- Email: [email protected]
Study on Vibro-acoustics Characteristics of Bamboo-based Violin
Available online at www.sciencedirect.com
ScienceDirect Procedia Engineering 170 (2017) 286 – 292
Engineering Physics International Conference, EPIC 2016
Study on Vibro-acoustics Characteristics of Bamboo-based Violin Teguh Aditanoyoa, Iwan Prasetiyob*, Ida Bagus Ardhana Putrac a,b,c
Bandung Institute of Technology, Ganeca 10, Bandung, Indonesia
Abstract Bamboo is knownas fast-growing plant and can easily be obtained in Bandung. This situation leads bamboo to be material that commonly used for constructing various solid structures with particular strength including violin.It is interesting that bamboo violin has a unique sound quality that differs perceptually from common wooden violin. This research is focused on finding the physical parameters in order to get plausible explanations on that sound difference by conducting vibro-acoustic analysis. An automatic bow-moving machine is developed to provide a highly repeatable bowing strokes upon string. The frequency spectrum analysis is used.A piezoelectric is put on the violin resonator surfaces for recording excitation force of bridge while a microphone is used for recording sound pressure level produced by the resonator.This approach is considered in order to obtain frequency response function of soundbox as ratio of the sound pressure level to the vibration one. It is found that the frequency response function on overtones of both violins are different at mid and high frequencies. Meanwhile, at low frequencies it is seen that the both violins share similar pattern of frequency responsefunction hill peaks.
© 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). © 2016 The Authors.Published by Elsvier Ltd. Peer-review under responsibility of the organizing committee of the Engineering Physics International Conference 2016 Keywords:violin, bamboo, vibro-acoustics
1. Introduction Bamboogrows widely in Indonesia which around 15% of bamboo species in the world can be found in the archipelago[1]. Thus, bamboo has been chopped by locals for vast uses, including in musical instruments. Due recognized as fast-growing plant which is economically beneficial, bamboo then expected to replace wood material in the future. An approach of substituting wood has been done by locals pioneering in making bamboo violin. The soundbox or resonator is made of a pressed 14cm diameter of round bamboo tube as well as the other component almost completely made of bamboo. Despite having the same tune, bamboo violin surely has its own sound quality which differs from wooden violin in general. There are some chordophones (strings instrument) which equipped with bamboo as its resonator, for example the Chinese violin-like named jinghu or Madagascarian tube zither national instrument named valiha. Spruce, traditional material for violin top plate, has low density and low characteristic impendance, which makes it classified as the best material for radiating sound. Please note that sound radiation coefficient is speed of sound divided by density In addition, spuce has a similar characteristic to silver maple or curly maple, the traditional material for the bridge, back plate, and ribs. Maple is known as a well sound radiator and has sufficiently high characteristic impedance to act as a reflector for air oscillations in the hollow body. Some comparison of how bamboo performs well as soundboard material versus other common materials have been done by Wegst [2]. It was found that bamboo has a high sound radiation coefficient, closes enough to that soundboard materials, back plate materials. In addition, impedance matching of the strings and the soundboard must be done carefully, considering impedance is proportional to the material’s characteristic impedance and to the square of the soundboard’s thickness. Nevertheless, bamboo has a promising chance to be used both as soundbox in violin. In addition, bamboo as musical instrument’s material has been done in Indonesia. Glued bamboo board used for guitar soundboard stated as a potential subtitutive material [3].
* Corresponding author E-mail address:[email protected]
1877-7058 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of the Engineering Physics International Conference 2016
doi:10.1016/j.proeng.2017.03.029
Teguh Aditanoyo et al. / Procedia Engineering 170 (2017) 286 – 292
Theoretically, the sound generation of violin started by bowed strings. In tuned strings, whether the nut or the performer’s finger stops the string at one end that defines desired pitch while the bow strikes perpendicularly. The vibration of bowed string is caused by Helmholtz wave, a bending point that race around the string on curved path [4]. The bridge, which its tip is the other end of the string, then transmits the vibration in form of saw-tooth wave force to the soundbox [4]. It is the saw-tooth wave which provides integer harmonics in violin. As the wave propagates through the bridge, filtering is occurred due to bridge’s resonance. The wave then excites the soundbox of the violin and radiates sound. Research on violin characterization has been done worldwide. A book by Rossing [4] can be a reference of general knowledge of violin. Jansson [5], Hutchins[6], and Woodhouse [7] are three notable researchers in finding important violin vibration characteristics. General wooden violinsshare similar modes which radiate sound effectively and make this bowed instruments sounds as violin, as they stated. Those are:A0 Helmholtz air resonance at around 280Hz; T1 or B1- body resonance at around 460Hz; C3 or B1+ body resonance at around 530Hz; and bridge resonance at around 3000Hz. In this paper, vibro-acoustics characteristics of a bamboo-based violin are studied particularly related withthe soundbox as a acoustic resonator by analyzing its spectrum. The spectrum consist of fundamental frequency along with overtones at integer multiples of the fundamental. The fundamental frequency defines the pitch while the overtones gives the sensation of timbre.A comparison of results to a wooden violin is also provided.It is expected that the sound characteristic of bamboo violin can be described in more detail. 2. Methods Only a bamboo violin and a wooden violin are considered in this paper. The bamboo violin is made by Indonesian Bamboo Community, a Cimahi based group of craftsmen specialized in making bamboo musical instruments, which dated on 2015. It is gombongbamboo (Gigantochloapseudoarundinacea), that is flattened, used as the soundbox. The common size and feature of wooden violin is almost fully imitated. Due to structural consideration, the soundpost of bamboo violin is glued to the back plate (wooden violin’s soundpost is adjustable and not attached to any plate) and the bassbar is not only glued on the top part but also extended to connect one rib to another rib at the opposite (wooden violin’s bassbar only glued on top plate). A Chinese-made wooden violin, dated on 2011, made by Ming-Jiang Zhu with fair price (around 830$ USD) and sufficient satisfying sound is used for comparison. Providedhammer impulse on the tip of bridge has been being the method in finding the vibrational characteristics of bestknown violin such as Stradivarius [5] and Guarneri del Gesu[8]. The result of those previous researcheswere a mechanical properties called mobility (the opposite of admitance), velocity measured at one edge of the bridge per unit force excited by a hammer at the other edge. This method has been reproduced in many researches and the mobility graph in frequency domain is considered as the “fingerprint” of the violin. In the other hand, a recent study suggests that direct measurement of radiated sound pressure with bowing excitation is more representative compared to the subjective assesment of the tone of violin [9].
Fig. 1. Photograph of experiment set for bamboo violin, which taken from above (left) for overall view and close to the violin for empashizing the placement of sandwiched piezoelectric disc (right). The brown box next to violin is the automatic bow-moving machine enclosed by rockwool for suppressing mechanical noise. Wooden violin is set carefully the same
In this paper, the experiment has been doneby bowing the strings using an automatic bow-moving machine for ensuring the same bowing parameters were applied for both violins. It is important to control such three basic parameters: bow velocity, bowbridge distance, and bow force [10]. The bow velocity sets the string amplitude in combination with the bow-bridge distance. The bow force determine the high frequency content of the bowed string, thus complexing the ideal Helmholtz wave and the saw tooth bridge force. The provided parameters from the automatic bow-moving machine were 35cm/s in bow velocity and 45mm in bow-bridge distance. The movement of bow was provided by a DC motor, which sensitive to torsional load. Since the bow
287
288
Teguh Aditanoyo et al. / Procedia Engineering 170 (2017) 286 – 292
always stopped automatically when the force needed for striking the sting exceed the torque of the DC motor, the bow force could be considered the same. The violin was supported firmly at the neck, using a rubber padded clam, and at the end button. The same strings set and bow were used for both violins. Each of four strings played freely or known as open string, exciting note at G3 (196Hz), D4 (293Hz), A4 (440Hz), and E5 (660Hz). While one string was stroke, the other strings were damped using soft foam tucked on the fingerboard. Simultaneously, radiated sound was measured with an omnidirectional microphone placed 50cm above the violin bridge; and vibration response was measured with a 21mm diameter piezoelectric thin disc sandwiched between bridge’s bass leg and the top surface of violin. All of the measurement was done in an anechoic chamber in order to avoid undesired acoustical noise. The set of measurement can be seen in Figure 1. 3. Results and Discussion Before manipulating into spectrum, the recorded data was cleaned. Only 400ms of relatively steady waveform of each down strokes were averaged and transformed using DFT (Discrete Fourier Transfromation) and absolutized. In particular ofopen string excitations, there were approximately 50 – 60 repetition for each strings to reduce the effect of nonliniearities of bowed string. Please note that all the vibration response recorded from piezoelectric disc was the transmitting vibrations that does not described in SI unit. Figure 2and Figure 3show that the bamboo violin radiating the same pitch as the fundamental frequencies of each strings matched with the wooden violin. The sound of integers overtones are occured which confirming the typical sound quality of bowed string chordophone. Eventhough of having the same pitch and giving the sensation of violin-like sound, subjectively bamboo violin’s timbre is different compared to the wooden violin’s. The sound pressure level peaks of overtones for the same pitch for both violins are variant, as that case can cause the different timbre. The bridge and the soundbox are the major notions of differentiator, since the two components made from bamboo. Moreover, the geometry of flattened tube surely differs the resonance from the common-shaped violin soundbox.
Fig. 2. Comparison of sound pressure level and vibration response on open string excitation of bamboo violin (a) G3 (196Hz) ;(b) D4 (293Hz) ;(c) A4 (440Hz) (d)E5 (660Hz)
289
Teguh Aditanoyo et al. / Procedia Engineering 170 (2017) 286 – 292
Fig. 3. Comparison of soundpressure level and vibration response on open string excitation of each 4 strings of wooden violin, G3 (196Hz) (a), D4 (293Hz) (b), A4 (440Hz) (c), E5 (660Hz) (d)
The height of peaks of sound pressure levelof bamboo violin seems to be random. The only recognizable pattern is rough reduction of peak height proportional to increasing frequency. In the other hand, its peaks of vibration response have a peculiar pattern. In the low to mid frequency, below 1000Hz, the peak heights is not decreasing proportional to frequency increment as we can clearly see at Figure 2(a) dan (b). The acceptable explanation is the bridge acts as a rigid body, allowing lateral force the strings act directly on the soundbox, as stated in Rossing [4]. In contrast to bamboo violin, the vibration response’s peaks of wooden violin shows a broad hill. This happens due to higher flexibility of wooden violin’s top plate, since its bassbar is not as long as bamboo’s and the bassbar end is not fixed at the two opposite ribs, as explained in Section 2.The piezoelectric disc would go up and down along with the wooden violin’s top plate in the low frequency, rather than squeezed on stiffer top part of bamboo violin. InFigure 2, in the frequency ranged from 2000 – 3000Hz, a hill, which consists of bamboo violin’s vibration peak response, is occured for all of the four strings. The second peaks hill is shown in 4000 – 5000Hz. As depicted in Figure 3, the similar two hills for wooden’s are shown, which occured at 1000 – 1500Hz (resembles nasal hill [11]) and around 3000Hz for the bridge resonance. Whether one of two hills recorded from vibration response of bamboo violin can be the effect of bamboo bridge resonance, with shifted frequency. Due to a relatively small amplitude of force, the soundbox can be assumed as a linear system of acoustial resonator. The characteristics of violin soundbox is approached by making a ratio between the yielded sound pressure level and the vibration response, as shown in Figure 4 and Figure 5. The ratio can be considered as the frequency response function (FRF) of violin’s soundbox, defining how an amount of sound pressure level is well converted per unit force from bridge. By comparing two peaks of each coincidence (or adjacent) frequency in Figure 4, the bamboo’s frequency response function seems generally shorter than the wooden’s. With presumably having the same thickness at the top and back part, it is kind of confirming that the spruce has more radiation coefficient than bamboo. Another plausible conjecture is the spruce has smaller loss coefficient compared to the bamboo, since loss coefficient effect is moreemphasized in high frequency and the figure shows more damped in bamboo’s transfer function.
290
Teguh Aditanoyo et al. / Procedia Engineering 170 (2017) 286 – 292
Fig. 4. Frequency response function of bamboo violin soundbox and wooden violin one on open string excitation of each 4 strings, G3 (196Hz) (a), D4 (293Hz) (b), A4 (440Hz) (c), E5 (660Hz) (d)
Fig. 5. Stacked frequency response functionof violin soundbox on 4 open string excitation: (a) bamboo violin ; (b) wooden violin
Teguh Aditanoyo et al. / Procedia Engineering 170 (2017) 286 – 292
After a careful observation in the graph in Figure 4, there were found some overtones with flat transfer function compared to the neighboring frequency ranging from 100 – 5000Hz. On G3 (196Hz) open strings excitation, there are five points of flat overtone transfer function in bamboo violin: at the 8th overtone (1564Hz), the 14th overtone (2738Hz), the 18th overtone (2738Hz), the 21st overtone (4107Hz), and the 24th overtone (4693Hz); there is only one point of flat overtone transfer function in wooden violin: at the 9th overtone (1760Hz). Next, on D4 (293Hz) open string excitation, there is no flat overtone transfer function in bamboo violin; while there is only one point of flat overtone transfer function in wooden violin: at the 8th overtone (2347Hz). There is no flat overtone transfer function both in two violins on A4 (440Hz) and E5 (660Hz) open string excitation. These absence of transfer function at some high frequency overtones can be the clue hinting the diffrerent timbre. For radiation to occur, combined dissplacement of body modes at a certain frequency must not be zero. It is known that body modes become denser proportional to frequency increment, which require more complex calculation to understand the sound radiation.As termed by Weinreich et al. in Rossing [4], the frequenzy region in which sparse monopole radiation predominate is below 1000Hz. Focusing in around that region in Figure 5, bamboo violin’s soundbox roughly depicted as a good radiator indicated by high peaks of tranfer function start at 300 – 700Hz followed by some shorther peaks at 700 – 900Hz and very low peaks at 900 – 1100Hz. There are also another hill peaks at 1100 – 1400Hz. In contrast, wooden violin shows high peaks ranging in about 200 – 700Hz, with an extremely high peak at 300Hz, and followed by peaks gap at 700 – 850Hz. The second peaks hill can be found standing at 850 – 1500Hz. The high peaks in wooden violin can be explained reasonably since body modes at these range resonances great sound radiation, especially the effect of the A0 air resonance. Interestingly, the peaks hill of bamboo violin resembles the pattern of wooden’s; as there is a hill around the monopole frequency region, a gap, and another hill around 1000Hz in both transfer functions. Meanwhile, there is notenough study about modes and resonances which occured in this bamboo violin.Referred from Schelske [11] about timbre subjective description, the overall transfer function of bamboo violin in Figure 5 depicts bamboo resonator’s thinner and chirpier sound (Helmholtz resoncance at 270Hz), along with more spacious and hollow sound (corpus resonance at 450 – 550Hz), and powerless or covered sound (nassal resonance at 1000 – 1800Hz) also dull and dark sound (brilliance region at 2000 – 3500Hz) compared to the wooden’s. 4. Conclusions The breakthrough of bamboo violin has been supplemented with objective measurements done by this research. Though having the same pitch and violin-like rich harmonics sound characteristic, the bamboo violin has different timbre compared to the wooden violin. By considering the soundbox as linear system resonator, a frequency response function (FRF) is provided as the ratio of sound pressure level against the bridge-topplate vibration response; both are recorded simultaneously.Bamboo, as violin soundbox material, shows less radiative and more damped resonator. In addition, there are some flat magnitude in the expected integers overtones (played at the same fundamental frequency) that occured differently in both transfer function. In a highligthed result, bamboo violin’s resonator has a similar pattern of peaks around the monopole region with different amplitude and shifted frequencies. The differences can be occured since the bamboo violin made from bamboo and has a distinctive soundbox shape. Thus the modes shall act diversely. The only comparable resonance is the bamboo violin’s bridge hill with shiftedin frequency range. Further study about modes in bamboo violin is needed for more advanced explanations about timbre differences. Acknowledgements The authors would like to express gratitude for Mr. Adang, the chairman of IBC (Indonesian Bamboo Community), and Mr. Alvino, the chief craftmen of IBC who provide bamboo violin samples for this research. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]
E. A. Widjaja, “Bamboo Diversity And Its Future prospect in Indonesia,” presented at the The Third International Wood Science Symposium, Kyoto, 2000, pp. 235–240. U. G. K. Wegst, “Bamboo and Wood in Musical Instruments,” Annu. Rev. Mater. Res., vol. 38, pp. 323–350, 2008. I. Kusumaningtyas, H. Yordaniansyah, and T. A. Purwanto, “Acoustical properties of petung bamboo for the top plate of guitars,” Appl. Acoust., vol. 112, pp. 123–130, 2016. T. D. Rossing, The science of string instruments. 2010. E. V. Jansson, T. högskolan i Stockholm., and musik och hörsel. Tal, Acoustics for violin and guitar makers. Stockholm: Kungl. Tekniska högskolan, Dept. of Speech. Music and Hearing, 2002. C. M. Hutchins, “The air and wood modes of the violin,” J. Audio Eng. Soc., vol. 46, no. 9, pp. 751–765, 1998. J. Woodhouse, “Body Vibration of the Violin—What Can a Maker Expect to Control?,” Catgut Acoust. Soc. J., vol. 4, no. 5, pp. 43–49, 2002. J. A. Moral and E. V. Jansson, “Eigenmodes, input admittance, and the function of the violin,” Res. Pap. Violin Acoust. 1975-1993 Ed. Carleen Maley Hutchins Assoc. Ed. Va. Benade Vol 1, pp. 453–461, 1997. N. Harris and F. Fahy, “A Comparative Study of the Hammered Bridge Response and the Bowed String Response of the Violin,” J. Acoust. Soc. Am., vol. XXII, no. 4, 2009. E. Schoonderwaldt, “Mechanics and acoustics of violin bowing : freedom, constraints and control in performance,” Datavetenskap och kommunikation, Kungliga Tekniska högskolan, Stockholm, 2009.
291
292
Teguh Aditanoyo et al. / Procedia Engineering 170 (2017) 286 – 292 [11]
M. Schelske, “Master Studio for Violinmaking - Martin Schleske Munich, Germany » Tonal color and the resonance profile.” [Online]. Available: http://www.schleske.de/en/research/handbook-violinacoustics/tonal-color-and-the-resonance-profile.html. [Accessed: 27-Aug-2016].
ScienceDirect Procedia Engineering 170 (2017) 286 – 292
Engineering Physics International Conference, EPIC 2016
Study on Vibro-acoustics Characteristics of Bamboo-based Violin Teguh Aditanoyoa, Iwan Prasetiyob*, Ida Bagus Ardhana Putrac a,b,c
Bandung Institute of Technology, Ganeca 10, Bandung, Indonesia
Abstract Bamboo is knownas fast-growing plant and can easily be obtained in Bandung. This situation leads bamboo to be material that commonly used for constructing various solid structures with particular strength including violin.It is interesting that bamboo violin has a unique sound quality that differs perceptually from common wooden violin. This research is focused on finding the physical parameters in order to get plausible explanations on that sound difference by conducting vibro-acoustic analysis. An automatic bow-moving machine is developed to provide a highly repeatable bowing strokes upon string. The frequency spectrum analysis is used.A piezoelectric is put on the violin resonator surfaces for recording excitation force of bridge while a microphone is used for recording sound pressure level produced by the resonator.This approach is considered in order to obtain frequency response function of soundbox as ratio of the sound pressure level to the vibration one. It is found that the frequency response function on overtones of both violins are different at mid and high frequencies. Meanwhile, at low frequencies it is seen that the both violins share similar pattern of frequency responsefunction hill peaks.
© 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). © 2016 The Authors.Published by Elsvier Ltd. Peer-review under responsibility of the organizing committee of the Engineering Physics International Conference 2016 Keywords:violin, bamboo, vibro-acoustics
1. Introduction Bamboogrows widely in Indonesia which around 15% of bamboo species in the world can be found in the archipelago[1]. Thus, bamboo has been chopped by locals for vast uses, including in musical instruments. Due recognized as fast-growing plant which is economically beneficial, bamboo then expected to replace wood material in the future. An approach of substituting wood has been done by locals pioneering in making bamboo violin. The soundbox or resonator is made of a pressed 14cm diameter of round bamboo tube as well as the other component almost completely made of bamboo. Despite having the same tune, bamboo violin surely has its own sound quality which differs from wooden violin in general. There are some chordophones (strings instrument) which equipped with bamboo as its resonator, for example the Chinese violin-like named jinghu or Madagascarian tube zither national instrument named valiha. Spruce, traditional material for violin top plate, has low density and low characteristic impendance, which makes it classified as the best material for radiating sound. Please note that sound radiation coefficient is speed of sound divided by density In addition, spuce has a similar characteristic to silver maple or curly maple, the traditional material for the bridge, back plate, and ribs. Maple is known as a well sound radiator and has sufficiently high characteristic impedance to act as a reflector for air oscillations in the hollow body. Some comparison of how bamboo performs well as soundboard material versus other common materials have been done by Wegst [2]. It was found that bamboo has a high sound radiation coefficient, closes enough to that soundboard materials, back plate materials. In addition, impedance matching of the strings and the soundboard must be done carefully, considering impedance is proportional to the material’s characteristic impedance and to the square of the soundboard’s thickness. Nevertheless, bamboo has a promising chance to be used both as soundbox in violin. In addition, bamboo as musical instrument’s material has been done in Indonesia. Glued bamboo board used for guitar soundboard stated as a potential subtitutive material [3].
* Corresponding author E-mail address:[email protected]
1877-7058 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of the Engineering Physics International Conference 2016
doi:10.1016/j.proeng.2017.03.029
Teguh Aditanoyo et al. / Procedia Engineering 170 (2017) 286 – 292
Theoretically, the sound generation of violin started by bowed strings. In tuned strings, whether the nut or the performer’s finger stops the string at one end that defines desired pitch while the bow strikes perpendicularly. The vibration of bowed string is caused by Helmholtz wave, a bending point that race around the string on curved path [4]. The bridge, which its tip is the other end of the string, then transmits the vibration in form of saw-tooth wave force to the soundbox [4]. It is the saw-tooth wave which provides integer harmonics in violin. As the wave propagates through the bridge, filtering is occurred due to bridge’s resonance. The wave then excites the soundbox of the violin and radiates sound. Research on violin characterization has been done worldwide. A book by Rossing [4] can be a reference of general knowledge of violin. Jansson [5], Hutchins[6], and Woodhouse [7] are three notable researchers in finding important violin vibration characteristics. General wooden violinsshare similar modes which radiate sound effectively and make this bowed instruments sounds as violin, as they stated. Those are:A0 Helmholtz air resonance at around 280Hz; T1 or B1- body resonance at around 460Hz; C3 or B1+ body resonance at around 530Hz; and bridge resonance at around 3000Hz. In this paper, vibro-acoustics characteristics of a bamboo-based violin are studied particularly related withthe soundbox as a acoustic resonator by analyzing its spectrum. The spectrum consist of fundamental frequency along with overtones at integer multiples of the fundamental. The fundamental frequency defines the pitch while the overtones gives the sensation of timbre.A comparison of results to a wooden violin is also provided.It is expected that the sound characteristic of bamboo violin can be described in more detail. 2. Methods Only a bamboo violin and a wooden violin are considered in this paper. The bamboo violin is made by Indonesian Bamboo Community, a Cimahi based group of craftsmen specialized in making bamboo musical instruments, which dated on 2015. It is gombongbamboo (Gigantochloapseudoarundinacea), that is flattened, used as the soundbox. The common size and feature of wooden violin is almost fully imitated. Due to structural consideration, the soundpost of bamboo violin is glued to the back plate (wooden violin’s soundpost is adjustable and not attached to any plate) and the bassbar is not only glued on the top part but also extended to connect one rib to another rib at the opposite (wooden violin’s bassbar only glued on top plate). A Chinese-made wooden violin, dated on 2011, made by Ming-Jiang Zhu with fair price (around 830$ USD) and sufficient satisfying sound is used for comparison. Providedhammer impulse on the tip of bridge has been being the method in finding the vibrational characteristics of bestknown violin such as Stradivarius [5] and Guarneri del Gesu[8]. The result of those previous researcheswere a mechanical properties called mobility (the opposite of admitance), velocity measured at one edge of the bridge per unit force excited by a hammer at the other edge. This method has been reproduced in many researches and the mobility graph in frequency domain is considered as the “fingerprint” of the violin. In the other hand, a recent study suggests that direct measurement of radiated sound pressure with bowing excitation is more representative compared to the subjective assesment of the tone of violin [9].
Fig. 1. Photograph of experiment set for bamboo violin, which taken from above (left) for overall view and close to the violin for empashizing the placement of sandwiched piezoelectric disc (right). The brown box next to violin is the automatic bow-moving machine enclosed by rockwool for suppressing mechanical noise. Wooden violin is set carefully the same
In this paper, the experiment has been doneby bowing the strings using an automatic bow-moving machine for ensuring the same bowing parameters were applied for both violins. It is important to control such three basic parameters: bow velocity, bowbridge distance, and bow force [10]. The bow velocity sets the string amplitude in combination with the bow-bridge distance. The bow force determine the high frequency content of the bowed string, thus complexing the ideal Helmholtz wave and the saw tooth bridge force. The provided parameters from the automatic bow-moving machine were 35cm/s in bow velocity and 45mm in bow-bridge distance. The movement of bow was provided by a DC motor, which sensitive to torsional load. Since the bow
287
288
Teguh Aditanoyo et al. / Procedia Engineering 170 (2017) 286 – 292
always stopped automatically when the force needed for striking the sting exceed the torque of the DC motor, the bow force could be considered the same. The violin was supported firmly at the neck, using a rubber padded clam, and at the end button. The same strings set and bow were used for both violins. Each of four strings played freely or known as open string, exciting note at G3 (196Hz), D4 (293Hz), A4 (440Hz), and E5 (660Hz). While one string was stroke, the other strings were damped using soft foam tucked on the fingerboard. Simultaneously, radiated sound was measured with an omnidirectional microphone placed 50cm above the violin bridge; and vibration response was measured with a 21mm diameter piezoelectric thin disc sandwiched between bridge’s bass leg and the top surface of violin. All of the measurement was done in an anechoic chamber in order to avoid undesired acoustical noise. The set of measurement can be seen in Figure 1. 3. Results and Discussion Before manipulating into spectrum, the recorded data was cleaned. Only 400ms of relatively steady waveform of each down strokes were averaged and transformed using DFT (Discrete Fourier Transfromation) and absolutized. In particular ofopen string excitations, there were approximately 50 – 60 repetition for each strings to reduce the effect of nonliniearities of bowed string. Please note that all the vibration response recorded from piezoelectric disc was the transmitting vibrations that does not described in SI unit. Figure 2and Figure 3show that the bamboo violin radiating the same pitch as the fundamental frequencies of each strings matched with the wooden violin. The sound of integers overtones are occured which confirming the typical sound quality of bowed string chordophone. Eventhough of having the same pitch and giving the sensation of violin-like sound, subjectively bamboo violin’s timbre is different compared to the wooden violin’s. The sound pressure level peaks of overtones for the same pitch for both violins are variant, as that case can cause the different timbre. The bridge and the soundbox are the major notions of differentiator, since the two components made from bamboo. Moreover, the geometry of flattened tube surely differs the resonance from the common-shaped violin soundbox.
Fig. 2. Comparison of sound pressure level and vibration response on open string excitation of bamboo violin (a) G3 (196Hz) ;(b) D4 (293Hz) ;(c) A4 (440Hz) (d)E5 (660Hz)
289
Teguh Aditanoyo et al. / Procedia Engineering 170 (2017) 286 – 292
Fig. 3. Comparison of soundpressure level and vibration response on open string excitation of each 4 strings of wooden violin, G3 (196Hz) (a), D4 (293Hz) (b), A4 (440Hz) (c), E5 (660Hz) (d)
The height of peaks of sound pressure levelof bamboo violin seems to be random. The only recognizable pattern is rough reduction of peak height proportional to increasing frequency. In the other hand, its peaks of vibration response have a peculiar pattern. In the low to mid frequency, below 1000Hz, the peak heights is not decreasing proportional to frequency increment as we can clearly see at Figure 2(a) dan (b). The acceptable explanation is the bridge acts as a rigid body, allowing lateral force the strings act directly on the soundbox, as stated in Rossing [4]. In contrast to bamboo violin, the vibration response’s peaks of wooden violin shows a broad hill. This happens due to higher flexibility of wooden violin’s top plate, since its bassbar is not as long as bamboo’s and the bassbar end is not fixed at the two opposite ribs, as explained in Section 2.The piezoelectric disc would go up and down along with the wooden violin’s top plate in the low frequency, rather than squeezed on stiffer top part of bamboo violin. InFigure 2, in the frequency ranged from 2000 – 3000Hz, a hill, which consists of bamboo violin’s vibration peak response, is occured for all of the four strings. The second peaks hill is shown in 4000 – 5000Hz. As depicted in Figure 3, the similar two hills for wooden’s are shown, which occured at 1000 – 1500Hz (resembles nasal hill [11]) and around 3000Hz for the bridge resonance. Whether one of two hills recorded from vibration response of bamboo violin can be the effect of bamboo bridge resonance, with shifted frequency. Due to a relatively small amplitude of force, the soundbox can be assumed as a linear system of acoustial resonator. The characteristics of violin soundbox is approached by making a ratio between the yielded sound pressure level and the vibration response, as shown in Figure 4 and Figure 5. The ratio can be considered as the frequency response function (FRF) of violin’s soundbox, defining how an amount of sound pressure level is well converted per unit force from bridge. By comparing two peaks of each coincidence (or adjacent) frequency in Figure 4, the bamboo’s frequency response function seems generally shorter than the wooden’s. With presumably having the same thickness at the top and back part, it is kind of confirming that the spruce has more radiation coefficient than bamboo. Another plausible conjecture is the spruce has smaller loss coefficient compared to the bamboo, since loss coefficient effect is moreemphasized in high frequency and the figure shows more damped in bamboo’s transfer function.
290
Teguh Aditanoyo et al. / Procedia Engineering 170 (2017) 286 – 292
Fig. 4. Frequency response function of bamboo violin soundbox and wooden violin one on open string excitation of each 4 strings, G3 (196Hz) (a), D4 (293Hz) (b), A4 (440Hz) (c), E5 (660Hz) (d)
Fig. 5. Stacked frequency response functionof violin soundbox on 4 open string excitation: (a) bamboo violin ; (b) wooden violin
Teguh Aditanoyo et al. / Procedia Engineering 170 (2017) 286 – 292
After a careful observation in the graph in Figure 4, there were found some overtones with flat transfer function compared to the neighboring frequency ranging from 100 – 5000Hz. On G3 (196Hz) open strings excitation, there are five points of flat overtone transfer function in bamboo violin: at the 8th overtone (1564Hz), the 14th overtone (2738Hz), the 18th overtone (2738Hz), the 21st overtone (4107Hz), and the 24th overtone (4693Hz); there is only one point of flat overtone transfer function in wooden violin: at the 9th overtone (1760Hz). Next, on D4 (293Hz) open string excitation, there is no flat overtone transfer function in bamboo violin; while there is only one point of flat overtone transfer function in wooden violin: at the 8th overtone (2347Hz). There is no flat overtone transfer function both in two violins on A4 (440Hz) and E5 (660Hz) open string excitation. These absence of transfer function at some high frequency overtones can be the clue hinting the diffrerent timbre. For radiation to occur, combined dissplacement of body modes at a certain frequency must not be zero. It is known that body modes become denser proportional to frequency increment, which require more complex calculation to understand the sound radiation.As termed by Weinreich et al. in Rossing [4], the frequenzy region in which sparse monopole radiation predominate is below 1000Hz. Focusing in around that region in Figure 5, bamboo violin’s soundbox roughly depicted as a good radiator indicated by high peaks of tranfer function start at 300 – 700Hz followed by some shorther peaks at 700 – 900Hz and very low peaks at 900 – 1100Hz. There are also another hill peaks at 1100 – 1400Hz. In contrast, wooden violin shows high peaks ranging in about 200 – 700Hz, with an extremely high peak at 300Hz, and followed by peaks gap at 700 – 850Hz. The second peaks hill can be found standing at 850 – 1500Hz. The high peaks in wooden violin can be explained reasonably since body modes at these range resonances great sound radiation, especially the effect of the A0 air resonance. Interestingly, the peaks hill of bamboo violin resembles the pattern of wooden’s; as there is a hill around the monopole frequency region, a gap, and another hill around 1000Hz in both transfer functions. Meanwhile, there is notenough study about modes and resonances which occured in this bamboo violin.Referred from Schelske [11] about timbre subjective description, the overall transfer function of bamboo violin in Figure 5 depicts bamboo resonator’s thinner and chirpier sound (Helmholtz resoncance at 270Hz), along with more spacious and hollow sound (corpus resonance at 450 – 550Hz), and powerless or covered sound (nassal resonance at 1000 – 1800Hz) also dull and dark sound (brilliance region at 2000 – 3500Hz) compared to the wooden’s. 4. Conclusions The breakthrough of bamboo violin has been supplemented with objective measurements done by this research. Though having the same pitch and violin-like rich harmonics sound characteristic, the bamboo violin has different timbre compared to the wooden violin. By considering the soundbox as linear system resonator, a frequency response function (FRF) is provided as the ratio of sound pressure level against the bridge-topplate vibration response; both are recorded simultaneously.Bamboo, as violin soundbox material, shows less radiative and more damped resonator. In addition, there are some flat magnitude in the expected integers overtones (played at the same fundamental frequency) that occured differently in both transfer function. In a highligthed result, bamboo violin’s resonator has a similar pattern of peaks around the monopole region with different amplitude and shifted frequencies. The differences can be occured since the bamboo violin made from bamboo and has a distinctive soundbox shape. Thus the modes shall act diversely. The only comparable resonance is the bamboo violin’s bridge hill with shiftedin frequency range. Further study about modes in bamboo violin is needed for more advanced explanations about timbre differences. Acknowledgements The authors would like to express gratitude for Mr. Adang, the chairman of IBC (Indonesian Bamboo Community), and Mr. Alvino, the chief craftmen of IBC who provide bamboo violin samples for this research. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]
E. A. Widjaja, “Bamboo Diversity And Its Future prospect in Indonesia,” presented at the The Third International Wood Science Symposium, Kyoto, 2000, pp. 235–240. U. G. K. Wegst, “Bamboo and Wood in Musical Instruments,” Annu. Rev. Mater. Res., vol. 38, pp. 323–350, 2008. I. Kusumaningtyas, H. Yordaniansyah, and T. A. Purwanto, “Acoustical properties of petung bamboo for the top plate of guitars,” Appl. Acoust., vol. 112, pp. 123–130, 2016. T. D. Rossing, The science of string instruments. 2010. E. V. Jansson, T. högskolan i Stockholm., and musik och hörsel. Tal, Acoustics for violin and guitar makers. Stockholm: Kungl. Tekniska högskolan, Dept. of Speech. Music and Hearing, 2002. C. M. Hutchins, “The air and wood modes of the violin,” J. Audio Eng. Soc., vol. 46, no. 9, pp. 751–765, 1998. J. Woodhouse, “Body Vibration of the Violin—What Can a Maker Expect to Control?,” Catgut Acoust. Soc. J., vol. 4, no. 5, pp. 43–49, 2002. J. A. Moral and E. V. Jansson, “Eigenmodes, input admittance, and the function of the violin,” Res. Pap. Violin Acoust. 1975-1993 Ed. Carleen Maley Hutchins Assoc. Ed. Va. Benade Vol 1, pp. 453–461, 1997. N. Harris and F. Fahy, “A Comparative Study of the Hammered Bridge Response and the Bowed String Response of the Violin,” J. Acoust. Soc. Am., vol. XXII, no. 4, 2009. E. Schoonderwaldt, “Mechanics and acoustics of violin bowing : freedom, constraints and control in performance,” Datavetenskap och kommunikation, Kungliga Tekniska högskolan, Stockholm, 2009.
291
292
Teguh Aditanoyo et al. / Procedia Engineering 170 (2017) 286 – 292 [11]
M. Schelske, “Master Studio for Violinmaking - Martin Schleske Munich, Germany » Tonal color and the resonance profile.” [Online]. Available: http://www.schleske.de/en/research/handbook-violinacoustics/tonal-color-and-the-resonance-profile.html. [Accessed: 27-Aug-2016].