I showed how it represented the musical circle of fifths publicised by Johann David Heinichen, 1683-1729, a famous German musician who lived and worked in Weissenfels at the same time as Bessler. See the first two figures below. MT 137 on left, modern version of Heinichen's circle of fifths to the right
In part two of the same page of the website at
http://www.theorffyreuscode.com/html/mt_137_part_two.html, I showed how Bessler had included a hidden septagram or heptagram, which is a seven-pointed star drawn with seven straight strokes, and sometimes drawn inside a circle. Deleting the black lines on the original MT 137, or circle of fifths illustration, as in the middle figure below, and redrawing them to skim the edge of the inner black circle produces a heptagram, as shown in the third figure below. This geometric figure has numerous associations with occult and religious symbolism, but lack of space prevents those discussions here at this moment.
What I had not appreciated was just how difficult it is to draw a circle with seven equal divisions, and that means that the inclusion of the heptagram in MT 137 cannot be considered as a coincidence, but is deliberate. A circle divided into seven equal segments has seven interior angles of 51.428571 degrees. This makes it impossible to get an accurate measured angle and there is no system available using ruler and compass, although you can get an approximation by dividing the circumference by seven and walking a set of compaases around it, or simply dividing the circle into seven angles of 51.5 degrees. I drew a heptagram and tried inscribing a circle within it to match the inner circle in MT 137, it is not at all easy!
The two figures lend themselves to a simple code - draw the connecting lines from one point numbered 1 and then follow the logical progression clockwise or anticlockwise and you get, for instance in the septagram,
1 to 4
4 to 7
7 to 3
3 to 6
6 to 2
2 to 5
5 to 1 . The same applies to the dodecagram using the numbers 1 to 12.
Curiously the sides of the Great Pyramid is said to have a slope angle which is close to one-seventh of a circle, i.e. 51.4°, so I guess a reasonable approximation could be 51.5 degrees.
The number 51.42857 contains six repeating digits of 1/7, and is the best-known cyclic number in base 10. If it is multiplied by 2, 3, 4, 5, or 6, the answer will be a cyclic permutation of itself, and will correspond to the repeating digits of 2/7, 3/7, 4/7, 5/7, or 6/7 respectively.
1 × 142,857 = 142,857
2 × 142,857 = 285,714
3 × 142,857 = 428,571
4 × 142,857 = 571,428
5 × 142,857 = 714,285
6 × 142,857 = 857,142
7 × 142,857 = 999,999
The last one, 7 times, is a surprise.. (found at http://en.wikipedia.org/wiki/142857_(number) )
So another mystery beckons - why did Bessler include a heptagram in MT 137? 5 or 7 mechanisms?
JC
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