Table Of ContentGiuseppe Cuzzucoli
Mario Garrone
Classical Guitar
Design
Classical Guitar Design
Giuseppe Cuzzucoli Mario Garrone
(cid:129)
Classical Guitar Design
123
Giuseppe Cuzzucoli Mario Garrone
Pianezza,Turin, Italy AcquiTerme, Alessandria, Italy
Translated byPietro Ivaldi
ISBN978-3-030-32991-4 ISBN978-3-030-32992-1 (eBook)
https://doi.org/10.1007/978-3-030-32992-1
Translation from the Italian language edition: La Progettazione della Chitarra Classica by Giuseppe
CuzzucoliaandMarioGarrone,©SpringerNatureSwitzerlandAG2020.AllRightsReserved.
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felix qui potuit rerum cognoscere causas
Virgil (70–19 BC) II Georgic
Preface
The miracle of creating an outstanding musical instrument cannot be explained by
science.Wekeptthatinmindwhilewritingthefirstpartofthisbook(Chaps. 1–6)
whereweillustratedthephysicalandacousticworkingsoftheclassicalguitar.The
miracle of creating an outstanding musical instrument arises primarily from the
experience, sensibility and creativity of the luthier.
However, we believe that all of us (guitar-makers included) can go beyond
personalexperience,stilltakingadvantageofit.Ifwedonotreach outofwhatwe
learned,andwealways didwell,experience—though endowedwithcreativity and
sensibility—willturnintoacage.Onthecontrary,ifwegrabthechancetoexplore
newpaths,thenknowledge(ifnotscience)willbetheguidebeyondourlimits.This
is the purpose in the second part of the book: trying to connect knowledge with
experience, never disregarding the value of personal creativity and sensibility.
The title may be surprising: Classical Guitar Design. We normally think of a
bridge, or a car engine, being designed. Commonly, a musical instrument must be
just built.
The starting point in designing is our idea of the features and performances we
expect from the final object. Secondly, we manufacture it according both to
experience and to processing of new information. In order to get a detailed
knowledgeoftheobject,wemustusepropermodelsandsimulations.Wealsoneed
to apply suitable technological tools to assess the potential performances in
pre-construction laboratory tests. This will enable us to take the steps required to
fulfil our expectations.
Of course, we need a good deal of sensibility and creativity. What we suggest
here is in the first place an intellectual and cultural approach, which will guide us
through the guitar manufacturing procedure.
Allguitar-makershavean‘expectedperformance’:theconceptofthesoundthey
demand from their instruments. How can we express this concept in measurable
parameters?Wefirstlyexaminedtheguitarsoundanddevelopedqualityevaluation
criteria that can be applied to any instrument. Then we got a deeper knowledge
vii
viii Preface
of the instrument to be created: the implementation of proper models and mea-
surement methods (both hardware and software) allows in-progress evaluation
oftheinstrumentperformanceandrevealsthenecessarystructuraladjustments.We
examined the resonator elements separately, and then we assembled them in order
to estimate the guitar resonator as a global object. New tools, and how they assist
traditional construction techniques are also illustrated here. For example, a partic-
ularshape forin-progressfine-tuningofthebackandsoundboard.Workingonthe
soundboardwhenmountedontheframe(withouttheback)isaveryimportantand
usefulprocedurebecause,thisway,allinternalelementscanbeeasilyreached and
modified.Anin-depthstudyofthebackboardresponseisalsopresentedinthetext,
aswhenproperlysized,thiscomponentcanfavourablyaffectthequality ofsound.
Furthermore, quantitative parameters are provided for the evaluation of timbers
employedinlutherie.Finally,thesamemethodisappliedtotheanalysisoffinished
guitars, some of which being very important in the guitar-making history. This
reverse engineering process provides much noteworthy information about engi-
neering guidelines that inspired the construction of these guitars.
Thisbookismainlyaddressedtoguitar-makers.Manyamongthemfeeltheneed
to go beyond the limits of their experience and gain a better understanding of the
workings in the instrument they are manufacturing. This turns into a more con-
sciousandrationalexperimentation.Ifthisbookcontributestoenlargethiscategory
of luthiers, a first and most important goal will be achieved.
Secondly, this book is addressed to guitar-players—whether professionals,
amateurs or students who will maybe find an answer to some questions they have
about the guitar sound. Moreover, they will cast a look upon the ‘magic’ realm of
guitar-making(whichisnotso‘magic’,actually).Maybe,followingtheindications
exposed here, some ofthem will try tobuild up aguitarof their own, even if their
aimisnottobecomeprofessionalluthiers.Stepbystep,theywillbeconqueredby
how some wooden parts change into a guitar. They will learn how to design,
experiment, act on this object under construction right to the finished, playable
instrument! If the book answers questions and encourages initiative, our second
purpose will be fulfilled.
Lastbutnotleast,thebookisaddressedtoreaders having atechnicaleducation
in Physics or Engineering, who are curious about how some basic notions can
explain the acoustic workings in a musical instrument. We apologize for inaccu-
racies or omissions they may find in the text, hoping they will report them to us.
Mathematical formulae were reduced to a minimum and demonstrations omitted,
being the whole subject available in specific textbooks and essays.
After all, this book is not ‘just’ concerned with classical guitar building, nor is
the mere description of a physical model, disconnected from the manufacturing
practice. In both cases, plenty of publications are available. We tried to develop
theoretical analysis and manufacturing practice as two parallel melodic lines that
intertwine, interact and sometimes superpose to build the harmony of a piece of
music.Ifthereadersharesthisfeeling—tosomeextent,atleast—ourthirdgoalwill
be reached.
Preface ix
Wetriedtoofferthemostdetaileddescriptionofthehardwareandsoftwaretools
employed in the examination and fine-tuning of instruments. Should our explana-
tions appear incomplete or, hopefully, arouse new questions, we are available for
constructive discussion.
The following list of sources is just a selection of the most important publica-
tions that support our investigation. Readers willing to expand their knowledge
of the subjects discussed in the book can refer to these authors. On our part, we
wishforresearchaimingtoforwardtheknowledgeandengineeringoftheclassical
guitar.
Pianezza, Italy Giuseppe Cuzzucoli
Acqui Terme, Italy Mario Garrone
Suggested Readings
1. Caldersmith, G. (1978). Guitar as a reflex enclosure. Journal of the Acoustical Society of
America,63(50).
2. Caldersmith, G., Freeman, E. (1990). Wood properties from sample plate measurements.
CatgutAcousticSocietyJournal,1(5).
3. Christensen, O. & Vistisen, B. B. (1980). Simple model for low frequency guitar function.
JournaloftheAcousticalSocietyofAmerica,68(30).
4. CremerL.(1984).Thephysicsoftheviolin.Cambridge:TheMITPress.
5. Cuzzucoli,G.,Lombardo,V.(1999).Aphysicalmodeloftheclassicalguitar,includingthe
player’stouch.ComputerMusicJournal,23(2).
6. Fletcher,N.H.&Rossing,T.D.(1991).ThePhysicsofacousticalinstruments.NewYork:
Springer-Verlag.
7. Garrone,M.(1994).Lacostruzionedellachitarraclassica.Ancona:EdizioniBèrben.
8. Jansson,E.V.(1971).Astudyofacousticalandholograminterferometricmeasurementson
thetopplatevibrationsofaguitar.Acustica,25.
9. Jansson,E.V.(2002).Acousticsforviolinandguitarmakers.www.speech.kth.se/music.
10. Meyer,J.(1985).Akustikdergitarreineinzeldarstellungen.Frankfurt:VerlagE.Bochinsky.
11. Morse,P.M.&Ingard,K.U.(1968).Theoreticalacoustic.NewYork:McGraw-Hill.
12. Righini,P.&Righini,G.U.(1974).Ilsuono.Milano:TamburiniEditore.
13. Rossing, T. D. (1983) An introduction to guitar acoustic. Guild of American Luthiers
Quarterly,11(4).
14. Rossing, T. D., Popp, J. & Poltein, D. (1985). Acoustical response of guitars. Proceedings
SMAC83.Stockholm:RoyalSwedishAcademyofMusic.
15. Sali,S.&Kopac,J.(2002).Positioningofbracesonaguitarsoundboard.ProceedingsIMAC
XX709–715.
Contents
1 The Sound. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Fundamental Sound Parameters . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Elementary Sounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Sound Representations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4 The Sound of the Guitar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.4.1 The Waveform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.4.2 The Spectrum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.4.3 The Sound Spectrogram and the Variation
of Harmonics Over Time . . . . . . . . . . . . . . . . . . . . . . 12
1.5 The Quality of Timbre in a Guitar. . . . . . . . . . . . . . . . . . . . . . 17
1.6 Relation Between Quality and Physical Parameters. . . . . . . . . . 18
1.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2 The String. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.1 The Ideal String . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.2 The Real String . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3 Oscillating Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.1 Natural Frequencies in Oscillating Systems . . . . . . . . . . . . . . . 43
3.1.1 Modal Frequencies . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.1.2 Adding a Longitudinal Wood Strip . . . . . . . . . . . . . . . 51
3.1.3 Arching the Table . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.2 The Resonance Phenomenon . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.2.1 The Transient Response . . . . . . . . . . . . . . . . . . . . . . . 61
3.3 Multiple Resonances and Antiresonances . . . . . . . . . . . . . . . . . 66
4 The Resonator Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.1 Vibration of the Air in the Guitar Body . . . . . . . . . . . . . . . . . . 70
4.1.1 Measurement of Oscillation Modes in the Cavity . . . . . 72
4.1.2 Mode 〈0 1〉 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
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xii Contents
4.1.3 Mode 〈1 0〉 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.1.4 Mode 〈0 2〉 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.1.5 Mode 〈1 0〉 in the Upper Volume . . . . . . . . . . . . . . . . 77
4.1.6 Helmholtz Resonance (Mode 〈0 0〉) . . . . . . . . . . . . . . 79
4.2 Fundamental Vibration Modes of the Soundboard. . . . . . . . . . . 83
4.2.1 Vibration Modes and Natural Frequencies of the
Fastened Table. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.3 Fundamental Vibration Modes of the Back. . . . . . . . . . . . . . . . 87
Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5 The Resonator as a Global System . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.1 Fundamental Resonances. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.2 Nature of the Fundamental Resonances . . . . . . . . . . . . . . . . . . 101
5.3 Coupled Oscillators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5.4 The Resonator Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
5.4.1 Fundamental Resonator Parameters . . . . . . . . . . . . . . . 117
5.4.2 The Vibrating Surface. . . . . . . . . . . . . . . . . . . . . . . . . 118
5.4.3 The Vibrating Mass . . . . . . . . . . . . . . . . . . . . . . . . . . 119
5.4.4 Soundboard Mean Stiffness. . . . . . . . . . . . . . . . . . . . . 121
5.4.5 Assessment of the Vibrating Surface . . . . . . . . . . . . . . 122
5.4.6 The Coupling Coefficient . . . . . . . . . . . . . . . . . . . . . . 123
5.4.7 Sound Pressure Level . . . . . . . . . . . . . . . . . . . . . . . . . 124
5.4.8 Overview of the Resonator Parameters. . . . . . . . . . . . . 126
5.4.9 From Soundboard Natural Frequency to Basic
Resonances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
5.5 The Back (Unveiling a Mystery) . . . . . . . . . . . . . . . . . . . . . . . 130
5.5.1 The Back as a Helmholtz Resonator Wall . . . . . . . . . . 131
5.5.2 Influence of the Back on Basic Resonances . . . . . . . . . 134
5.5.3 TheBehaviouroftheBackWhenFastenedtoaRigid
Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
5.6 Contribution of the Back to Resonances. . . . . . . . . . . . . . . . . . 140
5.6.1 Resonances of the Back. Mode 〈0 0〉. . . . . . . . . . . . . . 140
5.6.2 Resonances of the Back. Modes 〈0 1〉 and 〈0 2〉 . . . . . 146
5.6.3 Other Resonances from the Closed Back Response . . . 147
5.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
6 Upper Resonances. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
6.1 Resonances in the Mid-High Register . . . . . . . . . . . . . . . . . . . 161
6.1.1 The Guitar Resonance in Mode 〈0 1〉 . . . . . . . . . . . . . 161
6.1.2 The Guitar Resonance in Mode 〈2 0〉 . . . . . . . . . . . . . 164
6.1.3 Resonance of the Back at 610 Hz . . . . . . . . . . . . . . . . 167
