Chambers: Scores by Alvin Lucier

10. Still and Moving Lines of Silence in Families of Hyperbolas

STILL AND MOVING LINES OF SILENCE IN FAMILIES OF HYPERBOLAS STILL AND MOVING LINES OF SILENCE IN FAMILIESOF HYPERBOLAS (1973-74) for singers, players, dancers, and unattended percussion. Create standing waves in space caused by constructive and destructive interference patterns among sine waves from loudspeakers. With single sine wave oscillators, amplifiers, and pairs of loudspeakers, design sound geographies for dancers consisting of troughs and crests of soft and loud sound that form in outward-arching, symmetrically mirrored hyperbolic curves between the loudspeakers, the size and number of which are determined by the frequencies of the sine waves and the distances between the loudspeakers.Add loudspeakers,creating additional sets of hyperbolas, some of which intersect. When necessary, clear pathways for dancers by slightly changing the frequenciesof the sine waves, shifting the locations of the hyperbolas. Any number of dancers discover troughs of quiet sound along axes of pairs of loudspeakerswhich they may follow, changing directions, if they wish, at intersections. If bumps of sound occur due to reflections from walls or other surfaces, search for open paths or wait for troughs to shift. Play any number of sine tones, simultaneously in chords or clusters, or sequentially, through any configuration of loudspeakers. Any number of singers sing long pure tones in near-unison above or below the given sine tones so asto produce audible beating, forming continually variable rhythmic patterns. Sing within intervals, beating upper pitches at one speed, lower ones at another, creating double rhythms. Closely tune any number of oscillators, causing hyperbolas between loudspeakers to spin in elliptical patterns through space at speeds determined by the tunings and in directions toward the lower-pitched loudspeakers. Balance oscillator and amplifier volumes to achieve maximum and minimum amplitudes including silences, if possible, during beating cycles. Play any number of brass and wind instruments in such a way asto create and spin hyperbolas toward and away from your instruments and sounding loudspeakers. Pluck any number of stringed instruments, including electric guitars, to create series of beats, the speeds and numbers of which are determined by the tunings and amplitudes of the plucked sounds and sine tones. 128 Deploy any number of snare drums (metal snares) anywhere in space. Search for resonant frequencies of the drums and spin hyperbolas of those frequencies across them, the crests of which cause sympathetic vibrations , creating rhythmic patterns determined by the speeds of the beatings. Parts of this work may be performed singly or in any combination simultaneously , in any order. 129 This page intentionally left blank I'd like to ask you about your new piece, Still and Moving Lines of Silence in Families of Hyperbolas. What struck me the first time I heard the idea, standing waves and variations on them in a space, was that it reminded me of tile designs in floors. You've just come back from the land of tile, Italy; was there a visual image that began the piece for you? Well, if not visual spatial. The piece exists almost completely on a spatial plane. What's important is the making of simple to complex and still to moving sound geographieswith sine waves. You know that if you have a simple sound wave and a reflective surface , under certain circumstances, depending on the frequency of the sound and the distance between the source of the sound and the reflective surface, you can create standing waves. If the wavelengths of the frequencies are in simple proportion to the size of the room, then the sound bouncing off a reflective surfacereturns in synchronization with another wave as it's going out, and it amplifies itself. It's as if the reflective surfacewerfe a second source at the samefrequency which interferes constructively with the first to produce a rise in amplitude. If the distance between the sound source and the reflective surface is not in simple proportion to the wavelength, then you get destructive interference; asthe wave bounces back, it interferes with the wave that goes out. Under ideal circumstances, if it were 180° out of phase, it would attenuate the outgoing wave and completely eliminate it. You never get an ideal situation in a room because you're surrounded by reflective surfaces and because sound propagates all over, it doesn't go out in a line, it goes out concentrically , so you get reflections from all over. And if it's a highly reflective room, it's as if there were...