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Page 00000001 Piano Case, Keyboard, And Strings: Separation-Derived Musical Instruments In An Interactive Composition Juraj Kojs University of Virginia, USA Aalborg University Copenhagen, Denmark jukoc)rnqedia.ýauý. k Medialogy, ABSTRACT This paper proposes analysis as an effective technique for creating new instruments. Acoustic piano components such as the case, strings, and keyboard mechanism are defined as independent acoustic separation-derived musical instruments. Enhancement of the instruments via digital signal processing and synthesis is also discussed. Friction driven physical model of the string is used to complete the string separation-derived instrument. Expressive potential and characteristic sonorities of these instruments are exemplified in Three Movements for unprepared piano and electronics. 1. INTRODUCTION The separation-derivation technique for creating new musical instruments is based on a simple proposition that an instrument consists of at least two components: an exciter and resonator. When separated, these components can be identified and explored as individual stand-alone instruments. In an example of piano, these instruments are the case with the frame, resonant plate, soundboard, strings, keyboard mechanism, and pedals. This effective technique marks a continuation of inquiries about unusual use of the instrument accomplished by the composers such as Henry Cowell, John Cage, George Crumb, Curtis Curtis-Smith, and Eleanor Hovda. New sonic properties arise when digital signal processing and physical modelling are employed to extend an acoustic separation-derived instrument. In such cases, the acoustic instrument may additionally function as a controller of its computer-based complement. Characteristics of piano separation-derived instruments and their extended digital applications in Three Movements for unprepared piano and electronics are described in the following sections. 2. PIANO SEPARATION-DERIVED INSTRUMENTS Acoustics of piano is described in . It identifies three primary agents involved in piano sound production: striking mechanism (keyboard and hammers), strings, and piano case with soundboard, frame, and plate. Strings piano instrument Case Figure 1. Synthesis graph for piano sound production It can be summarized that the keyboard and hammer represent the excitation part of the sound production. The strings and case belong to the resonating area as explained in , , , and . The following figure displays how a piano complex instrument can parent a variety of separation-derived instruments. Soundboard Case /instrument instrumentrme " Frame instrument lKeboard instrument piano Hammer instrument instrument String instrument Pedal instrument Figure 2. Separation-derived instruments These instruments naturally retain certain sonic characteristics of their parent. Yet, new attractive sonorities emerge when the characteristic qualities of a separation-derived instrument are developed, amplified, and digitally enhanced. In this paper, the case instrument is considered as one instrument. Pedal and hammer instruments are not discussed. 3. THREE MOVEMENTS The piano case, keyboard, and strings were explored in Three Movements (2004) for piano and electronics.' Each of these instruments is employed with certain I The author used other separation-derived acoustic musical instruments such as piano lid and piano pedal in Dynamisms for piano and orchestra.
Page 00000002 dominance in one of the movements. Thus, spectra of resonating piano body enliven in Palms on the strings (movement one). In Sliding quietly (movement two) the silent keyboard is used as a primary instrument. The result of sliding and playing on the keys without producing any pitch is a set of characteristic percussive sonorities positioned on the threshold of hearing. The physical model of string prevails over the silent keyboard in Bowed fingertips (movement three). 3.1. Palms on the Strings In the opening movement, the piano case is defined as a percussion instrument. The performer uses its frame, soundboard, metal dividers, and strings in variety of performance modes such as dynamically varied rubbing, tapping, and hitting with palms and fingers. Keeping the sustain pedal down throughout the movement allows the slightest excitation to enliven the case. Most satisfying sonorities occur at these miniscule excitations. A microphone is positioned inside the case. It screens and transfers the sounds to MAX/MSP  for amplification and signal processing. In MAX/MSP, an artificial resonator is created out of a bank of band pass filters with center frequencies derived from the identified frequencies of resonant metal dividers. Coupled with spectra of frequencies that belong to the pitch design of the composition (described briefly later in the paper), a specific resonant space arises. The case instrument additionally functions as a controller of a comb filter series with high feedback coefficients. The filters are applied to the signal coming from the case instrument. Their level is linearly dependent on the amplitude level of performed gestures analyzed by the fiddle- object . Thus, a strong attack on the divider will result in a sound resembling a pulsating didgeridoo. Combination of the amplified sound and the filters completes a digitally extended case instrument with new resonant characteristics. The following figure displays a portion of the Palms on the Strings score. The horizontal bracket frames the system of two staves: electronics (top) and piano (bottom). Vertical orientation of the system represents time measured in seconds. Horizontal orientation of the computer music part indicates amplitude fluctuation (centered around invisible line 0 in the middle of the system). The top system represents transformations in computer-processed sounds as follows: pre-recorded string models, sampled piano, and filters. Figure 3. The piano part is scored in three lines and three spaces. These represent performance regions inside the grand piano case: three metal dividers (spaces) and strings areas positioned between them (lines). In addition to the case instrument sound, a set of the friction string models is present in a pre-recorded and pre-processed form. These construct a supplemental background spectrum for evolving case instrument sonorities. The relationship is largely defined by the performance media distribution: the case instrument is a real-time active component, while pre-recorded, thus fixed-to-respond, string models are a passive one. More active role of the model can be seen in the second and third movements. Here, the interaction is provided by the alignment between the model's bow pressure and amplitude analysis of the case instrument gestures. Thus, the higher amplitude in the case instrument part is mapped to the higher bow pressure and often results in high friction sound. 3.2. Sliding Quietly In this movement, the keyboard is identified as a separation-derived musical acoustic instrument. The performer slides their nails, knuckles and palms on top of the keys without fully depressing them. (In the third movement, the pianist performs in normal mode without depressing the keys in full.) Since the hammer never strikes the string, no pitch is produced. Instead, an array of slightly pitched percussive sonorities is generated. A range of these sonically original nuances forms the expressive range of the instrument. The pitch arises with the increased velocity of performed glissando gestures. As the sound is positioned at the threshold of hearing and needs to be amplified, two microphones are positioned on the sides of the keyboard. Similarly to the first movement, sliding the silent keys becomes an excitation mechanism for computer-based resonator: in this case the physical model of a string. The string model is a combination of three digital waveguides connected in parallel. It is excited by a friction mechanism. The friction interaction is a described in .
Page 00000003 Stefania Serafin implemented the model in MAX/MSP as an external object squeaking~ with the following inputs: frequency elements, bow force, bow velocity, bow position, and residual component. In MAX/MSP, amplitudes of the Sliding Quietly gestures are tracked by fiddle-  and mapped to the bow pressure, position and velocity of the model. This results in a simulation of either saltando or plucked string sonorities. The frequency spectrum of the model is pre-assigned and corresponds with the pitch design of the composition. As opposed to the third movement, the keyboard instrument controls the model in Sliding Quietly without variation. The following figure exemplifies notation of the saltando and plucked string (the wave form in the center), piano samplers (the outer lines), friction string (the inner line), and piano part (the bottom system). in MAX/MSP and provide the real-time frequency input for the model. Performed pitches, their durations and distance between them and between their repetitions are systematically arranged. Multidirectional rotation of pitches B, A, C, and B flat and their octave transpositions constitute the skeleton for vertical and horizontal design of the piano part and model's input. By feeding the string model with the input provided by real strings, the separation driven instrument of a string is proposed. The real strings function as an exciter and the virtual model as the resonant space. Figuratively, the resonant space of the piano case is removed and replaced by the virtual string. Amplitudes of the real string control the changes in pressure and velocity of the virtual one. The frequencies of the real string are transposed to the extremities before induced to the model. Thus the model produces pitches normally unavailable at the piano. Further, repetitive looping of the sampled and cross-synthesized models enhances the overall sonic tapestry of the movement. -------------------- 1 A0......... --------------------------------------......... --------------------- -------------............. --------- - - ------------ -- - - - - -- - - - - -- - - - - - The following figure exemplifies the signal of piano driven friction string model (dense centered wave) and string samplers (the lines). The bottom system displays the piano part. The cross note heads indicate nondepressed key performance, while the filled ones require full key depression. Figure 4. Performance technique such as sliding the keys with palms sidewise without producing any pitch can be applied to the keyboard separation-derived acoustic musical instrument. Straight lines connecting initial and ending points of the gesture represent such glissando technique. This instrument has a capacity to produce an attractive set of sonorities. It is digitally enhanced by functioning as a controller for the physical model of the string. The keys represent the exciters that constantly enliven saltando and plucked string. 3.3. Bowed Fingertips In the third movement the keyboard real-time control over the friction driven physical model of a string is expanded. The model is proposed to be the complete resonant space of the keyboard instrument. The produced sonorities are constantly sustained. Additionally, using the model presents a complete separation of the string component from the real instrument's complex identity. In the opening section, the pianist who performs on the keys in normal mode without producing any pitch controls the model. The model responds to the analyzed piano keyboard impulses similarly as in the second movement. Later in the movement, however, the pianist depresses keys and produces pitches. These are analyzed ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ________________________________________..............................................................................................................................................................................\.*...4",\.....ý"------------I 4, ý ------------ ----- ------- i............................................................................................................................................................................................................................................................................................................................ ------------- - - - ------ ---- ---- -- - ------- ---- - Figure 5. Emergence of pitched piano material is indicated in the filled note heads. Interaction between the real and virtual string is given by strict compositional control over the material. In pairing the two, a digitally enhanced separation-derived string instrument, is proposed. The real string presents an exciter and physical model functions as a resonator. 4. CONCLUSION In this paper, separation-derivation technique for creating new musical instruments is proposed. The instruments originate as an individual component of complex musical instruments. They have a potential to produce attractive and expressive sonic territories. The piano case, keyboard, and string were identified as such instruments and exemplified in the context of a music composition. Coupling the acoustic instruments with
Page 00000004 digital resonators dramatically enhances their sonic qualities and expressiveness. Thus, extending the separation-derived musical instruments by means of digital synthesis techniques such as physical modeling suggests an up-coming horizon for timbral explorations and composition. 5. REFERENCES  Askenfelt, editor. Five lectures on the acoustics of piano. Royal Swedish Academy of Music. 1990. Retrieved from: http://www.speech.kth.se/music/5_lectures/  Conklin H.A. Jr. Design and tone in the mechanoacoustic piano. Part 1. Piano hammers and tonal effects. Journal of Acoustic Society in America, 99(6), 1996.  Conklin H.A. Jr. Design and tone in the mechanoacoustic piano. Part 2. Piano structure. Journal of Acoustic Society in America, 100(2), 1996.  H. Fletcher, E.D. Blackham, and R. Stratton. Quality of piano tones. Journal of Acoustic Society in America, 34(6), 1961.  N. Fletcher and T. Rossing. The physics of musical instruments. Springer Verlag, New York, 1998.  Puckette, M. and Apel, T. "Real-time audio analysis tools for Pd and MSP". Proceedings of ICMC. San Francisco. 1998.  Serafin. S. The sound of friction. Real-time models, playability and musical applications. PhD diss., Stanford University, 2004.  Zicarelli D. and Puckett M. Max/MSP. Version 4.5, 2004.