Page  00000540 The Fujara: A Physical Model of The Bass Pipe Instrument in An Interactive Composition Juraj Kojs1 and Stefania Serafin2 1McIntyre Department of Music, University of Virginia, USA koj 2Medialogy, Aalborg University Copenhagen, Denmark Abstract In this paper, we propose a physical model of the fujara, a native Slovak folk instrument. The main motivation for building such a model is to establish and explore musical environment in which physical and virtual fujaras can interact. Firstly, we describe the acoustic properties of the instrument. Then we explain how the digital waveguide technique excels in modeling the instrument. The discussion of the composition Air for the real-time physical and virtual fujaras concludes the paper. Introduction The fujara is a native Slovak folk bass pipe instrument originating from the times of the Great Moravian Empire in the 10th century (Macak 1995). In the later centuries, the fujara was predominantly made and performed by the mountain shepherds, who used the instrument to musically express solitude and pastoralism of their daily life (Kresanek 1997). Original solo fujara repertoire emphasized slowly paced music material, simple rhythms, sustained notes, descending melodic structures, intervallic particularities of the mixolydian scale, and rich ornamentation. To these days, the fujara has been widely performed in the folk music and designed all around Slovakia. 1.1 Instrument's structure The fujara is a wooden pipe made of hard wood from indigenous trees such as mountain elder, ash, pear, and plum. The instrument ranges from 130 to 180 cm in length and from 2 to 5 cm in the inner pipe diameter. The parameters of the standard fujara in G are approximately 170 cm (length) and 3 cm (width). Traditional fujara has three toneholes, although fujaras with as many as 9 toneholes may be found in some Slovakian regions (Plavec 2003). The fujara belongs to the family of fipple flute instruments together with the recorder, the Native American flute, and Irish tin whistle. Different from the other fipple instruments, the fujara is much longer and produces lower and softer sounds. The instrument is performed while held in a vertical position. The performer blows air to the instrument through a shorter side pipe, which is attached in parallel to the main pipe. The side pipe length measures approximately one third of the length of the entire instrument. The instrument makers added the side pipe primarily for ergonomic reasons. Given the length of the instrument, it would be impossible for the player to reach the toneholes when blowing the air from the top of the instrument. The fujara playing technique is illustrated in Figure 1. 1.2 Tone Production The fujara has three toneholes that can be fully covered or open. Various fujara makers take different approaches in calculating positions of the toneholes, in particular the initial one. The fujara maker P. Paciga suggests dividing the instruments resonator length L by 2 and placing the first hole 4/7 of L below the top edge of the instruments bottom half. The following toneholes are placed 1/7 of L below the top one. M. Nosal also proposes dividing the length L by 2. However, he positions the top hole 2/7 of L and the inner diameter below the top edge of the instruments bottom half. J. Durecka recommends splitting L to three equal parts. Subtracting half of the diameter from the top edge of the instruments bottom third marks the placement of the bottom tonehole. Durecka positions the top tonehole in the center of the instrument's middle third and drills the middle tonehole in the center of the two toneholes (Elschek 1991). M. Filo recommends yet another approach. Firstly, Filo divides length L by 14. The resulting number I constitutes the distance between the toneholes 1 and 2. The distance between the bottom edge of the tube and the first tonehole I1 is given by addition of the inner 540

Page  00000541 I 4 5 6 Figure 1: Performance technique for the fujara. tube diameter D and 21. The third hole sits I + the tonehole diameter d above the second hole (Filo 2004). Abandoning the equidistant approach is no novelty in the fujara design. The comparative fujara studies proved that the distances between the toneholes of instruments with different length are not equal. While the distances between the toneholes in fujaras around 160 cm long are equal, the shorter fujaras reveal larger space between the hole 2 and 3. The distance value between the first and second tonehole is larger with the fujaras longer than 160 cm. Averaged values for the tonehole distances of the studied instruments were encapsulated in a number of referential tables, which became the primary source of Figure 3: Physical dimensions of a fujara. 1. length of resonator (L), 2. inner diameter of the instrument (D) 3. total length (Lc) 4. tone-hole diameter (d) 5. distance between the tone-holes (I) 6. distance between the bottom end of the fujara and the first tone-hole (11). The notation corresponds to Table 1. Adapted from (Filo 2004). consultation to the fujara makers (Elschek 1991). A set of tones that can be produced by fujara are derived from the harmonic series tuned to a particular fundamental frequency. As with the other open ended tubes in which the fundamental frequency does not sound, the first resonating tone on the fujara is the first harmonic (the octave). Individual tones of the series are produced when the toneholes remain in the same position (covered, open, or combined) at all times, and the air pressure is continuously increased. The tones thus result from overblowing. Spacing among the three toneholes ensures that covering and opening them in sequence will produce the initial major tetrachord. A simultaneous variation of air-pressure and fingering facilitates upward and downward stepwise motion. While constantly increasing the air pressure and changing the fingering properly, the performer can play * 0 @0o 0 0 * @ @00 @00 0 * *00 0*0 0*@ 0*@000 *oa 0 00 00aea 0 00 0 0 Figure 2: Tuning of the fujara. Adapted from (Filo 2004). 541

Page  00000542 an ascending major scale in the first octave and the mixolydian scale (major scale with the seventh lowered scale degree) in the second octave on the traditional fujara. Figure 2 displays the tones and fingering for a fujara in G. The newer tuning method developed by Tomas Kovac suggests the correction of the second octave to the major scale. Table 1 shows the dimensions of the fujara from Figure 1, which we used for our simulation. Table 2 displays the position of the instruments toneholes. tical point of view, the side pipe affects mainly the amplitude of the excitation pressure provided by the player. The excitation pressure gets filtered through the propagation along the pipe. The short pipe thus acts as a delay and input pressure attenuator. In the simulation, it is connected to the resonator in series. To simulate the excitation mechanism, we adopted a model recently proposed in (Cuadra 2005). In this model the jet formation is simulated using an exponential growth. As suggested in (Cuadra 2005), the second-order peaking and shelving filters facilitate efficient real-time implementation of the mechanism. The characteristic noise of the instrument is simulated by white noise filtered through the passive resonances of the instrument. The model is driven by the input pressure. Figure 4 shows different components of the fujara physical model. Tone G fo 97.97 D 3.00 L 161.6 Lec 168.7 Table 1: Physical dimensions of the fujara used in this paper fo =fundamentalfrequency (Hz), D = internal diameter (cm), L = internal length (cm), Lc = total length (cm). I 11.83 I1 26.67 Kx 4.08 Kh 4.98 Kk 0.9 OUTPUT SOUND Table 2: Position of the toneholes for the fujara. I = distance between toneholes, I- = distance between lower end and first tonehole. Figure 3 shows the different components of a fujara. The length L of the main resonator is calculated as L 2C, where c is the speed of sound in air and fo is the fundamental frequency. Based on empirical observations, the fujara makers modify the equation by adding three adjustment factors as follows: L =foKx, where Kx is an adjustment factor, Kx =Kk~+Kh where Kk =, 3D and Kh 1,36D. In the previous equation, D represents the inner diameter of the instrument (for the fujara in G, D = 3 cm) and L the physical length of the instrument (in cm)(Filip 1998). Figure 4: Block diagram of the physical model of thefujara. 2.1 Instrument's timbre A physical model of the fujara Given the strong similarity with flute instruments, we determined that one-dimensional digital waveguide (Smith 2006) is the most efficient modeling technique to simulate the fujara. Low-pass digital filters are used to describe radiation and visco-thermal losses inside the bore of the instrument. As in traditional flutes, the length of the long tube governs the fundamental frequency. Controlling the length of the digital waveguide we can simulate fujaras of different ranges. We added three tone holes into the model to replicate tones as produced by the original instrument. To achieve this goal, we adopted the tonehole model firstly proposed in (Scavone and Smith. 1997). The short pipe mounted in parallel to the long resonator was also simulated with a digital waveguide. From the acous We implemented the fujara model as an extension to the real-time synthesis environment Max/MSP'. As described in the previous section, the physical model of the fujara shares its main structural elements with the flute physical model. In addition to the control of the instruments length, we implemented varying pulse noise into the excitation mechanism to simulate fujaras characteristic timbre. Its unique timbre is most prominent during the blow (rozfuk in Slovak) gesture. Fast air injection into the pipe results inma set of simultaneously sounding multiphonics (both harmonics and subharmonics) based on the fingered fundamental. Figure 5 shows how the harmonic multiphonics resolve into the fundamental with the decreasing air pressure. Strict control over the blowing pressure assists in replication of this effect. Further, the model facilitates control over the number and type of the constituent harmonics and their individual weight. Such extensions aid in generation of novel timbres, which do not exist in the physical reality. Moreover, all the parameters can be modified in real-time. ' 542

Page  00000543 Conclusion __R II_~ ~_ I III i I Illb In this paper, we focused on contextualization of a historical instrument in the interactive computer music arena. We described the acoustical properties of the fujara, an exotic bass pipe instrument. Understanding the instrument's sound production allowed us to simulate the virtual fujara using the digital waveguide modeling approach. The model was implemented as an external object in Max/MSP. The physical and virtual fujaras were paired to produce novel timbres and textures in the real-time music composition Air.. ~. rnm'H^T.^,T>*ew>^C^,w>,^f.^^ ---- 00'00"500 5 Acknowledgments 00'00"000 00'00"250 Figure 5: Spectrogram of the fujara while performing descending harmonics. Musical Application Air is a composition scored for the physical and virtual fujaras. As mentioned above, the idiomatic fujara sound is produced by the overblowing technique. The composition presents elaborations on breathing and overblowing patterns of various durations, shapes, and intensities. The virtual fujara extends the frequency range, amplitude envelope contour and duration, and timbre of the physical instrument. The model further facilitates circular breathing, an effect that is impossible to achieve by the physical fujara. Pitch material of Air is derived from three Slovak folk songs. Formally, the composition follows the trajectory from the idiomatic sound of the physical fujara to the sounds produced by extended performance techniques, and, finally, to the sonorities of the physical model. The physical fujara functions as a controller for the physical model in real-time. A microphone positioned close to the opening of the instrument transmits the audio signal to Max/MSP, where it is pitch and amplitude tracked by the fiddler object (Puckette and Apel 1998). The object works efficiently as the tracked tones show stable fundamental frequencies and amplitudes. In addition, up to three higher sinusoidal components are extracted from the tones spectrum. Transposed or not, these are mapped as the fundamental frequencies of the models. Mapping of the amplitudes to the model is periodically shifted in order to highlight the component frequencies within the resulting tones thus, producing unusual timbres. In addition to the real-time sounds of physical and physically modeled fujara, textures of Air present pre-processed sonorities of the physical instrument. The authors would like to thank the fujara maker Tomas Kovac for providing information about the acoustics of the instrument and the fujara described in the paper. References Cuadra, P. D. L. (2005). The sound of oscillating air jets: Physics, modeling and simulation in flute-like instruments. Stanford University. Elschek, 0. (1991). Slovenske Ludove Pistaly (Slovak Folk Whistles). Bratislava.: VEDA. Filip, M. (1998). Analyza Zvuku (Sound analysis). Bratislava.: Narodne Hudobne Centrum. Filo, M. (2004). Fujary, Pistalky. (Fujaras and whistles). Bratislava.: Ustredie Ludovej Umeleckej, Vyroby. Kresanek, J. (1997). Slovenska Ludova Piesen zo Stanoviska Hudobneho (Slovak Folk Song from Musical Perspective.). Bratislava.: Narodne Hudobne Centrum. Macak, I. (1995). Dedicstvo Hudobnych Nastrojov (The Heritage od Musical Instruments). Bratislava.: Slovenske Narodne Muzeum a Hudobne Muzeum. Plavec, M. (2003). Majstri: Vyrobcovia Ludovych Hudobnych Nastrojov na Slovensku (The Masters: Slovak Folk Music Instrument Makers). Bratislava.: Eurolitera. Puckette, M. and T. Apel (1998). Real-time audio analysis tools for pd and msp. In Proc. ICMC. Scavone, G. and J. O. Smith. (1997). Digital waveguide modeling of woodwind tone- holes. In Proc. ICMC. Smith, J. 0. (2006). Physical Audio Signal Processing. Available online at jos/pasp/. 543