Paul Vigay provides a quick introduction to diatonic ratios and their relevance to crop circle patterns

First proposed by retired professor of astronomy at Boston University, Gerald Hawkins, the theory of linking crop circles to diatonic ratios became quite a big portion of my research. On this page I hope to describe some background research and what diatonic ratios are.

One of the first researchers to point out links with musical scales was Gerald Hawkings, a retired professor of astronomy at Boston University. Having worked at the Harvard-Smithsonian Observatory in the 1960's, he had already done much research on the astronomical importance of Stonehenge. After earning a subsidiary degree in Pure Mathematics from London University he analysed aerial photographs and ground surveys of crop circles and was surprised to spot a clue to their possible origins - lying in the ratios of musical notes.

The first link Gerald made to crop circles was in November 1990 when he discovered that, to his surprise, the ratios of musical notes showed up in the crop fields of England, in two different ways - for concentric rings it was in the relationship of the area of the larger to the smaller circles, and for satellite circles around larger circles it was in the diameters. Interestingly, numbers representing sharps and flats in music did now show up in the crop patterns.

Gerald stated that if we examine the exact frequency of the white notes on a piano we will find that, with perfect tuning, the note middle C has a pitch of 264Hz (vibrations per second). If we play the C note in the octave above (C') we will find that the frequency is 528Hz. This is exactly double, giving a ratio of 2:1.

If we now examine every note in the major scale we will find an elegant, yet exact, diatonic ratio - shown in the diagram below.

Using these ratios between the notes, we find that each note has a unique frequency;

Note Ratio Frequency (Hz)C 1 264 D 9/8 297 E 5/4 330 F 4/3 352 G 3/2 396 A 5/3 440 B 15/8 495 C' 2 528

These ratios are fundamental to music because as we rise each octave above middle C, exactly the same ratios are used but doubled. For example, E' (each ' is used to represent the rise of one octave) has a ratio of 10/4 and A'' gives 20/3. These ratios also give the intervals in all the notes in the other major keys too.

When we started analysing the ground surveys of crop formations we started to find that the same diatonic ratios started showing up in the relationship between various elements of the formation - either the ratio of a circle to it's ring, or perhaps a large circle surrounded by smaller satellite circles. Gerald analysed the entire sample of circles accurately measured by Colin Andrews and Pat Delgado between 1981 and 1988. Out of a total of 18 formations, 11 gave diatonic ratios.

In 1988 a formation was discovered at Corhampton in Hampshire which not only contained diatonic ratios, but also precise Euclidian mathematics. This ultimately gave rise to five crop circle theorems and also gave me the inspiration for my music composed from crop circles.

The tuning by which notes are related by whole number ratios is known as *just intonation*, and are what the human auditory system recognises as *consonance*. The significance of *just intonation* has been recognised for at least 5000 years.

My research has led me to investigate this and other types of musical tuning methods, such as the more modern *equal temperament* tuning system. Much of this is outside the scope of this introductory article. However, I hope to write up some of my more advanced notes in the near future.

- Tuning Systems - Catherine Schmidt-Jones' overview of music tuning systems.
- Frequency of Middle C - an interesting look at the varying frequencies for middle C.
- Diatonic scale - Wikipedia entry.
- Just intonation - Wikipedia entry.
- Equal temperament - Wikipedia entry.

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