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 YoshikawaÃ, 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 Ãe-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 instru- ments 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 spruceà 532 560 16 116 5300 0.11 6.2 sitka spruceà 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 mapleà 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 rosewoodà 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 ÃReference [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; Â: substitute wood for the Satsuma biwa. are used for the violin and cello back plate.