Tuning Gann’s Law of Vibration
The Search for the Musical System behind the Markets
By William Bradstreet Stewart
Those who have explored the subject of Gann analysis for some time will have discovered that there are several core subjects that are essential for understanding the science behind the markets. These core sciences were best defined by the great Pythagoras around 500 BC and called the Quadrivium: Arithmetic, Music, Geometry and Astronomy. Most Gann researchers are well versed in Gann’s use of geometry and astronomy in the markets and his unusual use of numbers behind his cycles and calculations has been an ongoing study for us all.
However, the subject of music as it applied to the markets has remained the most abstract and undefined of these essential studies, even though Gann’s characterization of his market science as The Law of Vibration makes a powerful allusion to the subject of music, since vibration is the basis of music itself. In fact, in all historical studies within the Esoteric Tradition, it is rather common to find numerous books on the subjects of esoteric geometry, or sacred geometry, alternative mathematics or numerology, as well as astronomy and astrology, but the subject of esoteric music theory has remained the lost cousin of the Quadrivium family, with very few studies of this key subject having been developed across history.
Aside from a few ancient texts on harmonics like that of Nicomachus and some vague references in Plato’s Dialogues, for 1000’s of years very few works in this field were produced. The post-Renaissance era saw Michael Maier’s alchemical work, Atlanta Fugiens, and of course, everyone has probably seen the beautiful artwork of Dr. Robert Fludd, presenting his musical theory of nature and the universe, with his “Divine Monochord”. But it is really not until the modern era that any serious studies of the esoteric nature of music were developed.
These probably began with Albert von Thimus’ historical survey of the subject, The Harmonical Symbolism of Antiquity (Die harmonikale Symbolik des Alterthums, 1870), which was the inspiration for the breakthrough work of Hans Kayser, but this work, like most others, has never been translated into English. As such, it is only in the last century that we saw the likes of Ernest McClain and the amazing series of works on universal harmonics by Hans Kayser begin to fill the historical gap in this tradition. Really, it has primarily been the numerous books of Joscelyn Godwin, Professor Emeritus of Music at Colgate University, that have brought us the main historical overview and analysis of the fragmented remnants of this almost unknown tradition.
It was Dr. Baumring in his 1980’s seminar series, Gann Harmony: The Law of Vibration, who first introduced Ernest McClain and Hans Kayser as containing critical insights into work of W. D. Gann. Since then, many Gann researchers have sought the only English translation of Kayser’s work, a small introductory book called Akroasis: The Theory of World Harmonics, causing it’s price on the used book market to soar into the multiple hundreds of dollars for the few rare copies in existence, as it had been pulled from publication due to textual inaccuracies.
Then in the mid-1990’s there was one book, Russell Smith’s Cosmic Secrets, which presented an analysis of G. I Gurdjieff’s system of harmonics as presented by Gann List author, P. D. Ouspenski in his wonderful work, In Search of the Miraculous, that inspired a flurry of new research into the application of harmonics to market price levels. But the conclusions of this research, while interesting and rather hopeful, never really developed any particularly breakthrough insights or applications, and the subject again fell into obscurity.
This led us, in the early 2000’s to develop the Sacred Science Translation Society, to translate Hans Kayser’s great 700-page masterpiece, The Textbook of Harmonics, from German into English through the funding of our tight-knit Gann community. This finally gave us access to the greatest work on Pythagorean harmonics, essentially THE Textbook on the Law of Vibration, and inspired a new interst in harmonics for the first time in millennia. Interst in the subject was primarily by serious Gann researchers and led to the funding of a further series important translations, including five further Kayser texts, the latest being our own recent, properly retranslation version of Akroasis: The Theory of World Harmony, this time by Professor Godwin himself, who is considered the leading expert on the subject, finally making it more affordable and easily accessible to the public. (See here for Dr. Godwin’s new Akroasis translation…)
With this new collection of works on harmonics finally available to the Gann community, we assumed that a much more direct pathway would be laid for the study of Gann’s Law of Vibration, and that the deeper implications and applications of Ganns’ work would be more easily accessible. Yet still, we saw very little new insight into Gann’s mysteries evolve through these works, and we continued to wonder when someone would finally crack this subject once and for all and reveal what Gann was really doing with these vibrational theories.
Well, that doorway has finally been broken wide open with the new work of Johannes Sundberg, The Harmonic Trader: Unlocking the Secrets of Gann's Law of Vibration. Past readers of Tradersworld may remember some of Sundberg’s articles over the prior years as he was engaged in deep research into the field of music and harmonics in preparation for this new work.
Initially, his musical work had been a long and rather convoluted chapter in his first book, The Secret Science of Squaring: W. D. Gann’s Lost System of Market Forecasting, which developed Gann’s system of mapping planetary phenomena onto market charts, showing what Gann angles really were and how, when overlaid with his with Gann’s principles of mathematical squaring, produced high-quality trade setups like Gann was famous for predicting and capturing.
However, by the time Squaring was finished, the book already exceeded 500 pages, and this final chapter on music was determined to be incomplete and in need of further research and development, so it was saved to be better developed in his second book. Little did either of us realize what a gold mine of wisdom was lurking behind those initial ideas, and how far they would develop with another 2 years of research on top of his prior 25 years. Neither of us imagined that this work, centered around music theory, would evolve into the utterly profound text that it has become, even surpassing in quality and application the ideas in his first book.
Sundberg, in his research of the last year and a half, dove more deeply into music theory than any Gann analyst I have seen do so up to this point. Besides studying the traditional sources mentioned above, he researched the entire history of harmonics and tuning theory to discover that there were no fewer than 14 core “tuning systems” developed over the past 2500 years with even more variants. The music that we are familiar with in the modern western world is merely ONE of these dozens of different possibilities, with that system alone possessing 12 differing tonal scales, which remains the only tuning system that has ever been applied to Gann analysis.
In exploring Gann’s original work, Sundberg also discovered that, as usual, Gann himself provided very little guidance and technical detail for his harmonic analysis. Students of Gann analysis will be familiar with Gann’s 1/8 divisions of price, essentially representing the 8-note division of the octave. Gann would then throw in the 1/3 and 2/3 levels, giving us a scale model much like Dr. Fludd’s model above. But that was essentially all he openly laid out in his teachings, which was not much to go by to say the least…
Those who have worked with these levels in the markets will attest to the fact that while the 50% retracement (a sub-octave) or a doubling of price (an octave) is quite common in the markets, ongoing divisions of 1/8ths are not all that reliable as absolute support and resistance levels. Really, it’s hit and miss at best, and not something that provides much practical use for trading. It soon became clear that Gann had presented nothing more than a conceptual template for a basic harmonic grid but without ever clearly defining any further specifics, unless you look very closely into the details and know exactly what you are looking for, as Sundberg came to understand.
Such specifics, to begin with, would be what particular scale the harmonic structure would represent. This is important because, as anyone who actually plays music will realize, the sequence of steps between each note varies according to which key the scale is played in. This can be easily seen on a piano keyboard where there are 8 white keys and 5 black keys in each octave, as shown above.
However, you will note that some white keys have a black key between them, and some do not which is where the variations in the sequences derive from. Each step between white keys measures a whole-tone, and each step between a white and black key measures a half-tone. Therefore, if you count 8 steps from one particular note to its repeat on a higher or lower octave, depending upon which note you begin with, or which scale you are playing, you will get a different sequence of mathematical tone-intervals from one start to end point vs. another.
What this means is that each different “key” of the scale has a different mathematical sequence between the notes and, in fact, can also have a different number of potential “steps” from start to finish in that particular “key”, as shown in the image to the left, where the red dots show the mathematical sequence of the notes in each scale.
In modern western music, you don’t have to worry about this because, due to the “equal-temperament scale” with a set sequence of intervals, musicians could just change to the same “key” and all play together in harmony.
But in the markets, we have to consider this issue more carefully, since the layout of the mathematical sequence will completely shift our support and resistance levels depending on what “key” the market is “tuned” to and the sequence of support/resistance levels that it will produce.
The simplified template that Gann presented with his 1/8 divisions represented nothing more than a basic C-Major scale, and the similar problem with the Russell Smith’s popular book, Cosmic Secrets, was that the entire book also concentrates upon nothing but a base C-Major scale, then develops its entire thesis from that basic scale sequence. Smith also provides some highlighted importance to the whole-step white-key intervals as a sort of “pause” followed by a new “impulse force” or “shock” at these mathematically inconsistent points. Many Gann researchers thought sounded a lot like market action and sought within the markets, looking for such a “pause” and new “impulse shock” after this whole-tone step, which sometimes occurred but often was just not there.
It never seemed to occur to these researchers that by changing from this base C-Major scale template to one of the dozen other musical “keys/scales”, that the placement of these “pause/impulse” points would shift around to different locations within the sequence, producing completely different mathematical variations within each key, which would very likely lead to discovering the proper mathematical sequence of price expansion within each specific market.
If you are applying these principles to measuring (or predicting) support and resistance levels in the financial markets, these variations will make all the difference in the world between providing the correct support and resistance or not! Measuring a market in the wrong “key” will produce mediocre if not useless results, mediocre only because the “equal temperament” turning of this system still has equal steps between many of the notes which will seem to show order, with the variants shifted around to different places according to the particular key.
But depending upon where the sequence begins and where the variants are then placed within the sequence, differing results will be produced which will vary anywhere from “sometimes working” to “totally off” depending upon what key you are using with what market, since different markets have different “keynotes”, as Gann and Baumring both taught us. So, finding the proper “keynote” of the market and then applying the proper scale will give the answer that provides the right or wrong interval structure to a market’s price expansion. This is why being able to derive the proper “keynote” of a market is critical to doing any harmonic analysis at all.
So, when people use Gann’s simple 1/8 divisions without understanding the underlying nature of musical scales and octaves, they are applying a generalized and often incorrect C-Major scale template to the markets which will only be correct perhaps 1/12 of the time, since there are 12 different keys in the octave. At times it may happen to fit okay, which is what most simple experiments find, but for a highly predictive and accurate application, it is almost useless. This is why very few consider this Gann application to be anything particularly important.
However, this is not the only issue at hand. Understanding the market’s “keynote” and what specific scale you should be using for each market is a critical step, but it is not the first step. There is a higher order consideration which must also take place prior to this analysis, and this is where few, if any, Gann researchers have explored. That issue is what specific TUNING should be applied on any or all markets, which takes the analysis to another dimension!
As discussed above, both Gann and Smith presented a C-Major template based upon the western “equal-temperament” tuning system (though Gann added the 1/3 and 2/3 intervals too), developed in the 18th century primarily so that the newly developed keyboard instruments could easily be played together with string instruments. But is this the proper “tuning” that we should be using for the financial markets? This subject has remained unexplored until the recent work by Johannes Sundberg, who has now answered this question once and for all…
When one looks back over the history of the development of musical systems, one discovers that there have been a good 30 different turning systems that have been developed across the past 2500 years in the western world alone. Each of these tuning systems presents a different sequence of notes between, say, C to C, as the base scale, with varying values for the half-tone and whole-tone steps. Each of these “tuning systems” produces a different “sounding” music since the tones that make up the scales have different tonal or frequency relationships. The chart above shows various “tuning systems” plotted on a 360° grid. It looks strangely like Gann’s 360° Spiral Chart! Could Gann’s chart actually be a harmonic grid?
In modern days, we are all accustomed to the standardized “equal temperament” tuning system mentioned above, and all modern music created over the last couple 100 years has been written according to these tonal relationships. But prior to this there were multiple systems in competition with each other, each with different mathematical sequencing, so could it be possible that one of these other “tuning” systems might be more functionally appropriate for market analysis, or perhaps even several of them, according to different market types? This is the study that Sundberg dug deeply into, and it turns out that the answer is a resounding YES!
So, before even beginning to experiment with finding the proper “scale” to overlay upon a market, you first have to know which “tuning” system to use to generate those “scales”. Once the researcher understands the proper “tuning system” to apply, he must then identify the “keynote” of the market he is analyzing which determines the “scale” to use matching the “keynote”. With this sequence of steps properly applied, a new level of precision is attained, one that is shockingly powerful and accurate. It was surely this procedure that Gann was using himself in his harmonic analyses, though he leaves nothing but thin and veiled instructions as to how to come up with all of this, that seemingly no one before Sundberg ever completely figured out.
Now, having discovered this series of steps to determine the correct harmonic structure to overlay upon the market, the first tool this insight produces is a set of powerful support and resistance levels in the markets where excellent trades can be taken with very tight stop loss placement. However, this is only the first step, though probably the only application most analysts have ever considered in using this sort of tool.
The next and more powerful insight is that when one has the properly attuned octave set to the keynote of a market, the market will bounce through these harmonic levels quite beautifully, but more importantly, Sundberg discovered a powerful rule which identifies a “signal line” right where the final high will occur in the market. This is one of the most simple but powerful trade setups you ever see in the markets.
In fact, over the past year while experimenting with these harmonic grids, I watched and documented Sundberg trade well over a dozen, perhaps two dozen, of these simple setups, which are documented at this link, and I cannot remember ever seeing him have even one losing trade with this simple technique. Let me provide you with a few examples following.
This first chart was done by one of Sundberg’s first pre-order clients for the new book and sent to me just the other day as Gold hit its all-time-high. It shows how the “signal line” perfectly caught the new top on COMEX Micro Gold Futures.
You can see a sequence of harmonic lines run up the chart from the last low, ending with Sundberg’s special “signal line” perfectly calling the final top. A short trade would have been placed at that exact trigger point with an extremely tight stop, and indeed the market even closed at the low of the huge bar that day with 110-point profit, and we’ve seen a 191-point drop over the last 5 days since the top.
Now, just because this “signal line” was triggered, it does not mean that there is still not a potential for higher prices in Gold. When the “signal line” is hit, it will generally produce a nice tradable pullback from that point, but when it comes back up again, IF this “signal line” is broken to the upside, it provides even a more powerful buy signal, because when that trigger point is broken, as the market then enters a new growth phase, and it’s natural inclination will be to make a good run into new territory, providing an excellent opportunity to trade the bull side breakout, or the bear run if it were a downside break of a “signal line”.
One would also note that this is the 4th time that Gold has topped around this level, and we all know what Gann says about the “4th time at the same level”. So, in knowing where these “signal lines” are placed and remembering Gann’s rules, we will carefully watch for the first violation of this level as high-probability trade setup will come if the “signal line” is broken on the upside.
One will also find that these harmonic levels integrate beautifully with the planetary Gann angles Sundberg taught in his first book. When I sent this client’s prior “signal trigger” to him, Sundberg replied by sending back the above chart showing the long-term planetary angles from his first book which cross-confirmed the same trigger point using an entirely different technique, but demonstrating that the “signal line” would have also been crossed by a planetary angle, providing an even more reliable indication of a key resistance level.
This led to the next step in generating even more and better high-probability trade setups using the combined input of the musical harmonics, the signals lines, and the proper application of Gann angles as planetary angles. Sundberg discovered that combining these multiple techniques led to the creation of an endless array of powerful turn signals in the markets which worked on any time level, even intraday. In fact, it seemed that the crossing of planetary lines and harmonic interval lines produced even better turn indications than just the crossing planetary lines with each other.
But could there be even more such lines? Sundberg realized that the more activated “crossing elements” could be found, the more high-quality trade setups could be generated. As he explored further, he discovered there were a number of different types of “diagonal angles”, as Gann called them, besides just Gann’s planetary angles, that worked beautifully to generate different kinds of turns at different points in the market according to what style of line was used. This began to explain the purpose behind Gann’s different approaches to generating angles, whether geometrically, harmonically or astronomically, as each different type of line produced crossing points on the harmonic grid at different points in price and time, identifying different key points or turns in the structure of the market. Sundberg managed to find out how Gann´s different, seemingly uncorrelated techniques, actually fit together in perfect harmony. This is shown on the chart to the right, which is NOT using a planetary line, but still provides excellent turn signals at each crossing.
The difficulty was in knowing what “tuning” of the harmonic lines was going to produce the most accurate turns with each type of “crossing angle”, and this was what led to the 18-month search for the “tuning” system with the highest accuracy. It further led to the recognition that even with the proper tuning, one also had to have the harmonic scale set to the “keynote” of that specific market, as well as sequenced with the “tone” of the starting point on the chart, so determining all of this became a much more complex puzzle than it first appeared to be.
But the payoff was beyond any expectation, because once the proper musical scale was set, not only did the planetary lines generate beautiful turns at each harmonic crossing, but each different type of projected angle generated perfect turn signals over and over again IF the right tuning system was used.
The charts shown here provide excellent examples. Note that every time these angles cross a harmonic line, we have a tradable turn in the market, marked by red arrows or vertical lines. And each of the angles shown here is generated by a different technique.
There is only room for a few examples here, but we have dozens more sample charts compiled at this link. But the absolute key to this application was the development of the correct tuning system for the markets, followed by the scaling of the harmonic intervals to the “keynote” of the market. Without these steps, or using Gann’s standard 1/8 and 1/3, 2/3 divisions, it doesn’t work.
After discovering these applications, Sundberg realized that this could likely be what Gann was intending with his plastic “Master Chart Overlays” that he was developing in the mid-1950’s near the end of his life. In his last marketing brochure, Gann mentions a new set of tools that did NOT require following all his other rules. This was something new for Gann, since he often said in his older courses, “you must use all of my rules all of the time”. But with these new plastic overlays, Gann changed his perspective entirely and created something that was a standalone tool and completely based upon diagonal and horizontal angles and the crossing of those lines alone.
These plastic overlays have harmonic divisions drawn horizontally up the chart, with sets of diagonal angles projected from the different corners. Gann’s 4 templates that have survived show geometrical angles, but anyone who understands how to adjust geometrical angles to astronomical angles could easily have drawn these overlays to show any one of Gann’s various “diagonal angles” sets. And the horizontal harmonic lines could easily have been drawn according to the specific harmonic scales that were “tuned” to the “keynote” of the market the overlay was built for. With this logic, each market would have its own original set of “Master Chart Overlays”, something like that shown on the chart below, which could be easily reused.
Could this be the final advanced tool set that Gann advertised in the last days of his life called The Master Mathematical Formula for Market Predictions? We know he had one of those specific overlays that was “tuned” to the Soybeans all-time low of 67-cents. Perhaps this gives us confirmation that Gann did actually make his own “Bespoke Master Charts” for each market he traded. This next chart shows an example of a “Bespoke Bitcoin Chart” where each of the elements of the Master Chart was drawn according to the specific requirements for the Bitcoin market. Gann could have easily done this for each different market using his “plastic overlays”.
Anyway, these are just a few examples of at least a dozen brilliant new Gann techniques that Sundberg discovered with his latest explorations into the depth of music theory conjoined with planetary charting. But this work provides a perfect example of how some simple and subtly implied reference of Gann’s can lead to a plethora of powerful trading techniques that literally no one in the Gann community has ever figured out or used before, even 70 years after Gann’s death.
For more information about Johannes Sundberg’s work please see his author page at the Institute of Cosmological Economics at this link or to reach out to him directly, send an email to insitute@cosmoeconomics.com and I will forward it on to him. His new course is being publicly released this month, December 2023.
