction: A Van der Pol Self-Sustained Oscillator
			5.4.2 State-Space Representations of the Elementary Brass Playing Model
			5.4.3 Linear Stability Analysis Applied to Brass Instruments
			5.4.4 The Trombone Pedal Note Regime
			5.4.5 Bifurcation Diagrams of Reed and Brass Instruments
			5.4.6 Multiphonics
	6 Shocks and Surprises: Refining the Elementary Model
		6.1 Why Brass Instruments Sound Brassy
			6.1.1 Brassy Sounds in Music
			6.1.2 Experimental Evidence for Shock Waves in Brass Instruments
			6.1.3 To Infinity and Beyond: Nonlinear Propagation in Tubes
			6.1.4 The Brassiness Potential Parameter
			6.1.5 Elephants, Exhausts and Angels: Some Surprising Sources of Brassy Sounds
		6.2 Going Further: Nonlinear Propagation
			6.2.1 From the Fundamental Fluid Dynamic Equations to the Nonlinear Wave Propagation Equation
			6.2.2 The Burgers Equations
			6.2.3 Brassiness of Flaring Bells
		6.3 The Player's Windway
			6.3.1 Coupling of Upstream and Downstream Resonances
			6.3.2 Tuning of Windway Impedance Peaks
			6.3.3 Other Effects of the Player's Windway
			6.3.4 Respiratory Control
		6.4 Improving the Lip Model
			6.4.1 Evidence from Mechanical Response Measurements
			6.4.2 Evidence from Measurements of Threshold Playing Parameters
			6.4.3 Models with More Than One Degree of Freedom
		6.5 Playing Frequencies of Brass Instruments
		6.6 The Influence of Wall Material on Brass Instrument Performance
			6.6.1 Factors Affecting the Choice of Wall Material
			6.6.2 Experimental Studies of Brass Instrument Wall Vibrations
			6.6.3 Pathological Wall Vibration Effects in Wind Instruments
			6.6.4 Frequency-Localised and Broadband Effects of Structural Resonances in Brass Instruments
			6.6.5 Mechanical Vibration at the Lip-Mouthpiece Interface
		6.7 Going Further: Analytical Modelling of Vibroacoustic Coupling in Ducts
			6.7.1 Basic Vibroacoustic Theory
			6.7.2 Effect of Vibroacoustic Coupling on Input Impedance
			6.7.3 Some Experimental Tests of Vibroacoustic Modelling
Part III Historical Evolution and Taxonomy of Brass Instruments
	7 The Amazing Diversity of Brass Instruments
		7.1 What Are Important Features of Brass Instruments?
			7.1.1 Taxonomic Labels Based on Tube Length
			7.1.2 Bore Profile and Brassiness
		7.2 The Different Kinds of Brass Instrument
			7.2.1 Instruments with the Shortest Tube Lengths
			7.2.2 Instruments with Very Short Tube Lengths in C and B
			7.2.3 Instruments with Short Tube Lengths in G, F, E and D
			7.2.4 Instruments with Short Tube Lengths in C and B
			7.2.5 Instruments with Medium Tube Lengths in G, F, E and D
			7.2.6 Instruments with Long Tube Lengths in C and B
			7.2.7 Instruments with Long Tube Lengths in G, F, E and D
			7.2.8 Instruments with Very Long Tube Lengths in C and B
			7.2.9 Instruments with Very Long Tube Lengths in G, F, E and D
		7.3 Families
		7.4 Mouthpieces
		7.5 Going Further: Trumpets and Cornets—Are They Different?
		7.6 Going Further: Alternative Taxonomies
		7.7 Going Further: Mouthpiece Parameters
		7.8 Going Further: The Bass Brass Instruments of Berlioz
			7.8.1 The Trombone
			7.8.2 The Serpent
			7.8.3 The Ophicleide
			7.8.4 The Bass Tuba
			7.8.5 Berlioz and Pedal Notes
	8 How Brass Instruments Are Made
		8.1 Materials
		8.2 Design
		8.3 Metal Forming
		8.4 Valves
		8.5 Assembly
	9 Looking Back and Looking Forward
		9.1 Brass Instruments in the Ancient World
			9.1.1 Etruscan Cornu and Lituus
			9.1.2 The Celtic Carnyx
		9.2 Brass Instruments in the Digital World
			9.2.1 Optimisation in Instrument Design
			9.2.2 Modification of Instruments Using Active Control
			9.2.3 Live Electronics and Augmented Instruments
			9.2.4 Epilogue
References
Index