The Physics of Musical Instruments

Front Cover
Springer Science & Business Media, Jan 1, 1998 - Music - 756 pages
7 Reviews
While the history of musical instruments is nearly as old as civilization itself, the science of acoustics is quite recent. By understanding the physical basis of how instruments are used to make music, one hopes ultimately to be able to give physical criteria to distinguish a fine instrument from a mediocre one. At that point science may be able to come to the aid of art in improving the design and performance of musical instruments. As yet, many of the subtleties in musical sounds of which instrument makers and musicians are aware and remain beyond the reach of modern acoustic measurements. Indeed, for many musical instruments it is only within the past few years that musical acoustics has achieved even a reasonable understanding of the basic mechanisms determining the tone quality, and in some cases even major features of the sounding mechanism have only recently been unravelled. This book describes the results of such acoustical investigations-intellectual and practical exercises of great fascination. Addressed to readers with a reasonable grasp of physics who are not put off by a little mathematics, this book discusses most of the traditional instruments currently in use in Western music. This second edition has been thoroughly revised to take into account the insights arising from recent research, and to generalize or clarify the presentation in many places. The book should continue to serve as a guide for all who have an interest in music and how it is produces as well as serving as a comprehensive reference for those undertaking research in the field.
  

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A superb book. I am a researcher in music acoustics, and I use it regularly. We have a couple of copies in the lab and they are very busy. But most of its readers are obviously not researchers: if you have an interest in music and any sort of background in physics, this book will excite you. Clear, well written, thorough. It's a good read, too.  

Contents

Free and Forced Vibrations of Simple Systems
3
11 Simple Harmonic Motion in One Dimension
4
12 Complex Amplitudes
6
13 Superposition of Two Harmonic Motions in One Dimension
7
14 Energy
10
15 Damped Oscillations
11
16 Other Simple Vibrating Systems
13
17 Forced Oscillations
18
112 The Harp
336
113 The Harpsichord
340
114 Harpsichord Design Considerations
343
115 Harpsichord Characteristics
346
116 The Clavichord
347
References
350
The Piano
352
121 General Design of Pianos
353

18 Transient Response of an Oscillator
21
19 TwoDimensional Harmonic Oscillator
23
Lissajous Figures
25
111 Normal Modes of TwoMass Systems
26
112 Nonlinearity
28
Appendix
29
References
32
Continuous Systems in One Dimension Strings and Bars
34
22 Transverse Wave Equation for a String
36
Traveling Waves
37
24 Reflection at Fixed and Free Ends
38
25 Simple Harmonic Solutions to the Wave Equation
39
27 Energy of a Vibrating String
40
29 Struck String
44
210 Bowed String
46
Impedance
50
212 Motion of the End Supports
52
213 Damping
53
214 Longitudinal Vibrations of a String or Thin Bar
56
215 Bending Waves in a Bar
58
216 Bars with Fixed and Free Ends
60
Rotary Inertia and Shear Deformation
63
218 Vibrations of a Stiff String
64
Cutoff Frequency
65
220 Torsional Vibrations of a Bar
66
References
68
TwoDimensional Systems Membranes Plates and Shells
70
Degeneracy
72
33 Circular Membranes
73
Stiffness and Air Loading
75
35 Waves in a Thin Plate
76
36 Circular Plates
78
37 Elliptical Plates
80
39 Square Plates
83
310 Square and Rectangular Plates with Clamped Edges
85
311 Rectangular Wood Plates
88
312 Bending Stiffness in a Membrane
91
313 Vibration of Shells
92
314 Driving Point Impedance
96
References
99
Coupled Vibrating Systems
102
42 Normal Modes
103
43 Weak and Strong Coupling
105
44 Forced Vibrations
107
45 Coupled Electrical Circuits
111
46 Forced Vibration of a TwoMass System
115
47 Systems with Many Masses
116
48 Graphical Representation of Frequency Response Functions
117
49 Vibrating String Coupled to a Soundboard
119
410 Two Strings Coupled by a Bridge
120
APPENDIX
125
References
131
Nonlinear Systems
133
51 A General Method of Solution
134
52 The Nonlinear Oscillator
136
53 The SelfExcited Oscillator
139
54 Multimode Systems
140
55 Mode Locking in SelfExcited Systems
143
56 Nonlinear Effects in Strings
144
57 Nonlinear Effects in Plates and Shells
148
References
150
Sound Waves
153
Sound Waves in Air
155
61 Plane Waves
156
62 Spherical Waves
160
63 Sound Pressure Level and Intensity
161
64 Reflection Diffraction and Absorption
163
65 Normal Modes in Cavities
167
References
169
Sound Radiation
171
72 Pairs of Point Sources
174
73 Arrays of Point Sources
176
74 Radiation from a Spherical Source
179
75 Line Sources
181
77 Unbaffled Radiators
185
78 Radiation from Large Plates
186
References
189
Pipes Horns and Cavities
190
82 Wall Losses
193
83 Finite Cylindrical Pipes
196
84 Radiation from a Pipe
201
85 Impedance Curves
202
86 Horns
205
87 Finite Conical Horns
210
88 Bessel Horns
213
89 Compound Horns
216
810 Perturbations
218
811 Numerical Calculations
220
813 Measurement of Acoustic Impedance
222
814 The Time Domain
223
815 Network Analogs
227
References
232
String Instruments
237
Guitars and Lutes
239
92 The Guitar as a System of Coupled Vibrators
240
93 Force Exerted by the String
241
94 Modes of Vibration of Component Parts
245
TwoOscillator Model
248
ThreeOscillator Model
250
97 Resonances of a Guitar Body
251
98 Response to String Forces
253
99 Sound Radiation
256
910 Resonances Radiated Sound and Quality
258
911 A Family of Scaled Guitars
260
912 Use of Synthetic Materials
261
913 Electric Guitars
262
914 Frets and Compensation
263
915 Lutes
264
916 Other Plucked String Instruments
265
917 OneSided Bridge Constraints
268
References
269
Bowed String Instruments
272
102 Research on Violin Acoustics
273
103 Construction of the Violin
274
104 Motion of Bowed Strings
275
105 Violin Body Vibrations
285
106 Transient Wave Response of the Violin Body
294
107 Soundpost and Bass Bar
295
108 The Bridge
297
109 Sound Radiation
301
1010 The Bow
310
1011 Wolf Notes and Payability
312
1012 Tonal Quality of Violins
313
1013 Viola Cello and Double Bass
318
1014 Viols
319
1015 A New Violin Family
322
References
326
Harps Harpsichords Clavichords and Dulcimers
331
122 Piano Action
354
123 Piano Strings
362
124 Piano Hammers
366
125 The Soundboard
374
Interaction of Strings Bridge and Soundboard
383
127 Scaling and Tuning
387
128 Tuning and Inharmonicity
388
129 Timbre
390
1210 Electric Pianos
396
Wind Instruments
399
Sound Generation by Reed and Lip Vibrations
401
132 QuasiStatic Model
403
133 Generator Behavior at Playing Frequency
406
134 Free Reeds
413
135 Generators Coupled to Horns
415
136 LargeAmplitude Behavior
418
137 Nonlinear Analysis
422
138 Numerical Simulation
424
References
426
LipDriven Brass Instruments
429
142 Horn Profiles
431
143 Mouthpieces
433
144 Radiation
437
145 Slides and Valves
440
146 SmallAmplitude Nonlinearity
442
147 LargeAmplitude Nonlinearity
445
148 Input Impedance Curves
449
149 Transients
450
1410 Acoustic Spectra
453
1412 Performance Technique
455
References
459
Woodwind Reed Instruments
461
152 Finger Holes
464
153 Impedance Curves
470
154 Reed and Air Column Interaction
477
155 Directionality
480
156 Performance Technique
481
157 Acoustic Efficiency
484
159 The Clarinet
486
1510 The Oboe
491
1511 The Bassoon
494
1512 The Saxophone
496
1513 Capped Reed Instruments
497
References
500
Flutes and Flue Organ Pipes
503
162 Disturbance of an Air Jet
509
163 JetResonator Interaction
511
164 The Regenerative Excitation Mechanism
516
165 Rigorous FluidDynamics Approaches
521
166 Nonlinearity and Harmonic Generation
522
167 Transients and Mode Transitions
525
168 Aerodynamic Noise
528
169 Simple FluteType Instruments
529
1610 The Recorder
531
1611 The Flute
537
References
548
Pipe Organs
552
171 General Design Principles
553
172 Organ Pipe Ranks
557
173 Flue Pipe Ranks
559
174 Characteristic Flue Pipes
563
175 Mixtures and Mutations
564
176 Tuning and Temperament
566
177 Sound Radiation from Flue Pipes
568
178 Transients in Flue Pipes
569
179 Flue Pipe Voicing
570
1710 Effect of Pipe Material
571
1711 Reed Pipe Ranks
573
1712 Analysis of Timbre
575
1713 Tonal Architecture
577
References
578
Percussion Instruments
581
Drums
583
181 Kettledrums
584
182 Bass Drums
599
183 Snare Drums
602
184 TomToms
606
185 Indian Drums
609
186 Japanese Drums
615
187 Indonesian Drums
618
189 Tambourines
620
References
621
Mallet Percussion Instruments
623
192 The Marimba
624
193 Tuning the Bars
627
194 Resonators
633
195 The Xylophone
636
196 Vibes
638
197 Mallets
639
198 Chimes
641
199 Triangles and Pentangles
642
1910 Gamelan Instruments
645
References
647
Cymbals Gongs Plates and Steel Drums
649
202 TamTams
656
203 Gongs
660
204 Crotales
663
205 Bell Plates
665
207 Steel Pans
667
References
673
Bells
675
211 Modes of Vibration of Church Bells
676
212 Tuning and Temperament
681
213 The Strike Note
682
214 MajorThird Bells
685
215 Sound Decay and Warble
686
216 Scaling of Bells
688
217 Modes of Vibration of Handbells
691
218 Timbre and Tuning of Handbells
694
219 Sound Decay and Warble in Handbells
695
2110 Scaling of Handbells
696
2111 Sound Radiation
697
2112 Bass Handbells
699
2114 Ancient Chinese TwoTone Bells
700
2115 Temple Bells of China Korea and Japan
701
References
705
Materials
709
Materials for Musical Instruments
711
221 Mechanical Properties of Materials
712
222 Materials for Wind Instruments
717
223 Wood
719
224 Plastics and Composite Materials
726
225 Metals
728
226 Conclusion
732
References
733
Name Index
735
Subject Index
743
Copyright

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Page 673 - England in the 18th century. One early use of handbells was to provide tower bellringers with a convenient means to practice change ringing. In more recent years, handbell choirs have become popular in schools and churches-some 2000 choirs are reported in the United States.
Page 673 - Western musical instruments in the seventeenth century when bell founders discovered how to tune their partials harmonically. The founders in the Low Countries, especially the Hemony brothers (Francois and Pieter ) and Jacob van Eyck, took the lead in tuning bells, and many of their fine bells are found in carillons today. The carillon also developed in the Low Countries. Chiming bells by pulling ropes attached to the clappers had been practiced for some time before the idea of attaching...

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About the author (1998)

Fletcher-Australian National University, Canberra, Australia

Thomas D. Rossing completed his B.A. at Luther College in 1950, his M.S. and Ph.D. at Iowa State University in 1954. His dissertation was in the field of molecular physics. After graduating, he went into industrial research, and from there, he went to teaching. Currently, he is a professor at Northern Illinois University.

Professor Rossing has published more than 200 papers and ten books. He is a Fellow of the Acoustical Society of America and of the American Association for the Advancement of Science. He has held about a dozen research positions other than at his home institution--in national laboratories, in research universities, and in several other countries. The Acoustical Society of America awarded him the Silver Medal in Musical Acoustics.

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