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Page 491 ï~~Time-Stretching of Hyper-Resonated Sound Using a Real-Time Granulation Technique Barry Truax School of Communication & School for the Contemporary Arts Simon Fraser University Burnaby, B.C. Canada V5A IS6 Truax@sfu. ca ABSTRACT The combination of recursive waveguide resonators with granular time-stretching is used to process sampled sound such that its spectral components are emphasized and prolonged. As a result, the sound appears to be placed in a large space which resonates much higher frequencies than normal. If the feedback factor in the waveguide is set near its maximum value below saturation, the resonant frequencies resemble overtone singing. The author describes the use of this technique in a recent composition Powers of Two. 1. Waveguide Resonators The Karplus-Strong model of a recursive waveguide with filter has long been regarded as an efficient synthesis technique for plucked string sounds (Karplus & Strong, 1983). The basic model for the waveguide uses a delay line of p samples which determines the resonant frequency of the string, a low-pass filter which simulates the energy loss caused by the reflection of the wave, and the feedback of the sample back into the delay line. The initial energy input is simulated by initializing the delay line with random values, that is, introducing a noise burst whose spectrum decays to a sine wave at a rate proportional to the length of the delay line. The model applies equally to a string fixed at both ends or a tube open at both ends, at least in terms of the resonant frequencies all being harmonics of the fundamental. If the sample is negated before being fed back into the delay line, the resulting change of phase models a tube closed at one end, which results in only the odd harmonics being resonant, and lowers the fundamental frequency by an octave, since the negation effectively doubles the length of the delay line. For the basic model, the fundamental resonance equals SR/(p + 1/2) where SR is the sampling rate, and p is the length of the delay line. However, since the technique models a resonating tube as well as a fixed string, it is equally suited for processing sampled sound. Because an ongoing signal activates the resonator, rather than an initial noise burst, a feedback gain factor must be used to prevent amplitude overflow and to control the amount of resonance in the resulting sound. The current real-time implementation offers a choice of delay line configurations (single, in parallel or series), plus the options of adding a comb filter (to add or subtract a delayed signal) and signal negation (which lowers the fundamental frequency by an octave and produces odd harmonics). Particularly interesting effects occur when the length of the KarplusStrong delay and the comb filter delay are related by simple ratios. Each delay line has real-time control over its length, and hence its tuning, up to a maximum of 511 samples. The user also controls the feedback level which can be finely adjusted to ride just below saturation, in combination with the input amplitude which can be lowered to facilitate higher feedback levels. The use of sample negation also makes it easier to control high feedback levels since the length of the feedback loop is essentially doubled. The complex behaviour of these resonators, particularly when driven to their maximum feedback level (termed hyper-resonance) cannot be tracked by the ear at normal speed, compared to when ICMC Proceedings 1996 491 Truax
Page 492 ï~~such sounds are time-stretched, using the real-time granulation technique described by Truax (1994) with the DMX-1000 signal processor. Such processing lengthens the decay of the resonance to an arbitrary duration, hence suggesting a very large space, while keeping the resonant frequencies intact. That is, resonant frequencies associated with relatively short tubes appear to emanate from spaces with much larger volumes. Vocal sounds subjected to this processing resemble "overtone singing" in a reverberant cathedral, because the resonant frequencies are strong enough to be heard as pitches. The addition of simple harmonization at the granulation stage, such as an octave lower, enriches the sound further and gives the impression of a choir. 2. Compositional Use of the Technique A recent work, commissioned by and performed at ICMC 1995 in Banff, named Powers of Two: The Artist, is scored for two singers (lyric tenor and counter-tenor), female dancer, video tape and eight digital soundtracks. It is a piece of electroacoustic music theatre that is structured around four scenes, each of which includes a video tape, and an historical musical and poetic reference. In order, these are the 15th century French tune, L'homme arms (The Armed Man); Monteverdi's Combattimento di Tancredi e Clorinda; the Liebestod from Wagner's Tristan und Isolde; and the ending of Stravinsky's Oedipus Rex. However, the musical and visual materials are digitally processed in order to remove them from any attempt at historical verisimilitude and render them timeless. For instance, the musical quotations, recorded by the counter-tenor, are heavily resonated using a double delay line with a high level of feedback. This processed sound is then time-stretched with the granulation technique referred to above such that the original and resonant pitches do not change, only the duration of the sound and the apparent volume of the space in which it appears to originate. The result is that the musical line sometimes retains its melodic contour, and at other times is stretched into long resonant tones that appear to be reverberated in a cathedral or other diffuse sound field. The resonances are often so strong that they resemble harmonic singing where overtones become clearly audible as pitches. In the performance, the countertenor frequently sings the same musical line against the processed one. A spoken English version of the text of the music is not resonated, but only granulated and partially stretched. In contrast, the independent poetic texts in each scene are resonated but not stretched. 3. Conclusion Hyper-resonance and time-stretching both contribute to the perceived sense of increased volume in the sound without any necessary increase in amplitude. Thus, the source and its processing become interdependent to a greater extent than with other signal processing methods. Whereas most signal processing subjects the source material to an arbitrary transformation, with often little or no correlation between the characteristics of the source and the manner of processing, resonance and time-stretching both bring out only the inner qualities of the source material, the former in the frequency domain, and the latter in the time domain. Moreover, the magnified time scale allows the temporal behaviour of complex resonances to be clearly heard. This approach may allow an effective aural exploration of other complex frequencytime behaviours, and create aurally attractive enhancements of acoustic sounds. References Karplus, K. & A. Strong, 1983. Digital synthesis of plucked string and drum timbres. Computer Music Journal, 7(2). Truax, B. 1994. Discovering inner complexity: Time-shifting and transposition with a real-time granulation technique. Computer Music Journal, 18(2), 38-48. Truax 492 ICMC Proceedings 1996