Some Findings on Crop Circle Formations
By Colette M. Dowell  N.D.
Offered by permission of Borderland Science Research Foundation

I was in a relaxed state one evening when the words magnitude, alternate,
melodic, harmonic, intervals seemingly were narrated in my mind, along with
images of the crop circles.
Having a musical background I interpreted this as vibrational patterns that
could be notated in musical terms.  Later I read (then an unpublished paper, now
published in Crop Circle Secrets Vol 2 and Cosmos Journal, Vol 2, No 1) an
article by Professor Gerald S. Hawkins, astronomer and author of "Stonehenge
Decoded", stating his findings that after tabulating the diameters of the crop
circles as measured by Delgado and Andrews, the ratios directly corresponded to
the same ratios of the Major Diatonic Scale of Music.  (This being a scale of 7
notes repeating in sequence on the 8th step or octave which double the value of
the 1st step and so on.)
The key of the Major Diatonic Scale depends on the initiating frequency or tonic
of the 1st step.  Our modern western musical scale has been tempered with each
interval of the steps of progression having an equal value, creating a chromatic
scale of 12 steps.  The progression of the 12 step chromatic scale is based off
of the 12th root of 2; 1.059463, or rounded off to 1.06.
The equally t
empered scale was developed in the late renaissance for practical purposes of
standardizing instruments and notated music.  It was impossible to modulate to
another key remaining in a true major diatonic scale.  Music became monotonous,
and creativity was stifled.  Equally tempering the scale became the easy answer
to both maladies.  With this form of tempering, many of us in the western world
have been unaware of the existence of the true Major Diatonic Scale.  
If the Crop Circles are possibly suggesting we take another look at the ratios
of the Major Diatonic Scale, then what would the value of the initiating tonic
be and what are we to find?
Knowing that 360 is significant in both tetrahedral mathematics and the
revolving system in which we live, I chose 360 as the tonic for initiating the
ratios of the Major Diatonic Scale.  I set 360 at middle C, in representation of
C Major Diatonic Scale.  I calculated 10 octaves above and 10 octaves below
giving me a total of 21 octaves of numbers to review.  I was amazed at my
findings.
I had broken into a number system clearly corresponding to 5 and 6 fold
symmetry, angular measurements of tetrahedral mathematics, the diameter of our
moon, the given value of the precession of equinoxes, angular measurements of
the great pyramid and values for the Ancient Egyptian system of measures and
weights. (See figure 1)
My first Crop Circle surveys to review were measured and drawn by J.F. Langrish. 
These surveys were measured using both the metric system and the English
Measure.  On surveys measured in the English system (12 inch foot), I recognized
specific numbers of measure that directly corresponded to the numbers from the
360 Major Diatonic Cover Sheet.  I began looking at numbers as entities,
symbolic of a system of multi-level coding. Eg. #1, 3' 6" not as 3.5, but as 3.6
eg. #2, 21' 6" not as 21.5, rather 21.6.
I went further to even break up the numbers such as 36' 6" as individual
separate entities, e.g. 36 and 6, so I could then multiply, divide, add and
subtract them.  I began breaking into a seemingly mathematically coded process.
Exact numerical values corresponding to Earth, Moon, 5 and 6 fold symmetry and
aspects of logarithmic processes began repeating themselves.  I found that many
diverse techniques of analyzing these numbers still yielded the same significant
numbers.  At this point they could not be random.  There was a definite purpose
for these numbers to keep showing.  My response was to accept the numbers and to
now evaluate what their possible meaning and values are.  What are they trying
to convey? 
The Barbary Castle Crop Formation is unique in that it combines circles, a
spiral, spokes and a 2-D projection of a tetrahedron. It is kiltered off its
axis and exhibits 2 flex points; one on the middle left side of the tetrahedron,
point C, and one on the upper right side of the tetrahedron, point E.
Richard Hoagland had demonstrated flex point C, when designated as a polar
projection, maintains a latitude of 49.6 degrees when straightened into singular
line form from the upper top vertex of the tetrahedron point D, to the lower
left vertex point B.  (49.6  e/ radians), (The radian is a unit of angular
measure that uses the radius of a circle as its base unit.)  It is of further
interest that English measure of the vertical aspect of the tetrahedron's outer
satellite ring's outside diameter measures 49' 6".  49.6 repeated.  From the
same vertical aspect, the inside diameter of the satellite ring is 42' 6". 
Added to the 26' 8" vertical diameter of the inner circle, the sum equals 69'
4". (69.4 = e/ radians) (See figure 2.)
In viewing the stepped spiral, the inner circle's diameter is 7', added to the
inside diameter of the 1st step of 14' 6" the sum is 21' 6".  (2160 total corner
angles on a cube, 2160 miles mean diameter of our moon.)  The bearing from the
right vertex of the tetrahedron point A, to the center of the inside circle of
the stepped spiral point Y, is 108 degrees.  (1080 = M-+ total corner angles on a
cube, 1080 miles the mean radius of our moon.)  The bearing of 274 degrees
extending from the 3rd step from the inside circle breaks to 27 x 8 = 108.  
Extending the left vertex towards the center circle of the tetrahedron notice
the values given for the diameters of the satellite rings, along with the
extended inside vertex's of 4'.  A graphic has been provided to illustrate how I
broke the numbers to receive a value of 2592.  (25,920, total vertices from six
dimensional view of a Polytope 221; which is a multi-dimensional figure able to
project its tetrahedral and triangular form through many dimensionalities,
25,920 years projected value for Precession of Equinoxes.)  (See figure 2.)
Now returning to the flex points C and E, flex point C had exhibited a
particular purpose in expressing 49.6, but flex point E was still a mystery.  In
working with the numbers on the extended left inner vertex leg of the
tetrahedron point B, to the center point of the inside circle of the tetrahedron
point X, the number 148 kept repeating.  I recalled that the bearing from point
D, which is the vertical vertex of the tetrahedron, to flex point E, was 148
degrees.  I connected point B to point E with a straight line.  I began to see
in my mind many lines representing multiple tetrahedron.  In conversation with
my colleague Erol Torun, I asked if there was possibly a geometric figure which
could represent a multilevel (hyper) tetrahedron.  He suggested I might possibly
be referring to the 5 Cell (a hyper tetrahedron (4D) projected into 3 space.) 
He faxed me the 5 Cell and I knew immediately that it was the image I saw in my
mind.  I proceeded to illustrate the 5 Cell by continuing to connect the point
by means of following the mathematical guides.  A 5 Cell was to overlay the
tetrahedron by means of flex point E.  (See figure 3)
I felt there was more to find in connection with the flex points.  I drew a
straight line from the lower vertex of the tetrahedron point A, to flex point C,
from flex point C to flex point E.  I inverted the tetrahedron and matched up
the flex points, exhibiting a 2-D projection of two interlocking tetrahedra. 
This was significant, if the flex point were any higher or lower on the legs
they would not have lined to create in effect, an interlocking tetrahedron. 
(See figure 4)
Erol Torun's analysis of the stepped spiral showed it to follow the same
equiangular logarithmic spiral pertaining to the 12 step chromatic scale
progression of the 12th root of 2 ; 1.06.
My visual approach to the stepped spiral was to view it as being symbolic of the
Major Diatonic Scale, as well as the 12 step chromatic progression.  Notice that
beginning with the right side vertex of the tetrahedron point A which connects
to the spiral, there are 7 steps including the inner 7' diameter circle.  If you
include point A as a step you have a complete octave or 8 steps with 7
intervals.  Erol plotted the Major Diatonic Scale against the spiral and indeed
found it to closely maintain the same equiangular spiral.
Please note that the distance in feet from the center of the inner circle of the
tetrahedron point X, to the right side vertex point A, is 106 feet. (1.06 ; 12th
root of 2.)  This possibly suggesting that mathematically the analysis is
proceeding on the correct path.  I find this to be true in many instances where
a specific number repeating itself regardless of the equational process, repeats
itself once again in a line, angle, or bearing value in close proximity.  This
connection so far has only been true with the English measure not the metric. 
However, at this point I have done limited study on the metric surveys, so it
may be premature to make a hard statement suggesting that the English not the
metric, is the absolute preferred system for the decoding of the mathematical
equations.  There is however substantial evidence revealing that the English
measure, not the metric, is the correct approach to the underlying complexities
for some of the particular mathematical coding found thus far.
Professor Gerald S. Hawkin's finding of the ratios of the Major Diatonic Scale
in the earlier Crop Circle Formations were arrived at through 2-D geometry and
application of division of members within the various formations.  
Through my process of analysis I find that the later more complex formations are
repeating the same ratios.  Of further interest I have found structuring the
ratios with Middle C base tonic  of 360 as opposed to the modern conventional
Middle C tonic of 261.6, there is a direct mathematical correlation of line,
bearing and angle measurements within  the formations exhibiting the same
numeric values of cycles per second in the progression of steps (notes) of the
Major Diatonic Scale.  Once again, however, I have found this to be true using
the English system of measure, not the metric. 
This has been only and introduction of personal process in treatment and view of
the Crop Circle Formations.  In future articles, I will share my findings on
other Crop formations and various studies.