This blog is based on a draft version I wrote a couple of years ago and I’ve added a few illustrations to help my explanations. It’s more of an update on work I’ve done but not all of it has been shared before. I hope it’s of interest.
The presence of a pentagram in some of Bessler’s drawings is well established and it is generally recognised that it is at least an indication of Bessler’s intention to point out at every opportunity his fascination with the number five. See above for an example of the pentagram in a Bessler illustration. His frequent use of alphanumeric and the Hebrew atbash and albam codes also reflect this apparent obsession.
The angles in the pentagram are exclusively multiples of the number 18; thus the numbers are 18, 36, 54, 72, 90 and 108 - plus the number 5. With the the benefit of his various codes, Bessler could manipulate the number 5 as an ‘E’, the fifth letter of the alphabet, or as an atbash cipher, the letter ‘R’, which in turn becomes the number 18. The letter ‘R’ being the 18th letter of the alphabet chimes nicely with the smallest pentagram number. This applies to all the pentagram numbers Bessler used.
|The Golden Ratio in Merseburg Wheel - 24 squares and 24 rectangles, 24 numbers.|
The golden ratio is embedded within the construction of the pentagram and it is also present in all of Bessler’s publications, but one particular place where it seems to be absent is Bessler’s Maschinen Tractate, in particular MT 137. The illustration is a dodecagram, with no clues as to its role in the MT - it almost looks like an afterthought, with no discernible mechanical design or purpose.
My initial speculation which, I still firmly believe is correct, is that MT 137 illustrates something which is used by musicians today. Johann David Heinichen, 1683-1729, a German musician, introduced the concept known as the ‘circles of fifths’ in 1711 (he called it Quintenzirkel). He was born, raised and got married in Weissenfels, the same place which Bessler moved to after Draschwitz, and close to Obergreisslau. Despite his interest in music, Heinichen practiced law in Weissenfels until 1709. However, he maintained his interest in music and was at the samne time composing operas. In 1710, he published the first edition of his major treatise on the theory of music (Thoroughbass). This contained his theory of circle of fifths.
|A Modern version Heinichen’s circle of fifths.|
Bessler lived in Weissenfels in 1714 and had a history of building organs. In 1717 Heinichen became a colleague of Johann Sebastian Bach at the court of Prince Leopold of Anhalt-Cöthen, then went on to be Kapellmeister to the Elector of Saxony. In 1721, Heinichen married in Weissenfels. In between these events his success attracted the attention of Duke Moritz Wilhelm who appointed him to be court composer at Zeitz. As many who have read my biography about Bessler will know, Moritz Wilhelm’s court was home to many learned men who persuaded the great Leibniz to investigate Bessler’s claims. There is a lot hof correspondence about Bessler between those members of the Court at Zeitz.
So it seems highly likely although not proven, that MT 137 represents Heinrich’s ‘circle of fifths’. This fits in with Bessler’s obsession with the number 5. The ‘Circle of Fifths’ is an easy way to find out which key a song is in. It tells you how many sharps or flats are in a given key. It is called the ‘Circle of Fifths’ because as you go clockwise, you go up a fifth. Even though I don’t claim to know much about musical theory I understand that you start on, say middle C, then count round the edge of the circle five places which brings you to F. This same technique is applied for any note.
However there is more to MT 137 than meets the eye. Recently I discovered the reason for MT 137’s inclusion in MT and also why it was placed where it was. First, remember that Bessler had studied clocks and was able to repair them, also I have posted information here previously, about the presence of a hidden clock in two of Bessler’s drawings. Next note that MT 137 is a dodecagram, in other words it has twelve points on the circumference not unlike a clock.
So far then we have a clock, a circle of fifths and a possibly missing phi, or golden ratio. No where have I found any reference to phi being an integral part of the dodecagram and yet… MT 137 is a circle of 360 degrees. The number for Phi is about 1.618. If we divide 360 by 1.618 we get 137.5 degrees and 222.5 degrees. If you look at a clock face and you have the hour hand at twelve o’clock and the minute hand at five o’clock, the angle between them is 137.5 degrees, and the larger angle is 222.5 degrees.
Examples below of when the angle between the hands is 137.5 and 12.25. There are, in total 44 golden moments, that is, times when the angle between the hands of the clock equals the golden angle 137.5.