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Acoustical classification of woods for string instruments


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Two basic types of wood are used to make stringed musical instruments: woods for soundboards (top plates) and those for frame boards (back and side plates). A new way to classify the acoustical properties of woods and clearly separate these two groups is proposed in this paper. The transmission parameter (product of propagation speed and Q value of the longitudinal wave along the wood grain) and the antivibration parameter (wood density divided by the propagation speed along the wood grain) are introduced in the proposed classification scheme. Two regression lines, drawn for traditional woods, show the distinctly different functions required by soundboards and frame boards. These regression lines can serve as a reference to select the best substitute woods when traditional woods are not available. Moreover, some peculiarities of Japanese string instruments, which are made clear by comparing woods used for them with woods used for Western and Chinese instruments, are briefly discussed.
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Acoustical classification of woods for string instruments
Shigeru Yoshikawa
Department of Acoustic Design, Faculty of Design, Kyushu University, 4-9-1 Shiobaru, Minami-ku,
Fukuoka, 815-8540 Japan
Received 22 February 2007; revised 8 April 2007; accepted 2 May 2007
Two basic types of wood are used to make stringed musical instruments: woods for soundboards
top plates and those for frame boards back and side plates. A new way to classify the acoustical
properties of woods and clearly separate these two groups is proposed in this paper. The
transmission parameter product of propagation speed and Q value of the longitudinal wave along
the wood grain and the antivibration parameter wood density divided by the propagation speed
along the wood grain are introduced in the proposed classification scheme. Two regression lines,
drawn for traditional woods, show the distinctly different functions required by soundboards and
frame boards. These regression lines can serve as a reference to select the best substitute woods
when traditional woods are not available. Moreover, some peculiarities of Japanese string
instruments, which are made clear by comparing woods used for them with woods used for Western
and Chinese instruments, are briefly discussed. © 2007 Acoustical Society of America.
DOI: 10.1121/1.2743162
PACS numbers: 43.75.Gh, 43.75.Mn, 43.75.De NHF Pages: 568–573
Wood selection is the most important parameter in
stringed instrument design. The body of a stringed instru-
ment consists, in general, of a soundboard top plate and a
frame board back plate and/or side plate as illustrated in
Fig. 1. The lute or guitar family, shown in Fig. 1a,isa
typical example. Since the back plate is connected with the
top plate by a sound post in the fiddle and violin family as
shown in Fig. 1b, the back plate can function as part of the
soundboard as well as of the frame board. Modern pianos
depicted in Fig. 1c have a very rigid frame structure, in-
stead of a frame board, which firmly supports the sound-
board as the prime sound radiator. The modern piano’s single
soundboard structure is essentially different from other string
instruments, which have a common structure consisting of a
resonant box and a sound hole or sound holes. Note, how-
ever, that the fortepianos made by Bartolomeo Cristofori in
the 1720s maintain such a box-hole structure four big holes
are hidden below the keyboard as seen in the harpsichord
and clavichord.
Woods for string instruments are thus divided into two
groups: A woods for soundboards and B woods for frame
boards. Just as in human society we put “the right person in
the right place,” so in musical instrument design it is essen-
tial to put “the right wood in the right place,” especially in
string instruments. The objective of this paper is to propose a
new classification diagram that clearly discriminates the
acoustical characteristics of group A from those of group B.
A scheme that can successfully classify the woods tradition-
ally used for the highest-quality string instruments can also
serve to guide the selection of both substitute woods and
synthetic materials, with the next best, or possibly even bet-
ter, quality. Such selection criteria have not been hitherto
established. In the face of serious shortages of natural mate-
rials from endangered species, it is very important to develop
In addition, the proposed classification scheme can be
used to clarify and understand some of the differences be-
tween Western string instruments and East Asian ones.
though both the style and manner of playing string instru-
ments ultimately arises from differences in musical taste, it is
found that the wood material also has a strong influence.
A. Wood vibration and its transmission
Fletcher and Rossing
added Chap. 22, “Material of Mu-
sical Instruments,” to the second edition of their excellent
textbook. Section 22.3, “Wood Material,” provides concise
and useful information on wood science, but it does not give
a scheme to classify the two groups of woods. Neither Bu-
curs well-organized book
nor the anthology edited by
Hutchins and Benade
addresses the problem of acoustical
classification. It is hoped that the proposed classification
scheme can fill this gap.
Two parameters that can be used to clearly discriminate
between the two wood types are sought. In a good classifi-
cation scheme the two wood types ought to be “orthogonal”
because soundboards and frame boards have opposite vibra-
tional and acoustical properties.
Various parameters have been proposed to describe the
acoustical properties of traditional woods used for string in-
struments and of substitute woods.
Research has also
been done on artificial composites.
Among the various
parameters that have been proposed, the most plausible one
is Schelleng’s c /
, where c denotes the propagation speed of
the longitudinal wave along the wood grain, and
the wood density.
The relevance of c/
is confirmed in Ref.
4. Schelleng derived it by supposing that both the stiffness
and the inertia of the plate should be the same for the wood
substitute if its vibrational properties are to be the same.
568 J. Acoust. Soc. Am. 122 1, July 2007 © 2007 Acoustical Society of America0001-4966/2007/1221/568/6/$23.00
Since the vibration of a wood plate produces sound radiation,
may be called the “vibration parameter” or “radiation
Moreover, Schelleng
found a strong correlation be-
tween the resonant Q value and c /
. The Q value is the
reciprocal of the loss factor, which is determined by the in-
ternal friction of wood. Since cellulosic microfibrils are
highly crystalline in resonance wood, they have low damp-
ing, that is, high Q.
Although the Q is an important prop-
erty of resonance woods for soundboards, it is not a useful
parameter to classify soundboards and frame boards. The
higher c /
the greater the vibration and radiation. Good ra-
diators soundboards are good transmitters of vibration be-
cause the excitation is easily transmitted to the edge and
corner. As a result, soft woods are used for soundboards, but
hard woods are usually used for frame boards. Although hard
woods are dense and vibrations are not easily excited, they
are good transmitters of vibration and wave. For the back
plate of the violin, and the body plate and neck of the
Japanese shamisen three-string instrument, good transmis-
sion is needed to make their sounds.
Thus, the characteristic acoustic transmission of woods
is another important parameter for classifying woods for
string instruments. If the attenuation or damping is rela-
tively weak, the characteristic transmission is the reciprocal
of the attenuation constant
of the longitudinal wave. The
solution of the lossy wave equation gives
=2Q /k
k is the wave number;
is the angular
Barducci and Pasqualini
stressed the importance of the
ratio c / Q and concluded that c/Q is independent of both
direction and frequency. However, since c/Q has no physical
acoustical significance, we consider the product cQ instead.
Also, though the anisotropy is essential to the wood,
only the longitudinal wave that propagates along the wood
grain is analyzed because it has the primary acoustical im-
The acoustic conversion efficiency ACE proposed by
has also been used to characterize acoustic
This ACE is the ratio of acoustic energy ra-
diated from a beam to the vibration energy of the beam and
is proportional to cQ/
. Thus ACE is simply Schelleng’s
vibration parameter radiation ratio, c /
, multiplied by Q.
Therefore, ACE has the same meaning as the radiation ratio,
and it is different from cQ or cQ/
. It is thus proposed to
use cQ to characterize the vibration transmission character-
istic of wood. Obataya et al.
have also suggested that cQ
which they call the “relative acoustic conversion effi-
ciency” be used to characterize woods. Their cQ was intro-
duced to eliminate a strong dependence of ACE on
assuming that ACE does not reflect the microstructure of the
wood cell wall.
Since the Young’s modulus E generally increases with
, higher acoustic impedance
might be
required for frame boards.
On the other hand, excellent
soundboards must have a high value of E /
the values of
E and
c alone do not predict the performance
of soundboards and frame boards.
B. Transmission parameter and its measurement
Wood properties, such as c and Q, are usually measured
by observing the first-mode bending vibration of strip-shaped
sample plates with the free-free boundary condition.
Depending on the sample size, the frequency of the first
mode is about 500 Hz. Wood parameters, such as Young’s
modulus and the attenuation, are almost frequency indepen-
dent over the frequency range of 300 Hz to 1 kHz.
Thus it
is appropriate to select data measured at around 500 Hz and
to adopt cQ, instead of cQ/
, as a measure of the character-
istic transmission of wood because
itself does not repre-
sent one of the wood properties. From now on we call cQ the
“transmission parameter.”
It must be noted that Q is measured by observing bend-
ing vibrations, while c is the longitudinal wave speed. The Q
for longitudinal vibrations along the grain is required to ex-
actly define the attenuation constant
of longitudinal waves
along the grain. However, Q for vibrations along the grain is
the same for longitudinal vibrations and bending vibrations if
the frequency is the same and the mode frequency and mode
FIG. 1. Color online Cross-sectional schematics of typical structures of
stringed instruments. a Box–sound-hole structure in the guitar, harpsi-
chord, Cristofori’s fortepiano, etc.. b Box–sound-hole–sound-post struc-
ture in the violin family the sound post is depicted by a darker gray rect-
angle in the middle. c Soundboard—iron-frame structure in modern
pianos. A white rectangle indicates top plate or soundboard; a black or gray
rectangle indicates back and side plate or frame board.
J. Acoust. Soc. Am., Vol. 122, No. 1, July 2007 Shigeru Yoshikawa: Wood classification for string instruments 569
number of vibration is not too high. This is because most
bending deformations are due to the compression and dilata-
tion in the longitudinal direction particularly in lower fre-
The wood species investigated in this paper are summa-
rized in Table I. Common names of woods are used hereafter.
Traditional meaning traditionally “best suited” woods for
stringed instruments the upper eight species in Table I are
first considered. Their wood constants are also summarized
in Table II, where most numerical data on Western instru-
ments are taken from Ref. 10, and those on Japanese instru-
ments from Ref. 26. The measurement frequency is noted in
these references. Unfortunately, the data at about 500 Hz are
very limited.
Norway spruce and Sitka spruce are used for the violin
top plate, the piano soundboard, the guitar top plate, etc.
Paulownia kiri in Japanese is best for the Japanese 13-
stringed long zither koto or soh. Mulberry kuwa in Japa-
nese is traditionally used for the whole body, including top
and back plates, of the Japanese four-stringed lute Satsuma
biwa. Wood parameters
, E, and Q of mulberry were newly
measured by Professor T. Ono of Gifu University using two
samples best quality and medium quality provided by the
Italian biwa maker, Doriano Sulis, living in Fukuoka, Japan.
Measurements of E and Q were carried out by the free-free
bending vibration method
mentioned in the previous
section. The density
was measured after the sample was air
dried which usually leaves a moisture content of about
12%. The data for the best-quality and medium-quality
samples are given in Tables II and III, respectively. Note that
“mulberry M is used in Table III to indicate the medium-
quality sample.
On the other hand, the other four woods are used for
frame boards. Both Norway and Japanese maple are used for
the violin back plate. The amboyna wood karin in Japanese
is best suited for the body and neck of the Japanese three-
stringed lute, shamisen. Brazilian/Rio rosewood is tradition-
ally best suited for the guitar back and side plates.
Note that Table II gives the reciprocal of Schelleng’s
vibration parameter c /
. Because
/c is roughly proportional
we see that soft woods for soundboards are light while
hard woods for frame boards are heavy. We may call
which is a measure of the resistance to vibration, the “anti-
vibration parameter.” The higher the value, the greater the
resistance to vibration. When transmission parameter cQ is
plotted against
/c, a clear separation is seen between woods
used for soundboards and woods used for frame boards see
Fig. 2. This shows the effectiveness of our newly proposed
transmission parameter cQ.
In Fig. 2 the four points corresponding to soundboard
woods excluding mulberry yield the regression line
TABLE I. Common names and botanical names of woods investigated in
this paper.
Common name Botanical name
Norway spruce Picea abies
Sitka spruce Picea sitchensis
Paulownia Japanese kiri Paulownia tomentosa
Mulberry Japanese kuwa Morus alba
Norway maple Acer platanoides
Japanese maple Japanese kaede Acer sp.
Amboyna wood Japanese karin Pterocarpus indicus
Brazilian/Rio rosewood Dalbergia nigra
White pine Pinus albicaulis
Hemlock Tsuga sp.
Redwood Sequoia sempervirens
Western red cedar Thuja plicata
Camphor wood Japanese kusu Cinnamomum camphora
Zelkova Japanese keyaki Zelkova serrata
Italian cypress Cupressus sempervirens
Pear Pyrus communis
American cherry Prunus serotina
Black walnut Juglans nigra
Andaman paduc Ptercarpus dalbergioides
Balsa Ochroma pyramidale
TABLE II. Physical properties of traditional woods best suited for stringed
Wood name
Norway spruce
532 560 16 5300 0.11 116 6.2
Sitka spruce
484 470 12 5100 0.092 131 6.7
Sitka spruce
617 408 10.0 4940 0.083 144 7.1
569 260 7.3 5300 0.049 170 9.0
Mulberry 447 647 6.3 3130 0.21 70 2.2
Norway maple
470 620 9.8 4000 0.16 85 3.4
Japanese maple
447 695 11.8 4110 0.17 122 5.0
Amboyna wood
519 873 20.0 4770 0.18 155 7.4
Brazilian/Rio 354 830 17 4400 0.19 185 8.1
Reference 10.
Reference 26.
TABLE III. Physical properties of substitute woods for stringed instruments.
Wood name
White pine
514 380 10.0 5200 0.073 116 6.0
533 440 8.4 4400 0.100 126 5.5
1067 380 9.5 5000 0.083 209 10.4
Western red cedar
816 400 6.5 4000 0.100 174 7.0
Mulberry M 565 616 9.7 3960 0.16 121 4.8
Camphor wood
497 550 9.0 4060 0.14 121 4.9
439 720 12.6 4180 0.17 122 5.1
Italian cypress
430 450 5.7 3560 0.13 97 3.5
369 570 8.2 3800 0.15 67 2.5
American cherry
795 700 12.0 4100 0.17 137 5.8
Black walnut
522 680 20.0 5400 0.13 185 10.0
Andaman paduc
474 710 12.0 4400 0.16 185 8.1
Balsa high density
428 162 2.8 4170 0.039 140 5.8
Balsa compressed
538 771 22.0 5150 0.15 163 8.4
Reference 10.
Reference 26.
Reference 27.
570 J. Acoust. Soc. Am., Vol. 122, No. 1, July 2007 Shigeru Yoshikawa: Wood classification for string instruments
y = 50.5x + 11.4, 1
and the four points corresponding to frame-board woods
y = 143x 18.9, 2
where x =
/c and y =cQ/10
. These regression lines show a
remarkable correlation with the different functions required
by soundboards and frame boards. Soundboards require a
strong positive correlation of transmission parameter cQ
with vibration parameter c /
; frame boards require a strong
positive correlation of cQ with antivibration parameter
In other words, large values of c and Q are required by both
good soundboards and good frame boards, while the
soundboards should be much smaller than that of frame
boards cf. Table II. Although individual differences in
wood samples must still be taken into account, it can be seen
that the properties of traditional woods for string instruments
given in Table II fall on one of two regression lines discussed
above, and they fall naturally into one of two groups, either
soundboard woods or frame-board woods.
Large values of c and Q along the grain are mainly due
to the smaller fibril angles of the wood cell wall with respect
to the grain direction.
Therefore, in a cell wall model of
wood, small fibril angle seems to be the parameter that de-
termines the performance of frame boards and soundboards.
Thus the larger the transmission parameter cQ, the smaller
the fibril angle.
Mulberry wood lies outside the traditional wood groups,
and its position opposite Sitka spruce and Norway spruce
with respect to line 2 for frame boards may seem puzzling.
The idiosyncrasies of mulberry are discussed in Sec. V. It is
interesting to note that Norway maple lies near the intersec-
tion of lines 1 and 2. Thus Norway maple has unique
acoustical properties that make it suitable for both sound-
boards and frame boards. Such properties are very desirable
for the back plate of the violin.
Substitute woods are woods that are not traditionally
used for the best quality instruments, but alternative woods
including artificial composites are often used in medium to
high quality instruments. Table III lists the physical proper-
ties of typical substitute woods. Since Cristofori selected the
Italian cypress and Italian poplar, respectively, for the sound-
boards and frame boards of his fortepianos, neither of these
two woods has been used for modern pianos. Although,
strictly speaking, these two woods are not substitute woods,
it is, nevertheless, interesting to compare them with other
woods. The Italian cypress data were courtesy of the French
wood scientist Brémaud,
but data on the Italian poplar are,
unfortunately, not available.
White pine and hemlock are applied to violin tops.
Redwood and Western red cedar are sometimes used for gui-
tar tops,
although a majority of European guitar builders
exclusively use Western red cedar as well as European
The data for mulberry M were obtained from new
measurement of a sample used in medium-quality biwas.
Camphor wood kusu in Japanese and zelkova keyaki in
Japanese are very good for Japanese furniture and some-
times are used to make the biwa. The Canadian paulownia is
used for medium-quality kotos, but its mechanical data were
not available in the literature. The pear and American cherry
are sometimes used for violin backs.
The black walnut and
Andaman paduc may be used for guitar backs.
Balsa wood
can be applied to the top and/or back plate of string
particularly the violin,
but its mechanical
strength is questionable.
From the data in Table III we construct the scatter dia-
gram of Fig. 3, where the two regression lines given by Eqs.
1 and 2 are drawn for the reference. The closeness of data
points to each regression line implies an excellent match to
the “right wood.” Hence the Western red cedar, white pine,
and hemlock should be excellent substitutes for Sitka spruce
and Norway spruce. Although the balsa with its high density
has a very high value of the radiation ratio very small anti-
vibration parameter, it is not a good alternative for the top
plate and soundboard. If its transmission parameter cQ
probably its Q value could be increased perhaps by the
proper processing, balsa could be a promising substitute
candidate for paulownia, which is best suited for the Japa-
nese koto. On the other hand, redwood has too high a value
FIG. 2. Acoustical classification of traditional woods best suited for stringed
instruments. The regression line for soundboards full circles is almost
orthogonal to the regression line for frame boards open circles. Note the
position of mulberry, which is used for the top and back plates of the Japa-
nese Satsuma biwa.
FIG. 3. A scatter diagram of substitute woods for stringed instruments. The
regression lines given in Fig. 2 are drawn as the reference. The closer to the
regression line that a proposed substitute material lies, the better its perfor-
mance. Full circles indicate soundboard woods and open circles frame-board
woods. Crosses show the positions of various substitutes used for mulberry,
which is used for the best-quality Satsuma biwa.
J. Acoust. Soc. Am., Vol. 122, No. 1, July 2007 Shigeru Yoshikawa: Wood classification for string instruments 571
of cQ, and it seems less desirable as soundboard wood. How-
ever, this conclusion is based on data at high frequency—
1067 Hz see Table III. Italian cypress also has too high a
value of
/c, making it unsuitable for the modern piano
Concerning the frame-board substitutes, pear and Ameri-
can cherry may be excellent choices, although the pear data
point is in the opposite direction of the regression line given
by Eq. 1. On the other hand, black walnut, compressed
balsa, and Andaman paduc are not such good alternatives.
The three data points for mulberry M, camphor wood,
and zelkova are very close to each other, but very far from
the mulberry point of the best quality shown in Fig. 2. This
result seems to endorse a clear difference between traditional
wood and substitution wood. Nevertheless, the points of
mulberry M and zelkova in Fig. 3 suggest that these woods
might be excellent substitutes for frame-board woods.
As explained above, the classification diagram of Fig. 2
and the regression lines given by Eqs. 1 and 2 can be used
to judge the suitability of substitute woods. In addition, they
can guide the design of better quality artificial composite
substitutes for stringed-instrument woods.
As shown in Fig. 2, mulberry, which is used for the best
quality Japanese Satsuma biwa “Satsuma” is the old name
of the southernmost prefecture in Kyushu, lies far off the
quality criteria for Western string instruments, given by the
regression lines of Eqs. 1 and 2. Although this is partly
because mulberry is used for both the top and the back
plates, it nevertheless does seem extraordinary that mulberry
has a very high value of the antivibration parameter and a
very low value of the transmission parameter.
However, the poor vibrational properties of mulberry
seem to match the playing style of the Satsuma biwa, in
which the string is strongly struck with a large triangular
wooden plectrum bachi in Japanese instead of ordinary
plucking with a small pick as in the guitar. Striking the Sat-
suma biwa yields very characteristic impact tones. It should
be noted that the peculiarity low resonance nature of mul-
berry makes this playing style possible because the top plate
is simultaneously struck by a stroke of a large plectrum.
Also, since the mulberry body of the Satsuma biwa is a
poor resonator, a mechanism has been invented to compen-
sate. This mechanism is called the “sawari” “touch”, which
allows strings to vibrate against the neck or frets, creating a
reverberating high-frequency emphasis.
A few variants of
this sawari are seen as “jawari” in Hindi on the Indian sitar
and tambura,
and as “bray pins” on medieval harps.
Moreover, the peculiarity of the mulberry clearly dis-
criminates the Satsuma biwa from the Chinese pipa
a. The Chinese pipa,
with a top plate of paulownia
and a back shell of red sandal wood close to amboyna
wood or maple, has many frets and is played with a small
pick. This is quite similar to the Western guitar, although
harmonic enhancement in the pipa is controlled by designing
the top plate to have large resonances about one or two oc-
taves higher than the fundamental frequencies of four strings
, and A
The Japanese shamisen meaning “three-stringed”,
whose root is in the Chinese sanxian, has a long, unfretted
wooden neck and a small body whose front and back are
covered with white cat skin. The shamisen’s neck and body
are traditionally made of the amboyna wood, which is hard
and does not readily vibrate but which transmits vibrations
excellently Fig. 2.
The shamisen also has the sawari, but its mechanism
differs from that of the Satsuma biwa.
Most importantly,
the shamisen’s sawari is restricted to only the first lowest
string. However, when the vibrations of the second and third
strings are transmitted to the first string, the sawari effect is
accompanied by appreciable sympathetic resonances if they
are correctly tuned.
Receiving sawari on second and third
strings serves as a reference to judge whether the tuning is
correct or not. The amboyna wood is also the best material to
facilitate the very smooth movement of fingers on the
strings, and it very well transmits vibration once they have
been excited.
Paulownia, used for the Japanese long zither koto,is
diametrically opposite to mulberry, used for the Satsuma
biwa as indicated in Fig. 2. Thirteen strings, each about
1.5 m long, are stretched between two fixed bridges. In ad-
dition, a movable bridge is applied under each string for its
tuning. The paulownia, with its very smooth surface, facili-
tates the movement of the bridge on the top plate when a
chord change is required during the performance this may
also be the case for Korean gayageum and Chinese gu-
zheng. Also, the koto strings are plucked with small plectra
worn on three fingers the thumb, index, and middle finger
of the right hand. Since this plucking is not so strong, and the
koto body is very large, the material must support vibration
well to maintain the sound. Thus, the high resonance of the
paulownia seems to be a relevant requirement.
A new scheme to classify the woods used in stringed
instruments is proposed. Plotting
/c the antivibration pa-
rameter along the x axis, and cQ the transmission param-
eter along y axis, we obtain two regression lines that clearly
discriminate soundboard woods from frame-board woods
that are traditionally best suited for string instruments. These
regression lines, defined by the traditional woods, constitute
criteria to select substitute woods and synthesize artificial
composites when making string instruments with the next
best quality.
Since the propagation speed c of the longitudinal wave
along the wood grain is determined by Young’s modulus E
and the density
, the wood classification diagram is based
upon the fundamental physical quantities E,
, and Q. How-
ever, it should be remembered that the frequency used to
measure these quantities is assumed to be almost the same
for all wood samples. A frequency of around 500 Hz is prac-
tical for measurements.
572 J. Acoust. Soc. Am., Vol. 122, No. 1, July 2007 Shigeru Yoshikawa: Wood classification for string instruments
Moreover, based on the classification diagram for tradi-
tional woods Fig. 2, some peculiarities of Japanese string
instruments such as the Satsuma biwa, shamisen, and koto
emerge. In particular, mulberry for the Satsuma biwa and
paulownia for the koto correspond to the opposite extremes
on the regression line for soundboard woods. Such extreme
wood properties are seldom seen in Western stringed instru-
ments. Also, in comparing with the Chinese pipa, it may be
understood that the unique playing style and the resulting
tone of the Satsuma biwa depend strongly on mulberry’s
acoustical properties.
The author would like to express his thanks to the
prominent biwa maker, Doriano Sulis, for kindly providing
mulberry samples. Professor Teruaki Ono of Gifu University
measured the physical properties of the mulberry samples
and provided helpful references during our discussions on
wood science. Also, the author would like to thank Dr. Iris
Brémaud of the University of Montpellier II, France, who
provided many data on wood properties, and for stimulating
discussions on European and Asian woods. She provided
useful references and the correct botanical names of various
woods. The author thanks Professor Eiichi Obataya of
Tsukuba University, who patiently answered the authors
questions on wood properties. The author also thanks Profes-
sor Thomas Rossing of Stanford University for his encour-
agement of considering Asian stringed instruments. Further-
more, the author thanks Professor James B. Cole of Tsukuba
University for his careful and helpful editing of the English
expressions. Finally, the author would like to show his ac-
knowledgments to the anonymous reviewers and associate
editor Neville Fletcher for their relevant comments and sug-
gestions to improve the manuscript.
S. Pollens, “The pianos of Bartolomeo Cristofori,” J. Am. Musical In-
strum. Soc. 10,32681984.
S. Yoshikawa, “From the cembalo to the piano: Progress in early keyboard
instruments,” J. Acoust. Soc. Jpn. 57, 704–711 2001兲共in Japanese.
A. Odaka and S. Yoshikawa, “Acoustical characteristics of Chinese
stringed instruments and their Asian relatives,” J. Acoust. Soc. Am. 120,
3118 2006.
N. H. Fletcher and T. D. Rossing, The Physics of Musical Instruments, 2nd
ed. Springer-Verlag, New York, 1998.
V. Bucur, Acoustics of Wood, 2nd ed. Springer-Verlag, Berlin, 2006.
C. M. Hutchins and V. Benade eds., Research Papers in Violin Acoustics
1975–1993 Acoustical Society of America, Woodbury, NY, 1997,Vol.2,
Chap. J. Wood.
T. Ono, “Frequency responses of wood for musical instruments in relation
to the vibrational properties,” J. Acoust. Soc. Jpn. E 17, 183–193 1996.
T. Ono and M. Norimoto, “On physical criteria for the selection of wood
for soundboards of musical instruments,” Rheol. Acta 23, 652– 656 1984.
J. C. Schelleng, “The violin as a circuit,” J. Acoust. Soc. Am. 35, 326–338
D. W. Haines, “On musical instrument wood,” Catgut Acoust. Soc. News-
letters 31, 23–32 1979.
I. Dunlop, “The acoustic properties of wood in relation to stringed musical
instruments,” Acoust. Aust. 17, 37–40 1989.
C. Y. Barlow, “Materials selection for musical instruments,” Proc. Instit.
Acoust. 19, 69–78 1997.
T. Ono, S. Miyakoshi, and U. Watanabe, “Acoustic characteristics of uni-
directionally fiber-reinforced polyurethane foam composites for musical
instrument soundboards,” Acoust. Sci. and Technol. 23, 135–142 2002.
D. W. Haines and N. Chang, “Application of graphite composites in mu-
sical instruments,” Catgut Acoust. Soc. Newsletter 23, 13–15 1975.
C. Besnainou, “From wood mechanical measurements to composite mate-
rials for musical instruments: New technology for instrument makers,”
MRS Bull. 20, 34–36 1995.
E. Meyer and E.-G. Neumann, Physical and Applied Acoustics, translated
by J. M. Taylor, Jr. Academic, New York, 1972, pp. 14–15.
I. Barducci and G. Pasqualini, “Measurement of the internal friction and
the elastic constants of wood,” Nuovo Cimento 5, 416–466 1948; trans-
lated by E. B. Abetti in a Benchmark Book Series, Musical Acoustics, Part
I Violin Family Components, edited by C. M. Hutchins Dowden, Hutch-
inson & Ross, Stroudsburg, Pennsylvania, 1975.
B. A. Yankovskii, “Dissimilarity of the acoustic parameters of unseasoned
and aged wood,” Sov. Phys. Acoust. 13, 125–127 1967.
E. Obataya, T. Ono, and M. Norimoto, “Vibrational properties of wood
along the grain,” J. Mater. Sci. 35, 2993–3001 2000.
H. Aizawa, E. Obataya, T. Ono, and M. Norimoto, “Acoustic converting
efficiency and anisotropic nature of wood,” Wood Res. 85, 81–83 1998.
H. Yano, Y. Furuta, and H. Nakagawa, “Materials for guitar back plates
made from sustainable forest resources,” J. Acoust. Soc. Am. 101, 1112–
1119 1997.
D. W. Haines, “On musical instrument wood—Part II Surface finishes,
plywood, light and water exposure,” Catgut Acoust. Soc. Newsletter 33,
19–23 1980.
F. P. Kollmann and A. Cote, Jr., Principles of Wood Science and Technol-
ogy Springer-Verlag, New York, 1968, pp. 301–302.
R. F. S. Hearmon, “The influence of shear and rotatory inertia on the free
flexural vibration of wooden beams,” Br. J. Appl. Phys. 9, 381–388
E. Fukada, “The vibration properties of wood I,” J. Phys. Soc. Jpn. 5,
321–327 1950.
H. Aizawa, “Frequency dependence of vibration properties of wood in the
longitudinal direction,” master thesis, Faculty of Engineering, Kyoto Uni-
versity, 1998 in Japanese.
I. Brémaud, “Diversity of woods used or usable in musical instruments
making: Experimental study of vibrational properties in axial direction of
contrasted wood types mainly tropical—Relationships to features of mi-
crostructure and secondary chemical composition,” Ph.D. thesis, Mechan-
ics of Materials, University of Montpellier II, 2006 in French.
C. Waltham, personal communication on the balsa violin February 2007.
Y. Ando, Acoustics of Musical Instruments, 2nd ed. Ongaku-no-tomo-sha,
Tokyo, 1996, pp. 197–199, 202, 203, 208–210 in Japanese.
M. Campbell, personal communication November 2006.
S.-Y. Feng, “Some acoustical measurements on the Chinese musical in-
strument P
a,” J. Acoust. Soc. Am. 75, 599–602 1984.
J. Acoust. Soc. Am., Vol. 122, No. 1, July 2007 Shigeru Yoshikawa: Wood classification for string instruments 573
... The inverse of this coefficient is called the anti-vibration parameter according to Yoshikawa (2007). The Acoustic Conversion Efficiency ACE defines the efficiency with which vibrational energy is transformed into sonic energy and has been accepted as an overall estimate of acoustic properties (Aizawa et al., 1998;Rujinirun et al., 2005;Roohnia et al., 2011). ...
... The transmission parameter or relative acoustic conversion efficiency was also defined which according to Yoshikawa (2007) is given by expression (Equation 6). ...
... Also, coupling density and stiffness modulus, T. superba and H. floribunda can be used as back and side woods for guitars following the classification of Sproßmann et al. (2017) which categorized woods from 700 to 1100 kg m -3 and 9000 to 18000 MPa as back and side woods, and woods from 1000 to 13000 kg m -3 and 14000 to 26000 MPa as guitar fret woods. Yoshikawa (2007), in Japan, working on the wood species traditionally used for making stringed instruments (Picea abies, Picea sitchensis, Paulownia tomentosa, Morus alba, Acer platanoides, Acer sp., Pterocarpus indicus and Dalbergia nigra) and substitute species used in the same manufacture (Pinus albicaulis, Tsuga species, Sequoia sempervirens, Thuja plicata, Cinnamomum camphora, Zelkova serrata, Cupressus sempervirens, Pyrus communis, Prunus serotina, Juglans nigra, Ptercarpus dalbergioides, and Ochroma pyramidale) density, modulus of elasticity, and velocity values for the two groups of 260 to 873 kg m -3 ; 6300 to 20000 MPa; 3130 to 5300 m s -1 and 380 to 710 kg m -3 ; 2800 to 22000 MPa; 3500 to 5400 m s -1 . These values crossed with our average values recorded in the two previous tables predispose our wood species to certain potentialities in instrument making of stringed instruments whereas in the light of the work of Traoré et al. (2010) on veneer (Pterocarpus erinaceus Poir.) the density and the modulus of elasticity of these studied species remain weak and unsuitable for the manufacture of xylophone bars. ...
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Wood is important in several fields including sculpture and instrument making. In the last two fields, Terminalia superba, Cleistopholis patens, and Holarrhena floribunda are three of Benin's most used wood species. In this work, we have, on prismatic samples (500 mm × 20 mm × 20 mm) of the wood of these species, used the acoustic method Beam Identification by Non-destructive Grading (BING) of CIRAD-Forêt to determine the density ρ, Young's modulus E, shear modulus G and internal friction tan that allowed the evaluation of the specific stiffness modulus E/ρ and the other acoustic parameters. These tests showed that T. superba, C. patens and H. floribunda wood species have specific moduli of elasticity of 18 ± 3, 17 ± 2 and 15 ± 1 GPa, respectively; internal friction of the order of 10-2 and sound velocities of the order of 4000 m s-1. All these three species have an average acoustic strength above 1.40 MPa s m-1 with acoustic radiation above 7 m 4 kg-1 s-1 for a high ACE above 1000 m 4 kg-1 s-1 for T. superba and C. patens and low around 674 m 4 kg-1 s-1 for H. floribunda. All these species have a medium stability in service and a low propensity to deformation due to their shrinkage anisotropy. In view of these results, the wood of these species can be used in both structural and acoustic works specifically in sound insulation, art sculpture and instrument making.
... Since acoustic properties are determined by physic-mechanical characteristics, several studies focus on exploring indices and parameters (e.g. density and Young's modulus) that influence the acoustic response of wood by determining the speed and intensity of the sound [9][10][11][12][13]. ...
... This is in accordance with what has been observed by Refs. [6,13], i.e. that a high Young's modulus value in relation to the density is a critical feature for the soundboard since it enables the wood to vibrate more easily, resulting in a more efficient sound emission. ...
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Since the dawn of humanity, wood has been the material of choice for crafting musical instruments due to its favorable acoustic properties, workability, and aesthetic value. Acoustic guitars are among the most widespread musical instruments worldwide, and today are industrially manufactured by large companies with global markets. This study investigates the use of wood in modern acoustic guitars, with a focus on wood species and sustainability. The websites of the 14 most relevant manufacturers on a global scale were analyzed collecting data on 874 guitars and 4506 components. The purpose of the research is to provide a novel overview of the variety and relevance of woods employed in the sector, of the most common environmental issues associated with their use, and of the strategies adopted by companies to deal with sustainability concerns and to communicate their environmental commitment to the public. The results show that, overall, wood remains the material of choice for acoustic guitars, and a wide number of wood species are used. Sustainability aspects are often highlighted on websites. However, the taxonomy is ambiguous in several cases, and some endangered wood species are used with limited information about preservation. Therefore enhancing the research of alternative wood species and increasing the efforts on environmental commitment and on promoting end consumer sustainability awareness are relevant targets to further enhance the use of wood in a sector that already provides a great valorization of this renewable material.
... and of the shear moduli in the shearing planes LT:LR:RT for 4.5:2.9:1. The studies highlighted the mechanical and acoustic properties of resonance wood (spruce and maple), identifying the values of sound propagation speeds in the longitudinal and radial directions, as well as the values of the modulus of elasticity through the following different methods to determine the resonance frequency [15][16][17][18][19][20][21]: the intrinsic transfer matrix method used to simulate the propagation of continuous waves or finite impulse in homogeneous, inhomogeneous or multilayered elastic media [16][17][18][19], and the non-destructive evaluation method based on ultrasound [22][23][24][25][26][27]. ...
... and of the shear moduli in the shearing planes LT:LR:RT for 4.5:2.9:1. The studies highlighted the mechanical and acoustic properties of resonance wood (spruce and maple), identifying the values of sound propagation speeds in the longitudinal and radial directions, as well as the values of the modulus of elasticity through the following different methods to determine the resonance frequency [15][16][17][18][19][20][21]: the intrinsic transfer matrix method used to simulate the propagation of continuous waves or finite impulse in homogeneous, inhomogeneous or multilayered elastic media [16][17][18][19], and the non-destructive evaluation method based on ultrasound [22][23][24][25][26][27]. ...
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The wood used in the construction of musical instruments is carefully selected, being the best quality wood from the point of view of the wood structure. However, depending on the anatomical characteristics of the wood, the resonance of wood is classified into quality classes. For example, sycamore maple wood with curly grains is appreciated by luthiers for its three-dimensional optical effect. This study highlights the statistical correlations between the physical and anatomical characteristics of sycamore maple wood and its acoustic and elastic properties, compared to the types of wood historically used in violins. The methods used were based on the determination of the acoustic properties with the ultrasound method, the color of the wood with the three coordinates in the CIELab system and the statistical processing of the data. The sycamore maple wood samples were divided into anatomical quality classes in accordance with the selection made by the luthiers. The results emphasized the multiple correlations between density, brightness, degree of red, width of annual rings, acoustic and elastic properties, depending on the quality classes. In conclusion, the work provides a valuable database regarding the physical–acoustic and elastic properties of sycamore maple wood.
... However, different cultures use different wood species to make traditional musical instruments, with sometimes very different material properties (Brémaud 2012). For example, white mulberry (Morus alba L.) is a dominant species used by craftsmen for making stringed musical instruments in Iran (see Fig. S1 in Supplementary material), Central Asia, and Japan (Yoshikawa 2007, Karami et al. 2010, Se Golpayegani et al. 2012, Vahabzadeh 2018). Yet mulberry wood has nearly opposite vibro-mechanical properties to spruce when the species used for string instruments among the world are compared (Brémaud 2012). ...
... Reduced anisotropy for white mulberry (L/R ratio of moduli of 4) is already reported (Se Golpayegani et al. 2012), but the anisotropy for the specimens in the current study was, interestingly, even lower. In a comparison of several studies on vibrational properties of mulberry (Se Golpayegani et al. 2015), the lowest values of E' L /γ were found for a wood considered as of "superior quality" for instruments (Yoshikawa 2007). It can be suggested that the extremely low value of E'/γ in L direction, accompanied by rather high values in R direction, may reflect an exceedingly high microfibril angle. ...
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Thermal treatments can be considered as an accelerated ageing, bringing partly similar changes in properties as naturally aged wood. Thermal treatment was applied on white mulberry (Morus alba L.), a dominant species for making musical instruments from middle-East to Far-East, to investigate the effects on the vibro-mechanical and physical properties of this wood, and the results compared to previously published data on spruce (Picea abies Karst.) as a reference for the soundboard of Western string instruments. Thermal treatment (TT) at 150 °C and 0% of relative humidity was applied to five analogous groups of specimens with five different durations (2.5, 8, 24, 72, 261 hours). Humidity reconditioning of specimens was done to explore the re-versibility of TT effects. Physical and vibrational properties such as specific gravity (γ), equilibrium moisture content (EMC), CIELab colorimetric values, specific modulus of elasticity (E'/γ) and damping coefficient (tanδ) in longitudinal (L) and radial (R) directions, have been measured after stabilisation of samples in standard conditions (20 °C, 65% RH), before and after TT and then after reconditioning. Untreated mulberry had a low EMC, very low L/R anisot-ropy and low E'L/γ, and relatively low tanδ. Weight loss (WL) and CIELab values evolved similarly during TT for mulberry and for previous results on spruce, however, their EMC and vibrational properties were affected differently. This could be explained in part by the low anisotropy of mulberry, and in part by its particular extractives. The parts of irreversible effects, linked to chemical modification or degradation, and of reversible effects, linked to physical configuration , were different between mulberry and spruce. The applied treatments did not bring permanent "improvements" in vibrational properties of mulberry, yet its colour appearance was enhanced.
... The above choices of woods are typical for the construction of the Cretan lyra [5]. For cedarwood, the physical properties used for modeling in this study have been found in [26], and for mulberry, in [27]. All the physical properties have been included in Appendix B. In Figure 1a, a picture of the Cretan lyra used in this study is included. ...
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Cretan lyra is a stringed instrument very popular on the island of Crete, Greece, and an important part of its musical tradition. For stringed musical instruments, the air mode resonance plays a vital part in their sound, especially in the low frequency range. For this study, the air mode resonance of a Cretan lyra is investigated with the use of finite element method (FEM). Two different FEM acoustic models were utilized: First, a pressure acoustics model with the Cretan lyra body treated as rigid was used to provide an approximate result. Secondly, an acoustic–structure interaction model was applied for a more accurate representation. In addition, acoustic measurements were performed to identify the air mode resonance frequency. The results of this study reveal that the acoustic–structure interaction model has a 3.7% difference regarding the actual measurements of the resonance frequency. In contrast, the pressure acoustics solution is approximately 13.8% too high compared with the actual measurements. Taken together, the findings of this study support the idea that utilizing the FEM acoustic–structure interaction models could possibly predict the vibroacoustic behavior of musical instruments more accurately, which in turn can enable the determination of key aspects that can be used to control the instrument’s tone and sound quality.
... The published and widely used material characteristics, frequency response and vibrational properties for wood materials are outputs of measurements and structural models (e.g. [18][19][20][21][22][23][24]). Wood choice for instruments manufacturing is also affected by geo-cultural and economic motives (e.g. ...
The piano is a complex musical instrument consisting of several components influencing vibration and sound production. By understanding the sound production mechanism virtual instruments can be created (physics-based sound synthesis) and the design and manufacturing of soundboards can be supported (virtual prototyping). Based on previous results published in the literature, a piano model was built and extended by a near field sound radiation model capable for physics-based sound synthesis. In this paper a simplified piano model is presented, including hammer strike and hysteretic felt models, coupled lossy string model and a 2D FEM based stiffened plate model for soundboard. This paper contains a parametric study where the soundboard parameters, such as its material characteristics and boundary conditions, are modified and their effect on the soundboard's modal behavior and the radiated sound is analyzed. Instead of using only musical (qualitative) descriptors, e.g. brightness or coloring, the piano sounds are characterized based on standard quantitative descriptors (e.g. harmonic ratio, spectral centroid). It is shown that these descriptors are determined by soundboard admittance, string characteristics and position on the soundboard; radiated sound from wooden soundboards can be characterized as harmonic for wide range of initial material descriptors; the string position is essential, and the perceived sound can differ significantly for different listening positions, even for the same harmonic decay pattern.
... For simplicity we have disregarded the effect of the Poisson ratio in this formula. These quantities have been previously used to measure the effect of ageing [26,27], the effect of absorbed water [28] and the classification of woods for string instruments [29]. In the case of wood for soundboards, it should have low anisotropy ratio and high acoustic radiation [24]. ...
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One of the biggest challenges in guitar-making is consistency: even though two guitars are made of the same tree, with the same geometry and manufactured with exactly the same techniques, small material variations intrinsic to the wood will make them sound different. We want to address this variability through the structural design of wooden plates used in the manufacture of guitar tops, developing wood-based mechanical metamaterials. By means of simulations, we study the effect of different geometric patterns of holes on the mechanical parameters of a piece of Engelman Spruce, with special emphasis on the density, the radial and longitudinal stiffness, and derived quantities. We show how one can control the elastic properties of perforated wood boards used for mechanical, acoustic and/or aesthetic purposes in general, and not only guitar making. These results could open a new era of rationally designed wood-based panels, for instrument making and beyond.
... Thus, the wood used for fretboards should have a certain wear resistance, a high hardness and stiffness, and an excellent flexibility. The higher the wear resistance and hardness of the fretboard wood, the less prone it will be to pits on the surface during overuse, and the wear of high-pitched note positions will be reduced, thus, extending the life of the instrument (Tu 1983;Shigeru 2007). The commonly used fretboard woods of ebony, Indian rosewood and African blackwood have high hardness, rigidity and excellent wear resistance. ...
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The commercial applications of endangered wood species (e.g., ebony, Indian rosewood, and African blackwood) for string instrument fretboards have been limited due to their low yield, long growth cycle, and tight trade restrictions. However, the physical and mechanical properties of radiata pine modified by furfuryl alcohol (FA) are comparable to the tropical hardwood species that are commonly used for fretboards. Therefore, this study proposes performance indicators of fretboard material selection to evaluate the physical and mechanical properties of modified wood samples with different FA concentrations. The concentration of FA was optimized to make the modified wood satisfy the performance requirements of fretboards. The density of fretboard wood needs to be greater than 800 kg/m3, and have good dimensional stability. The surface color of the wood needs to be dark brown or jet black. The hardness of fretboard wood needs to be greater than 6.0 kN, and it should have superior abrasion resistance (the friction coefficient is about 0.72, and width and depth of the wear scars are 0.8 mm and 25.0 μm, respectively). The E' and \({G}_{LT}^{^{\prime}}\) of the fretboard wood were greater than 9.32 GPa and 1.21 GPa, respectively. The fretboard wood had higher tanδ values and lower \(\upsilon\) and R values. The results indicated that the density of the 70% FA modified wood was 850 kg/m3, and it had good dimensional stability, which met the physical performance requirements of fretboard selection materials. Only the 70% FA modified wood met the requirements of the main evaluation indicators for the mechanical and sound vibration properties of the wood for fretboards. However, the furfurylated wood had the drawbacks of high brittleness and low bending strength, which needs to be addressed in the future research through FA modification combined with other modification technologies to perfectly replace the fretboard wood species.
The acoustical properties of wood are primarily a function of its elastic properties. Numerical and analytical methods for wood material characterization are available, although they are either computationally demanding or not always valid. Therefore, an affordable and practical method with sufficient accuracy is missing. In this article, we present a neural network-based method to estimate the elastic properties of spruce thin plates. The method works by encoding information of both the eigenfrequencies and eigenmodes of the system and using a neural network to find the best possible material parameters that reproduce the frequency response function. Our results show that data-driven techniques can speed up classic finite element model updating by several orders of magnitude and work as a proof of concept for a general neural network-based tool for the workshop.
The acoustic properties of wood for musical instruments have been often studied to manufacture good quality soundboards. The soundboard of a musical instrument plays an important role in producing good quality sound. Sape which is a Sarawak traditional musical instrument is a string instrument that is mostly made of a single bole of wood. Local woods such as Adau, Tapang, and Merbau were often used by the Sape makers to make the structure and soundboard of Sape. In this research, the objectives are to identify the feature of the selected wood type, classify the woods using machine learning, and propose the best wood to make the sape soundboard. Free-free beam forced vibration test is carried out to obtain the sound data from 9 wood samples. Acoustics, vibration, and timbre features are then ascertained. Support Vector Machine (SVM) algorithm is used to classify the wood type and wood grade using the 13 features selected. Wood is graded according to loudness and period. Adau wood which has a longer period and higher loudness tends to be the best wood type as the soundboard wood for making sape. The results show that the classification of the wood type and wood quality can be predicted using sound data collected from the flexural vibration of the Sape soundboard using MATLAB simulation.
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This work aims at bringing a better knowledge of woods, mainly heavy tropical ones, used in instruments, and some proposals for a diversification in relation with difficulties in sustainable availability. It follows two complementary approaches: characterization of the diversity used or usable in musical instrument making (species, vibrational properties); study of microstructural and chemical (extractives) factors influencing the important properties. A database “woody species – uses in instruments” is drawn and started to be implemented with information about extra-European traditions in instrument making. Basic vibrational properties (specific Young's modulus and damping coefficient in the frequency range 200- 600Hz) in axial direction, equilibrium moisture content (at 20°C and 65% RH) and colour parameters CIELab and CIELCh are determined on 1400 probes of small dimensions covering 60 species and 70 wood types, including 70% of tropical woods. One half is provided by instrument makers, the other is pre-selected according to criteria linking mechanical, chemical and physical properties. The relationships between properties are analysed and the species are classified into similarity groups by multivariate analysis. Heartwood extractives are responsible for very low damping coefficients and moisture contents for the majority of the tropical woods under study. Simple predictive models are proposed that explain, on studied species, 85-90% of the observed variability in damping coefficients. Relationships between physico-mechanical properties and microfibril angle on normal and compression wood of 3 softwoods are globally in agreement with the literature but compression woods exhibit – at given specific modulus- lower damping than normal woods. Heartwoods of two species of Papilionaceae (Pterocarpus soyauxii Taub. ‘Padauk' et P. erinaceus Harms. ‘Senegal Rosewood') are compared in their native state and after being extracted in different solvents. The extractives from Padauk are –at given quantities- more efficient in reducing damping than those of Senegal Rosewood and conversely for moisture content. Hypothesis are formulated about possible mechanisms.
From the reviews of the 1st edition: "It will surely remain the most comprehensive work in this field for a long time to come. It belongs on the bookshelf of every material scientist and structural engineer." CAS Journal, USA "...[T]he author has done an admirable job, collecting, organizing, and reviewing the disparate literature on most aspects of the Acoustics of Wood." Journal of the Acoustical Society of America, USA
Several authors have conducted research to characterize the woods used for musical instruments. The principle of such studies is that acoustical qualities of musical instruments are linked to modal properties of the resonator, especially to the soundboard. Therefore, by knowing the mechanical parameters of materials, it is easy to deduce the frequencies of the eigen modes of a vibrating structure. Equation 1 requires only the geometrical dimension of a plate, the density, and Young's modulus to define a material: where l is length, b is width, d is thickness, E is Young's modulus, I (= bd ³ /12) is inertial momentum, ρ is density, n is partial number, and f n , is frequency mode(n). But, how do we choose the values of each parameter, since woods are variable materials with a large distribution of values-for samples coming from the same tree?
From the point of view of economics, a defect in wood is any feature that lowers its value on the market. It may be an abnormality that decreases the strength of the wood or a characteristic that limits its use for a particular purpose. There is a certain amount of risk involved in classifying an abnormality as a defect because what is judged to be definitely unsuitable for one application may prove to be ideal for a different or special use.