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Page 00000001 Real Time Extended Physical Models for the Composer and Performer Matthew Burtner 1,2, Stefania Serafin 1 1 CCRMA, Stanford University 2 VCCM, McIntire Department of Music, University of Virginia email:email@example.com, firstname.lastname@example.org Abstract In this paper we describe compositional and performancerelated issues for exploring extended techniques of a bowed string physical model. First, an extended waveguide physical model of a bowed string instrument was created. To explore new techniques for the physical model we perform it with the metasaxophone, a tenor saxophone retrofitted with an array of sensors tracking continuously changing performance data from the instrument in real time. Through instrumental controller substitution the physical model is forced to function in a different expressive space, and new timbral possibilities were therefore created. 1 Introduction Physical models of musical instruments become interesting for composers when sonorities that cannot be achieved with real instruments can be obtained. In this paper we explore extended techniques for bowed string physical models arising when a traditional instrumental controller is substituted for an entirely different type of controller. This technique of instrument controller substitution creates surprising real-time performance possibilities for the physical model, forcing it to function in unconventional ways and generating new timbral possibilities for the composer. 2 The bowed string physical model In order to create sonorities that cannot be obtained in real instruments we extended the waveguide bowed string physical model described in (5). Some extensions were already described in (1). In this paper we focus on how we modified the physical properties of the strings in order to be able to bow and pluck strings of different materials. Usually in instruments like the violin the role of stiffness is almost neglectable, so the corresponding models do not account for it. However we noticed that accounting for stiffness improves the quality of the model, especially in instruments like the cello with a higher stiffness coefficient, as we will show below. Moreover high stiffness coefficients allow the possibility of creating interesting sonorities that expand the usual sounds obtained by a real bowed string. 3 Designing allpass filters for dispersion simulation In order to account for dispersion in the digital waveguide model of a bowed string, we chose a numerical filter made of a delay line qr-ro, and a n-order stable all-pass filter H(q) = q-np(q-1)/P(q) where P(q) - po +... +pn-1n-1 + qn, and T and n are appropriately chosen. As proposed in (3), we want to minimize the oo-norm of a particular frequency weighting of the error between the internal loop phase and its approximation by the filter cascade: 6D = min IIWD(t)[pd(t) - (~D() + T)llo Pl,...Pm where oD(Q) is the phase of H(ej"), and WD(Q) is the frequency weighting (WD(Q) is zero outside the frequency range, i.e. [fc, U]). From an acoustical point of view, it is important to have a frequency weighting that approximates the way the auditory system perceives the difference between original and simulated phase dispersion. In order to restrict the approximation to the first few thousand hertz, Rocchesso and Scalcon (4) propose to use frequency warping (6). In our implementation, we chose a weighting function that stresses the accuracy at low frequencies, in order to provide a filter design technique that is both correct from a perceptual point of view and interesting from a musical point of view.
Page 00000002 3.1 Application to the bowed string model We inserted the estimated filters in the string loop as shown in figure 1. The transversal waves propagating toward the bridge are first filtered by the bridge filters for losses and then by the dispersion filters. Note how, since the string is a linear system, inverting the three blocks corresponding to the propagation of the waves in the bridge side of the string would not change the results of the simulation. DISPERSION --BRIDGE FILTER STRING jST NUT ILTER BOW-STRING INTERACTION BRIDGE FILTER STRIG STRIG NUT FILTER Figure 1: Block diagram of a digital waveguide model of a bowed string including the allpass filters for stiffness simulation. 3.2 Influence of stiffness in virtual bowed strings We run our digital waveguide model using the same cello D string as before, with bending stiffness B = 0.0004 Nm2 The string, starting from rest, is excited by a constant bow velocity vb = 0.05 m/s, a bow force of fb = 0.2 N and a normalized bow position of 0.08, where 0 represents the bridge while 1 represents the nut. Figure 2 shows the result of this simulation where the string velocity at the bridge has been captured after a steady state motion is achieved. The waveform on the top of figure 2 and 3 shows the velocity of a string with stiffness coefficient B = 4e - 2 Nm2, while the waveforms on the bottom shows a string with no stiffness. Note how the Helmholtz motion gets distorted in the case of the stiff string, which has a significant impact on the quality of the sound synthesis. 4 The Metasaxophone In an effort to explore extended techniques of the physical model we perform it with an original alternate controller, the metasaxophone. This allows the physical model to be controlled through a different expressive interface, that of a wind instrument. This in turn opens new expressive potentialities of the model. The metasaxophone tracks data from eight continuous controller force sensing resistors (FSR), five triggers, and a two dimensional accelerometer chip. The FSRs are located on the front B, A, G, F, E and D keys, and on the two thumb rests. Three triggers are located on the bell of the instrument, and one below each of the thumb rests. The ac Figure 2: Bottom: velocity of the string at the bridge point for a cello D string with B=0. Top: resulting spectrum. Figure 3: Bottom: velocity of the string at the bridge point for a string with B=3e-2 N m2. Top: resulting spectrum. celerometer chip measures left/right, up/down tilt of the saxophone bell. The data from these sensors are collected via a 26 pin serial connector by a microcontroller fixed to the bell of the instrument. The computer chip is a Basic Stamp BIISX microprocessor. Analog pressure data from the performer is converted to a digital representation and passed to the Basic Stamp through an RC circuit. Trim potentiometers calibrate the sensitivity of each individual circuit. The microprocessor is programmed in PBASIC and the software converts the sensor data into MIDI messages. The circuit board and a 9 volt battery are fit into a black box with openings for the serial cable inputs, a MIDI output, and a power switch. MIDI messages from the metasaxophone can be sent to any MIDI device and used as control data for live electronics. In addition to sending MIDI information, the metasax
Page 00000003 Figure 4: The Metasaxophone front and back views. ophone sends an audio signal through microphones located both inside and outside the instrument. MIDI and audio data are sent to some external computer or device for processing. These continuous controller MIDI messages from the metasaxophone are then used to drive the bowed string physical model controlling each parameter of the model by constantly varying degrees of finger pressure applied to the different metasaxophone keys. The metasaxophone and string physical model interact through a Max/MSP performance interface (figure 5) which allows for a highly flexible performance interface design and complete integration of MIDI control values and synthesis parameters. 5 Instrument controller substitution The input parameters of the physical model, i.e. the parameters of the excitation, the string inharmonicity, frictional properties, center frequency, and microtonal frequency variation are controlled by different sensors on the metasaxophone. By assigning each finger of the saxophone to a different parameter of the complex action in the model, this action is broken into a series of isolated tasks. This creates a reallocation of the parameters of a complex expressive action - the bowing - to another complex action - the fingering of keys. Consequently, simple motions such as the convergence of parameters occurring as, for example, when a bow is drawn across the strings can become difficult to execute, while impossible bowing configurations, such as for example dynamically linking the material transformation of the string to decreasing bow velocity, become possible. A series of expression tests of this nature were performed and the results presented at (1). These tests suggested new possibilities of exploring extended techniques for physical models using instrument controller substitution remappings. p metasaxophone ha. PluckedStrings.Bo.wedString pi]t~man~autii....................... Figure 5: Max/MSP performance interface for S-Trance-S. Furthermore, the acoustics of these results suggested additional extensions to the acoustic properties of the string physical model itself (2). 6 Composition: S-Trance-S In the musical composition, S-Trance-S (2001), written expressly for this instrumental configuration, we explore instrument controller substitution through the metamorphosis between "real" and physically modelled instruments. The metasaxohone keys are mapped to the physical model bowing parameters: bow force, bow position, bow velocity, frequency, two types of inharmonicity, and chaotic bow friction. This controller mapping then undergoes a series of remappings as the single virtual string grows into an ensemble of virtual strings, each one utilizing a different controller mapping. With regard to the physical model we identify two types of control parameters, 1) those that are intrinsically tied to the propogation of sound such as bow velocity and bow pressure, and 2) those that modify the mode of performance for expressive timbral richness such as inharmonicity, noise, bow position, and frequency. This observation was an important concern when creating the performance mappings because for a generally congruous sound certain keys must retain a propagatory role while others can be used as modifiers. Figure 6 illustrates the mappings as they occur in the piece and figure 5 shows the Max/MSP performance interface for S-Trance-S. The metasaxophone controls the transformation between three instruments: the acoustic saxophone, a string physical model played by the metasaxophone controllers, and acoustic bowed string timbres played by the computer. Two aspects of extended techniques for physical models are explored
Page 00000004 Alternate Controller Substitution Mappings in S-Trance-S etas,aKphfl.rie remaped to.an esemnbie of siris.- ph.ys:ira! mnoels $ ~ continuous Figure 6: Controller mapping in S-Trance-S - gestural transmutation of the instrumental controller, and signal transmutation as a result of instrumental cross synthesis. Through signal transmutation, the saxophone sound, the bowed string sound, and the combined metasax/string physical model sound are transformed into a series of hybrid instruments that are performed live by the saxophone and transfused into independent timbral screens. There are six such convolved timbral screens derived from the three archetypal models: -sax convolved with sax -string convolved with string, -physical model string convolved with physical model -string sax convolved with physical model string, -sax convolved with string -physical model string convolved with string. As these hybrid timbres evolve they are continuously mutated, forming a series of transformations. 7 Conclusions Instrumental controller substitution opens new paradigms for compositional timbral exploration using physical models. Rather than evaluating the musical effectiveness of the physical model in terms of its acoustic real-world counterpart, we propose a method for exploring the virtual instrument for its own complex and unique properties. Similarly, the instrumental controller when coupled with the physical model can be evaluated independently from its acoustic basis, solely as a controller for the redefined digital instrument. S-TranceS explores this paradigm of transmutation by seeking to occupy a timbrally rich musical space in which a dialectic is es tablished between control parameters and sonic parameters. This type of coupling is natural with all musical instruments but instrumental controller substitution opens the possibility of potentially unlimited hybrid electroacoustic instruments. References  Matthew Burtner and Stefania Serafin. Extended performance techniques for a virtual instrument. In Proceedings of DAFX, Verona, Italy, 2000.  Matthew Burtner and Stefania Serafin. Extended techniques for physical models using instrumental controller substitution. In Proceedings oflSMA, Perugia, Italy, 2001.  M. Lang. Optimal weighted phase equalization according to the 1-infinity norm. Signal Processing, 1992.  Davide Rocchesso and Francesco Scalcon. Accurate dispersion simulation for piano strings. In Nordic Acoustical Meeting, Helsinki, June 1996.  Stefania Serafin, Julius O. Smith, III, and Jim Woodhouse. An investigation of the impact of torsion waves and friction characteristics on the playability of virtual bowed strings. In IEEE Workshop on Signal Processing to Audio and Acoustics, New Paltz, NY, New York, Oct. 1999. IEEE Press.  Julius O. Smith and Jonathan S. Abel. Bark and ERB bilinear transforms. IEEE Speech and Audio Processing, pages 697-708, November 1999.