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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
共Received 22 February 2007; revised 8 April 2007; accepted 2 May 2007兲
Two basic types of wood are used to make stringed musical instruments: woods for soundboards
共top plates兲 and those for frame boards 共back and side plates兲. A new way to classify the acoustical
properties of woods and clearly separate these two groups is proposed in this paper. The
transmission parameter 共product of propagation speed and Q value of the longitudinal wave along
the wood grain兲 and the antivibration parameter 共wood density divided by the propagation speed
along the wood grain兲 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.
关DOI: 10.1121/1.2743162兴
PACS number共s兲: 43.75.Gh, 43.75.Mn, 43.75.De 关NHF兴 Pages: 568–573
I. INTRODUCTION
Wood selection is the most important parameter in
stringed instrument design. The body of a stringed instru-
ment consists, in general, of a soundboard 共top plate兲 and a
frame board 共back plate and/or side plate兲 as illustrated in
Fig. 1. The lute or guitar family, shown in Fig. 1共a兲,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. 1共b兲, the back plate can function as part of the
soundboard as well as of the frame board. Modern pianos
depicted in Fig. 1共c兲 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 共or sound holes兲. Note, how-
ever, that the fortepianos made by Bartolomeo Cristofori in
the 1720s maintain such a box-hole structure 共four big holes
are hidden below the keyboard兲 as seen in the harpsichord
and clavichord.
1,2
Woods for string instruments are thus divided into two
groups: 共A兲 woods for soundboards and 共B兲 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
alternatives.
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.
3
Al-
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.
II. PARAMETERS TO CHARACTERIZE WOOD
PROPERTIES
A. Wood vibration and its transmission
Fletcher and Rossing
4
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-
cur’s well-organized book
5
nor the anthology edited by
Hutchins and Benade
6
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.
7–12
Research has also
been done on artificial composites.
13–15
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
denotes
the wood density.
9
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 共1兲, July 2007 © 2007 Acoustical Society of America0001-4966/2007/122共1兲/568/6/$23.00
Since the vibration of a wood plate produces sound radiation,
c/
may be called the “vibration parameter” or “radiation
ratio.”
10,12
Moreover, Schelleng
9
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.
4,5
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 共soundboards兲 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 共and neck兲 of the
Japanese shamisen 共three-string instrument兲, 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 共or damping兲 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
␣
−1
=2Q /k
=2cQ/
共k is the wave number;
is the angular
frequency兲.
16
Barducci and Pasqualini
17
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,
4–6,9–12
only the longitudinal wave that propagates along the wood
grain is analyzed because it has the primary acoustical im-
portance.
The acoustic conversion efficiency 共ACE兲 proposed by
Yankovskii
18
has also been used to characterize acoustic
materials.
7,19,20
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 共radiation ratio兲, c /
, multiplied by Q.
Therefore, ACE has the same meaning as the radiation ratio,
7
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.
19
have also suggested that cQ
共which they call the “relative acoustic conversion effi-
ciency”兲 be used to characterize woods. Their cQ was intro-
duced to eliminate a strong dependence of ACE on
by
assuming that ACE does not reflect the microstructure of the
wood cell wall.
Since the Young’s modulus E generally increases with
density
, higher acoustic impedance
c关=共
E兲
1/2
兴 might be
required for frame boards.
21
On the other hand, excellent
soundboards must have a high value of E /
.
5,7,8
Therefore
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.
19,22–24
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.
25
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 共and mode
FIG. 1. 共Color online兲 Cross-sectional schematics of typical structures of
stringed instruments. 共a兲 Box–sound-hole structure in the guitar, harpsi-
chord, Cristofori’s fortepiano, etc.. 共b兲 Box–sound-hole–sound-post struc-
ture in the violin family 共the sound post is depicted by a darker gray rect-
angle in the middle兲. 共c兲 Soundboard—iron-frame structure in modern
pianos. A white rectangle indicates top plate or soundboard; a black or gray
rectangle indicates back 共and side兲 plate or frame board.
J. Acoust. Soc. Am., Vol. 122, No. 1, July 2007 Shigeru Yoshikawa: Wood classification for string instruments 569
number兲 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-
quencies.
III. CLASSIFICATION DIAGRAM OF TRADITIONAL
WOODS BEST SUITED FOR STRING INSTRUMENTS
The wood species investigated in this paper are summa-
rized in Table I. Common names of woods are used hereafter.
Traditional 共meaning traditionally “best suited”兲 woods for
stringed instruments 共the upper eight species in Table I兲 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 共kiri in Japanese兲 is best for the Japanese 13-
stringed long zither 共koto or soh兲. Mulberry 共kuwa in Japa-
nese兲 is traditionally used for the whole body, including top
and back plates, of the Japanese four-stringed lute 共Satsuma
biwa兲. Wood parameters
, E, and Q of mulberry were newly
measured by Professor T. Ono of Gifu University using two
samples 共best quality and medium quality兲 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
19,22–24
mentioned in the previous
section. The density
was measured after the sample was air
dried 共which usually leaves a moisture content of about
12%兲. The data for the best-quality and medium-quality
samples are given in Tables II and III, respectively. Note that
“mulberry 共M兲” 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 共karin in Japanese兲
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
to
we see that soft woods for soundboards are light while
hard woods for frame boards are heavy. We may call
/c,
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 共see
Fig. 2兲. This shows the effectiveness of our newly proposed
transmission parameter cQ.
In Fig. 2 the four points corresponding to soundboard
woods 共excluding mulberry兲 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 共Japanese kiri兲 Paulownia tomentosa
Mulberry 共Japanese kuwa兲 Morus alba
Norway maple Acer platanoides
Japanese maple 共Japanese kaede兲 Acer sp.
Amboyna wood 共Japanese karin兲 Pterocarpus indicus
Brazilian/Rio rosewood Dalbergia nigra
White pine Pinus albicaulis
Hemlock Tsuga sp.
Redwood Sequoia sempervirens
Western red cedar Thuja plicata
Camphor wood 共Japanese kusu兲 Cinnamomum camphora
Zelkova 共Japanese keyaki兲 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
instruments.
Wood name
f
共Hz兲
共kg/m
3
兲
E
共GPa兲
c
共m/s兲
/c
共kgs/m
4
兲 Q
cQ
共10
5
m/s兲
Norway spruce
a
532 560 16 5300 0.11 116 6.2
Sitka spruce
a
484 470 12 5100 0.092 131 6.7
Sitka spruce
b
617 408 10.0 4940 0.083 144 7.1
Paulownia
b
569 260 7.3 5300 0.049 170 9.0
Mulberry 447 647 6.3 3130 0.21 70 2.2
Norway maple
a
470 620 9.8 4000 0.16 85 3.4
Japanese maple
b
447 695 11.8 4110 0.17 122 5.0
Amboyna wood
b
519 873 20.0 4770 0.18 155 7.4
Brazilian/Rio 354 830 17 4400 0.19 185 8.1
Rosewood
a
a
Reference 10.
b
Reference 26.
TABLE III. Physical properties of substitute woods for stringed instruments.
Wood name
f
共Hz兲
共kg/m
3
兲
E
共GPa兲
c
共m/s兲
/c
共kgs/m
4
兲 Q
cQ
共10
5
m/s兲
White pine
a
514 380 10.0 5200 0.073 116 6.0
Hemlock
a
533 440 8.4 4400 0.100 126 5.5
Redwood
a
1067 380 9.5 5000 0.083 209 10.4
Western red cedar
a
816 400 6.5 4000 0.100 174 7.0
Mulberry 共M兲 565 616 9.7 3960 0.16 121 4.8
Camphor wood
b
497 550 9.0 4060 0.14 121 4.9
Zelkova
b
439 720 12.6 4180 0.17 122 5.1
Italian cypress
c
430 450 5.7 3560 0.13 97 3.5
Pear
a
369 570 8.2 3800 0.15 67 2.5
American cherry
a
795 700 12.0 4100 0.17 137 5.8
Black walnut
a
522 680 20.0 5400 0.13 185 10.0
Andaman paduc
a
474 710 12.0 4400 0.16 185 8.1
Balsa 共high density兲
b
428 162 2.8 4170 0.039 140 5.8
Balsa 共compressed兲
b
538 771 22.0 5150 0.15 163 8.4
a
Reference 10.
b
Reference 26.
c
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, 共1兲
and the four points corresponding to frame-board woods
yield
y = 143x − 18.9, 共2兲
where x =
/c and y =cQ/10
5
. 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
/c.
In other words, large values of c and Q are required by both
good soundboards and good frame boards, while the
of
soundboards should be much smaller than that of frame
boards 共cf. Table II兲. 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.
19
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 共2兲 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 共1兲 and 共2兲. 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.
IV. CLASSIFICATION DIAGRAM FOR SUBSTITUTE
WOODS
Substitute woods are woods that are not traditionally
used for the best quality instruments, but alternative woods
共including artificial composites兲 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,
27
but data on the Italian poplar are,
unfortunately, not available.
White pine and hemlock are applied to violin tops.
10
Redwood and Western red cedar are sometimes used for gui-
tar tops,
10
although a majority of European guitar builders
exclusively use Western red cedar as well as European
spruce.
27
The data for mulberry 共M兲 were obtained from new
measurement of a sample used in medium-quality biwas.
Camphor wood 共kusu in Japanese兲 and zelkova 共keyaki in
Japanese兲 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.
10
The black walnut and
Andaman paduc may be used for guitar backs.
10
Balsa wood
can be applied to the top and/or back plate of string
instruments,
9
particularly the violin,
28
but its mechanical
strength is questionable.
12
From the data in Table III we construct the scatter dia-
gram of Fig. 3, where the two regression lines given by Eqs.
共1兲 and 共2兲 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 共very small anti-
vibration parameter兲, it is not a good alternative for the top
plate and soundboard. If its transmission parameter cQ
共probably its Q value兲 could be increased 共perhaps by the
proper processing兲, 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 共full circles兲 is almost
orthogonal to the regression line for frame boards 共open circles兲. 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 共see Table III兲. Italian cypress also has too high a
value of
/c, making it unsuitable for the modern piano
soundboard.
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. 共1兲. On the other hand, black walnut, compressed
balsa, and Andaman paduc are not such good alternatives.
The three data points for mulberry 共M兲, 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 共M兲 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. 共1兲 and 共2兲 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.
V. UNIQUE PROPERTIES OF JAPANESE STRING
INSTRUMENTS
As shown in Fig. 2, mulberry, which is used for the best
quality Japanese Satsuma biwa 共“Satsuma” is the old name
of the southernmost prefecture in Kyushu兲, lies far off the
quality criteria for Western string instruments, given by the
regression lines of Eqs. 共1兲 and 共2兲. 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 共bachi in Japanese兲 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 共low resonance nature兲 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” 共“touch”兲, which
allows strings to vibrate against the neck or frets, creating a
reverberating high-frequency emphasis.
3,29
A few variants of
this sawari are seen as “jawari” 共in Hindi兲 on the Indian sitar
and tambura,
3,4
and as “bray pins” on medieval harps.
30
Moreover, the peculiarity of the mulberry clearly dis-
criminates the Satsuma biwa from the Chinese pipa
共p
⬘
i-p
⬘
a兲. The Chinese pipa,
31
with a top plate of paulownia
and a back shell of red sandal wood 共close to amboyna
wood兲 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
共A
2
,D
3
,E
3
, and A
3
兲.
31
The Japanese shamisen 共meaning “three-stringed”兲,
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 共Fig. 2兲.
The shamisen also has the sawari, but its mechanism
differs from that of the Satsuma biwa.
29
Most importantly,
the shamisen’s sawari is restricted to only the first 共lowest兲
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.
29
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 共koto兲,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 共this may
also be the case for Korean gayageum and Chinese gu-
zheng兲. Also, the koto strings are plucked with small plectra
worn on three fingers 共the thumb, index, and middle finger兲
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.
VI. CONCLUSIONS
A new scheme to classify the woods used in stringed
instruments is proposed. Plotting
/c 共the antivibration pa-
rameter兲 along the x axis, and cQ 共the transmission param-
eter兲 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 共Fig. 2兲, some peculiarities of Japanese string
instruments such as the Satsuma biwa, shamisen, and koto
emerge. In particular, mulberry 共for the Satsuma biwa兲 and
paulownia 共for the koto兲 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.
ACKNOWLEDGMENTS
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 author’s
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.
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