THE ACOUSTICS AND PSYCHOACOUSTICS OF THE GUITAR Howard Wright Doctor of Philosophy

270 Pages·2002·4.68 MB·English

THE ACOUSTICS AND PSYCHOACOUSTICS
OF THE GUITAR
by
Howard Wright
A thesis submitted to
the University of Wales
for the degree of
Doctor of Philosophy
Department of Physics and Astronomy,
University of Wales, College of Cardi(cid:11)
September 1996
Declarations
This work has not previously been accepted in substance for any degree and is not being
concurrently submitted in candidature for any degree.
Signed ....................................................................................
Date ......................................................................................
All the work presented in this thesis is the result of my own investigations, except where
otherwise stated. References are given where other sources are acknowledged. A bibliography
is appended.
Signed ....................................................................................
Date ......................................................................................
I hereby give consent for mythesis, if accepted, to be available for photocopying and for inter-
library loan, and for the title and summary to be made available to outside organisations.
Signed ....................................................................................
Date ......................................................................................
Acknowledgements
Iwould liketo thank mysupervisor, Dr. B.E.Richardson, for his helpand support throughout
my period of research. The work presented in this thesis owes much to his enthusiasm and
careful guidance.
I am indebted to Professor R.H. Williams for providing research facilities at the Department
of Physics and Astronomy at UWCC, and to EPSRC for provision of the grant which funded
my research period.
I am also grateful to Professor D. Jones for advice on the preparation and presentation of the
sounds for the psychoacoustical tests, and to Dr. M. Greenhough for allowing me to use the
recording equipment and facilities at UWCC for both work and pleasure.
I would also like to thank all who volunteered for the psychoacoustical tests. It is your
perceptions that have provided some of the most important results. I am grateful to Ed
Burges, Matt Nisbet and Dan Jones, guitarists from the Welsh College of Music and Drama,
who took part in the psychoacoustical work and provided useful feedback from the guitarist’s
perspective.
I thank all the friends and colleagues who have shared in the wonderful times I have spent in
Cardi(cid:11). To Ali and Jon, it was a pleasure to live with such caring and fun-loving (cid:13)atmates.
Manythanks forthe good timeswe shared at number11. Specialthanks goes to Maria, Simon
and Ian, joint founders of the Bedford Street Musical Acoustics Fan Club, and friends with
whom I have shared much music, laughter and alcohol. Many thanks to Mario Antonioletti
who was generous with his time in helping me to overcome a variety of computing problems.
Thanks also to Oona and family for their friendship and support, and to all who sailed with
me on ‘the good ship Bracken Hill’ for helping me to make it through my (cid:12)rst degree.
Finally, thanks to my brother Gordon who helped to stimulate my interest in music and
guitars many years ago, and to my parents for their love and support for the last 25 years.
There is no such thing as music divorced from the listener. Music, as such, is unful(cid:12)lled until
it has penetrated our ears.
Yehudi Menuhin.
Summary
The work presented in this thesis is concerned with the relationships between the perceived
tone qualityof classical guitars and the vibrational behaviour of the guitar body. A numerical
model is described which calculates the sound pressure response of a guitar when a sinusoidal
force is applied to one of its strings. The response of the body is described in terms of its
modes of vibration, eachmode being characterisedby four parameters: a resonance frequency,
an e(cid:11)ectivemass, an e(cid:11)ectivemonopole area and a Q-value. Coupling between the string, top
plate and fundamental modes of the back plate and air cavity is included.
The output of the model represents the sound of a plucked note as heard by a listener at a
givendistanceinfront oftheguitar. Usingnotessynthesisedfromthemodel,psychoacoustical
listening tests are performed which examine the e(cid:11)ect on tone quality of a variety of changes
to the mode parameters.
The thesis is divided into nine chapters. Chapter 1 outlines the aims and methods of the
research. Chapter 2 reviews the literaturerelating to stringed musicalinstruments. Chapter 3
presents a description of the processes that occur in the guitar during sound production.
Chapter 4 outlines the theory for the numerical model. Chapter 5 describes experimental
measurementsof the frequency responses of two guitars and the curve-(cid:12)tting techniques used
toobtain valuesofthefourmodeparametersfora numberofbody modes. Chapter6 describes
experimentalmeasurementsof the coupling between string and body. Chapter 7 describes the
four psychoacoustical listeningtests. Chapter 8 discusses the results of the listeningtests, and
establishes connections between the properties of the body modes and certain characteristics
of tone quality. Chapter 9 presents a brief summary of the conclusions reached, and also
outlines topics for future work.
Contents
Title page 1
Declarations 2
Acknowledgements 3
Quotation 4
Summary 5
Table of contents 6
1 Introduction 1
1.1 Aims of the research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Numerical methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Anatomy and evolution of the classical guitar . . . . . . . . . . . . . . . . . . 6
1.4.1 The top plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.4.2 The back plate and sides . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.4.3 The neck and strings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.4.4 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.5 The ‘quality’ of an instrument . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.6 Sound production in the classical guitar . . . . . . . . . . . . . . . . . . . . . . 12
1.7 The guitar, guitar-player and acoustic environment . . . . . . . . . . . . . . . 13
1.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
CONTENTS 7
2 Previous work on stringed instrument acoustics 18
2.1 Modal analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2 Coupling between top plate and air cavity . . . . . . . . . . . . . . . . . . . . 25
2.3 The string . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.4 Coupling between string and body . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.5 Radiation of sound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.6 Evaluation of an instrument’s sound quality . . . . . . . . . . . . . . . . . . . 39
2.7 Previous work at Cardi(cid:11) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3 The functioning of the guitar: an overview 49
3.1 Plucking of the string . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.2 Transverse string modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.3 Decay rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.4 Coupling between string and body . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.5 Normal modes of the body . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.6 Coupling between air cavity, back plate and top plate . . . . . . . . . . . . . . 60
3.7 Radiation of sound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4 An oscillator model of the classical guitar 63
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.2 Simple model of the top plate . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.3 Coupling between top plate and air cavity . . . . . . . . . . . . . . . . . . . . 65
4.4 Adding a coupled back-plate piston to the system . . . . . . . . . . . . . . . . 68
4.5 Fluid loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.6 The vibrating string . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5 Experimental work: the guitar body 81
5.1 The guitar body . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.2 Velocity response measurements and curve-(cid:12)tting . . . . . . . . . . . . . . . . 83
5.2.1 Mode identi(cid:12)cation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
5.2.2 Coupling between the top and back plates . . . . . . . . . . . . . . . . 93
5.3 Sound pressure responses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
CONTENTS 8
5.4 Back plate response curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.5 Comparisons between measured and synthesised response curves . . . . . . . . 97
5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6 Experimental work: string-body coupling 111
6.1 The free string . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
6.1.1 Decay rates of the string modes . . . . . . . . . . . . . . . . . . . . . . 112
6.2 Response of the bridge to an applied plucking force . . . . . . . . . . . . . . . 115
6.3 Response of the body to a sinusoidal force applied to the string . . . . . . . . 120
6.3.1 Opto-switch callibration . . . . . . . . . . . . . . . . . . . . . . . . . . 120
6.3.2 Callibration of the PC’s analogue to digital converter . . . . . . . . . . 122
6.3.3 Measuring the vertical and horizontal string displacements . . . . . . . 125
6.3.4 Measurements of the coupling between string and body . . . . . . . . . 128
7 Psychoacoustical listening tests 133
7.1 General aims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
7.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
7.3 First listening test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
7.3.1 Aims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
7.3.2 Selection of parameter changes . . . . . . . . . . . . . . . . . . . . . . 142
7.3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
7.3.4 Summary of results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
7.4 Second listening test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
7.4.1 Aims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
7.4.2 Discussion of validity of parameter changes . . . . . . . . . . . . . . . . 150
7.4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
7.4.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
7.4.5 Coincidence of string and body modes . . . . . . . . . . . . . . . . . . 160
7.4.6 Global and local changes . . . . . . . . . . . . . . . . . . . . . . . . . . 164
7.4.7 The body transient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
7.4.8 Summary of results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
7.5 Third listening test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
CONTENTS 9
7.5.1 Aims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
7.5.2 Results: magnitude of the changes in tone . . . . . . . . . . . . . . . . 173
7.5.3 Results: nature of the changes in tone . . . . . . . . . . . . . . . . . . 178
7.6 Fourth listening test: guitarists’ test . . . . . . . . . . . . . . . . . . . . . . . 188
7.6.1 Aims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
7.6.2 Results: magnitude of the changes in tone . . . . . . . . . . . . . . . . 189
7.6.3 Results: nature of the changes in tone . . . . . . . . . . . . . . . . . . 195
8 Discussion: mode properties and tone quality 198
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
8.2 Limitations of the model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
8.3 Summary of listening test results . . . . . . . . . . . . . . . . . . . . . . . . . 203
8.4 In(cid:13)uence of the mode parameters on the response of the guitar . . . . . . . . . 204
8.5 In(cid:13)uence of the body modes on tone quality . . . . . . . . . . . . . . . . . . . 211
8.5.1 Fundamental air-cavity mode: T(1,1)1 . . . . . . . . . . . . . . . . . . 211
8.5.2 The T(1,1)2 mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
8.5.3 The T(1,2) mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
8.5.4 The T(3,1) mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
8.5.5 The T(2,1) mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
8.5.6 Modes of the back plate . . . . . . . . . . . . . . . . . . . . . . . . . . 227
8.5.7 Mid-frequency top-plate modes . . . . . . . . . . . . . . . . . . . . . . 228
8.5.8 High-frequency top-plate modes . . . . . . . . . . . . . . . . . . . . . . 232
8.6 Implications for the guitar maker . . . . . . . . . . . . . . . . . . . . . . . . . 234
8.6.1 Mode frequencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
8.6.2 Altering the body modes . . . . . . . . . . . . . . . . . . . . . . . . . . 237
9 Conclusions 242
9.1 Linking the properties of the body modes with tone quality: a summary. . . . 242
9.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
A Theory detail 247
A.1 Solution for the motion of coupled top-plate and air-cavity pistons . . . . . . . 247
A.2 Solution for the system of coupled top-plate, back-plate and air-cavity pistons 249
CONTENTS 10
B Equipment speci(cid:12)cations 253
B.1 Equipment used for acoustic measurements . . . . . . . . . . . . . . . . . . . . 253
B.2 Equipment used for psychoacoustical listening tests . . . . . . . . . . . . . . . 255