The Science of String Instruments

1. Auflage 2010
ISBN: 978-1-4419-7110-4
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 470 Seiten

Thomas D. Rossing String instruments are found in almost all musical cultures. Bowed string instruments form the backbone of symphony orchestras, and they are used widely as solo inst- ments and in chamber music as well. Guitars are used universally in pop music as well as in classical music. The piano is probably the most versatile of all musical inst- ments, used widely not only in ensemble with other musical instruments but also as a solo instrument and to accompany solo instruments and the human voice. In this book, various authors will discuss the science of plucked, bowed, and hammered string instruments as well as their electronic counterparts. We have tried to tell the fascinating story of scienti?c research with a minimum of mathematics to maximize the usefulness of the book to performers and instrument builders as well as to students and researchers in musical acoustics. Sometimes, however, it is dif?cult to “translate” ideas from the exact mathematical language of science into words alone, so we include some basic mathematical equations to express these ideas. It is impossible to discuss all families of string instruments. Some instruments have been researched much more than others. Hopefully, the discussions in this book will help to encourage further scienti?c research by both musicians and scientists alike. 1.1 A Brief History of the Science of String Instruments Quite a number of good histories of acoustics have been written (Lindsay 1966, 1973; Hunt 1992; Beyer 1999), and these histories include musical acoustics.

Autoren/Hrsg.

Inhaltsverzeichnis

1;The Science of String Instruments;3
1.1;Contents;5
1.2;Contributors;7
1.3;Chapter 1: Introduction;9
1.3.1;1.1 A Brief History of the Science of String Instruments;9
1.3.1.1;1.1.1 Bowed String Instruments;10
1.3.1.2;1.1.2 Lutes and Guitars;11
1.3.1.3;1.1.3 Harpsichords, Clavichords, and Dulcimers;13
1.3.1.4;1.1.4 Piano;14
1.3.1.5;1.1.5 Electric and Virtual String Instruments;15
1.3.2;1.2 Modal Analysis of String Instruments;15
1.3.2.1;1.2.1 Experimental Modal Testing;15
1.3.2.2;1.2.2 Mathematical Modal Analysis;16
1.3.2.3;1.2.3 Sound Field Analysis;17
1.3.2.4;1.2.4 Holographic Modal Analysis;17
1.3.3;References;17
1.4;Chapter 2: Plucked Strings;19
1.4.1;2.1 Transverse Waves on a String;19
1.4.1.1;2.1.1 Impulsive Waves, Reflection, and Interference;20
1.4.1.2;2.1.2 Standing Waves;20
1.4.2;2.2 Plucked String: Time and Frequency Analyses;22
1.4.3;2.3 Force Exerted by the String;23
1.4.4;2.4 Plucking;24
1.4.5;References;26
1.5;Chapter 3: Guitars and Lutes;27
1.5.1;3.1 Acoustic Guitars;27
1.5.1.1;3.1.1 The Guitar as a System of Coupled Vibrators;28
1.5.1.2;3.1.2 Force Exerted by the Vibrating String;28
1.5.1.3;3.1.3 Frequency Response of Guitars;29
1.5.2;3.2 Vibrations of the Guitar Body;30
1.5.2.1;3.2.1 Normal Modes of Vibration;30
1.5.2.2;3.2.2 Modes of Component Parts;31
1.5.2.3;3.2.3 Coupling of the Top Plate to the Air Cavity: Two-Oscillator Model;34
1.5.2.4;3.2.4 Coupling to the Back Plate: Three-Oscillator Model;35
1.5.2.5;3.2.5 Low-Frequency Resonances of a Guitar Body;35
1.5.2.6;3.2.6 Modal Shapes;36
1.5.3;3.3 String Forces;37
1.5.4;3.4 Sound Radiation;38
1.5.5;3.5 Quality;40
1.5.5.1;3.5.1 Influence of Design and Construction;41
1.5.5.2;3.5.2 The Bridge;41
1.5.5.3;3.5.3 Thickness of the Top Plate and Braces;41
1.5.5.4;3.5.4 Asymmetrical and Radial Bracing;42
1.5.6;3.6 A Family of Scaled Guitars;43
1.5.7;3.7 Synthetic Materials;45
1.5.8;3.8 Other Families of Guitars;45
1.5.9;3.9 Electric Guitars;45
1.5.9.1;3.9.1 Body Vibrations and Dead Spots;47
1.5.9.2;3.9.2 Electric Bass;47
1.5.10;3.10 Lutes;48
1.5.10.1;3.10.1 Acoustics of the European Short Lute;49
1.5.10.2;3.10.2 Acoustics of the Turkish Long-Necked Lute;49
1.5.11;3.11 Concluding Remarks;52
1.5.12;References;52
1.6;Chapter 4: Portuguese Guitar;54
1.6.1;4.1 Origins;54
1.6.2;4.2 Types and Characteristics;55
1.6.3;4.3 Vibroacoustic Behavior;56
1.6.4;4.4 Subjective Acoustical Quality Evaluation;59
1.6.4.1;4.4.1 Objective Parameters;60
1.6.4.2;4.4.2 Listening Tests;60
1.6.4.3;4.4.3 Test Conditions;61
1.6.4.3.1;4.4.3.1 Subjective Parameters Used;61
1.6.4.3.2;4.4.3.2 Conditions of the Guitars;62
1.6.4.4;4.4.4 Test Procedure;62
1.6.5;4.5 Results;63
1.6.5.1;4.5.1 Subjective Tests;63
1.6.5.2;4.5.2 Objective Tests;63
1.6.6;References;64
1.7;Chapter 5: Banjo;65
1.7.1;5.1 Introduction;65
1.7.2;5.2 Banjo Anatomy;66
1.7.3;5.3 Banjo Sound;67
1.7.4;5.4 Head Modes;71
1.7.5;5.5 Harmonics Analysis;73
1.7.6;5.6 Resonators;74
1.7.7;5.7 Bridges;77
1.7.8;5.8 Tone Rings, Rims, and Neck;79
1.7.9;5.9 Summary;80
1.7.10;References;81
1.8;Chapter 6: Mandolin Family Instruments;82
1.8.1;6.1 Introduction;82
1.8.2;6.2 Types of Mandolins;83
1.8.2.1;6.2.1 Neapolitan Mandolins;84
1.8.2.2;6.2.2 Flatback Mandolins;85
1.8.2.3;6.2.3 Cylinderback Mandolins and Other Unique Designs;86
1.8.2.4;6.2.4 Archtop Mandolins, Oval Sound Hole;86
1.8.2.5;6.2.5 Archtop Mandolins, f-Holes;86
1.8.2.6;6.2.6 Mandolas, Octave Mandolins, and Mandocellos;87
1.8.3;6.3 Normal Modes of Vibration and Holographic Interferometry;88
1.8.4;6.4 Normal Mode Shapes in Mandolins;89
1.8.5;6.5 Normal Mode Frequencies in Different Types of Mandolins;92
1.8.6;6.6 Sustain in Mandolins;97
1.8.7;6.7 Other Mandolin Family Instruments: Normal Modes in Two Mandolas;100
1.8.8;6.8 Mandocellos;101
1.8.9;6.9 Summary and Conclusions;102
1.8.10;References;102
1.9;Chapter 7: Psalteries and Zithers;104
1.9.1;7.1 Introduction;104
1.9.2;7.2 Influence of Stresses in Strings on the Instrument´s Shape;105
1.9.3;7.3 Plucking Stiffness, and Strength of a Plucked String;105
1.9.4;7.4 String Materials;106
1.9.5;7.5 Acoustical Study of Carved Baltic Psalteries;107
1.9.5.1;7.5.1 History of the Carved Baltic Psaltery;108
1.9.5.2;7.5.2 Playing Techniques;109
1.9.5.3;7.5.3 Body Resonances of Some Carved Baltic Psalteries;110
1.9.5.4;7.5.4 Coupling of Strings to Body Resonances;114
1.9.5.5;7.5.5 Experiments with Distribution of Sound Holes;116
1.9.5.6;7.5.6 Some Conclusions and Applications;117
1.9.5.7;7.5.7 Features of Proposed New Traditional-Style Designs;118
1.9.5.8;7.5.8 A More Radical Design from Finland;119
1.9.6;7.6 Zithers;120
1.9.6.1;7.6.1 Zithers Without Fretboard;120
1.9.6.2;7.6.2 Fretted (Alpine) Zithers;121
1.9.7;7.7 Hammered Dulcimers;122
1.9.8;7.8 Modernized Baltic Psalteries;122
1.9.8.1;7.8.1 Diatonically Tuned Versions;122
1.9.8.2;7.8.2 Chromatic Baltic Psalteries;123
1.9.9;References;126
1.10;Chapter 8: Harpsichord and Clavichord;128
1.10.1;8.1 Introduction;128
1.10.2;8.2 The Harpsichord;129
1.10.2.1;8.2.1 General Design;129
1.10.2.2;8.2.2 Plucked Strings;132
1.10.2.3;8.2.3 Soundboard and Radiation;135
1.10.2.4;8.2.4 Acoustic Balance;137
1.10.2.5;8.2.5 Design Extensions;139
1.10.3;8.3 The Clavichord;141
1.10.3.1;8.3.1 General Design;141
1.10.3.2;8.3.2 String Excitation in the Clavichord;144
1.10.4;8.4 Keyboard Tuning;145
1.10.5;8.5 Conclusion;147
1.10.6;References;148
1.11;Chapter 9: Harp;149
1.11.1;9.1 Introduction;149
1.11.2;9.2 Overview;149
1.11.2.1;9.2.1 Origins and Development;149
1.11.2.2;9.2.2 Structure;150
1.11.3;9.3 Strings;154
1.11.3.1;9.3.1 History;154
1.11.3.1.1;9.3.1.1 Diatonic Versus Chromatic Stringing;155
1.11.3.1.2;9.3.1.2 Sharping Mechanisms;155
1.11.3.2;9.3.2 Basic String Considerations;156
1.11.3.3;9.3.3 String Motion and Its Influence on the Sound Spectrum;157
1.11.3.4;9.3.4 String Motion and Temporal Development of the Sound;160
1.11.4;9.4 Soundboard and Soundbox;160
1.11.4.1;9.4.1 Evolution of the Soundboard;160
1.11.4.2;9.4.2 Vibrational Behavior of the Soundboard;162
1.11.4.3;9.4.3 Helmholtz and Pipe Resonances of the Soundbox;162
1.11.4.4;9.4.4 Vibroacoustic Behavior of the Soundbox;164
1.11.5;9.5 The Harp as a Whole;167
1.11.5.1;9.5.1 Strings and Soundbox;167
1.11.5.2;9.5.2 Sound Radiation;168
1.11.5.3;9.5.3 The Sound of the Harp;169
1.11.6;9.6 Conclusion;169
1.11.7;References;170
1.12;Chapter 10: Burmese Arched Harp;171
1.12.1;10.1 History;171
1.12.2;10.2 Construction and Playing Techniques;172
1.12.3;10.3 Scales and Tunings;173
1.12.4;10.4 Measurements of Plucked Tones;174
1.12.5;References;175
1.13;Chapter 11: Plucked String Instruments in Asia;176
1.13.1;11.1 Classification of Asian Musical Instruments Based on Construction Material;176
1.13.2;11.2 Japanese Satsuma Biwa;179
1.13.2.1;11.2.1 Structural Response;181
1.13.2.2;11.2.2 Sawari Mechanisms and Their Effects on High-Frequency Emphasis;183
1.13.2.3;11.2.3 Examples of Characteristic Sounds;188
1.13.2.4;11.2.4 Brief Comparison with the Chinese Pipa;189
1.13.3;11.3 Japanese Shamisen;189
1.13.3.1;11.3.1 Shamisen as an Overall String-Bridge-Membrane System;190
1.13.3.2;11.3.2 Sawari and Its Effect on the Tuning;192
1.13.4;11.4 Japanese Koto and Korean Gayageum;193
1.13.5;11.5 Concluding Remarks;196
1.13.6;References;196
1.14;Chapter 12: Bowed Strings;199
1.14.1;12.1 Kinematics of the Bowed String;199
1.14.2;12.2 Dynamics of the Bowed String;204
1.14.3;12.3 Bowing to Achieve Anomalous Low Frequencies;205
1.14.4;References;209
1.15;Chapter 13: Violin;211
1.15.1;13.1 History;211
1.15.2;13.2 Research;212
1.15.3;13.3 Evaluating Violins;213
1.15.4;13.4 Sound Analysis;214
1.15.5;13.5 Frequency Response;215
1.15.6;13.6 Tone Quality;215
1.15.6.1;13.6.1 Sizzle;217
1.15.6.2;13.6.2 Directional Tone Color;217
1.15.6.3;13.6.3 Projection;218
1.15.7;13.7 Playability;219
1.15.7.1;13.7.1 Helmholtz Motion;220
1.15.7.2;13.7.2 Bow Force Limits;221
1.15.7.3;13.7.3 Damping and Playability;222
1.15.8;13.8 Violin Body Vibrations;222
1.15.8.1;13.8.1 Normal Modes of Vibration;223
1.15.8.2;13.8.2 Vibrational Models;224
1.15.8.3;13.8.3 A Three-Dimensional Model of Vibration;226
1.15.8.4;13.8.4 Modal Analysis;226
1.15.8.5;13.8.5 What Modes Can a Maker Control?;227
1.15.9;13.9 Component Parts;228
1.15.9.1;13.9.1 Top and Back Plates;228
1.15.9.2;13.9.2 Tap Tones;229
1.15.9.3;13.9.3 The Mass of a Violin;231
1.15.9.4;13.9.4 Enclosed Air;232
1.15.9.5;13.9.5 Bridge;232
1.15.9.6;13.9.6 Ribs;235
1.15.9.7;13.9.7 Fingerboard;235
1.15.9.8;13.9.8 Bass bar and Soundpost;236
1.15.10;13.10 Measuring Sound Radiation;237
1.15.11;13.11 Low-Frequency Radiation;240
1.15.12;13.12 High-Frequency Radiation;241
1.15.13;13.13 Radiation Damping;242
1.15.14;13.14 Electric and Virtual Violins;243
1.15.15;References;244
1.16;Chapter 14: Cello;247
1.16.1;14.1 The Cello;247
1.16.2;14.2 Modal Analysis of Cellos;249
1.16.2.1;14.2.1 Frequency Response;249
1.16.2.2;14.2.2 Modes of Vibration;250
1.16.2.3;14.2.3 Observing the Modes;251
1.16.2.4;14.2.4 Labeling the Resonances;251
1.16.3;14.3 Modes of Component Parts;252
1.16.3.1;14.3.1 Cello Plate Modes;252
1.16.3.2;14.3.2 Cello Air Cavity Modes;252
1.16.4;14.4 Cello Body Modes;253
1.16.4.1;14.4.1 Comparison with Violin Resonances;256
1.16.5;14.5 Sound Spectra of the Cello;256
1.16.6;14.6 Mobility (Admittance) at the Bridge;257
1.16.7;14.7 The ``New Violin Family´´;258
1.16.8;14.8 Conclusion;258
1.16.9;References;258
1.17;Chapter 15: Double Bass;260
1.17.1;15.1 Modes of Vibration;260
1.17.1.1;15.1.1 The Modes in Playing;261
1.17.1.2;15.1.2 Mobility Curves and Instrument Identity;262
1.17.2;15.2 The Double Bass Compared to the Violin and Cello;264
1.17.3;15.3 Double Basses of Different Quality;265
1.17.4;15.4 The Violin Octet;269
1.17.5;15.5 The Player´s Support;270
1.17.6;15.6 Scaling;271
1.17.7;15.7 Body Size and Radiated Sound;272
1.17.8;15.8 Stage Risers;274
1.17.9;15.9 Directional Radiation;276
1.17.10;15.10 Further Reading;278
1.17.11;References;278
1.18;Chapter 16: Bows, Strings, and Bowing;279
1.18.1;16.1 The Bow;279
1.18.1.1;16.1.1 Effect of Camber on Transverse Hair Stiffness;279
1.18.1.2;16.1.2 Wood;281
1.18.1.3;16.1.3 Tonal Quality;281
1.18.1.4;16.1.4 Effect of Hair Elasticity and Surface Roughness;282
1.18.1.5;16.1.5 Rosin/Friction;282
1.18.2;16.2 Strings;283
1.18.2.1;16.2.1 The Concept of Wave Resistance or Wave Impedance;283
1.18.2.2;16.2.2 Tension;284
1.18.2.3;16.2.3 Damping;285
1.18.2.4;16.2.4 Torsion;287
1.18.3;16.3 Bowing Techniques;287
1.18.3.1;16.3.1 The Main Three Bowing Parameters;287
1.18.3.2;16.3.2 Flautando;290
1.18.3.3;16.3.3 Harmonics;290
1.18.3.4;16.3.4 Harmonics and Intonation;291
1.18.3.5;16.3.5 Double Stops;292
1.18.3.6;16.3.6 Tone Onsets, Attacks;292
1.18.3.7;16.3.7 Détaché;294
1.18.3.8;16.3.8 Martelé;295
1.18.3.9;16.3.9 Light Bowing;295
1.18.3.10;16.3.10 Spiccato/Sautillé/Ricochet;295
1.18.3.11;16.3.11 Bouncing Rate;296
1.18.3.12;16.3.12 Parameters That Affect the String´s Spectrum;297
1.18.4;References;299
1.19;Chapter 17: Viols and Other Historic Bowed String Instruments;300
1.19.1;17.1 Medieval Bowed String Instruments;301
1.19.1.1;17.1.1 Medieval Fiddles;301
1.19.1.2;17.1.2 Rebecs;302
1.19.1.3;17.1.3 Acoustics of Medieval Bowed String Instruments;303
1.19.1.3.1;17.1.3.1 Acoustical Properties of the Medieval Fiddle;304
1.19.1.3.2;17.1.3.2 Acoustical Properties of the Rebec;305
1.19.2;17.2 Renaissance Viols;306
1.19.2.1;17.2.1 The Development of the Renaissance Viol;306
1.19.2.2;17.2.2 Acoustics of Renaissance Viols;308
1.19.3;17.3 Baroque Viols;309
1.19.3.1;17.3.1 Development of the Baroque Viol;310
1.19.3.2;17.3.2 Acoustics of the Baroque Viol;311
1.19.3.2.1;17.3.2.1 The Baroque Treble Viol;311
1.19.3.2.2;17.3.2.2 The Baroque Tenor Viol;312
1.19.3.2.3;17.3.2.3 The Baroque Bass Viol;312
1.19.4;References;313
1.20;Chapter 18: The Hutchins-Schelleng Violin Octet After 50 Years;315
1.20.1;18.1 Introduction;315
1.20.2;18.2 Brief Octet History;317
1.20.2.1;18.2.1 Identification of Important Resonances;318
1.20.3;18.3 What Do We Know Now?;319
1.20.3.1;18.3.1 Summary of Octet-Related Developments, 1964-2007;319
1.20.3.2;18.3.2 How Bowed-String Instruments Radiate;322
1.20.3.3;18.3.3 Where Do Materials Come in?;323
1.20.3.4;18.3.4 A1 Radiation in the B1 Region;324
1.20.4;18.4 Scaling Basics;325
1.20.4.1;18.4.1 Scaling Assumptions;325
1.20.4.2;18.4.2 The Practicalities;326
1.20.4.3;18.4.3 Flat Plate Scaling Equations;327
1.20.4.4;18.4.4 Important A0 Scaling Equation Modification;328
1.20.4.5;18.4.5 Similarity of Shape;329
1.20.5;18.5 Modal and Acoustical Analyses;330
1.20.5.1;18.5.1 Modal and Acoustical Analyses of the Octet;331
1.20.5.2;18.5.2 A0 and A1: Coupling;334
1.20.5.3;18.5.3 Wall Compliance and Cavity Mode Frequencies;335
1.20.5.4;18.5.4 Rib Heights and Pressure Ratios;336
1.20.5.5;18.5.5 Clarifying A1 Status;336
1.20.5.6;18.5.6 Fat Bottoms, Wall Compliance, and Pressure Ratios;338
1.20.6;18.6 Future of the Violin Octet;340
1.20.7;18.7 Conclusions;341
1.20.8;References;342
1.21;Chapter 19: Hammered Strings;344
1.21.1;19.1 Dynamics of the Hammer-String Interaction;344
1.21.2;19.2 Piano Hammers;346
1.21.3;19.3 String Excitation by a Piano Hammer;347
1.21.4;19.4 Hammer Position on the String;348
1.21.5;19.5 String Excitation in a Hammered Dulcimer;349
1.21.6;References;349
1.22;Chapter 20: Some Remarks on the Acoustics of the Piano;350
1.22.1;20.1 Introduction;350
1.22.2;20.2 History of the Instrument;350
1.22.3;20.3 Overall Design;352
1.22.4;20.4 Vibrating Strings;353
1.22.5;20.5 The Hammers;357
1.22.6;20.6 The Soundboard as a Speaker;360
1.22.7;20.7 How We Perceive Piano Tones;364
1.22.8;20.8 Modeling of the Piano;365
1.22.9;20.9 Lessons;366
1.22.10;References;367
1.23;Chapter 21: Hammered Dulcimer;368
1.23.1;21.1 History;368
1.23.2;21.2 The Basic Instrument;369
1.23.3;21.3 Inharmonicity and Scaling;371
1.23.4;21.4 Lateral Stability;372
1.23.5;21.5 Instrument Warp;373
1.23.6;21.6 Tuning Stability;375
1.23.6.1;21.6.1 Tuning Stability: Temperature;375
1.23.6.2;21.6.2 Tuning Stability: Humidity;377
1.23.6.3;21.6.3 String-Bridge Friction;379
1.23.7;21.7 The Percussive Sound: Hammer and String Interaction;379
1.23.8;21.8 Hammers and Course Spacing;381
1.23.9;21.9 String Coupling and Resonance Time;382
1.23.10;21.10 Sound Board and Body Modes;384
1.23.11;21.11 Sound Board Materials, Back Plates, and Design;386
1.23.12;21.12 Bridges, Bridge Caps, and Bridge Vibrations;386
1.23.13;21.13 Pin Blocks, Pins, and Hitch Pins;387
1.23.14;21.14 Sound Radiation Patterns;388
1.23.15;21.15 Unimportant Characteristics: Sound Holes, Special Finishes, Peglegs, and Perfect Fifths;388
1.23.16;References;389
1.24;Chapter 22: Electric Guitar and Violin;390
1.24.1;22.1 Historical Background;391
1.24.2;22.2 The Electric Guitar;392
1.24.3;22.3 The Electric Violin;396
1.24.4;22.4 Acoustic, Magnetic, and Piezoelectric Pickups;399
1.24.4.1;22.4.1 Acoustic Pickups;399
1.24.4.2;22.4.2 Magnetic Pickups;400
1.24.4.3;22.4.3 Special Sound Effects;403
1.24.4.4;22.4.4 Piezoelectric Pickups;404
1.24.4.5;22.4.5 Other Types of Pickups;407
1.24.5;22.5 The Electric Violin as a Research Tool;408
1.24.5.1;22.5.1 Multiresonant Filter Characteristics;409
1.24.5.2;22.5.2 Sound Perception and Acoustical Properties;410
1.24.5.3;22.5.3 Real-Time Synthesis of Cremonese Instruments;411
1.24.6;References;412
1.25;23: Virtual String Synthesis;413
1.25.1;23.1 Introduction;413
1.25.2;23.2 Nomenclature;414
1.25.2.1;23.2.1 Digital Signals;415
1.25.2.1.1;23.2.1.1 Sampling;415
1.25.2.1.2;23.2.1.2 Sum of Sinusoids;416
1.25.2.2;23.2.2 Digital Filtering;418
1.25.3;23.3 Elements of Stringed Instruments;418
1.25.3.1;23.3.1 Vibrating String;419
1.25.3.1.1;23.3.1.1 D´Alembert´s Wave Equation;419
1.25.3.1.2;23.3.1.2 The Delay Line;421
1.25.3.1.3;23.3.1.3 Digital Waveguide Models;422
1.25.3.1.4;23.3.1.4 Natural Decay of the String;423
1.25.3.1.5;23.3.1.5 Modeling Two Planes of Vibration;424
1.25.3.1.6;23.3.1.6 Varying the Digital Waveguide;425
1.25.3.2;23.3.2 Plucking the String;426
1.25.3.2.1;23.3.2.1 Theoretical Plucks;426
1.25.3.2.2;23.3.2.2 Complexities of Real Plucks;427
1.25.3.3;23.3.3 Body Resonance;428
1.25.3.3.1;23.3.3.1 Driving-Point Admittance;428
1.25.3.3.2;23.3.3.2 Filtering with the Driving-Point Admittance;428
1.25.3.3.3;23.3.3.3 Bidirectional Interaction;429
1.25.3.3.4;23.3.3.4 String-Body Scattering Junction;430
1.25.3.4;23.3.4 Pressure Radiation;431
1.25.4;23.4 Measurements;432
1.25.4.1;23.4.1 String Vibration;432
1.25.4.2;23.4.2 Bridge Impedance;433
1.25.4.3;23.4.3 Body Vibration;434
1.25.4.4;23.4.4 Pressure Radiation;435
1.25.5;23.5 Parameter Estimation;435
1.25.5.1;23.5.1 Short-Time Fourier Transform;435
1.25.5.2;23.5.2 Excitation;436
1.25.5.2.1;23.5.2.1 The Statistical Spectral Interpolation Method;438
1.25.5.3;23.5.3 String;440
1.25.5.3.1;23.5.3.1 Loop Filter Estimation;440
1.25.5.4;23.5.4 Body Resonator;443
1.25.5.4.1;23.5.4.1 Low-Order Filter Implementations;445
1.25.5.5;23.5.5 Radiated Sound Pressure;446
1.25.5.5.1;23.5.5.1 Low-Order Filter Implementations;447
1.25.5.5.2;23.5.5.2 Combining and Interpolating Between Measurements;448
1.25.6;23.6 Summary and Conclusion;449
1.25.7;References;449
2;Index;452