6 Lissajous Figures — Images as Sound

The basis of analog-electronic audiovisuality is a signal simultaneously made visible and audible via loudspeakers and cathode ray tubes. The principle of the orthogonal superimposition of two vibrations is essential for the electronic image. A waveform is affixed both to the abscisse and the ordinate, spanning the image plane. The specific composition of the signals can emerge in different ways, as the variety of video formats demonstrates. In principle however, cathode ray tubes can be used to present arbitrary waveforms. These picture formats are all subject to the general theory of oscillation, which makes them comparable to older types of images.

In 1815 the mathematician Nathaniel Bowditch described for the first time the functions of the perpendicular superimposition of harmonious swings of the pendulum. Following this discovery, a wide range of different mechanical instruments was constructed for the creation of such Bowditch curves — including numerous so-called harmonographs^[26] and Charles Wheatstone’s Caleidophone (1827) — and in order to directly observe oscillation patterns of light on resonant metal staves. The curves finally became known as Lissajous figures, when Jules Antoine Lissajous examined them in 1857/1858 in the context of acoustic experiments concerning the oscillation behavior of solid objects. With Karl Ferdinand Braun’s invention of methods for electronic image production in 1897, the waveforms of electric signals could also be observed. As a result, the oscilloscope was developed as a physical quantifying instrument for determining alternating voltage.

Similar to the transfer of visual patterns into sound that occurs in optical sound, electronically generated audiovisuality works with a specific interaction of medial operability and perception processes. The perpendicular superimposition of oscillations as a form of two-dimensional representation, which serves to make acoustic processes in the electronic image medium visually accessible, has always constituted an interference of two signals, which deflect the point of light in two different directions — horizontal and vertical. In addition, the oscillation movement of a Lissajous figure appears static when the level is higher than the fusion frequency of the human eye (approx. 18 Hz), while the human ear is not able to perceive spectral components below this frequency. Thus a Lissajous figure does not represent a particular frequency and there is no clear correlation between the pitch and figure. Nevertheless, sound and image can be compared within other factors, such as the relationships between frequencies (intervals) and phase relations in the lower frequencies. Depending on the complexity of the matter to be audiovisually perceived, specific convergences between media-technical and perception-related aspects can arise. For an aesthetic approach to electronic audiovisuality precisely these intersections are of interest, in order to expose the perspective on mediality, the constructed nature of the transfer. Intuitively comprehensible convergences are created, for example, as a result of the precise simultaneity of sound and image, which is guaranteed by the precision of the analogue electromagnetic interconnection and which cannot be achieved in digital coupling systems. The same applies to the magnification of the figures at higher volumes, caused by the heightened amplitude. Finally, the growing complexity of the Lissajous figures when harmonic frequency relations become more complex corresponds to the impression made on the ears. These kinds of correlations are often simulated in the algorithmic parameter mapping of digital audiovisual systems.

Electronic image synthesis was initially explored as an aesthetic strategy in the older medium of film, which by the 1930s had established itself also as an abstract art form. Mary Ellen Bute^[27] and, in the 1950s, Hy Hirsh and Norman McLaren integrated Lissajous figures into their animations by filming oscilloscope screens. In addition, the possibilities presented by geometric image synthesis also interested practitioners of Op art, kinetic art, and early computer graphics.^[28] Cathode ray oscillography was also tested in music visualizations in electronic studios in Berlin by Fritz Winckel (1960s) and in Paris by Pierre Schaeffer (La Trièdre Fertile, 1975).^[29] Reynold Weidenaar continued to use analogue synthesizers and oscilloscopes for audiovisual compositions (1979) and Bill Hearn’s video synthesizer VIDIUM (1969), an audio synthesizer modified especially for this purpose, enabled the precise synthesis of complex Lissajous figures. Due to their ability to couple electronic sounds and image signals without inertia, cathode ray tubes were used by Nam June Paik and David Tudor for live participatory and performative purposes. Paik’s experiments with the audiovisual interconnection of television sets, audiotapes, and microphones in his first solo exhibition Exposition of Music — Electronic Television (1963) are now seen as the notorious beginning of video art. In 1966 David Tudor, in collaboration with Lowell Cross, realized the performance piece Bandoneon! (a combine), on the occasion of 9 Evenings: Theatre and Engineering, for which several audiovisual transformation processes were deployed. For the Pepsi-Cola Pavilion at the Expo 1970 in Osaka, Tudor and Cross together with the physicist Carson D. Jeffries developed a multiple deflection system for laser rays. The system operates on the same principles as the electronic image generation mentioned before. Finally, with a hybrid analogue-digital linking system, Robin Fox extended the possibilities for synthesizing Lissajous figures in his video series Backscatter (2004) and, like media artist Edwin van der Heide,^[30] has been experimenting increasingly with deflection systems in laser-sound performances. In his audiovisual performances, Fox expands the boundaries of the screen-centered projection by using rooms filled with smoke-machine generated haze as projection volumes. Once again Moholy-Nagy demonstrated particular foresight when, as early as 1936, he conceded in his essay “probleme des neuen films” that: “it is certainly conceivable that smoke or vapour can be hit at the same time by different projection apparatus, or that figures of light can appear at the points where different cones of light meet.^[31]