Thursday, 25 July 2013

Johann Bessler's small world of paragrams and chronograms.

It was while seeking for corroborative evidence that Bessler's MT 137 was derived from David Heinichen's circle of fifths (see my page at ) that I found a thesis describing how JS Bach, a friend and colleague of Heinichen, had included in his works a system known as alphanumerics; the subject of numerology and the old Hebrew system of Gematria involved the use of similar alphanumeric manipulation ..and of course so did Johann Bessler.

In 1947 Friedrich Smend, published the first of four studies in which he presented his theory that Johann Sebastian Bach had used a alphanumerics to incorporate significant words into his music as part of a grander scheme of compositional number symbolism. Smend collected historical testimonies and musical examples which confirmed his theory,

By the seventeenth century, alphanumeric were known about in many parts of Europe. They seem to have been most popular in German-speaking countries, where they were most frequently used as a means of solving mathematical puzzles,decoding cryptographic messages, in cabbalistic gematria and in the poetical paragram. It is common knowledge that Bessler was fascinated by paragrams and used them extensively throughout his works, most obviously in the form of chronograms.

These paragrams were described by a certain professor Christian Weise, in one of his many publications. He was headmaster of the school In Zittau that Bessler attended. He became Bessler's mentor and his teachings had a profound effect on him.  Professor Christian Weise was famous as a German writer, dramatist, poet, and teacher.  Although he was Rektor of the Zittau school, he had previously worked at the court of Duke Augustus at Weissenfels.  Following his success at designing, building and exhibiting his perpetual motion machine at Gera and Draschwitz, Bessler had moved to Wesenfels in 1714, where he worked on the new two-way version of his wheel.

JS Bach applied for the position of the organist in Weissenfels but failed to obtain the post then, although he wrote works in praise of the Duke later, so there was no bad feeling between them. In 1717 David Heinichen became a colleague of Johann Sebastian Bach and in 1721, Heinichen married in Weissenfels where he had been born and where he lived for much of his life. I continue to believe that Heinichen passed on to Bessler his ideas on the circle of fifths because they all lived and worked in close proximity to each other and their fields of interest, music and organs overlapped, but I suspect that the alphanumeric system so popular in Germany at the time was also discussed.

It seem to have been a small world in which Bessler lived.  His headmaster worked for many years in Weissenfells, where JS Bach and David Henichen also flourished. Bach used some of Weise's poetry in his operas.  He wrote his own version of the circle of fifths which, although it bore no similarity to Heinichen's was based on the same theory.  Weise wrote knowledgeably about paragrams and it would seem unlikely that Bessler would not have leaned all about these popular number-alphabets directly from his mentor.

I'm writing a longer article examining these paragrams as they may hold one of the keys to deciphering much of Bessler published te xts. I'll publish it later on one of my websites.

PS the above information I culled from a varierty of web sites too numerous to mention, other than wikipedia.




  1. If MT137 IS an allusion to the circle of fifths (and as you've revealed there's compelling reasons to suppose so) then there's two particular interpretations that seem most consistent to me:

    1) He / it's pointing to the 3:1 ratio of a perfect fifth - again, we have the recurrent 'clover' ideogram, per the three lobes of the Apologia wheel

    2) It could be another reference to inner (minor) and outer (major) loops of the cycle. Comments in Machinen Tractate seems to place particular emphasis on these types of configs. My current favourite hypothesis is a CF vs G asymmetry, the outer loop playing centrifugal force against gravity in the inner loop.

    I think pictographic hieroglyphics (as opposed to real, phonetic ones) is the main code MT is designed around. It defines elements in the earlier plates, then reorganises them into instructions in the later ones, that would otherwise seem nonsensical. These later contraptions aren't mechanisms but more abstract concepts. For instance i now think the scissorjack glyph refers to power conversions, per se.

    It's a culturally and language-agnostic means of encoding ideas, after all. While i don't doubt there may be cryptic paragrams and all manner of cabalistic cyphers besides, he surely wouldn't have placed too much stock in such culturally-subjective and temporal terms and concepts - not exclusively so, at any rate.. putting your vital message in a leaky bottle defeats the whole purpose.

    Not to deride the possible value of the search for such leads, amongst those capable of finding them. It's beyond my paygrade though..

  2. Thanks Mr Vibe. I agree that Bessler would not have wished to obscure his message in a confusion of cyphers overlaying his principle purpose which seems to have been the desire to leave sufficient information behind him to allow someone to work out how his wheel worked and thus prove that he was genuine and not the fraud history has labelled him.

    For me the problem lies in trying to decide how much of the apparently cabalistic content holds genuine information and how much, if not all of it, is simply Bessler showing off his knowledge of the subject. My feeling is that it is more than likely the latter.


  3. Just before i scoot off to work this morning; last night i noticed more possible consistencies between my current hypothesis and the Gera / Merseburg wheels:

    I'm thinking there's two CF weights, and two G weights, and each cycle contains one interaction in each field.

    So we have 4 strokes per cycle; a GPE output, a GPE input, a CF-PE output and corresponding input. We can then shuffle these four strokes and see if anything interesting falls out - and indeed, we may note that the one-directional wheels ostensibly self-started under a GPE output (there seems little other option)... whereas the bi-directional wheels, by all accounts (but particularly Wolff's) required a threshold of input CF-PE to be initiated.

    So 4 weights per cycle, choreographed into 4 actions. You can accelerate a wheel with a single weight given the right timing (was playing with such a system last night in WM2D), but somehow, doing it with two pairs, which must, logically, move up, down, in and out, in tandem in some special sequence... these inputs all cancel.

    There's four possible sequences (as depicted in the toys page MT138-141) for these inputs and outputs in the two fields.. one at least, will be interesting (tho i'm guessing its inverse may be a non-thermodynamic loss cycle)..

    Gotta go work, laters..

  4. John,
    here's a strange idea that's just occurred to me, do you think that Bessler may have come up with a device that vibrated sympathetically with the Schumann Resonance ?
    It may have been discovered by accident in his instrument making days.
    Hence the musical reference to the wheel of fifths.

    1. Just checked out sympathetic resonance on Wikipedia, very interesting, any musicians out there who can link them to the wheel of fifths etc.?

    2. Kinda - what immediately springs to mind is the Nice model (as in Nice, France) of planetary dynamics. This is the currently accepted 'standard' model for explaining planetary distributions (particularly those of our own system, Sol).

      From memory, the key mechanism of the theory is a 2:1 resonance in the orbital periods of the gas giants Saturn and Jupiter, and the combined gravitational effects of such conjunctions upon the inner planets.

      Hence, if the intended clue is the harmonic interval of the fifth (rather than the actual 'circle of fifths' mnemonic), it might be correlated with the combined centrifugal tug of say a 3:2 (equivalent to a factor of three of a given fundamental) orbital resonance between outer and inner wights - so for 3 cycles of the outer weights, we'd have 2 conjunctions with the inner ones, or 1.5:1 /cycle.

      This isn't quite the same thing as sympathetic resonance though, where energy exchange is facilitated by maximising the incident phase between resonator and wave. It might give a periodically boosted centrifugal tug on the inner weights, but can't increase the net energy of the system. Any gain in energy would have to come from the quantum fields that manifest the forces doing the extra work. Hence we wouldn't actually be synchronising with any 'latent' frequencies of the fields themselves.

      The schumann EM resonance (of the atmosphere's electrical activity) would presumably amount to a very low amplitude at any given location. There just wouldn't be anywhere near enough power available to explain that of Bessler's wheels, even if he had modern knowledge and materials to hand.

      Hence, rather than external resonances, if the 3:2 ratio is significant it must pertain to an internal resonance, between its own parts and/or dimensions. The actual mechanism and form of energy influx though would be entirely conventional force/displacement work, though.

      So for instance, perhaps a 3:2 ratio between the excursion distances, down vs up, of the gravitating and centrifugal weights, is the key. Or perhaps it alludes to the symmetry break Bessler found, a difference in force or energy between gravitating weights and centrifugally-flung ones, under certain constraints - ie. 3 units of output energy for each 2 units input, or perhaps a "3 steps forward, 2 steps back" dynamic.

      The actual angular distance between increments of fifths around the mnemonic is of course too small for anything significant to arise in a single mechanism - it's the same /12 increment size of a standard clock face, and not much could be happening between any two adjacent fifths as expressed in such terms of angular intervals.

      The simplest two methods for deriving the fifth (or the entire harmonic series) are, as i've suggested, ascending inverse-proportion integer ratios (so 2:1, 3:2, 4:3 etc), or, my own preference, ascending (or descending) integer factors of a given fundamental frequency (so starting with a 100Hz fundamental, a factor of two gives the first octave at 200Hz, a factor of three gives the first fifth at 300Hz, a factor of four gives the second octave at 400Hz, a factor of five gives the first fourth at 500Hz, and so on (NB. 300Hz / 100Hz, a 3:1 ratio, is equivalent to a 3:2 ratio (300Hz / 200Hz because of the octave equivalence principle between freqs in a factor of two relationship - hence 100Hz and 200Hz are 'equivalent' pitches, sharing the same pitch class as 400Hz, 800Hz etc. upwards, and 50Hz, 25Hz, 12.5Hz etc. downwards).

      As i've explained though, i think if MT137 alludes to the circle of fifths, or specifically, the fifth itself, it's more likely indicating a spatial relationship than a temporal one. Of course 3 is only .14 away from Pi... perhaps that's significant (ie. radial vs axial translations between CF and G fields, or something like this)...

  5. PS just a quick clarification of the above - i know this is all terribly tedious but if the MT137-circle of fifths correlation is valid then this basic aspect of music theory is worth making clear:

    It does seem incongruous that a 3:1 ratio could be 'equivalent' to a 3:2 ratio - obviously, we're not talking about their actual numerical values here; the basis of the equivalence is perceptual.

    Hence a harmonic ratio of 300Hz to 100Hz (3:1) is equivalent to a ratio of 300Hz to 200Hz (3:2) because of the paradoxical percept of equivalence between 100Hz and 200Hz - all halvings or doublings of a given frequency sound harmonically equal to it; so if one corresponds to say G3 then the others will be G2 and G4 etc etc.

    Thus, while most derivations of the harmonic series will describe the perfect fifth as a 3:2 interval, in reality 3:1, 3:0.5, 3:0.25 and 3:4, 3:8 etc etc. are also all perfect fifths in precisely the same pitch class.

    Any and all of these frequency ratios are fifths. This might seem an unnecessary over-complication, if only it didn't throw the range of possible interpretations so wide open..

  6. In my opinion it is not the use (profession) of the figure, but the properties of the figure itself that is of most importance. There are several professions that have used this circle (Musicans is just one of them). And as a frindly tip: It is also used as a seers tool.

  7. You're probably right. Still, continuing on the subject of resonance, over the past couple of days i've been playing around with a number of different systems and by far the most interesting ones are those with springs.

    They can have weird properties, speeding up and slowing down again chaotically. One particular clue that might fall into place here is that of a "bolt screwed into the axle to regulate its motion" - perhaps such a mechanism might've been used to fine-tune a spring's tension, to 'zone in' on an interesting point of resonance between internally-moving masses and distances etc. as a function of CF and G forces.

    My current most interesting config has two equal masses connected by a rigid rod, both sliding on the same diametric rail. The rod separating them is slightly longer than the radius, such that the innermost weight lies just slightly over on the opposite side of the wheel when its twin is at the rim. A single spring pushes this carriage to one side of the wheel.

    The interesting behaviour arises when the spring is balanced against CF and G forces such that at a given RPM the carriage can drop slightly against gravity as its force peaks at TDC, before weakening and thus allowing CF plus the spring to push it back against its rim stop.

    It's just a WM2D model but the damn thing keeps going until i run out of memory. No gain yet though. Just holds onto whatever energy you give it at start.

    No banana yet, but i'm sure i can smell it...


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