In the first instalment of this series on technical building blocks we introduced the basic principles of W.D. Gann and Elliott Wave theory, and we broke down the X and Y graph coordinates and discussed how to define market peaks, troughs and trend reversals. Here we dig a little deeper and discuss the Law of Vibration and The Symmetry of Coordinate X vs. the Asymmetry of Y.

The tool introduced by Gann was his Square-of-9 spiral that ties together the movements of price and time.

The key feature of the square’s spiral is the identical shape and size of its blocks.

It assigns one block to one unit of time making no distinction between one minute, hour, day, week or month. Intervals however cannot be mixed; apples must be compared to apples.

Whereas the time factor takes no notice of wave magnitudes, the Law of Vibration does. It ensures that all throughout the cycle same scale-order waves land upon the same cardinals and diagonals of the square. An interval-pair measured from a time-peak to a time-trough, and from a time-trough to the time-peak, maps onto the square at a 360° or 180° angle, depending upon its location within the Elliott cycle (more about it later).

Intervals terminating at a 360° angle manifest a co-axial alignment upon one of the square’s cardinals or diagonals. Intervals terminating at a 180° angle form an “opposition” upon two of the square’s cardinals or diagonals.

Swing-pairs failing to map at 180° or 360° angles are either incorrectly measured, incomplete or belong to a greater/lesser scale-order phase of the cycle.

The Law of Vibration is subject to Time Dilation — a time discrepancy between “real time travel” in space and travel on Earth (time passes more slowly for bodies moving quickly relative to bodies that are within the gravity well where the Earth’s physical speed and time slow down).

It often becomes necessary to adjust the waves’ day-count to the nearest cardinal or diagonal on the square (see “Crude intervals,” below).

Complete Intervals:

- Feb. 9, 1999 — Jul. 15, 2008 = 3440cd NC (Not displayed)
- July 15, 2008 — Feb.18, 2009 = 218cd NC = 360°
- June 28, 2012 — Jun. 16, 2014 = 716cd (718 NC) = 360°
- June 16,2014 — Feb. 19, 2016 = 613cd NC = 360°

Lesser scale-order Intervals:

- Apr. 29, 2011 — Jun. 28, 2012 = 426cd (421 NE)
- Feb.19, 2016 — Jun. 8, 2016 = 110cd (111 NE) = 360°
- June 8, 2016 — Aug. 2, 2016 = 55cd (57 SW) = 180°

The Feb. 19, 2016 interval represented a simultaneous termination of crude oil’s time and price-troughs.

### The Symmetry of Coordinate X vs. the Asymmetry of Y

Each ring of the Archimedean spiral expands twice during one 360° rotation. The first expansion takes place upon the square’s northwest diagonal and the second, 180° opposite, in the southeast. The Archimedean spiral does not permit fractions. It allocates one whole block to one unit of time. The perimeter of each ring expands by two whole blocks (two whole number integers) during one 360°rotation.

Coordinate Y lacks the symmetry of coordinate X. As it adheres to the logarithmic spiral, the number 1 at the center (from where the first ring begins to radiate) is the only whole-number-integer point on the spiral. The ring’s end value is + 61.8% (equivalent to the Fibonacci ratio) — a fractional number incompatible with the square’s blocks. The asymmetry of the logarithmic spiral makes projecting coordinate Y’s values difficult (see “Picture this,” below).

Gann, however, found a way to forecast the values of coordinate Y’s peaks and troughs without resorting to the Golden Mean or the Dow Theory (the Wave Principle did not emerge until the 1950s). The Law of Vibration showed him the way.

Knowing that all the resonances in the universe are encoded onto the square’s cardinal and diagonal lines and that none can bypass this law, Gann reasoned that the vibration of price, like any other, ought to correspond to the Square’s matrix.

He wrote: “By knowing the exact vibration of each individual stock, I am able to determine at what point each will receive support and what point the greatest resistance is to be… After years of patient study I have proven to my entire satisfaction as well as demonstrated to others that vibration explains every possible phase and condition of the market… After much researcher of the known sciences, I discovered that the Law of Vibration enabled me to accurately determine the exact points to which stocks or commodities should rise and fall within a given time. The working out of this law determines the cause and predicts the effect long before the Street is aware either.”

It importnat to note that the square of 9 is essential to building on the works of Gann and Elliott. By applying the Law of Vibration and understanding the distinction between coordinates X and Y, you can begin to understand the work of the masters. Our next and final feature in this series will examine how Elliott applied the square of 9 in creating the Elliott Wave Principle.