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CYMATICS: by th "Chladni figures" THE SCIENCE OF THE FUTURE? ecsish a» by Peter Pettersson © 2005 What was the significance of | translated by Yarrow Cleaves this discovery? Chladni demon- “sr strated once and for all that - Is there a connection between sound, vibra - sound actually does affect phys- tions and physical reality? Do sound and _ ical matter and that it has the d > Fi = vibrations have the potential to create? In quality of creating geometric oK t | this article we will see what various __ patterns. : researchers in this field, which has been :, - named Cymatics, have concluded. Bowditch Curves and Lissajous Figures , ; 1] ¢ Chladni Figures In 1815, the American mathe- Et \. he —_ n 1787, the jurist, musician and physi- matician Nathaniel Bowditch of 5 —— fs [« Ernst Chladni published began studying the patterns cre- nd “ + 5 Entdeckungen iiber die Theorie des ated by the intersection of two Klanges (Discoveries Concerning the _ sine curves whose axes are per- 1? : Theory of Music). In this and other pio- _ pendicular to each other. These eo neering works, Chladni, who was born in are sometimes called "Bowditch _ 1 1756 (the same year as Mozart) and died in curves", but more often are Pa / 1829 (the same year as Beethoven), laid the known as "Lissajous figures" foundations for that discipline within (see overleaf)—named after the physics that came to be called acoustics, French mathematician Jules- the science of sound. Among Chladni's Antoine Lissajous who, independently of rhythms or periods coincide. If, on the successes was finding a way to make visi- Bowditch, investigated them in 1857-58. other hand, the curves have different fre- ble what sound waves generate. Both concluded that the condition for these quencies and are out of phase with each With the help of a violin bow which he designs to arise was that the frequencies, or other, intricate web-like designs arise. drew perpendicularly across the edge of flat oscillations per second, of both curves stood These Lissajous figures are all visual plates covered with sand, he produced in simple whole-number ratios to each examples of waves that meet each other at those patterns and shapes which today go _ other, such as 1:1, 1:2, 1:3 and so on. right angles. In fact, one can As I pondered the connection between produce Lissajous _ these figures and other areas of knowledge, figures evenif the I came to think about the concept that frequencies are not exists in many societies and their mytholo- in perfect whole- gies around the world, which describes the number ratios to world as aweb. For example, many of the each other. Mesoamerican people regarded the various If the difference is parts of the universe as products of spin- insignificant, the ning and weaving: "Conception and birth phenomenon that were...compared with the acts of spinning arises is that the and weaving; all the Aztec and Mayan cre- designs keep chang- _ ation and fertility goddesses were described ing their appearance. as great weavers."' A number of waves They move. What crossing each other at right angles looks creates the variations _ like a woven pattern, and it is precisely that in the shapes of they meet at 90-degree angles that gives these designs is the _ rise to Lissajous figures. phase differential, or the angle between Dr Hans Jenny and Cymatics the two curves—in In 1967, Hans Jenny, a Swiss doctor, other words, the way artist and researcher (now deceased), pub- in which their _ lished the bilingual book Kymatik: Wellen Chladni figures CYMATICS: THE SCIENCE OF THE FUTURE? by Peter Pettersson © 2005 translated by Yarrow Cleaves ie =—s 4 —_y in Chladni figures Dr Hans Jenny and Cymatics In 1967, Hans Jenny, a Swiss doctor, artist and researcher (now deceased), pub- lished the bilingual book Kymatik: Wellen NEXUS = 43 FEBRUARY — MARCH 2006 www.nexusmagazine.com