article
Savart Journal
Article
1
Effect of Vibration Treatment on Guitar Tone:
A Comparative Study
B.M. CLEMENS
1
, J. KADIS
2
, D.M. CLEMENS
3
, E. POLLAK
1
, P. CLARK
1
,
AND
J.R. GROVES
1
Abstract-- In order to study the widely-held belief that the sound of a guitar evolves with use due to vibration-
induced changes in the guitar, the tone of guitars subjected to controlled vibrations is investigated. The study uses
three pairs of guitars, where each of the two guitars in the pair is the same make, model and year. One guitar
from each pair is treated using a commercial device for effecting a tone change through imposition of vibrations.
The guitars are evaluated before and after the treatment using double-blind player evaluations and physical property
measurements. The player evaluations showed no statistically-significant changes in the differences between the two
guitars in each pair. Fourier analysis of instrumented hammer strikes were used to extract the frequency response
function. Statistical analysis showed no significant change in the correlation between treated and untreated guitars
due to the vibration treatment. It is therefore concluded that this vibration treatment had no significant effect on the
guitar tone. It is suggested that the evaluation approach used here could be useful for studies of other instruments
or treatments.
I. INTRODUCTION
It is a common belief that the tone of wooden string instruments improves with time, and that playing the instrument
enhances this improvement [1][5]. The evidence for this is mainly anecdotal and qualitative, but, for guitars in
particular, improvements in sustain, ease of playing, loudness, and tone have been claimed. The term "opening up"
has been coined to describe this effect [6][8]. Several physical changes have been suggested as being responsible
for this effect, including crystallization of resins or sap in the wood of the guitar, creep of the wood or glue joints,
and weakening of the structure allowing for greater movement of vibrating elements.
In order to investigate the effect of vibration on the maturation of guitar tone we conducted a study involving three
pairs of guitars. We subjected one guitar from each pair to a vibration treatment from a device that is marketed as
improving instruments through vibration. We performed physical tests and player evaluations on the guitars before
and after the treatment to comparatively evaluate any changes in guitar performance. This study creates a framework
for future studies regarding maturation of tone quality of guitars, and is extensible to the study of other wooden string
instruments such as violins.
II. EXPERIMENTAL
PROCEDURE
The study used three pairs of new guitars, with the two guitars in each pair being the same make, model, and year.
The three guitar pairs covered a range of guitar designs and construction. All had solid spruce tops. One pair (Taylor
110 guitars) had laminated sapele sides and back, solid hardwood neck and a modified dreadnought body design. A
second pair (Martin D-1) had solid sapele back and sides, a Stratabond neck (multiple thin strips of wood laminated
together) and a dreadnought body design. The final pair (Collings OM2H) had solid rosewood back and sides, solid
mahogany neck and an OM ("orchestra model") body design. The list prices range from approximately $700 to $3500.
One guitar from each pair was selected at random to be the control guitar (guitar "A") and the other was given
a vibration treatment (guitar "B"). The vibration treatment used a commercially available device made specifically for
vibrating musical instruments, and was used following the mounting and operation instructions from the manufac-
turer. This device imparts a 60 Hz vibration to the strings of the guitar, which then causes vibration of the sound
1
Department of Materials Science and Engineering, Stanford University, 476 Lomita Mall, Stanford, CA 94305-4045
2
Center for Computer Research on Music and Acoustics, Stanford University, 660 Lomita Court, Stanford, CA 94305-8180
3
Department of Molecular and Cell Biology, University of California, Berkeley, MC 3200, Berkeley, CA 94720-3200
Manuscript received July 29, 2014
Article published: September 3, 2014
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Savart Journal
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2
producing guitar structure. For treatment, the three B guitars were placed in guitar stands and the vibration device
was fixed to the strings near the bridge. The guitars were treated for 348 hours, which is nearly five times the
minimum recommended by the manufacturer. Three different vibration devices of the same make were used (one
first generation model and two third generation models), and the devices were cycled so each of the three treated
guitars had approximately equal time with each device. During treatment, the three A, or control, guitars were also
placed in guitar stands in the same room as the guitars being treated.
Photo 1 - Guitar testing set-up, showing instrumented ham-
mer, accelerometer mounted to guitar top, microphone, gui-
tar cradle, strumming apparatus and foam string dampers.
Several different testing procedures were used, based on
similar previously-used approaches for analyzing guitar re-
sponses [9][14]. A calibrated, instrumented impact hammer
(PCB Piezotronics, Inc, Model 086B01) was used to impart an
impulse to the guitar tops by striking the guitars on the bridge
just below where the strings are attached. The response of
the guitar was measured using a calibrated accelerometer
(PCB Piezotronics, Inc. Model 352B22) mounted with wax to
the centerline of the guitar top 10 cm below the saddle. The
mass of the accelerometer was 0.5 g. The time response of
the hammer accelerometer and guitar top accelerometer were
recorded using dedicated preamplifiers (PCB Piezotronics
480E09) fed into a digital mixer console (Yamaha DM2000)
and digitized with 24 bits at 48 kHz sampling rate for input to
Protools. The sonic output of the guitar was also measured
using an omnidirectional microphone (B&K 4006) mounted 61
cm above the strings, directly above the guitar sound hole,
fed into the same recording setup. The guitars were held in
a cradle that contacted the guitars at specific points on the
guitar sides and in the middle of the neck, allowing unhindered motion of the top and back plates. To record the
response of the guitar body without the interference of the ringing of the strings, some hammer strikes were performed
with the strings damped using several foam dampers between the strings along the neck and at the headstock.
Hammer strikes without the string dampers were also performed. For each test, several hammer strikes were recorded
to check for consistency and to allow for averaging.
-300
-200
-100
0
100
200
300
A
c
c
e
l
e
r
a
t
i
on

(
m/
s
2
)

(
St
r
u
m)
4.70
4.65
4.60
4.55
4.50
Time (s)
-3
-2
-1
0
1
2
3
A
c
c
e
l
e
r
a
t
i
on

(
m/
s
2
)

(
V
i
b
r
a
t
i
on
)
Strum
Vibration Treatment
Figure 1 - Output of the guitar-top mounted accelerometer
as a function of time during a gentle strum from the strum-
ming device and during vibration treatment. Note that the
scale for the acceleration during vibration treatment (right
axis) is 100 times more sensitive than that for the strum
(left axis).
The response of the guitars to a plectrum strum was also
recorded. To achieve a consistent strum, the guitar cradle
was fitted with a pivoting arm that swung a guitar plec-
trum through an arc designed to replicate the arc of the
string height set by the curved saddle of the guitars. This
device imparted a gentle, repeatable strum for a given
guitar. However the magnitude of the strum was a sen-
sitive function of the height of the pick, making quanti-
tative comparisons between guitars difficult. For this rea-
son the hammer strikes were used for quantitative mea-
sure.
Each test was performed on each guitar before and after the
vibration treatment. Each guitar was measured in the same
pre-treatment and post-treatment test sessions. The post-
treatment was performed about 16 hours after stopping the
vibration treatment. New strings (D'Addario phosphor bronze
lights for the Collings OM, and D'Addario phosphor bronze mediums for the Martin and Taylor dreadnoughts) were
put on each guitar the night before each of the two test sessions.
In addition to the above tests, the apparatus described above was used to measure the acceleration of the guitar
top and the sound emanating from the guitar during the vibration treatment. Figure 1 shows the acceleration of
the guitar top as a function of time during a gentle strum and the acceleration of the guitar top during vibration
treatment. The acceleration values were extracted using the calibration of the accelerometer and a 10 mV signal
played through the same signal chain as the actual data. The magnitude of the acceleration during the vibration
Article published: September 3, 2014
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3
treatment is about 100 times smaller than that due to the gentle strum. The sound emanating from the guitar during
the vibration treatment and that from the strum showed the same relative magnitudes, consistent with observation
that sound from a guitar results largely from motion of the guitar top. Also the frequency of the vibration treatment
(60 Hz) is significantly different from the frequencies produced by the strum. Hence the vibration treatment is much
more gentle than regular guitar playing and might not be expected to have the same effect.
The guitars were also evaluated by 9 accomplished guitar players, with an average of 24 years of playing experience.
Included in this group were advanced amateur, semi-professional and professional guitarists, guitar salespersons,
guitar technicians, contributors to popular guitar literature, and players that evaluated guitars as part of their
professional duties. The players were asked to evaluate each guitar on five metrics: volume, sustain, warmth,
brightness and clarity on a scale of 1 to 5, with 5 corresponding to the highest value. These are somewhat subjective
terms, reflecting the difficulty in describing and quantifying the concept of guitar tone, but reflective of the qualities
that aging and opening up are purported to change in guitars.
Each player had at least two evaluation sessions; one before the vibration treatment and one after. Some of the
players performed two evaluations before treatment to assess consistency of rating. For the trial performed after the
vibration treatment, the players were told that one of the guitars of each pair had been given a vibration treatment
meant to improve the guitar performance, but not told which guitar of the pair was treated. To ensure that no
subconscious clues were given, the person running the evaluation also did not know which of the guitars had been
treated, making this a "double-blind" study. In addition to evaluating the guitars on the five metrics, the players were
asked which of the two guitars they thought had been treated.
III. ANALYSIS
APPROACH
The frequency response function (FRF) of an instrument is its output magnitude in response to a stimulus at a given
frequency [15]. This serves as an acoustic fingerprint for the tone an instrument delivers in response to, for example,
the input of the vibrating strings. This is frequently used to evaluate and compare instruments, including guitars and
violins [15][25].
In this study, Fourier analysis was used to obtain the instrument frequency response function from the hammer
strike data. In the time domain, the observed microphone or accelerometer signal
s(t)
is the convolution of the
hammer input
h(t)
with the frequency response behavior
r(t)
, that is:
s(t) = h(t) r(t)
Taking the Fourier transform we find:
F [s(t)] = F [h(t)] F [r(t)]
where, due to the convolution theorem, the convolution becomes a simple multiplication. Hence the frequency
response function of the guitar can be found as:
R(f ) = F [r(t)] =
F [s(t)]
F [h(t)]
(1)
Numerical fast Fourier transforms (FFT) of the hammer, accelerometer, and microphone signals were performed
using commercial software (IGOR, Wavemetrics, Inc.), and the frequency response functions were computed and
averaged for 5 or more hammer strikes. Due to the normalization in equation 1, the frequency response functions
were consistent from strike to strike, even though the hammer strike magnitude varied considerably, consistent with
the behavior of a linear system. Each FFT was performed over the same time period to insure consistent frequency
resolution. The time interval was chosen to begin before the hammer strike, and end after cessation of output signal,
so no filtering function was required in the analysis to extract the frequency response functions. The frequency
response functions from the microphone (measuring the sound output of the guitar) and accelerometer (measuring
the deflection of the guitar top) were similar but not identical for a given guitar. However, the conclusions drawn from
comparisons of the frequency response functions between different guitars and between guitars before and after
treatment were the same for both output measures.
Article published: September 3, 2014
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To facilitate the comparison between the frequency response functions of guitars, the Pearson's
r
correlation coef-
ficient was calculated using the standard expression:
r =
n
(R
1
(n) - R
1
) (R
2
(n) - R
2
)
n
(R
1
(n) - R
1
)
2
n
(R
2
(n) - R
2
)
2
where
R
i
(n)
is the
n
th frequency data point for the
i
th frequency response function, and
. . .
refers to sample
average of the quantity. The Pearson's
r
correlation coefficient measures the correlation, or linear dependence,
between two variables. Here we used it to quantify the differences and similarities between the frequency response
functions of different guitars, and to quantify changes in the frequency response functions of one guitar before and
after treatment. Our Pearson's
r
values were in the range
0 < r < 1
, where a value of 0 would correspond to no
correlation and a value of 1 to perfect correlation. Guitars that have similar spectral response functions would give a
Pearson's
r
correlation coefficient close to unity, and would also be expected to have similar tone. A treatment that
significantly changed the tone of a guitar would also be expected to reduce the Pearson's
r
correlation coefficient
calculated between the frequency response function of the guitar taken before and after the treatment.
Practically, we find that the extracted Pearson's
r
correlation coefficient varies with the maximum frequency used, and
examination of repeated data for the same guitar revealed that fluctuations in the measuring and analysis procedure
made the correlation unreliable for frequencies above about 5 kHz. Hence the Pearson's
r
correlation coefficients
we report here are extracted using the frequency response function data between 0 and 5 kHz.
IV. RESULTS
A. Player Evaluations
It was clear from their comments during the player evaluation tests that players had a hard time distinguishing which
of the guitars had been treated. Comments such as "I am just guessing" and "this one might be the one that was
treated" were common. This is also reflected in their lack of success in identifying the treated guitar. Of the nine
players, one player missed on all three pairs, five players identified one correctly, three players identified two correctly,
and one player identified one correctly, one incorrectly, and thought the third pair was indistinguishable in tone. No
player was able to identify the treated guitar for all three guitar pairs. For each of the three guitar pairs, five out of
the nine players identified the incorrect guitar as the one that had been treated. A tenth player that played the guitars
before and after, but not in a monitored trial, also was unable to identify which of the guitars had been treated. So it
is clear that the players were unable to consistently identify which of the guitars had been treated, which suggests
that they were unable to detect the effect of the vibration treatment on the sound of the guitar.
The inability to consistently identify a change in tone associated with the vibration treatment is also reflected in
the player-assigned scores for the five metrics. Figure 2 shows the averaged player-assigned scores for the guitars
before and after the treatment. To account for differences in player scoring and player mood in different trials, the
player-assigned scores are divided by the average for that player for that metric at that trial. The scores on the
metrics (volume, sustain, warmth, brightness, clarity) show significant variations reflected in the estimated standard
error of the mean (SEM).
To evaluate the statistical significance of the vibration treatment on the player evaluations of the guitars, a two-way
MANOVA was applied. The comparisons were made between guitars before and after treatment, where the treatment
was application of the vibration treatment or a control treatment where nothing was done to the guitar between the
two testing days. The results indicate that there was no statistically significant effect of the vibration treatment on any
of the five measured qualities of the guitars (p=0.89). The analysis indicates that there are statistically significant
differences between the three guitar models as scored by the players. The Collings guitars scored better than
the Martins in the Brightness and Clarity categories in both comparisons. The Collings guitars scored better than
the Taylors in the Sustain category in both comparisons. The never-treated Collings guitar scored better than the
never-treated Marin guitar in the Sustain category, and the Collings A guitar scored better than the Taylor A guitar
both before and after treatment. Since the trials were not brand blind (the players knew which brand of guitar they
were playing, but not whether it had been treated) it is not possible to discount the effect of brand biases. The guitar
players were all sophisticated in the guitar market and aware that, for instance, the Collings guitars were high-quality,
expensive instruments from a small manufacturer known for its consistency, while the Taylors were near the bottom
of the model line from a large factory producer. It is also important to note that these differences, while evidence
Article published: September 3, 2014
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5
Figure 2 - Average player-assigned scores for the guitars before and after the treatment. In each case, guitar "B" received the vibration
treatment and guitar "A" did not. To account for differences in the players and the player moods in different trials, the player assigned scores
are normalized by the player average for that metric for that trial before being averaged. The error bars are the estimated standard error of
the mean.
of the ability of the players to discern differences between various guitars, are not necessarily indicative of general
differences between these guitar models but are comparisons of the specific guitars used in this study.
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
C
h
a
n
g
e

i
n

A
v
e
r
a
g
e

Sc
or
e
V
ol
ume
Su
st
ai
n
W
ar
mt
h
Brightne
ss
Cl
ari
ty
Control
Treated
Figure 3 - Change in normalized score between the
trials after and before the vibration treatment of one
guitar from each pair. The scores were averaged
over all the guitar pairs and over all the players. Since
the scores were normalized by averaging over all
guitars for each player for each metric, the increase
or decrease in the average score will be equal and
opposite for the untreated and treated guitars. The
error bars show the 95% confidence intervals.
To evaluate equivalence of the two treatments (vibration treat-
ment and control), the differences of means and 95% confidence
intervals were calculated using the TukeyHSD test. The resul-
tant differences of means were plotted with error bars repre-
senting the 95% confidence intervals (Figure 3). In this type of
analysis, two treatments are considered equivalent if the 95%
confidence intervals lie entirely within the range of scientific ir-
relevance. The range of scientific irrelevance should be cho-
sen such that changes within the range, regardless of sta-
tistical significance, are too small to be considered interest-
ing.
In this study, the scored differences between guitar models are
on the order of 0.1, or 10 percentage points. Presumably it is
worthwhile for guitar aficionados to purchase a more expensive
guitar based on a perceived change of 10 percentage points.
Some musicians may claim that changes more subtle than 10
percentage points are interesting. However even the most refined
instrumentalist, when subjected to blinded tests, has trouble dis-
cerning differences of less than 10 percentage points. [2] It is
reasonable, then, to set the range of scientific irrelevance at
10 percentage points. To repeat, this range does not
imply that changes of less than 10 percentage points are statistically insignificant; it merely suggests that changes
on this order are uninteresting in the context of evaluating structural differences between instruments.
The 95% confidence intervals of all of the mean differences in this study fall within the
10 percentage point
range (Figure 3), and so the effects of treatment with the vibration device and the effects of control treatment can
be considered equivalent.
B. Physical Measurements
The frequency response functions (FRF) for all guitars before and after treatment were extracted from both the
accelerometer and microphone measurements of the guitar response. Since both response measurement techniques
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6
300
200
100
0
I
n
s
t
r
u
me
n
t

Re
s
p
on
s
e
1000
800
600
400
200
0
Frequency (hz)
Taylor A
Before
After
300
200
100
0
I
n
s
t
r
u
me
n
t

Re
s
p
on
s
e
1000
800
600
400
200
0
Frequency (hz)
Taylor B
Before
After
300
200
100
0
I
n
s
t
r
u
me
n
t

Re
s
p
on
s
e
1000
800
600
400
200
0
Frequency (hz)
Martin A
Before
After
300
200
100
0
I
n
s
t
r
u
me
n
t

Re
s
p
on
s
e
1000
800
600
400
200
0
Frequency (hz)
Martin B
Before
After
300
200
100
0
I
n
s
t
r
u
me
n
t

Re
s
p
on
s
e
1000
800
600
400
200
0
Frequency (hz)
Collings A
Before
After
300
200
100
0
I
n
s
t
r
u
me
n
t

Re
s
p
on
s
e
1000
800
600
400
200
0
Frequency (hz)
Collings B
Before
After
Figure 4 - Frequency response function magnitude for all six guitars before and after the vibration treatment or non-treatment period. For
each pair, guitar A was the un-treated, control guitar, and guitar B is the guitar subjected to the vibration treatment. The frequency response
functions were extracted from the microphone response from hammer hits with damped strings.
yield the same relative behavior and lead to the same conclusions, for brevity we discuss here only the results from
the microphone data. The frequency response functions extracted from microphone data for all six guitars before and
after vibration treatment (or non-treatment period) are shown in Figure 4. To help with comparing and interpreting
these curves, the Pearson's
r
correlation coefficient is tabulated in Table 1 for several pairs of guitars. To clarify, the
numbers in Table 1 are comparisons between two guitars, not absolute measures of guitar quality. Furthermore there
are statistical uncertainties and repeatability variations in these numbers. For example the Pearson's
r
correlation
coefficient value for the frequency response function for different hammer hits of the same guitar was typically
in the range 0.97 - 0.99. For some guitars we performed several sequences of hammer hits, and the Pearson's
r
correlation coefficient between the averages of frequency response function was also in this range. The pure
statistical uncertainty was in the range of 0.01 - 0.02, with larger uncertainties for smaller correlation coefficients.
Therefore changes of a percent or two are probably not significant. Nonetheless, there are clear differences in the
frequency response functions that can be observed in the graphs and tabulated correlation coefficients.
Turning first to comparisons between different guitars, we see that the two guitars in the Collings pair are the most
similar to each other, followed by the two guitars in the Taylor pair and the two guitars in the Martin pair. Interestingly
Talyor A is also close to Martin A, and both Martin guitars are closer to both Taylor guitars than they are to the
Collings guitars. These comparisons hold for both before and after the treatment, as shown by the near-symmetry in
Table 1. This is perhaps not surprising due to the similarity of body size and design for the large Martin and Taylor
dreadnoughts compared to the smaller, OM-size Collings.
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Taylor
Martin
Collings
vs
A
B
A
B
A
B
Taylor
A
0.92
0.84
0.75
0.69
0.40
0.40
B
0.81
0.89
0.72
0.60
0.39
0.35
Martin
A
0.79
0.70
0.93
0.80
0.45
0.43
B
0.69
0.59
0.81
0.93
0.29
0.29
Collings
A
0.41
0.39
0.47
0.27
0.92
0.95
B
0.45
0.45
0.50
0.30
0.92
0.90
Table 1 - Table of Pearson's r correlation coefficients for the frequency
response functions from 0 to 1000 Hz for the six guitars before and af-
ter treatment or non treatment period extracted from microphone data.
The "A" guitars were given the control treatment (no vibration), and
the "B" guitars were given the vibration treatment. The bold, italicized
numbers are comparisons between the same guitar before and after
the treatment. The plain numbers are comparisons between different
guitars before the treatment, and the italicized, non-bolded numbers
are comparisons between different guitars after the treatment.
Turning next to comparisons between the same guitar
before and after the treatment period, we find that
there are changes in the frequency response function
for all the guitars, mainly in peak height differences
and small changes in peak position. However, there
is no significant difference between the changes for
the control treatment (no vibration) and the changes
from the vibration treatment. For all six guitars, the
Pearson's
r
correlation coefficient that compares
the frequency response before treatment versus af-
ter treatment is about 0.91
0.02, independent of
whether the guitar was vibrated or not. Furthermore,
even though the changes due to the control and
vibration treatment are significant, a given guitar after
the treatment is significantly more similar to the same
guitar before the treatment than it is to any of the
other guitars, including the other guitar of the pair.
An exception is the Collings pair, where there is remarkable similarity between the two guitars of the pair both before
and after the treatment. So, in other words, the change in frequency response function due to the control treatment
is indistinguishable from that due to the vibration treatment, and the difference in frequency response behavior
associated with either the control or vibration treatment is less than or equal to the frequency response behavior
differences between guitars of a matched pair. The frequency response functions extracted from the accelerometer
showed this same behavior.
V. DISCUSSION AND
CONCLUSION
We performed player evaluations and physical property measurements on three matched pairs of guitars, before and
after subjecting one guitar from each pair to a vibration treatment. We find no discernible difference in the changes
due to this vibration treatment from those due to a control or "null" treatment. Players were not reliably able to tell
which guitar of the pairs had been subjected to the vibration treatment - for each of the three guitar pairs, five out of
the nine players identified the incorrect guitar as the one that had been treated. Statistical analysis of the evaluations
by the players on the five metrics of guitar tone showed no significant difference in the before and after changes
due to either the vibration or control treatment. While there were differences in the averages of the metric scores,
with the vibration treatment resulting in a decrease for four out of the five metrics, the 95% confidence intervals for
both control and vibration treatment lie within the range of scientific irrelevance.
Changes due to the vibration treatment were also not discernible with our measurements of physical properties,
despite the demonstrated sensitivity to measure the subtle differences between guitars of the same make and model
as well as changes due to weather or a relatively short aging and playing time. Comparisons of the frequency
response function for different guitars before and after treatment was made using the Pearson's
r
correlation
coefficient, and while it may be fair to say that the Pearson's
r
correlation coefficient does not represent all the
complexity of comparing the frequency response functions in Figure 4, and that the frequency response behavior in
the graphs in Figure 4 does not represent the full complexity of a guitar sound, we maintain that these quantitative
measures should exhibit significant changes if the guitar sound is influenced by a given treatment. Indeed, significant
differences can be detected between matched guitars of the same make, model and year.
Interestingly, subtle but significant changes are also observed for the guitars before and after treatment. However,
these changes were essentially the same whether or not the guitar was subjected to the vibration treatment. So these
differences are due either to the small amount of playing during the player trials (about 1-2 hours total), the passage
of time (about three months), the changing of weather from late summer to fall in Palo Alto, or irreproducibility of
our measurement method. The later could be from the placement of the microphone relative to the guitar, mounting
of the accelerometer onto the guitar, or changes in the sonic characteristics of the testing environment. However
effort was made to be as consistent as possible in accelerometer mounting and microphone placement, and the
testing was performed in a controlled sound studio. Furthermore, some guitars were tested more than once on the
same day. This involved placing the guitar in the cradle, adjusting the microphone placement, and re-mounting the
accelerometer. These tests showed much better reproducibility than the tests done before and after the vibration
treatment or waiting period. Furthermore, the correlation in frequency response function between different guitars
Article published: September 3, 2014
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8
shows almost no change associated with the control or vibration treatment, so changes are not due to random
experimental error. Hence it is likely that the changes in frequency response function represent a real change.
However, there is no significant difference between the effects of the control treatment and the vibration treatment.
It is interesting to estimate the deflection and stress in the guitar structure to ascertain whether high cycle fatigue
could result from the vibration treatment. While a full elastic analysis is beyond the scope of this paper, we can
make simplifying assumptions to allow for an order of magnitude estimate. We first assume the guitar is exhibiting
harmonic oscillation at the peak resonance frequency of
200 Hz. In this case the maximum acceleration
a
max
and maximum deflection
x
max are related through:
x
max
=
a
max
(2)
2
Taking the maximum strum and vibration accelerations from figure 1 to be
a
strum
max
= 200 m/s
2
and
a
vibration
max
= 2 m/s
2
we find:
x
strum
max
= 140 m
and
x
vibration
max
= 1.4 m
Next we calculate the maximum stress associated with this deflection. We take a grossly simplified structural model
of the guitar and replace the top and bracing structure with a single beam with the length
l
equal to that of the
lower guitar bout and the height
h
equal to that of the guitar bracing. From elementary beam mechanics we find the
stress:
=
6E
Y
x
max
h
l
2
where
E
Y is the Young's modulus of the wooden bracing. Taking
h = 1 cm
,
l = 40 cm
, and using the modulus
for sitka spruce
E
Y
= 11 GPa
, we find:
strum
max
= 400 kPa
and
vibration
max
= 4 kPa
The yield stress of sitka spruce is about
yield
= 86 MPa
, so the maximum stresses from the strum and vibration
treatment are about 0.5% and 0.005% of the yield stress respectively. Wood is thought to have good fatigue
resistance, and and can withstand cyclic stresses of
0.4
yield for
10
8 cycles. Thus our simple analysis
here indicates that the stress during the vibration treatment, with a duration of
7.5 10
7 cycles, was extremely low
relative to stresses that cause changes in elastic modulus or strength of wood. Sobue and Okayasu have measured
the effect of vibration on the elastic modulus and loss modulus of wood, and find that imposing vibrational stresses
of the order of 300 kPa does not change the elastic modulus, but does reduce the loss modulus by 5-15% [26].
This, combined with our simple analysis here, suggests that the vibrational stresses associated with normal, gentle
playing might result in a modest decrease in the loss modulus of wood, but that the stresses from the vibration
treatment, which are two orders of magnitude lower, are unlikely to produce changes. So it is not surprising that we
were unable to detect any changes in guitar tone associated with this vibration treatment.
We therefore conclude that any changes associated with the vibration treatment we performed are negligible. We
do not make conclusions on the origin of the widespread anecdotal reports of improvements in sound associated
with this vibration treatment, but note that the well-established effects of the power of suggestion and marketing
[27], as well as the lack of double-blind, control testing might be a factor in these anecdotal reports. We also do not
make conclusions about possible effects of more vigorous vibration treatment, including that of playing the guitar for
decades, or of the effects of simple aging on guitar tone. We do however suggest that the methods utilized in this
study can be used to investigate the effects of these treatments and others on wooden string instruments of various
types.
ACKNOWLEDGEMENTS
The authors would like to gratefully acknowledge Gryphon Stringed Instruments of Palo Alto California for providing
the instruments used in this study.
Article published: September 3, 2014
http://SavartJournal.org/index.php/sj/article/view/22/pdf
Savart Journal
Article
9
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Article published: September 3, 2014
http://SavartJournal.org/index.php/sj/article/view/22/pdf