Gann Science
The Periodic Table & The Law of Vibration

Eric Penicka

Sample Charts & Content



·        Chapter 3 & 8 – The concept of the Law of 3 and law of 7. This is the beginning base leading to the more complex analysis in Chapter 20.

·        Chapter 9 – Atomic theory, how to find, test, and prove the numbers, then breaking down the triads, and generating the Master Number Set.

·        Chapter 10 – Keely’s harmonic, octave and third, the 3, 6, 9 secret is attributed to Tesla, but it was Keely’s main tool.

·        Chapter 11 – Biblical ties to the theory. Time, times, half a time. More on application of Keely concepts.

·        Chapter 12 – Russell Periodic Table, the circle of fifths analogy, and phi price and time expansions and contractions.

·        Chapter 13 – Luo Clements’ name and date numerology, testing the harmonic number theory, defining the keynote.

·        Chapter 14 – New ratios and Time Cycles. Various indications for support and resistance and turn times.

·        Chapter 15 – Defining Composite Cycles and applying them to the market to develop a new approach not based upon market price but upon the Master Number Set.

·        Chapter 16 – Creation of composite cycles not using any price action. Creating price action composites and using them in tandem.

·        Chapter 17 –Gravity centers from the periodic table, Keely’s neutral center, triangulation as proof of cause.

·        Chapter 18 – Volume as the third dimension, not volume as in shares or contracts traded. A new dimension.

·        Chapter 19 – A look at AAPL in the key of ---, checking harmony and dissonance.

·        Chapter 20 – The Jonah riddle explored, the meaning of the 3 days and 3 nights. Time, times, and half a time as an integration of a Biblical verse to markets.

·        Chapter 21 – Gann fans, vibration of the market set by number. The true source of vibration and its application according to Clements’ number harmonics.

·        Chapter 22 & 23 – The grand synthesis. How to integrate these techniques into a practical analysis and trading methodology.







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A recent swing trade setup example using the periodic table method.

Tesla (TSLA) is a popular and volatile stock that offers good trading opportunities.

At the time this trade was setting up there was a lot of negative news coming out that Tesla was about to go bankrupt.  This news sent the stock plummeting.

This is further proof that news doesn’t drive the market.  Natural law drives the market and the news is just a byproduct that may have a temporary influence but is not a causal factor.

A trade on this stock was indicated as TSLA was trading down and a potential low was possibly coming due on April 2nd, 2018.

There were multiple time points and 3 price indications coming into play on that day.

The price points were derived from the primary method which projected the low not to exceed 245.  Two octave structures indicated a price level convergence at 244.

This gives 3 price points converging at 244, 244 and 245.

There are also two price measurements that are called “Keely Harmonics” that converge at this low which are illustrated in the Gann Science book and are powerful enough to be used as stand-alone reversal projection points.

The time structures used will not be presented here.

Gann would have said in The Ticker Interview in 1909 that Tesla will not penetrate below 244 without a significant reaction in the upward direction.  This is exactly how the calls he made on stocks like US Steel, Auburn Motors, and Union Pacific were made.

The stock traded down to 244.59 on the morning of April 2nd.  A trade could be taken at that level with minimal risk.

On this day the US stock indices were trading down and made morning lows. TSLA hit 244.59, a low which was coincident with the indices and started trading up. 

The indices traded up as well but then they rolled over and continued down. Tesla held its ground strongly and did not go lower.  The stock proceeded to run up hard for six consecutive trading days in the face of all the bad news.

The swing high area after the trade was put on was also known in advance as a short-term target at 308.  The actual high was 309.50. 

Lost motion is a bit more nowadays than at the time of Gann due to larger group of market participants, program trading, and the additional trading activity not in the market in the early days.

This trade had a potential of a $65 profit most of which could have been garnered by users of this method in six days.

These calculations are made without the use of the Square of Nine nor any of the other number wheels.  This is not to say they don’t have a purpose. But only that they are not a necessary part of the Law of Vibration.

The chart below made with Wave 59 software identifies the entry and exit points for this trade.


Though the primary methodology presented in Gann Science is the technique of using the Periodic Table along with musical harmonics to trade, other science and math concepts are explored in Gann Science that traders can use to find further tradeable mathematical points of force in the market. These and other techniques presented in the book are still pretty powerful tools and can stand on their own legs as viable trading tools, even though considered secondary to the primary Law of Vibration technique taught in the book.

One of these ideas is the use of mathematical constants in trading.  These constants have great predictive value in their own right. Numerous scientific formulae and mathematical constants will work in the analysis of stocks and commodities. By using them as multipliers, or factors, traders can determine additional pressure points in the market.

These pressure points are what were referred to as “mathematical points of force” in the Faraday quote Gann often refers to. These numbers can be used to multiply measurements in price or time, including highs, lows, ranges, or vectors.

There is a chapter in Gann Science dedicated to proving out these numbers with examples of varied market applications. Numerous constants are used in those examples.

In this article, we will test only one mathematical constant, pi, to see how it may help with our trading. Pi is significant because of its connection to the circle and the octave.  In the examples following, we will be using pi as a multiplier (factor) to price and time measurements. 

In essence, the measurement of price or time would be the diameter of a circle, and when multiplied by pi, the resultant number is the circumference of that circle.  This is basically, circling the square, where the swing vector (diameter), would be the diagonal of the square.

This can also work in reverse, where the measurement may be divided by pi and used to take a circumference to find a diameter.

A series of tests will be made on the following charts of the stock of Tesla, (TSLA), the electric car company. This is a good trading stock because of its volatility and presents good options trading possibilities for short to intermediate term swing traders.


Pi as a Time Factor

The first test will be to measure some swing points, getting a bar count between highs and lows, and then measuring that count by pi and projecting it forward.

It is August 21, 2018 as this article is being written and there is a trade triggered yesterday by two pi time count projections coming together which is causing an up move in TSLA stock. There is both an expansion and a contraction projection. 

The low came in after the open on Monday 8-20-18. The projection of 23 days between two highs projected 72-bars to the low.  The contracting (division) projection took a 49-bar count between two lows to project a 15-bar count to the low. This can be seen at the far right of the chart. 

The measuring counts are marked with the gray bar counter, and the projections are done with a black bar counter.  All measurements are multiplied by pi, other than the one mentioned prior.

A dozen projections are made on this example chart. Ten of them caused reversals in the market’s price action. Although the projections made were high to high and low to low, there is no rule that says this is the only way this can be used.

There is a key point to mention having to do with the area where the red square is placed on the chart.  The area marked is where the 82 and 188 counts come together.  There was no reversal at this point which is what is normally expected. When this happens, generally, the continuation move will double the range of the swing in progress to that point.

In other words, the measurement indicates the approximate midpoint of a swing.  This is a good place to move into a stop and reverse mode, had a short been put into place. Reverse it into a long, and let it run to the expected target area.

In this example trading bars are used.  Calendar days can be used as well and in general are preferable. Trading bars were used to show they work as well.


Pi as a Price Factor

On the next chart, some price range projections will be added in to see how pi may affect price.

Four price projections will be made. 3 of them from small price ranges, and one from just the range of the high bar itself. This one is marked in text at the September 2017 high.

Each range is multiplied by pi, and then projected from the beginning and end of the swing range, or bar range.  Notice how these levels act as important support and resistance points and also many gaps take place at these areas.

The last projection off the June high minor range gave the area of the last two swing lows, confirming the two timing signals mentioned in the prior chart, triggering the 8-20-18 long trade.

It should be stated that these points were chosen randomly and are not to be construed as the only valid points to be used.  Any other swing ranges not shown in the examples are also applicable and will give different points of force.

It should also be noted that there are multiple points on a chart that when found will tie the various numbers together and act as the best support and resistance areas in price and in time due to their harmonic connection.

Pi as a Slope to Set Gann Fans

The following chart brings into the analysis the popular “Gann fan” concept.  Most traders are trying to calculate a 45 degree angle but that is not the true method of finding a correct slope.

A 1:1 relationship is also not a necessary way to begin. Squaring of time and price can be done in a lot of different ways.

One method is to use pi as the slope.  On the following chart, two fans are plotted using a slope of .314.  Floating the decimal is necessary to fit the fan to the price level of the chart in question.

No prices or high or low are used. Only the slope is input of .314. These can be anchored at any pivot and will give results.

The fans are shown on a separate chart for clarity.  The confluent points between the price and time counts along with the fans gives many good trade opportunities. Notice the 8-20-18 low is confirmed by the fan line.  Fan lines not involved in the price action were removed.

This is one good use, but maybe not the best construct for these fans.  A full chapter dedicated to the proper set up and use of Gann fans is included in the Gann Science book, in the Chapter on Pitch: The Fourth Dimension.

This particular analysis of Tesla has been done using nothing but pi as a multiplier or factor.

This simple mechanism using pi could be developed into a trading system by itself.  The nice thing about it is that it only uses simple arithmetic and can be done with a calculator in a few minutes.


Using Pi as a Setting on Technical Indicators

Traders who use indicators can use derivatives of pi to set up their indicators with.

On the following chart, two AMA, adaptive moving averages set at 31 and 314 have been plotted. Two oscillators, a CCI, and a cyclic RSI have been set at 31 length.

Lastly, another fan set from the first top of the double top not used as a fan anchor on the prior chart does a nice job of displaying the vibrational tendencies of the price action.  Looking at both of the down fans from the two charts, different angles from the two fans caught some of the same pivot points.

The slope is again .314.

The trend lines on the cyclic RSI are indicating divergence points.

For readers interested in furthering these concepts, try using the prices of highs and lows and multiplying and dividing by pi and its increments to find important support and resistance levels.

The Pi number can be used as a measuring stick by itself. Checking back off the 8-20 low, 315 trading and calendar days hit swing lows.  The inclined reader may wish to test planetary longitude.  Using Mercury and measuring back 315* geocentric degrees ties back to a high 11-17-17.  These points are shown on the indicator chart.  These are good confirmations of the pi projection measurements from the first chart.

These techniques can be used in any time frame. The best trades on a daily bar are set up by numbers coming together on a weekly chart.  The entry on the daily bar can be fine-tuned by some calculations made on an intraday chart.  The best use of this material is to know the position of the market in these various time frames which will lead to very precise trading setups.



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