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the laws of the former govern the mathematical intervals that the Pythagorean Table, it defines the exact relationships between make up the notes in Western musical scales, also known as musical harmonics and mathematical ratios (see figs 2a, 2b). diatonic ratios. Physical reality, it seems, is governed by But it was a convincing crop circle etched in barley at geometric arrays related to sound frequencies. Goodwood Clatford, England, in 1996—which had its plants bent One of the mathematical minds studying crop circles was the six inches from the top—that gave the proverbial nod to sound, late Professor Gerald Hawkins. In February 1992 he published an for here was a representation of a cymatic pattern (see fig. 3). interesting challenge to the half a million subscribers of Science Cymatics is the study of sound waves and their interaction with News. Prof. Hawkins had studied the work of Euclid, a Greek physical substances. One of its modern pupils was Swiss scientist mathematician of the third century BC, whose treatises on mathe- Hans Jenny who, throughout the 1950s to 1960s, painstakingly matics pretty much form the basis of our knowledge today. He captured on film the effects of sound as it interacted with powders used the principles of Euclid to prove that four geometric theo- and liquids. He observed how sound vibration created geometric rems can be derived from the relationships of design elements in shapes: a low frequency produced a simple circle encompassed crop circles. More significantly, he by rings, whereas a higher frequency discovered a previously unknown increased the number of concentric fifth theorem from which he could icc j rings around a central circle. As the derive the other four. Euclid himself Cymatics is the study of frequencies rose, so too did the had not written it in his 13 treatises sound waves and their interaction complexity of shapes, to the point on mathematics, and yet Prof. with physical substances. where tetrahedrons, mandalas and Hawkins showed that a gap existed in other sacred geometric forms could Euclid's work where logically it Low frequencies produce a simple e discerned. ought to have fitted. circle encompassed by rings, Just as the Egyptians had once Despite an open challenge to the whereas higher frequencies described geometry as "frozen high IQ readership of Science News , . . no one was able to create this fifth | increase the number of concentric theorem. Needless to say, it came as rings around a central circle. a slight shock when it materialised as a 160,000-square-foot crop circle at ing for, since many of the vibrational Litchfield, England, in 1995 (see fig. 1). atterns captured in his photos mimic Incredibly, the theorem did not appear overtly, and, just like the their designs: from the simple circle surrounded by concentric challenge laid by Hawkins, the Circlemakers required it to be rings, typical of early 1980s designs, to the tetrahedron and the music", so Jenny now enabled umanity to see it. Jenny also pro- vided a physical connection to the creation of crop circles I'd been look- decoded from within their own design. complex star fractals of the 1990s (see fig 4). By their nature, the crop circle theorems produce diatonic Visually, then, the connection is undeniable. But what evi- ratios, so a link now exists between crop circles and musical dence links sound and crop circles at a physical level? notes, which are the by-product of sound frequencies. And by 1995, crop circles bearing unmistakable physical associations Sonic Effects in the Field and in the Laboratory with sound began to appear. One contained a curious ratchet fea- | * Audible sound ture from which is extracted a musical diagram, the Lambdoma, Many accounts exist of a trilling sound heard by the 80 reported dating to the ancient Egyptian mystery schools. Also known as witnesses to crop circles fi is unusual noise, which Cymatics is the study of sound waves and their interaction with physical substances. Low frequencies produce a simple circle encompassed by rings, whereas higher frequencies increase the number of concentric 1995, crop circles bearing unmistakable phys associations Sonic Effects in the Field and in the Laboratory with sound began to appear. One contained a curious ratchet fea- | * Audible sound ture from which is extracted a musical diagram, the Lambdoma, Many accounts exist of a trilling sound heard by the 80 reported dating to the ancient Egyptian mystery schools. Also known as witnesses to crop circles forming. This unusual noise, which sounds like a cross between a cicada and a waterfall, was captured on magnetic tape in 1989 during a night watch of a field at Cheesefoot Head, England, by a group of researchers. It was duly sent to NASA's Jet Propulsion Laboratory in Pasadena, where it was brought to the atten- tion of Robert Weiss, the man who had previously analysed the famous Watergate tapes. He concluded that the noise was not related to any type of bird or insect, and due to its looping, rhythmic nature it appeared to be of intelligent, mechanical origin. Further, it contained a frequency of 5.0-5.2 kHz. Later that summer, the trilling sound was captured again—this time by a BBC cameraman whilst recording an interview inside a crop circle. A few seconds after its appearance, it rendered his US$55,000 camera useless. According to the technicians who later rebuilt the equip- ment, the sound frequency had interfered with the circuitry to such a degree that the camera would not work after that episode. Interestingly, many latter-day Australian Aborigines relate to this trilling sound. During their ceremonies to ——— contact their "sky spirits", a specially shaped piece of wood = called a bora is attached to the end of a long string and Figure 1: Crop circle at Litchfield near Dunley, Hampshire, UK, formed 4 July 1995. whirled, creating a noise practically identical to the crop Photograph © Steve Alexander 1998. circle sound. It was later discovered that not only have 50 + NEXUS rings around a central circle. www.nexusmagazine.com AUGUST - SEPTEMBER 2005