Ebony vs. Rosewood: experimental investigation about the influence of the fingerboard on the sound of a solid body electric guitar

Full text

Ebony vs. rosewood: experimental investigation about the influence of the
fingerboard on the sound of a solid body electric guitar
Arthur Pat´
e, Jean-Lo¨
ıc Le Carrou, Benoˆ
ıt Fabre
LAM / Institut Jean Le Rond d’Alembert
UPMC Univ Paris 06, CNRS UMR 7190
pate@lam.jussieu.fr
ABSTRACT
Beyond electronics, lutherie also has something to do with
the sound of the solid body electric guitar. The basis of
its sound is indeed the conversion of the string vibration to
an electrical signal. The string vibration is altered by cou-
pling with the guitar at the neck. Electric guitar lutherie
being a huge topic, this paper focuses on the influence of
the fingerboard on the string vibration. An experimen-
tal study is carried out on two guitars whose only inten-
tional difference is the fingerboard wood: ebony or rose-
wood. The well-known ”dead spot” phenomenon is ob-
served, where a frequency coincidence of string and struc-
ture at the coupling point leads to an abnormal damping
of the note. Striking is the different behaviour of each fin-
gerboard wood about dead spots: affected notes, as well as
how much they are affected, differ with the wood.
1. INTRODUCTION
Physical studies about the solid body (without soundbox)
electric guitar have been mainly focused on electronics,
whether it is on the string transduction by the pickup [1,2],
the effects and processing chain [3] or the amplifier [4],
often with the purpose of doing numerical synthesis. The
characteristics of the pickup (transducing the velocity of
the string into an electrical signal), effect pedals (trans-
forming this signal with endless possibilities), amplifier
(far away from high-fidelity), loudspeakers (reproducing
and distorting the final sound) are of course of significant
importance. But lutherie is at least partially responsible
for the sound. The vibration of the string is altered by the
coupling to a moving structure (the guitar) at its ends. The
structure may vibrate and exchange energy with the string,
like it is the case for e.g. the classical guitar [5] or the harp-
sichord [6].
The coupling of a string to a structure is described in [7].
The admittance of the structure at the coupling point causes
the frequencies and dampings of the coupled-string partials
to differ from those in the uncoupled case (string with two
rigid ends). This admittance at the coupling point is known
as the ”driving-point admittance”. It is defined by the ra-
tio in the frequency domain between the velocity V(ω)of
Copyright: c
2013 Arthur Pat´
e et al. This is an open-access article distributed
under the terms of the Creative Commons Attribution 3.0 Unported License, which
permits unrestricted use, distribution, and reproduction in any medium, provided
the original author and source are credited.
the structure at the coupling-point and the force F(ω)ap-
plied on the same point. Driving-point admittance can be
obtained by classical measurements on relevant coupling
points between the string and the structure, typically on the
neck [8,9]. The real part of this driving-point admittance is
called the driving-point conductance. It provides addition-
nal damping to the string [7]. Measurements in [9] qualita-
tively link a measured high conductance value at a specific
frequency with the fast decay of the note at the same fre-
quency, when fretting point and measurement point are the
same. Notes affected by an abnormally big damping are
known as ”dead spots”. Damping inhomogeneity among
notes is known to be disturbing for the players.
The vibrational behaviour of the structure, seen by the
string as end conditions, is influenced by many parame-
ters. Electric guitars can differ in many things [10]: shape
of the body and headstock, wood used for body, finger-
board or neck, bridge type, nut material, size and material
of the frets, neck profile. . . Each of these lutherie parts
changes the vibrational behaviour of the structure and then
may alter the sound.
Fleischer and Zwicker [8] studied a Gibson Les Paul and
aFender Stratocaster, which have been the two reference
models in the electric guitar industry [10]. Differences in
modal behaviour are found and are attributed to the sym-
metry of the headstock. However, these two guitars dif-
fer not only in the headstock shape, but also in the wood
species, the body shape, . . .
In order to draw conclusions about the influence of a
lutherie parameter, this parameter should be the only vary-
ing one. This paper is part of a broader project [11, 12]
aiming at studying the influence of each lutherie parameter
taken separately. Here the spotlight is on the study of the
fingerboard wood on the sound. An experimental investi-
gation of ebony and rosewood fingerboards is presented.
These are two out of three (the other one being maple) typ-
ical woods used for solid body fingerboards.
Section 2 gives a simple model of string-structure cou-
pling and its consequences on string frequency and dam-
ping. Section 3 describes the experimental protocol, and
quantitatively checks the model of section 2: the string
damping value can be predicted from the conductance value.
Section 4 discusses the change in sound induced by the
change in fingerboard wood.

2. MODEL
A simple model of a stiff lossy string connected at one
end to a moving body is proposed. The moving-end string
model is derived as small perturbations of the stiff string
model simply-supported at its two ends. The theory has al-
ready been detailed by [7] and it is briefly described here.
Let xbe the axis of the string at rest position and yits mo-
tion normal to the fingerboard plane. The string is simply-
supported at x= 0 and x=L. It is stretched with tension
T. The string is also characterised by its mass per unit
length ρL, second moment of area Iand Young’s Modulus
E. The dispersion relation is:
ω0
n=ck0
n1+(k0
n)2EI
2T(1)
where c=qT
ρLis the wave velocity, κ=qT
EI is the
stiffness term and k0
n=nπ
Lis the quantized (nis a posi-
tive integer) wavenumber for simply-supported end condi-
tions.
The string loses energy through three damping mecha-
nisms: visco-elasticity, thermo-elasticity and air damping.
Let ξ0
nbe a damping coefficient taking into account those
three damping mechanisms. It is frequency-dependent be-
cause it depends on the partial number n. The damping
ξ0
nis generally added as the imaginary part of the complex
angular frequency, so that the dispersion relation becomes:
ω0
n=ck0
n1+(k0
n)2EI
2T−2jξ0
n(2)
Yet the string is not simply-supported at its ends. One end
is connected to the bridge and the other end is connected
at the neck to a fret or to the nut. What [8, 9] showed was
checked: most of the time the motion of the end connected
to the bridge is small compared to the motion of the end
connected to the neck. The bridge end (at x= 0) is still
assumed to be rigid whereas the other end (at x=L) is
connected at the neck to the admittance of the moving gui-
tar. The moving end at x=Lonly causes small perturba-
tion δkn1to the wavenumber k0
n, so that the corrected
wavenumbers kn=k0
n+δknare used.
At x=L, the string’s admittance is defined as the ratio
between its velocity and the force being applied on it:
Ystring (L, ωn) =
∂y
∂t (L, t)
−T∂y
∂x (L, t)=jtan(knL)
Zc
(3)
where Zc=√ρLTis the characteristic impedance of the
string. At x=L, the string and the structure are connected
and must have the same admittance. Letting Y(L, ω)be
the admittance of the structure at the connection point, one
has :
Y(L, ω) = Ystring (L, ω)(4)
Remembering that tan(k0
nL)=01and assuming that
ZcY(L, ωn)12, equation 3 leads to the expression of
1k0
nis the the simply-supported end solution for the wavenumber
2The impedance of the structure is much greater than the characteristic
impedance of the string, resulting in a reflection of travelling waves in the
string at the connection point
kn:
kn=k0
n+δkn=nπ
L−jY(L, ωn)Zc
L(5)
with which equation 1 becomes:
ωn=nπc
L1 + n2π2E I
2T L2−2jξ0
n−jY(L, ωn)Zc
nπ (6)
ωnare the complex angular frequencies of a stiff lossy
string having a moving end. Modal frequency is defined
as :
fn=Re(ωn)
2π=nc
2L1 + n2π2
L2
EI
2T+Zc
nπ Im(Y(L, ωn))
(7)
and modal damping as:
ξn=−Im(ωn)
2knc=ξ0
n+Zc
2nπ Re(Y(L, ωn)) (8)
The imaginary part of the body admittance implies a shift
in the simply-supported string frequencies, affecting the
inharmonicity [13]. Nevertheless, measured admittance
imaginary parts on the tested guitars never lead to a fre-
quency shift larger than 1Hz. For this reason this paper
only discusses the influence of the real part of the admit-
tance, the conductance.
3. EXPERIMENTAL STUDY
The main effect of string-structure coupling is the damping
due to the conductance. The experimental study identifies
the conductance terms C(ω) = Re(Y(ω)) at the points
where the strings couple to the structure 3, that is on the
fingerboard.
3.1 The two guitars of the study
This experimental study is intended to determine what dif-
fers in the sound when changing the fingerboard wood.
The fingerboard should therefore be the only varying lu-
therie parameter. In order to fulfil this recommendation,
a collaboration with instrument-makers was developped.
Two guitars were made by luthiers from Itemm 4, a french
leading lutherie training-center. The two guitars follow the
specifications of the Gibson Les Paul Junior DC, a ver-
sion of one of the two most important solid body electric
guitars in history [10]: original shape, quartersawn ma-
hogany for body, neck and head, set-in neck, same equip-
ment (bridge, bone nut, P-90 pickup). The only inten-
tional difference between the two guitars is the fingerboard
wood. One guitar has an ebony fingerboard (E) and the
other one a rosewood fingerboard (R). It should be kept
in mind that other parameters may differ between the two
guitars, mainly because of the wood variability and the
handmade process. For schedule reasons, the guitars could
not be measured prior to the gluing of the fingerboard.
3Measurements of this section are made at the connected end of the
string, so the dependence in Lof Y(L, ω)is no longer specified.
4http://www.itemm.fr

impact point
woodpiece bridge
accelerometer
nut
Figure 1. Setup for driving-point conductance measure-
ment along the 5th string’s axis, at a particular fret. An
accelerometer is put on the one side of the fret. The ham-
mer strikes at the other side of the fret. A very light piece
of wood moves aside the strings and allows the accelerom-
eter to stay between the two strings.
Samples of the woods used for the fingerboards were pro-
vided. Ebony density ρE=1180kg.m−1and rosewood
density ρR=751kg.m−1are simply measured. Longi-
tudinal Young’s moduli EE= 3.02 1010Pa and ER=
2.30 1010Pa are identified with simple bending test. The
two fingerboard woods have different characteristics: fit-
ting the neck with one or another fingerboard wood may
then change the vibrational behaviour of the instrument.
3.2 Experimental setup
The experimental setup is sketched in figure 1. The con-
ductance is measured at every potential coupling point be-
tween string and structure, that is at every fret-string cross-
ing on the neck. As in [9], only the conductance normal
to the plane of the fingerboard is studied. Only the cou-
pling of the string polarisation in this direction is studied
in this paper. As usual, force F(ω)is applied with an im-
pact hammer equipped with a force sensor, and velocity
V(ω)is measured with an accelerometer. Impact and mea-
surement points must be as close as possible in order to ob-
tain actual driving-point conductance. The modal domain
(where peaks and modes are well identified) is from 20Hz
to 700Hz. The useful impact bandwidth is from 20Hz to
2000Hz. It is decided to consider the coupling of only the
fundamental frequency with the structure, so that n= 1 in
all equations of the section 2. The guitar is laid on elastic
straps supported by a frame. Resonant frequencies of the
system {frame-straps}is below the resonant frequencies of
the guitars, so that this setup provides a good approxima-
tion for free boundary conditions. Modeling clay is put on
the pegs and on the screw of the truss rod to prevent them
from vibrating. Paper is used to avoid string vibrations,
which are unwanted here for the study of the guitar only.
Section 3.3 experimentally checks the model of section
2.
100 200 300 400 500 600 700 800 900 1000
0
0.01
0.02
0.03
0.04
0.05
0.06
Frequency [Hz]
Re(Y) [m.s−1.N−1]
f0(F4) = 349 Hz
E
R
Figure 2. Driving-point conductance at the 6th fret along
the 2nd string’s axis. Solid line is used for the guitar E
and dashed line for the guitar R. Gray line highlights the
fundamental frequency of the F4 played at this place.
3.3 Validation of the model
In order to validate the model of section 2, a simple check
is done. Figure 2 is an example (further discussed in sec-
tion 3.4) of measured driving-point conductance: here at
the 6th fret along the 2nd string for both guitars. The cor-
responding note is F4 with fundamental frequency fF4=
349Hz. This note is also recorded by picking the string
with a guitar pick, fretting the 6th fret with a capo and
taking the output signal of the guitar pickup. Figure 3
shows the temporal evolution of the fundamental of this
note. This temporal evolution is extracted from the recorded
signal. It is obtained by computing a short-time Fourier
transform of the signal and determining the envelope of
the bin centered on the fundamental frequency. The time
constant τ, defined as the time needed for the amplitude to
get divided by Euler’s number e, can be estimated from the
fundamental envelope signals for guitars E and R. The esti-
mation of the global damping terms ξE
F4= (2πfF4τE
F4)−1=
2.8 10−4and ξR
F4= (2πfF4τR
F4)−1= 1.4 10−3is straight-
forward. Superscripts ”R” and ”E” refer to guitar R and E
respectively. Subscript refers to the note.
Identical string sets provided the string for both guitars.
String damping ξ0
F4is then assumed to be the same for
both guitars. The magnetic pickup could be a cause of
string damping as well. Since the guitars are equipped with
pickups of the same model series, the magnetic damping is
assumed to be the same for both guitars. This magnetic
damping can be included in ξ0
F4. According to equation 8
with C(ω) = Re(Y(ω)), one expects :
ξR
F4−ξE
F4=Zc
2πCR(2πfF4)−CE(2πfF4)(9)
Estimating the conductance values from measurements pre-
sented in figure 2 (CE(2πfF4)=1.9 10−3m.s−1.N−1and
CR(2πfF4)=3.2 10−2m.s−1.N−1) leads to:
ξR
F4−ξE
F4= 1.1 10−3(10)
Zc
2πCR(2πfF4)−CE(2πfF4)= 1.0 10−3
ξ0
F4can be identified by subtracting the term Zc
2πC(2πfF4)
from the experimental ξF4. The line with crosses in figure

012345
10−4
10−3
10−2
10−1
100
Time [s]
Normalised amplitude
Measure (E)
Measure (R)
Model with rigid ends
Figure 3. Temporal evolution of the fundamental fre-
quency of the F4 (6th fret and 2nd string) played on both
guitars. Solid line is for guitar E, dashed line is for gui-
tar R, crosses show the computed decay of the same string
with rigid ends.
3 is the decay curve with identified ξ0
F4= 2.3 10−4.
The small difference between the two lines of equation
10 can be explained by our estimation of τ, and by the ac-
curacy of our measurements. Nevertheless, the two values
are quite close and the model of section 2 is validated.
3.4 Observation of dead spots
Figure 2 shows that at the fundamental frequency of the
note, the conductance takes a low value for the guitar E.
Thus the factor Re(Y)in equation 8 is small and so should
be the string damping due to coupling with support. This is
checked in figure 3 and in the calculations of section 3.3:
the experimental computed decay is close to the intrinsic
decay (i.e. the rigid-ends case).
On the other hand, figure 2 shows a high conductance
value for the guitar R. Figure 3 and calculations of section
3.3 confirm the ”abnormal” damping of the fundamental.
This damping is indeed higher for the guitar R, and the de-
cay curve exhibits two slopes instead of the single slope
decay for ”normal” cases.
These two phenomena are consistently checked on the
two guitars: a low conductance value leaves the note’s
decay unperturbed (live spot), a high conductance value
makes the decay of the note shorter (dead spot).
When looking at other notes, it is found that both finger-
boards exhibit dead spots. However, the note studied in
this section showed a difference between the two finger-
board woods: for the same note at the same place on the
neck, a guitar exhibited a live spot whereas the other ex-
hibited a dead spot. Section 4 deals with the differences in
sound that may appear between the two guitars.
4. SOUND DIFFERENCES BETWEEN THE TWO
FINGERBOARDS
The two fingerboard woods lead to the same dead/live spot
phenomenon. However, it does not break out the same way
depending on the instrument.
Figure 4. Guitar E: driving-point conductance values in
the frequency range [20Hz–1000Hz] for all frets along the
2nd string. White crosses spot the fundamental frequencies
of the notes played at each fret of the 2nd string. Unit of
conductance is m.s−1.N−1.
Figure 5. Rosewood-fingerboard guitar: driving-point
conductance values in the frequency range [20Hz–
1000Hz] for all frets along the 2nd string. White crosses
spot the fundamental frequencies of the notes played at
each fret of the 2nd string. Unit of conductance is
m.s−1.N−1.
4.1 Dead spot location
Section 3.4 indicates that a difference between the two gui-
tars is the places where dead spots occur. Since the repre-
sentation of figure 2 is hard to handle if one wants to have
an overview of every fret of one string, figures 4 and 5 pro-
pose a synthetic view of the string-structure frequency co-
incidences, a ”dead spot map”. The frequency-dependant
driving-point conductance values at every fret along one
string are represented on the same plot. Conductance value
is transcribed as a continuous color coding from blue (very
low conductance) to red (conductance peak). For each
fret, the fundamental frequency of the note is plotted with
a white cross. Hence, whenever a white cross gets close
enough to a red spot, a dead spot is reached.
Figures 4 and 5 can be used to quantify the number of
dead spots of a guitar. Here on the 2nd string, the rosewood-
fingerboard guitar has one dead spot (6th fret) and none at
any other place. ”Corresponding” dead spot for the gui-
tar E is moved to the 7th and 8th frets. A first remark can
be done, when looking at the ”dead spot maps” for all six
strings (five are not showed in this paper): the number of

110 120 130 140 150 160 170 180 190 200 210
0
0.02
0.04
0.06
0.08
Frequency [Hz]
Re(Y) [m.s−1.N−1]
f0(D#3) = 155 Hz E
R
Figure 6. Driving-point conductance at the 1st fret along
the 4th string’s axis. Solid line is used for the guitar E and
dashed line for guitar R. Gray line highlights the funda-
mental frequency of the D#3 played at this place.
dead spots is roughly the same between the two guitars, but
their locations often slightly (one or two frets) differ.
A second remark is that the conductance peaks (for ex-
ample figures 4 and 5 around 400Hz and between 600Hz
and 700Hz) seem to be higher for the guitar R than for the
guitar E. This is the purpose of section 4.2.
4.2 Dead spot dangerousness
Another kind of difference between the two fingerboard
woods is the amplitude of conductance peaks, that is the
potentially high damping of the note. That is what we
call the ”dangerousness” of a dead spot. Most of the mea-
surements show that higher values of driving-point con-
ductance are reached for the rosewood-fingerboard guitar.
Figure 6 illustrates this tendency. It shows the measure-
ment at 1st fret along the 4th string for both guitars. The
conductance at the frequency of the note (D#3,155Hz) is
high for both guitars. Estimation of experimental damping
coefficient ξas in section 3.3 leads to ξE
D#3 = 1.0 10−3
and ξR
D#3 = 2.4 10−3in this case. ξ0
D#3 is estimated as
in section 3.3: ξ0
D#3 = 3.0 10−4. For both guitars, ξD#3
is much higher than ξ0
D#3: this clearly reveals a common
dead spot. However, the dead spot is more pronounced for
the guitar R than for the guitar E. Guitar R’s conductance
peak is closer to the frequency of the note than guitar E’s
one, and guitar R also has a higher peak guitar E’s one.
Whatever the tuning (determining the frequencies of the
notes) is, the string-structure coupling still occurs because
the neck conductance still takes non-zero values. In order
to characterise this conductance amplitude difference ten-
dency between guitars E and R in a more tuning-indepen-
dent way, a mean conductance value is computed. For each
measurement (each fret) along a string, the mean of the
conductance is computed in the frequency range [20Hz–
2000Hz]. Figure 7 presents these computed mean conduc-
tance values as a function of the place on the neck along
the 2nd string. For every fret the guitar R clearly stands
out from the guitar E with systematically higher mean con-
ductance. This would mean that whatever the tuning is, the
rosewood-fingerboard guitar is likely to grasp more vibrat-
ing energy from the string.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
0
1
2
3
4
x 10
−3
Fret number
Mean Re(Y) [m.s−1.N−1]
E
R
Figure 7. Mean value of conductance in the fre-
quency range [20Hz–2000Hz] as a function of fret num-
ber/measurement place along the 2nd string. Solid line is
used for the guitar E and dashed line for the guitar R.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
� [s]
Fret number
E
R
Figure 8. Computed time constants τfor each note of the
2nd string. A bandpass filter ([20Hz-2000Hz]) was applied
to each note. Solid line is used for the guitar E and dashed
line for the guitar R.
In figure 7 it can be seen that above 15th fret, the two
curves become closer and the mean conductance tends to
become smaller. This is because 15th fret and upper frets
are close to the neck-body junction, an area where the neck
motion is smaller.
These mean conductances can be linked to the computed
time constants τfor each note along the 2nd string showed
in figure 8. This computation is slightly different from sec-
tion 3.3: a bandpass-filter (20Hz to 2000Hz) is applied to
the pickup signal and τis computed from this filtered sig-
nal. Guitar E almost always has a higher time constant.
The smaller damping (for every partial in the frequency
range [20Hz-2000Hz]) due to the smaller mean conduc-
tance for guitar E results in a higher time constant τ.
The mean conductances and the time constants are com-
puted along the five other strings. The tendency is con-
firmed: the guitar E almost always has a lower mean con-
ductance value and a higher time constant. Rosewood might
then perturb the string more than ebony.
5. CONCLUSION
Previous results on the influence of the structure on the
vibration of the string have been confirmed. Because the

vibrational behaviour of the electric guitar is highly depen-
dent on the lutherie parts, which are numerous, it was de-
cided to focus on the influence of a single lutherie parame-
ter: the most prominent difference between the two guitars
of the study was the wood of the fingerboard (ebony or
rosewood). Comparative study of sound and driving-point
conductance on these two guitars indicate that the wood of
the fingerboard may have an influence upon the:
•dead spot location: the spatial and frequency coin-
cidence of string and guitar resonances happens at
different places depending on the fingerboard wood
•dead spot dangerousness: when this coincidence
happens, the string damping may be bigger for rose-
wood-fingerboard guitar
Experimental investigation about dead spots and the re-
lated discussion are naturally not only valid for the fun-
damental of the string but also for partials. As equation 8
shows, each string partial may couple with higher structure
modes. Hence the timbre is affected by the fingerboard.
The sound differences that may be induced by the change
of fingerboard wood can then have consequences in:
•instrument-making: the guitar maker could attempt
to change the resonance coincidences: for example
fingerboard thickness, shape (the so-called ”slim”
and ”slapboard” fingerboards by Fender) or sawing
angle are parameters changing the modes of the struc-
ture. Hence the instrument-maker can reduce the
differences between the woods or on the contrary in-
crease them.
•playing: the same note can be played at different
places on the neck. Depending on the location and
dangerousness of the dead spots, the player may be
forced to avoid certain places on the neck and to con-
form his playing to the guitars’ sound.
•tuning: actually, the frequency coincidence between
the string and the structure depends on the tuning of
the string. In order to avoid a too strong coupling,
the guitar player can slightly change the tuning of the
strings. This could be an explanation to the fact that
some guitar players say that a guitar sounds better
with a special tuning (e.g. all the strings a whole-
tone lower) than with the standard tuning A-440Hz.
A perceptual study involving the two guitars of this paper
has been carried out. The analysis is in progress and is
expected to tell us to what extent the differences found here
are perceptible for the guitar player.
Acknowledgments
The authors pay a special tribute to the luthiers Vincent
Charrier, Lo¨
ıc Keranforn, Lisa Marchand, Bela Pari, Alex-
andre Paul and Julien Simon and warmly thank as well
Yann-David Esmans, Fred Pons and Pierre Terrien from
Itemm. The efficient mediation of Vincent Doutaut made
the collaboration with instrument-makers possible.
The authors also thank R´
emi Blandin for his helpful con-
tribution to the measurements on the guitars, and Benoˆ
ıt
Navarret for fruitful discussion.
6. REFERENCES
[1] D. Queen, “From boom boxes to Beatles, Baez and
Boccherini, the electric guitar at the crossroads,” in
Proceedings of the 31st Convention of the AES, 1966.
[2] N. G. Horton and T. R. Moore, “Modeling the mag-
netic pickup of an electric guitar,” American Journal of
Physics, vol. 77 (2), pp. 144–150, 2009.
[3] O. Kr ¨
oning, K. Dempwolf, and U. Z ¨
olzer, “Analysis
and simulation of an analog guitar compressor,” in Pro-
ceedings of DAFx11, 2011.
[4] I. Cohen and T. H´
elie, “Real-time simulation of a guitar
power amplifier,” in Proceedings of DAFx10, 2010.
[5] C. Lambourg and A. Chaigne, “Measurements and
modeling of the admittance matrix at the bridge in gui-
tars,” in Proceedings of SMAC 93, 1993, pp. 448–452.
[6] N. H. Fletcher, “Analysis of the design and perfor-
mance of harpsichords,” Acustica, vol. 37, pp. 139–
147, 1977.
[7] A. Hirschberg, J. Kergomard, and G. Weinreich, Me-
chanics of musical instruments. Wien–New York:
Springer Verlag, 1995.
[8] H. Fleischer and T. Zwicker, “Mechanical vibrations
of electric guitars,” Acta Acustica united with Acustica,
vol. 84, 1998.
[9] H. Fleischer and T. Zwicker, “Investigating dead spots
of electric guitars,” Acta Acustica united with Acustica,
vol. 85, pp. 128–135, 1999.
[10] A. Pat´
e, B. Navarret, R. Dumoulin, J.-L. Le Carrou,
B. Fabre, and V. Doutaut, “About the electric guitar: a
cross-disciplinary context for an acoustical study,” in
Proceedings of Acoustics 2012, Nantes, France, 2012,
pp. 2717–2722.
[11] J.-L. Le Carrou, J. Frelat, A. Mancel, and B. Navar-
ret, “Guitare ´
electrique : quel r ˆ
ole pour les ´
el´
ements de
lutherie ?” in 10`
eme Congr`
es Franc¸ais d’Acoustique,
2010.
[12] A. Pat´
e, J.-L. Le Carrou, B. Navarret, D. Dubois, and
B. Fabre, “A vibro-acoustical and perceptive study of
the neck-to-body junction of a solid-body electric gui-
tar,” in Proceedings of Acoustics 2012, Nantes, France,
2012, pp. 2711–2716.
[13] C. E. Gough, “Acoustical studies of stringed instru-
ments using string resonances,” in Proceedings of
SMAC 83, 1983, pp. 19–45.