Leonardo

Leonardo, Vol. 11, pp. 301-303. 0Pergamon Press Ltd. 1978. Printed in Great Britain. 0024-094X/78/ 1001-0301 S02.00/0 DRAWINGS BASED ON LASER LISSAJOUS FIGURES AND THE LAMBDOMA DIAGRAM Barbara Hero* 1. In an earlier article in Leonardo, I described some nonfigurative paintidgs that I made whose patterns and colors were related in arbitrary ways to relative pitch in music [I]. A more extensive discussion of my work relating visual art and music is given in my book, Eyesf Ears=Ideas[2]. The starting point for the pictorial compositions is the Lambdoma or Pythagorian diagram, which dates back to Ancient Greece. For recent works I use the followingprocedure: I select a number of tones with the aid of the Lambdoma diagram, produce the tones electronically and make sketchesof their Lissajous figures, which are produced by means of a helium-neon laser scanner device and projected onto a wall or screen. Finally, I make a drawing based on the Lissajous figures with colors chosen according to an arbitrary code that identifies colors with frequencies. 2. A tone of a specific frequency is produced by an electronic sine-wave oscillator (Eico 379 solid state sine/square wave generator, Eico Electronic Instrument Co, Brooklyn, N.Y.). Sinusoidal wave forms may be produced in a frequency range from 20Hz to 2m Hz, but I do not exceed 1200 Hz. It is essential in my work that tones have wave forms with a minimum of overtones of the harmonic series. Therefore sinusoidal wave forms are preferred to square and triangular ones. I record the frequenciesof the harmonic tones from the Lambdoma diagram (Fig. l), one ofwhichis a fundamental , separately on each of two channels of a magnetic tape. Later, using a second tape recorder, I make mixtures of these tones, which I record on one channel of a magnetic tape and different mixtures of tones on the second channel. These two channels are used as input to the scanners that produce the Lissajous figures [3,4]. The production of Lissajous figures in response to music by means of a helium-neon laser beam scanner for projection on a screen has been described in Leonardo by Wagler [5]. He reported on the use of a Sonavision projector manufactured by Son:. ision, Ann Arbor, Michigan. I employ a Metrologic i;iser (model ML-600, 0.5 mw, Metrologic Instruments, Bellmaur, N.J.). The tape-recorded tones on two channels, called Xand Yare used as an input to an amplifier (Studio Standard CA-2100, Fisher, Long Island City, N.J.) having four outputs, two of which are speakers, enabling one to hear as well as to see simultaneously the sum of the two tape- *Artist, 48 Lawrence Strret, Boston, MA 02116, U.S.A. (Received 19 Nov. 1977.) ~ 301 recorded inputs. Two outputs from the amplifier, corresponding to X and Y, drive two galvanometers for laser scanning[31(General Scanning, Watertown, Mass.). One, rotating on a vertical axis, carries a mirror 7 x 7 mm; the other, rotating on a horizontal axis, carries a mirror 7 x 11 mm. The mirrors oscillate to the beats of the different frequendies received. The helium-neon laser beam impinges on one mirror, is reflected to the next and is finally reflected to a wall or a projection screen. The power of a laser (0.5 mW) is sufficient to produce a satisfactory image on a wall at a distance of 3-4.5 m. I calibrate the system so that the Lissajous figures can be analyzed, although I do not attempt to do so myself. 3. My aim is to produce Lissajous figures that are aestheticallypleasing as well as meaningful. It is desirable to minimize dissonances to obtain well delineateddesigns. The absence of dissonance is assured when only frequencies of the harmonic series are employed. The numerical values of the frequenciesof the harmonic series are obtained by multiplying the frequency of the fundamental tone (which I have chosen t obe 352 Hz) by the integers 1-16 and by dividing each of the products by the integers 1-16. This calculation, which is realistically restricted to integral multipliers and divisors below 17to provide frequencies covering eight octaves and...