Biwa Vs. Cello

Home , Biwa, Gayageum, Koto (instrument), Pipa, Shamisen

Acoust. Sci. & Tech. 29, 1 (2008) #2008 The Acoustical Society of Japan PAPER

A comparison of string instruments based on wood properties: Biwa vs. cello

Shigeru Yoshikawa, Masahiro Shinodukay and Takafumi Senda Department of Acoustic Design, Graduate School of Kyushu University ( Received 23 April 2007, Accepted for publication 23 August 2007 )

Abstract: The Satsuma biwa and the cello are compared from the viewpoint of their wood properties. According to the wood classiﬁcation diagram, the mulberry traditionally used for the biwa is very far from the Western criteria for the resonance woods such as sitka spruce and maple respectively used for the top and back plate of the cello. The structural responses of these instruments are investigated by measuring the driving-point mobility and the transmission mobility of the top plate. The cello is designed to stress the fundamental, while the biwa is constructed to sustain the higher harmonics that are generated by the ‘‘sawari’’ mechanisms applied to the nut and frets. Since the sawari tone yields a reverberating high-frequency emphasis, it is auditorily discriminated from the lower harmonics, which depend on the mode vibrations of the top plate and the bridge. In addition, the camphor-made biwa is compared with the mulberry-made biwa on their structural responses and the resulting sound spectrograms. The camphor wood is not an excellent substitute for the mulberry. Furthermore, the acoustical features of other Asian stringed instruments, where the paulownia and amboyna wood are used, are brieﬂy discussed in relation to the playing style and musical taste.

Keywords: Wood classiﬁcation diagram, Transmission parameter, Mobility measurement, Sawari mechanism, Satsuma biwa

PACS number: 43.75.Gh, 43.75.De, 43.75.Mn [doi:10.1250/ast.29.41]

been tried yet in the context of musical acoustics. 1. INTRODUCTION Although the cello is bowed and the biwa is plucked, String instruments are distributed worldwide. The such a difference in driving method is insignificant because features common to string instruments are easily found, our primary interest is in structural and material differences but at the same time various significant differences are of the instruments. First of all, the classification diagram observed between those in different races. For example, the of woods for different string instruments is proposed to guitar, the pipa, and the biwa are the plucked string demonstrate major differences between wood properties in instruments, but they have distinct differences in their next Sect. 2. wood material, playing style (plucking way), and tonal Physical properties of wood are directly reflected in taste corresponding to the racial difference [1]. As the structural responses of wood against the vibration excita- result, the philosophy of making string instruments is tion. These wood responses are relevantly measured as the definitely different between individual races. driving-point mobility (admittance) and the transmission The selection of wood seems to be the first importance mobility. Therefore, these mobilities are measured on the for making string instruments [2,3]. This is because a given biwa and cello in Sect. 3. The driving point is selected at string instrument was created by human beings living in the center of the bridge. Four strings of the cello are tuned a given natural environment. Hence, there are traditional as C2 (65 Hz), G2 (98 Hz), D3 (147 Hz), and A3 (220 Hz). wood materials for traditional string instruments. Spruce is On the other hand, the tuning of four strings of the Satsuma the best to the top plate of the guitar, violin, and cello. biwa (‘‘Satsuma’’ is the old name of the southernmost Mulberry is the best to the top plate and the shell-shaped prefecture in Kyushu) depends on player’s voice register. frame body of the Japanese Satsuma biwa. In this paper the However, one of typical tuning examples for male voice is ] ] ] ] cello and the biwa are compared with each other from the as C3 (139 Hz), G2 (104 Hz), C3 (139 Hz), and G3 (208 Hz). viewpoint of wood material. Such a comparison has not Hence, both instruments seem to have similar sounding ranges and to be reasonable objects for the comparison. It e-mail: [email protected] will be then understood that different woods lead different yCurrently with Kawai Musical Instruments Mfg. Co., Ltd. philosophies of instrument making in Sect. 3. Such under-

41 Acoust. Sci. & Tech. 29, 1 (2008) standings and suggestions on the interrelation between Table 1 Common names and botanical names of woods wood material and instrument making philosophy are the investigated in this paper. The Japanese name is given in the parenthesis with the Italic font. prime objective of this paper. It is well known that the mulberry (kuwa in Japanese) Common name Botanical name is the best wood (traditional wood) for the Satsuma biwa. Norway spruce Picea abies However, the camphor wood (kusu in Japanese) and Sitka spruce Picea sitchensis zelkova (keyaki in Japanese) are sometimes used as Paulownia (kiri) Paulownia tomentosa Norway maple Acer platanoides substitute wood. In order to understand the major differ- Japanese maple (kaede) Acer sp. ence between the traditionally best-suited wood and Amboyna wood (karin) Pterocarpus indicus substitute wood, two Satsuma biwas, respectively made Brazilian/Rio rosewood Dalbergia nigra of mulberry and camphor wood, are compared with each Mulberry (kuwa) Morus alba other in Sect. 4. Moreover, wood material largely affects Camphor wood (kusu) Cinnamomum camphora Zelkova (keyaki) Zelkova serrata the playing style. From this viewpoint some string instruments from the Asia are briefly compared with each other in Sect. 5. Conclusions are given in Sect. 6. Satsuma biwa. Note that ‘‘mulberry (M)’’ is used to 2. CLASSIFICATION DIAGRAM OF WOOD indicate its medium quality. Numerical data are taken from A fundamental structure of string instruments in the Refs. [5,7,8]. Asia and Western is a box-sound hole structure [4,5] as Sitka spruce and Norway spruce are used for almost seen in the harpsichord, guitar, violin, and biwa. The box all Western string instruments such as the violin, cello, usually consists of the top plate, side plate, and back plate. harpsichord, piano, guitar, etc. Paulownia (kiri in Japanese) The top plate is the soundboard radiating sound due to its is widely used for Asian string instruments, particularly vibration characteristics. The side and back plates (or shell- for long zither family such as the Japanese 13-stringed shaped body plate in the biwa) work as the frame board that koto (or soh), Korean 12-stringed gayageum, and Chinese supports the vibration of top plate, and form the cavity for 21-stringed gu-zheng. Also, the top plate of the Chikuzen air resonance, whose effect is radiated from the sound biwa and the Chinese pipa is the paulownia. Since this hole(s). Therefore, the string-instrument woods can be paulownia is very light, the speed of the longitudinal wave divided into two groups: soundboard woods and frame- c [¼ðE=Þ1=2] propagating along the grain is as high as board woods [5,6]. Norway spruce and sitka spruce (over 5,000 m/s). How- Wood species investigated in this paper are summariz- ever, mulberry (kuwa in Japanese), which has been used for ed in Table 1. Common names of woods are used hereafter. the whole body of the Japanese 4-stringed lute, Satsuma Table 2 summarizes fundamental wood properties (the biwa, and used for the back shell of the 5-stringed density , Young’s modulus E along the wood grain, and Chikuzen biwa, has such a very low c as about 3,100 m/s. the quality factor Q of the resonance) of traditional woods This is primarily due to its very low Young’s modulus. for string instruments with best quality and three substitute On the other hand, the following four woods are used woods [camphor, zelkova, and mulberry (M)] for the for frame boards: Both Norway maple and Japanese maple

Table 2 Physical properties of traditional woods for string instruments and three substitute woods for the Satsuma biwa.

f E Q c =c Wood name cQ (Hz) (kg/m3) (GPa) (m/s) (kgs/m4) (105 m/s) Norway spruce 532 560 16 116 5300 0.11 6.2 sitka spruce 484 470 12 131 5100 0.092 6.7 sitka sprucey 617 408 10.0 144 4940 0.083 7.1 paulowniay 569 260 7.3 170 5300 0.049 9.0 Norway maple 470 620 9.8 85 4000 0.16 3.4 Japanese mapley 447 695 11.8 122 4110 0.17 5.0 Amboyna woody 519 873 20.0 155 4770 0.18 7.4 Brazilian/Rio rosewood 354 830 17 185 4400 0.19 8.1 mulberryz 447 647 6.3 70 3130 0.21 2.2 mulberry (M)z 565 616 9.7 121 3960 0.16 4.8 camphor woody 497 550 9.0 121 4060 0.14 4.9 zelkovay 439 720 12.6 122 4180 0.17 5.1

Reference [7]; yReference [8]; zReference [5].

42 S. YOSHIKAWA et al.: STRING INSTRUMENTS AND WOODS: BIWA VS. CELLO

105 10 paulownia y = 143 x - 18.9 9 cQ for Brazilian/Rio 8 rosewood soundboards zelkova amboyna wood 7 sitka spruce Norway spruce for 6 frame boards y = - 50.5 x + 11.4 camphor x 5 x x Japanese maple 4 mulberry (M) Norway maple mulberry 3 2

Transmission Parameter 1 0 0 0.05 0.1 0.15 0.2 0.25 Anti-Vibration Parameter /c

Fig. 1 Classification diagram of string-instrument woods. : soundboard wood; : frame board wood; : traditional wood for the Satsuma biwa; : substitute wood for the Satsuma biwa. are used for the violin and cello back plate. Amboyna wood if the Q-value is sufficiently high, where k (¼ c=!) and (karin in Japanese) is the best for the body and long neck ! (¼ 2f ) denote the wave number and the angular of the Japanese 3-stringed lute, shamisen. Brazilian/Rio frequency, respectively [5,10]. See Ref. [5] for more rosewood is best suited for the guitar back and side plates. detailed discussion on the transmission parameter cQ and Substutute woods (camphor wood and zelkova) and other related parameters. mulberry (M) for the biwa with medium quality indicate The four points corresponding to soundboard woods much larger values of c and Q than the mulberry for the yield a regression line with a negative slope (y ¼50:5x þ best-quality biwa. 11:4 for x ¼ =c and y ¼ cQ=105) in Fig. 1. On the other A classification diagram of stringed-instrument woods hand, the four points corresponding to frame-board woods is illustrated in Fig. 1 on the basis of wood constants given form another regression line with a positive slope (y ¼ in Table 2. In Fig. 1 open circles indicate the frame-board 143x 18:9). It is well understood that two parameters =c woods, full circles the soundboard woods, and a square and cQ clearly separate the different functions required by symbol indicates the wood for the Satsuma biwa’s whole the soundboard wood and frame-board wood. However, body. In addition, three cross symbols denote substitute mulberry lies outside the traditional wood groups. More- woods for the Satsuma biwa. Yoshikawa [5,6] first over, it should be noted that the woods with almost proposed such a diagram for traditional woods. opposite characteristics (mulberry, paulownia, and amboy- In this paper only the outline of the classification na) are preferably used for Japanese stringed instruments. scheme is repeated. The abscissa is the ‘‘anti-vibration 3. STRUCTURAL RESPONSE parameter’’ =c and the ordinate is the ‘‘transmission OF CELLO AND BIWA parameter’’ cQ. Schelleng [9] derived the ‘‘vibration parameter’’ c= by supposing that both the stiffness and 3.1. Mobilities of the Cello the inertia of the plate should be invariant between At first, the driving-point mobility is measured at the different woods if their vibrational properties are to be bridge top of the cello. A block diagram for the measure- the same. Since the vibration of a wood plate produces ment is depicted in Fig. 2 [11]. A mini-shaker (B & K type sound radiation, Haines [7] called c= ‘‘radiation ratio’’. 4810), whose frequency and amplitude are given by an Higher c= implies higher degree of the vibration excita- oscillator (NF type 1930) and a power amplifier (B & K tion or the resonance. type 2718) respectively, drives the bridge top as depicted On the other hand, the transmission parameter cQ is in Fig. 2(b). An impedance head (B & K type 8001) is derived from the inverse of attenuation constant of the inserted between the shaker and the bridge. A stylus made longitudinal wave propagating along the wood grain [5]. of a small nail is applied to the bottom of the impedance The solution of a lossy wave equation approximately gives head to connect the bridge and then measure the driving force and the resulting acceleration with two measuring 1 ¼ 2Q=k ¼ 2cQ=! ð1Þ amplifiers (B & K type 2609).

43 Acoust. Sci. & Tech. 29, 1 (2008)

(a) power oscillator amplifier mini-shaker driving force measuring cello impedance head oscilloscope amplifier

acceleration measuring amplifier

(b) driving mini-shaker signal

acceleration driving force impedance head string bridge stylus

top plate

Fig. 2 Measurement diagram on the driving-point mobility of the cello. (a) Signal-ﬂow diagram. (b) An enlargement of the contact between the cello bridge and the measurement system.

It should be noted that a cello is horizontally placed on two heavy blocks through three small rubbers (two rubbers near the bottom edge of the back plate, and another near the top edge of the back plate). Also, a soft rubber is applied to the strings to avoid their sympathetic resonance. Two driving (measuring) points are selected: the real top of the bridge between the D and G strings; the notch of the C string after removing it. Moreover, the transmission mobility is measured by changing the accelerometer position to the lower part of the Fig. 3 Mobilities measured on the cello. (a): the driv- top plate (185 mm below the f-hole center on the A-string ing-point mobility; (b): the transmission mobility; side, corresponding almost to the center of the lower (c): the difference between (b) and (a). right part of the top plate) as well as by changing the accelerometer to a miniature one (B & K type 4374, 0.65 grams). The bridge top is driven by the sinusoidal signal in As clearly shown in Fig. 3(a), some peaks below 1-Hz step (from 10 Hz to 0.5 kHz) and in 5- to 10-Hz steps 500 Hz (at about 80, 155, 190, 300, 320, and 425 Hz) are (from 0.5 kHz to 4 kHz) for the measurement of the more prominent than appreciable peaks above 500 Hz. This driving-point and transmission mobilities. means that the fundamental frequencies (distributed from The measurement result on a Suzuki cello is illustrated 65 Hz to 440 Hz) of the tones produced by four strings of in Fig. 3. The ordinates of Figs. 3(a) and (b) indicate the cello are primarily emphasized. That is, the Western 20 log jYdj and 20 log jYtj respectively, where Yd is the ratio philosophy of making string instruments is in the emphasis of the vibration velocity at the driving point vd to the of the fundamental frequency, which yields the sensation driving force Fd, and Yt is the ratio of the vibration velocity of definite pitch. Such a statement is confirmed by the at the transmission point vt to the driving force Fd. The measurement result on another Benedict cello of medium values of Yd and Yt are calibrated based on the transducer quality [11] and by the measurement carried out by sensitivities. Therefore, the ordinate values correspond to Woodhouse [12]. Also, it may be said that there is no the calibrated absolute values. Also, Fig. 3(c), which plots significant difference between the results measured at the 20 log jYt=Ydj, shows the difference between Fig. 3(b) and bridge top and at the C-string notch [11]. Fig. 3(a). Since Yt=Yd ¼ vt=vd, the curve of Fig. 3(c) can Since the transmission always suffers the attenuation, suggest the loop or node of normal mode vibration and the 20 log jYt=Ydj tends to be negative in general. However, it sound radiation characteristic of the top plate. can take positive values in reality as shown below about

44 S. YOSHIKAWA et al.: STRING INSTRUMENTS AND WOODS: BIWA VS. CELLO

1 kHz in Fig. 3(c). This implies that there are resonant vibration modes of the top plate in this frequency range. Particularly, the resonance around 425 Hz must be easily detected. Also, according to Reinecke [13], two main resonances of a cello bridge are measured at 985 Hz and 2,100 Hz. Therefore, two peaks near 1,000 Hz and 2,400 Hz in Fig. 3(a) might imply the eﬀect of the bridge resonance. The frequency fB of a bending wave in a thin plate is approximately given by [14]

2 fB ¼ 0:0459hcLkn ð2Þ where h is the plate thickness, cL is the velocity of 2 1=2 longitudinal waves in an inﬁnite plate [cL ¼ c=ð1 Þ , where is Poisson’s ratio], and kn is the wave number corresponding to the normal modes of vibrations that Fig. 4 Experimental setup for the mobility measurement on the Satsuma biwa. The driving point is right depend on the boundary conditions of the plate. Therefore, over the short post situated between the bridge ( fukuju) h (as well as and E) is important to determine the and the top plate. An accelerometer for measuring the vibrational properties of soundboards. The thinness of top transmission mobility is placed on the centerline of the plates in the violin, cello, and guitar largely contribute to top plate and below the white line indicating the inner decrease their resonance frequencies. brace position.

3.2. Mobilities of the Mulberry-Made Biwa frequency range as shown in Fig. 5(c). A biwa string is extended between a nut (called The first (lowest) broad peak extends from about ‘‘tori-kuchi’’ in Japanese, meaning a bird bill) and a bridge 400 Hz to about 600 Hz. Since individual sharp peaks (called ‘‘fukuju’’, meaning a covering hand). The string appear at this frequency range in Fig. 5(b), these sharp length between the nut and bridge is about 0.85 m. It should peaks probably correspond to the resonance modes of the be noted that a short post connects the bridge with the top top plate. A distinct dip is seen at about 730 Hz in Fig. 5(a), plate as shown in Fig. 4. The driving point is located right but this dip changes into the highest peak in Fig. 5(c). Thus over this post. A small accelerometer for the transmission this dip possibly indicates a certain node frequency of the mobility measurement is also seen at the right-hand side of bridge. According to Taguti and Tohnai [15], the bridge Fig. 4. This accelerometer position is on the centerline of itself (made of mulberry) of the Satsuma biwa tends to the top plate and about 60 mm below a solid brace that is have three peaks (near 1 kHz, 1.4 kHz, and 2.1 kHz) and horizontally built under the top plate near its middle. The two dips (near 0.5 kHz and 2.0 kHz). Thus we may interpret location of this brace is usually indicated as a white line on the measured responses of the biwa as follows: the top plate (cf. Fig. 4). The measurement system and (1) The lowest broad peak consists of resonance modes procedure are the same as in the case of the cello. of the top plate (this is confirmed by analyzing The measurement result is shown in Fig. 5 just in the tapping tones of the top plate. See Table 3 in the same manner as Fig. 3. Comparing Fig. 3(a), we may Sect. 3.3). easily recognize that there are three distinct and broad (2) The response near 730 Hz is due to the first node of peaks in Fig. 5(a). The centers of these peaks are located the bridge. near 600 Hz, 1,900 Hz, and 2,800 Hz. Also, from Figs. 5(b) (3) The second and third broad peaks are due to the and (c) the vibration response of the top plate seems to be bridge resonances. Their frequencies seem to be divided by a very deep dip at around 2.6 kHz, which is raised by about 500 Hz when the bridge is integrated possibly given by a certain vibration node formed near onto the biwa body. The lowest peak of the bridge the acceleration position. Since there is a dip near 2.2 kHz itself near 1 kHz is obscure, but seems to appear near in Fig. 5(a), a frequency band of weak response can be 1.5 kHz. formed between about 2.2 kHz and about 2.7 kHz. The (4) The low response near 2.2 kHz in Fig. 5(a) is due to frequency range below this weak response band, which is the second node of the bridge. extended from about 0.4 kHz to about 2.2 kHz, probably (5) In relation to the resulting sound, the three frequency yields stronger responses and sustains the resulting sound bands mentioned in the previous paragraph are [cf. Fig. 5(c)]. In addition, a higher frequency range above important [cf. Fig. 5(c)]: A primary sound-sustaining the weak response band can sustain the sound, though the band (0.4–2.2 kHz), a sound-suppressing band (2.2– relative strength is about 10 dB less than that in the lower 2.7 kHz), and another secondary sound-sustaining

45 Acoust. Sci. & Tech. 29, 1 (2008)

driving-point mobility of the biwa shows very weak responses below 400 Hz. Thus the main importance in biwa making is not upon the fundamental frequency as in the cello making, but upon higher harmonics that are produced in the primary sound-sustaining band. Moreover, it will be revealed in next section that the secondary sound- sustaining band serves to support the sawari sounds. Also, the response shown in Fig. 3 indicates very minute change as the frequency is varied, while that in Fig. 5 looks rather smooth. Such a diﬀerence in the response seems to depend on the diﬀerence in wood material, that is, the high- resonance nature of spruce and the low-resonance nature of mulberry. Furthermore, since the thickness of the biwa top plate is about 10 mm, which is roughly three times the thickness of the cello top plate, the vibrational response of the biwa tends to be decreased below 500 Hz [cf. Eq. (2)].

3.3. Mobilities of the Camphor-Made Biwa First of all, as a prerequisite for the mobility comparison, it should be confirmed that our two experimental biwas have almost the same geometry and structure. Table 3 indicates the degree of their similarity. The camphor-made biwa is a little smaller and lighter than the mulberry-made one. Since the density of mulberry is relatively higher than that of camphor wood as shown in Table 2, a small difference in weight suggests that the top plate and the back shell are slightly thicker in the camphor- made biwa. This seems to be reflected in a lower value (790 Hz) of the second main tap-tone frequency of the camphor-made biwa. A slightly higher value (600 Hz) of the first main tap-tone frequency possibly reflect the smaller size of the camphor-made biwa. Moreover, since Fig. 5 Mobilities measured on the mulberry-made biwa. (a): the driving-point mobility; (b): the transmission the Helmholtz resonance frequency is very close to each mobility; (c): the difference between (b) and (a). other, the air cavity inside the biwa is almost the same between two experimental biwas. We may thus recognize Table 3 Important parameters indicating the geometry the geometrical and structural similarities between these and structure of two experimental Satsuma biwas. Note biwas. that their bridges are made of the same wood as their The driving point and the accelerometer position for bodies. transmission mobility are relatively the same as the Mulberry-made Camphor-made previous measurement. The measurement result is shown biwa biwa in Fig. 6. We can notice that the peak at around 1.9 kHz in Total weight 3.2 kg 3.0 kg Fig. 5(a) disappears in Fig. 6(a). Moreover, the response Maximum height 927 mm 910 mm from 1 kHz to 2 kHz shows a declining tendency in Maximum width 325 mm 308 mm Fig. 6(c), which is clearly different from the sound- Helmholtz resonance 103 Hz 110 Hz Main tap-tone 590 Hz 600 Hz sustaining band in Fig. 5(c), although the prominent peak frequencies 940 Hz 790 Hz near 730 Hz is seen in both figures. Also, a very deep dip is observed near 1.2 kHz in Fig. 6(b). This suggests a clear node of top-plate vibration in the camphor-made biwa. band (2.7–4.5 kHz). Although the result above 4.0 Such a strong node does not appear in the mulberry-made kHz is not shown here, the measurement was carried biwa. Taking these undesirable points into consideration, out up to 5.0 kHz, and it was confirmed that the we may say that the camphor-made biwa is definitely sustaining response was kept to about 4.5 kHz. inferior to the mulberry-made biwa in the structural Comparing Fig. 5 with Fig. 3, we know that the response.

46 S. YOSHIKAWA et al.: STRING INSTRUMENTS AND WOODS: BIWA VS. CELLO

say that the difference between our camphor-made biwa and the mulberry-made biwas is significantly larger than the difference among mulberry-made biwas. 4. BIWA SOUNDS In this section the differences between traditional wood (mulberry) and substitute wood (camphor wood) for the Satsuma biwa are discussed from sound examples. Figure 7 compares three examples of biwa sounds when the fourth string is pressed by a player’s finger at the upside of the third fret (counting from the nut) and then plucked by a large plectrum (bachi in Japanese): (a) string vibration without the sawari on the mulberry-made biwa; (b) string vibration with the fret-sawari on the mulberry-made biwa; (c) string vibration with the fret-sawari on the camphor- made biwa. Here the ‘‘fret-sawari’’ means that the upper end of the string is constrained by the fret surface (usually about 10 mm wide), and during the vibration the string touches the fret on and off. The degree of this fret sawari is carefully determined by subtly adjusting the height and the slope of the fret surface. When the fret is not used, the nut gives the sawari to an open string and produces the ‘‘nut- sawari’’ tone. See Ref. [16] for more explanations about the sawari (‘‘gentle touch’’ in Japanese). The biwa was played in an anechoic room of the Kyushu University by the Italian biwa maker, Doriano Sulis living in Fukuoka, Japan. The sounds were digitally recorded. Also, the following devices were used: A microphone B & K type 4191, a preamplifier B & K type 2669, and a measuring amplifier B & K type 2609. A microphone was set near the distance of about 1 meter from the biwa body and near the height of about 0.96 m from the Fig. 6 Mobilities measured on the camphor-made biwa. (a): the driving-point mobility; (b): the transmission floor (the player seated on a chair and the center of the mobility; (c): the difference between (b) and (a). biwa body was 0.70 m high from the floor). Spectrogram analysis in Fig. 7 is carried out by applying the Matlab software to the above digital data When the tapping tones of the top plate are analyzed, which are sampled with 48 kHz. The FFT length is 1,470 two peaks near 600 Hz and 800 Hz in Fig. 6(a) are points and the Kaiser window is used. The tone is D4 recognized as the plate resonances. This is almost the (about 294 Hz), though the fundamental frequency of same in the mulberry-made biwa as shown in Table 3 and (a) and (b) is about 306 Hz. Comparing Fig. 7(a) with Fig. 5. However, the decisive difference appears at the Fig. 7(b), we may easily recognize that the sawari yields resonance near 2 kHz, which demonstrates the significant a reverberating high-frequency emphasis. This sawari difference between the mulberry-made biwa and the effect is particularly evident in a frequency band between camphor-made biwa that are used in our present measure- 11th harmonic (about 3,370 Hz) and 15th harmonic (about ment. Also, when comparing them with other Satsuma 4,590 Hz). This frequency band tends to be decreased by biwas used in Taguti’s measurement [15], we know that about 1 kHz when lower notes are played on the mulberry- our two biwas have prominent peaks near 3 kHz as shown made biwa used for the measurement. This result well in Figs. 5(a) and 6(a), while Taguti’s three biwas have no agrees with that shown in Ref. [17], where it is reported such peaks. However, his results of the transmission that the harmonic levels around 10th harmonic are higher mobility are much similar to our mulberry-made biwa than the fundamental level by about 30 dB when the first than to our camphor-made biwa because our camphor- open string (A3 ¼ 220 Hz) is plucked. made biwa lacks an important peak near 2 kHz in the Importantly, this emphasized frequency band almost driving-point mobility as explained above. We may thus corresponds to the secondary sound-sustaining band (2.7–

47 Acoust. Sci. & Tech. 29, 1 (2008)

(a) 1

–1 amplitude 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 8000 40 7000 20 6000 0 5000 –20 4000

–40 3000

2000 –60 frequency (Hz) 1000 –80

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 (dB) time (s)

(b) 1

–1 amplitude 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 8000 40

7000 20 6000 0 5000 –20 4000 –40 3000 –60 2000 frequency (Hz) –80 1000

–100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 (dB) time (s)

–1 amplitude 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 8000 40

7000 20 6000 0 5000 –20 4000 –40 3000 –60 2000

frequency (Hz) –80 1000 –100 0 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 (dB) time (s)

Fig. 7 Spectrograms of the Satsuma biwa sounds (D4) played on the third fret of the fourth string. (a) string vibration without the sawari on the mulberry-made biwa; (b) string vibration with the fret-sawari on the mulberry-made biwa; (c) string vibration with the fret-sawari on the camphor-made biwa.

48 S. YOSHIKAWA et al.: STRING INSTRUMENTS AND WOODS: BIWA VS. CELLO

4.5 kHz) shown in Fig. 5(c). The response in this high- 3 kHz. The existence of such a frequency range, which frequency band depends on the vibrational characteristic of corresponds to the sound-suppressing band (2.2–2.7 kHz) the bridge itself as explained in Subsect. 3.2. Therefore, the described in Subsect. 3.2, may be decisive to make the structural coupling between the bridge and the top plate as biwa sound, in which the sawari components are discrimi- well as the adjustment of the fret (or nut) surface is very nated from the body components. important to support the reverberating sawari sound. The Chinese pipa (p’i-p’a) consists of the top plate of Comparing Figs. 7(a) and 7(b), we notice that the sawari paulownia and the back shell of red sandal wood (close to temporally sustains the sound very much. Both this sus- amboyna wood) or maple. It has many (over 20) frets, and taining sound and the high-frequency emphasis mentioned its strings are plucked with a small pick or player’s fingers. above yield the impression of reverberation. See Ref. [18] This is quite similar to the Western guitar. However, a for the sawari tones of the Chikuzen biwa, which are harmonic enhancement is designed in the pipa by adjusting relatively different from those of the Satsuma biwa because the top plate to have some resonances about one or two of the difference in wood materials and their properties. octaves higher than the string fundamental frequencies [19]. On the other hand, as shown in Fig. 7(c) the sawari Paulownia seems to be best suited to the top plate to the pipa sound of the camphor-made biwa cannot create a distinct in order to have the above resonance characteristics. high-frequency emphasis, though a weak emphasis around Paulownia is widely used for Asian long zither-type 3 kHz (9th to 11th harmonic) is appreciable. Note that this string instruments such as the Japanese koto, Korean frequency band around 3 kHz corresponds to a broad peak gayageum, and Chinese gu-zheng. As shown in Fig. 1, in the driving-point mobility as indicated in Fig. 6(a). paulownia is opposite to mulberry used for the biwa. The Comparing Fig. 7(c) with Fig. 7(b), we may understand high resonace quality of the paulownia seems to be a that the camphor-made biwa stresses the lower (4th to 7th) relevant requirement because the plucking with small harmonics. This should be due to the vibrational properties plectrums worn on three fingers or with fingernails is not of camphor wood, which are closer to those of Norway so strong, and the instrument body is very large. In addition, maple or Norway spruce as inferred from Fig. 1. As the since the paulownia provides very smooth surface, the result, the sound of the camphor-made biwa is appreciably movement of movable bridges, which are applied under different from that of the mulberry-made high-quality each string for the tuning, is well facilitated on the top plate biwa. Hence, it may be concluded that camphor wood when a chord change is required during the performance. cannot be used as good substitute wood for the mulberry The left-hand sections of the koto string are important which is best suited to the Satsuma biwa. to produce vibrato effects and interpolate semitones by pressing these sections with player’s left hand. The pitch 5. COMMENTS ON ASIAN STRING change by this technique is very drastic in the Korean INSTRUMENTS gayageum, which is usually played on the right leg of the The string of the Satsuma biwa is strongly struck with a player who is seating on the floor. Such characteristic pitch large triangular plectrum instead of being plucked with a fluctuation is peculiar to the Korean music, not found in the small pick or fingers as in the guitar, etc. Very character- Chinese and Japanese music. istic impact sounds are produced by this striking play. The An overall view of Asian stringed instruments gives an low-resonance nature of the mulberry, which is shown in important recognition that lutes with short neck (such as Fig. 1 by a large value of the anti-vibration parameter and the biwa and pipa) and those with long neck (such as the by a small value of the transmission parameter, makes this shamisen and sanxian) are not used in Korean traditional playing style possible because the top plate is simulta- music. This might be because the characteristic pitch neously struck with a large plectrum. fluctuation (bending) mentioned above is created much less The sawari mechanism has been invented to compen- effectively on these lutes than on long zither-type instru- sate this low-resonance nature by creating a reverberating ments such as the gayageum. On the other hand, a high- high-frequency emphasis. However, the situation is a little frequency emphasis is very important in traditional music complicated. The response of the mulberry body probably in India, China, and Japan. Such musical tendency can be supports the harmonic components below about 2 kHz [cf. understood from the fact that the sawari mechanisms are Fig. 5(a) and Fig. 7(a)]. The sawari mechanism tends to invented in Japanese biwa and shamisen, and the jawari strongly generate high-frequency components of string (in Hindi) mechanisms are invented in Indian sitar and vibration between about 3 kHz and about 4.5 kHz [cf. tambula [14], to produce unique reverberating high- Fig. 7(b)]. This high-frequency band is supported by the frequency emphasis. vibrational characteristic of the bridge (fukuju) [cf. 6. CONCLUSIONS Fig. 5(a)]. Thus relatively weak harmonics are usually observed in the frequency range between about 2 kHz and A classification scheme of woods for stringed instru-

49 Acoust. Sci. & Tech. 29, 1 (2008) ments [5] makes it clear that the Japanese stringed drastic pitch bending in traditional Indian, Chinese, instruments traditionally and preferably have used unique and Japanese stringed instruments such as the sitar, woods (mulberry, amboyna wood, and paulownia) with pipa, and biwa. almost opposite properties. On the other hand, the Western ACKNOWLEDGMENTS stringed instruments traditionally consist of the soundboard (top plate) and the frame board (back and side plates). Sitka The author thanks the Italian biwa maker, Doriano Sulis spruce used for the soundboard is close to paulownia, and for his construction of the mulberry-made biwa, for his maple and Brazilian/Rio rosewood used for the frame careful repair of the camphor-made biwa, and for his playing board are close to amboyna wood. Thus, the Satsuma biwa of them to carry out the research on the biwa acoustics. made of mulberry is a very unique stringed instrument. REFERENCES In order to examine the acoustical effects of these [1] A. Odaka and S. Yoshikawa, ‘‘Acoustical characteristics of differences in wood materials, the structural responses of Chinese stringed instruments and their Asian relatives,’’ J. the cello and the Satsuma biwa are compared with each Acoust. Soc. Am., 120, 3118 (2006). other by measuring the driving-point mobility and the [2] T. Ono and H. Yano, ‘‘Traditional wood for musical instru- transmission mobility. The experimental results imply ments and the future,’’ J. Acoust. Soc. Jpn. (J), 52, 356–361 (1996). distinct differences in the philosophy of making these [3] Y. Nagai, T. Ono and E. Obataya, ‘‘Materials for musical instruments. The fundamental frequency is always clearly instrument making,’’ J. Acoust. Soc. Jpn. (J), 62, 587–592 produced in the cello, and its harmonics are evenly (2006). emphasized according to the resonance nature of the top [4] S. Yoshikawa, ‘‘From the cembalo to the piano: Progress in J. Acoust. Soc. Jpn. (J) 57 plate. On the other hand, the fundamental frequency is early keyboard instruments,’’ , , 704– 711 (2001). always obscure in the mulberry-made biwa, and its [5] S. Yoshikawa, ‘‘Acoustical classification of woods for string response consists of the three frequency bands: A primary instruments,’’ J. Acoust. Soc. Am., 122, 568–573 (2007). sound-sustaining band (0.4–2.2 kHz); a sound-suppressing [6] S. Yoshikawa, ‘‘Sounding mechanisms and sound-framing band (2.2–2.7 kHz); a secondary sound-sustaining band designs in musical instruments,’’ Tech. Rep. Musical Acoust. Group, 25, MA2006-61 (2006). (2.7–4.5 kHz). [7] D. W. Haines, ‘‘On musical instrument wood,’’ Catgut Acoust. A comparison with the spectrograms of the biwa sounds Soc. Newsl., 31, 23–32 (1979). confirms that the ‘‘sawari’’ mechanism invented in the biwa [8] H. Aizawa, ‘‘Frequency dependence of vibration properties of creates the reverberating high-frequency emphasis in the wood in the longitudinal direction,’’ Master Thesis (Faculty of Engineering, Kyoto University, 1998). secondary sound-sustaining band. This sawari effect can be [9] J. C. Schelleng, ‘‘The violin as a circuit,’’ J. Acoust. Soc. Am., auditorily distinguished from the harmonics produced in the 35, 326–338 (1963). primary sound-sustaining band whose characteristic de- [10] E. Meyer and E.-G. Neumann, Physical and Applied Acoustics pends on the coupling between the top plate and the bridge. (Academic Press, New York, 1972, translated by J. M. Taylor, Moreover, a camphor-made biwa is measured to Jr.) pp. 14–15. [11] M. Shinozuka and S. Yoshikawa, ‘‘Measurement of the examine the validity of the camphor wood as one of driving-point admittance and study on wolf notes of the substitute woods for the mulberry. Its structural response cello,’’ Tech. Rep. Musical Acoust. Group, 25, MA2006-78 and sound spectrogram are largely different from those of (2007). the mulberry-made biwa. As the result, the sawari sound [12] J. Woodhouse, ‘‘On the playability of violins Part II: Minimum bow force and transients,’’ Acustica, 78, 137–153 (1993). cannot be clearly heard from the camphor-made biwa. It is [13] W. Reinecke, ‘‘U¨ bertragungseigenshaften des Streichinstru- thus concluded that the camphor wood is not an excellent mentenstegs,’’ Catgut Acoust. Soc. Newsl., 19, 26–34 (1973). substitute wood for the Satsuma biwa. [14] N. H. Fletcher and T. D. Rossing, The Physics of Musical Taking an overview of Asian stringed instruments, we Instruments (Springer-Verlag, New York, 2nd ed., 1998) p. 77, may recognize the following interesting points: 268, 269, 299. [15] T. Taguti and K. Tohnai, ‘‘Vibro-acoustic measurement of (1) The sawari mechanism is seen in the Japanese lutes and several biwas,’’ Tech. Rep. Musical Acoust. Group, 25, the jawari mechanism is seen in the Indian lutes, while MA2006-26 (2006). they are not seen in the Chinese and Korean lutes. [16] Y. Ando, Acoustics of Musical Instruments (2nd ed., Ongaku- (2) The sawari mechanism is applied to the neck and frets no-tomo-sha, Tokyo, 1996). pp. 197–199, 202, 203. [17] Y. Tohnai and K. Kishi, ‘‘Structure and examples of played in the Japanese biwa, while the jawari mechanism is waves of the Satsuma biwa,’’ Tech. Rep. Musical Acoust. applied to the bridge in the Indian sitar and tambula. Group, 12, MA93-19 (1993). (3) Lutes with short or long neck are not used in Korean [18] T. Taguti and K. Tohnai, ‘‘Acoustical analysis on the sawari traditional music, while long zither-type instruments tone of Chikuzen biwa,’’ Acoust. Sci. & Tech., 22, 199–207 (2001). such as the gayageum, which create the characteristic [19] S.-Y. Feng, ‘‘Some acoustical measurements on the Chinese pitch bending, are traditionally popular. musical instrument P’i-P’a,’’ J. Acoust. Soc. Am., 75, 599–602 (4) A high-frequency emphasis is more important than a (1984).