the acoustics of the steel string guitar

417 Pages·2007·3.8 MB·English

THE ACOUSTICS OF THE STEEL STRING GUITAR
By
Ra Inta
SUBMITTED IN TOTAL FULFILMENT OF THE
REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
SCHOOL OF PHYSICS
THE UNIVERSITY OF NEW SOUTH WALES
SYDNEY, AUSTRALIA
September 6, 2007
To the memory of Tamzin Sherwood
(1977-2000)
Sic Transit Gloria Astra
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Table of Contents
Table of Contents iii
Abstract vii
Acknowledgements viii
Why study the acoustics of the guitar? (An overview) 1
0.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
0.2 Outstanding problems of interest . . . . . . . . . . . . . . . . . . . . 4
0.3 The approach in this thesis . . . . . . . . . . . . . . . . . . . . . . . . 4
0.4 Overview. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1 Previous work 9
1.1 A brief history of the guitar . . . . . . . . . . . . . . . . . . . . . . . 9
1.2 Early work in acoustics . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.3 Previous work on stringed musical instruments and related systems . 15
2 How the guitar produces sound 29
2.1 The basic anatomy of the guitar . . . . . . . . . . . . . . . . . . . . . 29
2.2 Specialised anatomical features . . . . . . . . . . . . . . . . . . . . . 34
2.3 Excitation methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.4 The Helmholtz resonator . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.5 Soundboard-air cavity coupling: the two-mass oscillator model . . . . 46
2.6 Three-mass oscillator model . . . . . . . . . . . . . . . . . . . . . . . 56
2.7 The importance of bracing . . . . . . . . . . . . . . . . . . . . . . . . 58
2.8 General behaviour in various frequency regimes . . . . . . . . . . . . 62
2.9 Resonant modes of the guitar . . . . . . . . . . . . . . . . . . . . . . 65
2.10 Interpretation of response curves . . . . . . . . . . . . . . . . . . . . 74
2.11 Acoustic radiativity of the guitar . . . . . . . . . . . . . . . . . . . . 77
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2.12 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3 The Construction of the Guitar 82
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.2 Material used in construction . . . . . . . . . . . . . . . . . . . . . . 84
3.3 Damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3.4 Traditional techniques of construction . . . . . . . . . . . . . . . . . . 99
3.5 Recent innovations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
3.6 Phases of construction examined in this thesis . . . . . . . . . . . . . 122
4 Applications of the Finite Element Method to instrument construc-
tion 124
4.1 Methods and motives for using finite element calculations . . . . . . . 125
4.2 Inputs for the model . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
4.3 Brace scalloping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
4.4 Glue bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
4.5 The free guitar soundboard . . . . . . . . . . . . . . . . . . . . . . . 142
4.6 Guitar body . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
4.7 Conclusion: Applications of finite element simulations to instrument
construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
5 Experimental: Selection of Materials 152
5.1 Timber used in the guitars studied . . . . . . . . . . . . . . . . . . . 153
5.2 Measurement techniques . . . . . . . . . . . . . . . . . . . . . . . . . 155
5.3 Measuring and controlling the moisture content of wood . . . . . . . 162
5.4 Selection criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
5.5 Bracing material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
5.6 Soundboard material . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
5.7 Bridge material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
5.8 Neck material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
5.9 Fingerboard material . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
5.10 Back, sides, binding and other materials . . . . . . . . . . . . . . . . 188
5.11 Damping measurements . . . . . . . . . . . . . . . . . . . . . . . . . 188
5.12 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
5.13 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
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6 Experimental: Plates, bodies and the guitar 193
6.1 Experimental measurement techniques . . . . . . . . . . . . . . . . . 194
6.2 Simple plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
6.3 Free guitar soundboards . . . . . . . . . . . . . . . . . . . . . . . . . 205
6.4 Guitar bodies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
6.5 The thinned soundboard . . . . . . . . . . . . . . . . . . . . . . . . . 217
6.6 Binding the soundboard . . . . . . . . . . . . . . . . . . . . . . . . . 222
6.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
7 Experimental: Completed instruments and parameter evolution 231
7.1 Effects from the addition of the neck . . . . . . . . . . . . . . . . . . 231
7.2 Addition of the bridge . . . . . . . . . . . . . . . . . . . . . . . . . . 240
7.3 The polished instruments . . . . . . . . . . . . . . . . . . . . . . . . . 246
7.4 Effects of lacquer curing . . . . . . . . . . . . . . . . . . . . . . . . . 250
7.5 Short term ageing and playing in . . . . . . . . . . . . . . . . . . . . 254
7.6 The effects of brace scalloping . . . . . . . . . . . . . . . . . . . . . . 266
7.7 Parameter evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . 280
7.8 Results/Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290
8 A lexicon and a preliminary study of subjective responses to guitar
sounds 296
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
8.2 Study I—establishing a guitar timbre lexicon . . . . . . . . . . . . . . 298
8.3 Study II—evaluation of guitar sounds . . . . . . . . . . . . . . . . . . 308
8.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328
9 Conclusion and Further Work 330
A Some derivations and measurements 335
A.1 The Helmholtz resonator . . . . . . . . . . . . . . . . . . . . . . . . . 335
A.2 Soundboard-air cavity coupling parameters . . . . . . . . . . . . . . . 339
A.3 Two mass model for a cantilever beam driven at the base . . . . . . . 342
A.3.1 Change in frequency of bending mode of a profiled beam . . . 343
A.4 Measurements of dimensions of the guitar soundboards . . . . . . . . 350
B Vibratory data acquisition system (ACUZ) 351
B.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351
B.2 Design and operation . . . . . . . . . . . . . . . . . . . . . . . . . . . 352
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B.3 Impedance spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . 355
C Alternative methods of measuring mechanical properties of wood 356
D Soundboard thickness measurement device 361
D.1 Outline of soundboard thickness problem . . . . . . . . . . . . . . . . 361
D.2 The Hall effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364
D.3 Measurements of soundboard thinning . . . . . . . . . . . . . . . . . 368
D.4 The device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369
D.5 Methodology and usage . . . . . . . . . . . . . . . . . . . . . . . . . . 370
E Excitation and coupling apparatus 374
E.1 Magnetic coupling apparatus . . . . . . . . . . . . . . . . . . . . . . . 374
E.2 Cup-hook support mechanism . . . . . . . . . . . . . . . . . . . . . . 378
E.3 Magnetic support mechanism . . . . . . . . . . . . . . . . . . . . . . 379
E.4 Materials used in excitation stand . . . . . . . . . . . . . . . . . . . . 380
E.5 Design of excitation stand . . . . . . . . . . . . . . . . . . . . . . . . 380
E.6 Specific operating techniques . . . . . . . . . . . . . . . . . . . . . . . 382
F Lists of terms in describing the timbre of guitar sounds 383
F.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383
Bibliography 386
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Abstract
To improve the replication of acoustic guitars, measurements of three Martin OOO
style steel-string guitars were made at various stages of their construction. The
guitars were constructed in parallel, as similar to each other as possible, with the
exception of the soundboard material—which were made of Sitka spruce, Engelmann
spruce and Western Red cedar.
To improve the similarity of the instruments, methods were developed to measure
andcontrolthematerialpropertiesofkeycomponentsbeforetheirincorporationinto
the instruments, including a device to measure the thickness of a guitar soundboard
attached to the back and sides of the instrument.
Some of these measurements were compared to numerical models of the instrument
and, after the establishment of a lexicon to describe guitar sounds, some physical
factors contributing towards the timbre of guitar sounds were determined.
The results of these investigations may be developed to improve the consistency in
the manufacture of stringed musical instruments.
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Acknowledgements
TM
Thankfully, this is not an Academy Awards speech, so I am able to properly thank
the following, without whom this project would have been impossible. These truly
are debts I will not ever be able to repay.
First, I would like to thank my supervisor, Prof. Joe Wolfe, who was supportive
and generous well above and beyond the usual obligatory demands placed on super-
visors. Joe has not only been a mentor in my scientific life, but also contributed
much to my broader existence, both in the day-to-day, and the philosophical sense.
A true captain of men as well as sailing ships.
Gerard Gilet, my industrial supervisor: I am indebted to his extraordinary fore-
sight in recognising the importance of research on improving the construction of the
guitar—especially in an industry with such ‘slim overheads’. This is evident not only
in his support of this project, but in his history of supporting research in a collegial
and intelligent manner. I hope I have helped in some small way.
Dr John Smith, my co-supervisor: I am grateful for his continuous suggestions
and expertise offered, as well as his broad knowledge, which helped me solve innu-
merable problems with his many great ideas. One day I hope I will visit Mileto, too.
(The)JohnTann: NoamountofmuffinswouldequaltheaccumulatedhelpIhave
received from this man. From my very first day on this project (helping him make
an anechoic chamber) until the very(!) last minute, help support and inspiration
was ungrudgingly, nay, willingly, offered.
An acknowledgement of foresight and support rightly belongs to the Australian
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Research Council. This is not offered as a platitude: I really am grateful for support
to what may have looked like a high-risk venture!
I would also like to thank:
EmerySchubert: Forhelpwiththepsychoacousticalaspectsofthisproject. Itwould
have been a right SASS-P without him. David Vernet, Matthieu Maziere and Davy
Laille: It was a pleasure working with you all. I hope you remember your brief stay
in Australia fondly and wish you well for the future.
The people in the Music Acoustics Lab, including Paul Dickens, Attila Stopic,
Jane Cavanagh, Manfred Yew, Alex Tarnopolsky, Claudia Fritz, David Bowman,
Ben Lange, Romano Crivici, Michael Lea, Harry Vatiliotis, Ryan France, Pierre-
Yves Plac¸ais, Olivier Marnette and the many others who passed through in the time
I was there. You have all helped make my PhD life richer and more enjoyable in
innumerable ways.
The people at the Gilet Guitars workshop: Darrell ‘Deathride’ Wheeler, Michael
PrendergastandCharlesCilia, plusArjuna, CharlesMilne, Pete, andFrank. Iwould
have had a lot of expensive firewood without your help.
I would also like to thank the good people of the UNSW School of Physics, in-
cluding Jules, Tony Travolta, Cormac, Sue Hagon, Bosco, Steve ‘Yaarrgh’ Curran,
Dr Matty, Vincent, Gary Keenan, Tammy Reztsova and so many others for provid-
ing such a stimulating environment. So many good people. So many good times.
Of course, any acknowledgements would not be complete without especially
thanking Aunt Elly, Doug Lloyd-Jones, and Jim Williams for their continuous sup-
port and help through the years. I am grateful to your input and inspiration for so
many things.
More fundamentally, it would not have been possible without my parents, Frida
and Scotty, and my ‘little’ brothers Rory, Chad and Zigs. It must have seemed like
I have taken forever to write this!
I would also like to thank Professor Joseph Lai, Dr Theo Evans, and the CSIRO
Termite Group, for their patience and understanding while finishing this project at
the same time as embarking on another exciting adventure.
Sydney, Australia Ra Inta
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