The solution to Gann's Law of Vibration from the 1909 Ticker Interview. Penicka analyzes Gann’s exact words correlating them with the cutting edge science of Gann’s day to develop a system which identifies the “mathematical points of force” behind all market action. The Periodic Table of Elements determines a system of order based upon atomic structure which generates a master number set for each market defining its structure in price and time.

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Sundberg's The Secret Science of Squaring elaborates a major series of insights within the field of W. D. Gann’s astrological market forecasting. Sundberg has rediscovered an approach to the application Gann's of astro-geometric price/time conversion and projection principles which operates to square price and time on market charts using a system of planetary geometry and astronomical timing.

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Dr. Lorrie Bennett is one of the only Gann experts to have cracked the Law of Vibration! After 20 years of grueling research she discovered a complex code in Gann's texts which led her to the full solution. Following in Baumring's footsteps, Dr. Bennett lays out the science behind the Law of Vibration in an intensive 4 Volume Advanced Series revealing the Patterns, Numbers, Planets & Geometry behind Gann's secret trading system.

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The Application of Wave Mechanics
to Financial Market Forecasting A Brief Description of the Analysis of Theoretical Wave Mechanic Charts
and their Correlation of Financial Market Price Charts

As Taught By Dr. Jerome Baumring

Basic Wave Mechanic Observations (4 Wave Theoretical)

Composition

The composite or summational wave is the summation of the four component sinusoidal waves. Anytime one of the underlying component waves turns there is change in velocity in the composite wave except when two component waves simultaneously turn in opposite directions. The pattern of the composite wave is the result of the summation and changes of the various underlying waves. If you change the relationships of the length of the waves, the summational pattern will likewise change. If you change the phasing of any of the component waves, you change the pattern of the composite wave.

Wavelength

Wavelength or lambda refers to the underlying component waves. In this model there are four component waves. These waves have been chosen to have specific musical relationships to each other. Wavelengths are usually referred to by their 1/4 cycle lengths, the amount of time/distance from the 0 line to the maximum or minimum energy extreme. If a sinusoidal wave is seen as a circle cut in half with the bottom half slid forward the length of the diameter, one can then see the relationship between the circle and the wavelength or cycle. A 1/4 cycle can be seen to be also a 1/4 circle, a 1/2 cycle 1/2 of a circle, 3/4 cycle 3/4 of a circle, and a full cycle a full circle. This explains why we use degrees when referring to cycles with a 1/4 cycle being equal to 90 degrees, a 1/2 to 180 degrees and a full cycle equal to 360 degrees. These lengths are related to each other through musical harmonics. Harmonics are expressed as ratios such as 3/4, 2/3, 1/2, which relate to divisions of a vibrating string, or bell, or something of the sort.

Phasing

The phasing of the waves relates the beginning of the different component waves together. If all component waves began at 0 degrees, they would all begin by moving up, or phased up, according to our explanation above. If they all began moving downwards, they would all have begun at 180 degrees. At any point along the summational wave, you can look at the component waves and determine their phasing to each other which will be most easily expressed by whether the waves are moving up or down. If two or more waves are moving up or down simultaneously, they cause what is called either positive or negative constructive interference, respectively, meaning that the combined sum of the energies of these two or more waves creates a greater positive or negative amplitude summational wave. If one has two waves moving up and two waves moving down, you get destructive interference, meaning that there is an equilibration of energies causing a sideways movement on the chart.

Pattern Formation

It is the interaction of these component waves that forms the patterns of the summational wave on the charts. It will be noticed when you have a particular pattern of the summational wave on a chart, if you simply change one wave, whether large or small, it changes the whole summational pattern. For instance, compare charts 1 and 3. Notice that by changing the phasing of the smallest component wave it changes the pattern of the composite. The difference in the composite pattern depends upon which and how many of the component waves you change. Also notice that if you change all of the components the opposite direction, you get the same pattern but up-side-down. This is called an inverse pattern, and it should be easily noticed that there are only 8 patterns in this 4 wave theoretical with 8 inverses.

Market Applications

The wonderful thing about wave mechanics is that it serves as an excellent foundation for incorporating many concepts and ideas of the market. It acts as a sort of foundational schemata upon which one can build a good model of market behavior in simplified form.

Counting

One of the first things one learns to see in the markets after studying theoreticals is how to see energy vectors and from where to count them. We see that a bottoming or topping complex is always made from a number of energy vectors changing simultaneously (within the range of the top or bottom). Since we know that a directional movement is caused by combination of several component waves, we would not expect that the count from extreme top to extreme bottom to be the sole determinant of that move. Rather we would count from the few energy change points at the top to the few energy change points at the bottom, giving us a larger number of vector counts, some of which must be the lengths of some of the underlying components (or multiples thereof). If one were then to measure the different actions and reactions in this way, one would see the same numbers recurring and in that way determine some of the underlying intervals.

Reactions and Congestion

In the same way, a good place to discover smaller component lengths in is reactions against the major trend. The longer components will be determining the main trend, while the minor components either strengthen that trend or cause reactions against it. So measuring these reactions is a good way to uncover these smaller components. Also when you have a long congestion phase in which the longer components are equilibrating, you can often see the smaller cycles turning up and down in the range of the trend, so this is a good place to discover them.

Pattern Recognition

One of the most useful aspects of the theoreticals is in the study of pattern recognition. Since in the theoreticals we learn to see the cause and process of permutation of form or pattern, we can learn to extrapolate this experience into real market patterns. Two patterns which before might not have seemed similar now can be seen to be almost the same with one or two or more components flipped. We have a sense of the underlying causal structure of formations. For instance a broadening top formation or bed of accumulation at a bottom can be seen to be cases where you have a number of waves spread out over a longer period with most of them equilibrating until the last one or two turn down or up respectively causing the beginning of the reversal in trend. Or with a spike top or bottom, you know that you have the underlying components changing almost simultaneously causing the fast reversal in trend. Likewise, every pattern, whether top, bottom, directional trend, or congestion has an underlying combination of component waves which will cause that particular formation. Also, the slight irregularities one always finds in these patterns can be explained by changes in the underlying component relationships. These slight changes can also give you an idea what to expect in terms of permutations. Say you have on occurrence of a bottom which makes a clean downward half-circle, then you see later a bottom of the same time length but with a sideways S pattern rather than the full arc. You would recognize that you have a wave out of phase and that you should not expect the same movement away from the bottom, but, rather that you may get a different angle of attack and different ending to the upward movement due to this changed cycle. The trick is to be able to quantify all of this so as to use it correctly.

Angle of Attack

The angle of attack is the slope at which the market moves at any time. Baumring has said that the slope of a vector is its vibratory rate. It can easily be seen that the slope of the market is caused by the relative constructive or destructive interference of the underlying waves. A steep slope or angle of attack has a number of underlying components moving together in the same direction. A flat slope or congestion area only exists when you have an equilibration of underlying waves.

Larger Implications

There are many implications which come with the wave mechanics concept. One is the whole idea of cycles, harmonics, and the law of vibration. These underlying cycles must have some larger correlation to some cosmic or stellar phenomena. All of these waves have harmonic relationships between them showing the underlying order of the cosmos and its harmonic composition. This shows that the whole universe can be broken down in terms of the law of vibration, or the harmonic interrelation of time cycles as the causative foundation for mundane phenomena.

Cycles vs. Periodicity

The difference between cycles and periodicity is an important concept. Cycles are equivalent to what we look at as component waves on the theoreticals, energy vectors, or directional force fields, moving from a positive to a negative extreme at a regular time interval. Baumring said that there were 12 different stellar combinations of component waves. A periodicity is the recurrence of a pattern at some sort of time interval. This pattern is made of component cycle relationships which recur simultaneously in a period of time. This pattern is more like a sequence of events which occurs at the periodicity.

Geometric Structure

It is the harmonic relationships of these cycles which cause the geometric order underlying the structure of the market. These harmonic relationships build harmonic structures which grow like natural growth structures according to the geometry of nature.

Problems

In theory many of these ideas seem clear and logical but when it comes to applying them to the markets, the task is much more difficult. The theoreticals are a gross simplification of the real market, and the simple analyses which can be done on the theoreticals can become baffling when tried on a real market chart. Baumring would regularly repeat that the theoreticals are just theoreticals, and the market is different. If not, one could do Fourier analysis on the market and break out all of the components and know where it is going, but Baumring said that this would not work. Baumring also stated that the component waves were not sinusoidal, but were elliptical instead. This obviously changes the picture, but would seem to correlate more logically to planetary phenomena.

Notes

Page 1: Acceleration and Deceleration

Baumring used to talk about measuring acceleration and deceleration off of a median line. He would say to dray a vector or line from a high to a low and then the movements above and below that line should be symmetrical and be a measure of acceleration and deceleration which would identify some of the underlying waves.

Pages 2-3: Least Common Denominator

When you have two or more waves changing together or crossing a node and you multiply their 1/4 cycles together to find the LCD, then at that point of time in the future they will be changing direction again. So find where two cycles turn together and project the LCD both forward and backward and you will always see them turn together or cross a node together at their 1/4 cycles.

Page 5: Spatial Orientation

Baumring says that taking time counts allows us to measure the spatial orientation of the structure we are analyzing. So then we are able to see the structure and what precedes it and the next structure and what precedes that and then we measure the changes in torque between them.