In our first two articles on the building blocks of technical trading we examined the basics of W.D. Gann’s Square-of-9 Principle, how it can be used to define market peaks and ways to see it more clearly through understanding its coordinates and the Law of Vibration. Here we delve deeper into Elloitt’s Wave Principle.

The Square-of-9 and the Wave Principle are intimately related. A basic Elliott cycle constitutes five advancing (bull market) and three declining (bear market) waves that subdivide into lesser-degree cycles. The reduction process of the largest eight-wave cycle breaks down into 144 lesser scale-order wavelets (see “Charting waves,” below).

The most credible method of establishing a swing’s termination is to compare the day-count of two adjacent intervals by mapping them onto the Square-of-9. A complete interval-pair forms a 180° or a 360° angle.

“Market ups and downs,” (below) illustrates a typical Elliott eight-wave cycle.  Irrespective of numerical order or magnitude, peripheral waves C & 1, C & 5, 5 & A, 5 & 1, 5 & C, A & C and C & C map onto the Square-of-9 at a 360º angle.

Likewise, irrespective of numerical order or magnitude, inner waves 1 & 2, 2 & 3, 3 & 4, 4 & 5, A & B, and B & C map onto the square at a 180º angle.

The bull-market side of the Elliott cycle constitutes five waves: impulse waves 1, 3 and 5 and corrective waves 2 and 4. The bear-market side of the cycle constitutes a three-wave A-B-C correction made up of impulse waves A and C and countertrend wave B.

The eight-wave cycle is akin to Russian Dolls. Waves 1 and 2 of the first pair of the cycle subdivide into an eight-wave lesser-magnitude cycle that mirrors the original. Likewise, impulse waves 3, 5, A and C subdivide into five lesser-degree waves each, and corrective waves 2, 4 and B subdivide into three waves forming a lesser-magnitude ‘a-b-c’ correction in which waves a and c are longer than b.

An irregular Wave-B on the S&P 500 is still underway. The recent Nov. 9 rally altered the wave-count and labelling of the 2009 to 2017 advance. What appeared to be a three-wave pattern turned into a five-wave advance showing major Wave-B as the longest swing. “Turning points,” page shows two possible wave counts, each showing that Wave-b of B was, in fact, shorter than Waves “a” and “c” of B.

“Turning points” (below) also illustrates the distribution of different scale-order waves to their designated cardinals and diagonals on the Square showing major peaks and troughs alternating between the east and west cardinals.

  • Oct. 31, 2007 — Mar. 9, 2009, Wave-a of A, 496cd, EC
  • The failure of Wave-a of A to map at 360° with Wave-V (496 & 1702cd = 180°) signalled a temporary pause in the direction of the main trend.
  • Mar. 9, 2009 — Apr. 29, 2011, Wave-b of A, 781cd (785 SE)
  • Apr. 29, 2011 — Nov. 25, 2011, Wave-c of A, 211cd NE, Total = 1483cd, SE
  • The 360° angle between the short and long spans signalled Major Wave-A’s termination.
  • Nov. 25, 2011 — May 21, 2015, Wave-a of Major B, 1273cd (1279 SC) = longest span
  • (Alternative Count) Nov. 25, 2011 — Dec. 1, 2015, Wave-a of Major B 1467cd = longest span
  • May 21, 2015 — Feb. 11, 2016, Wave-b of B, 267cd (265 EC) = shortest span
  • (Alternative Count) Dec. 1, 2015 — Feb. 11, 2016, Wave-b of B, 72cd (73 NE) = shortest span
  • Wave-a of B = 1273 or 1467cd (depending on the count). Wave-b of B = 265cd (the shortest), and Wave-c of B currently heading for the Square east’s 411 will peak on March 28, 2017.
  • Feb. 11, 2016 — Mar. 28, 2017, Wave-c of Major B = 411cd EC, Total = 1950cd (1959 EC) = Wave B’s termination
  • A 360° angle between the short (411cd) and long (1950cd) spans, both c-waves, will mark Wave-B’s termination.
  • Waves V and B (1695cd, WC, Oct. 31, 2007) and (1950cd, EC, Mar. 28, 2017) must terminate at a 180° angle.
  • Given that a 360° angle between the overall span and the final interval indicates wave termination, the above forecast skips the east cardinal’s number 334 — the next inline following 265cd recorded on Feb. 11, 2016. A 334cd-interval, due on January 10, 2016, will make Wave-B 1873cd long, 79cd short of a 360° mapping.

360° mapping of price

Price and time peaks/troughs’ distribution to their designated axes on the square is controlled by the Law of Vibration.

As  “Logging Reversals,” below, shows on  a S&P 500 weekly chart, closing prices correspond to the numbers running along the Square’s cardinal and diagonal lines. They seem to appear in clusters, each possibly characterizing a different cyclic wave, yet the absence of input from coordinate-X shows no orderly swing distribution. The Index’s major waves gravitate towards the square’s diagonals, the intermediate ones alternate between east and west, while others, of a similar scale-order, adhere to the square’ north and south.

The S&P weekly chart shown in “Logging reversals” could stay, however delete the arrow pointing to August 2016, including the AUG. 16, 2016 on the top right and replace with Mar. 28, 2017 instead as shown below.

Forecasting the highest or lowest price a swing will reach relies on time. The Law of Vibration makes it possible to discern the axis upon which the peak/trough value will show close to the swing’s maturity date.

Having grown out of the Babylonian zodiac, the Square-of-9 is the world’s second measuring instrument. It is also a cosmic clock of space-time embodying every vibration in the solar system (see “Origins out of this world,” below).

When pulled from the number 1 at the center, it morphs into a pyramid revealing tiers laid out in an Archimedean spiral. Yet, as the pyramid rises from the base up, it does so logarithmically. The pyramids of Egypt, like all others around the world, are two-way spirals embodying the Time Factor and Law of Vibration. It seems that no matter how ancient civilizations with no contact with one another built pyramids, it enshrines the “X” and “Y” coordinates into them.

Elliott and Gann have been able to understand these basic principles and apply them to the world of markets. The best quote related to modelling price and time comes from Stephen Hawking and Leonard Mlodinov’s “The Grand Design“ (2010). They wrote: “A model is good if it: Is elegant, contains few arbitrary or adjustable elements, agrees with and explains all existing observations and makes detail predictions about future observations that can disprove or falsify the model if they are not borne out.”

The Great Pyramid of Egypt, like all others around the world, is a two-way spiral based on the Law of Vibration and Time-Factor. It embodies the cosmic clock of space-time — the mechanism controlling vibrations in the universe. As the pyramid rises from the base up, it follows a logarithmic spiral, however, the shape of its tiers follows an Archimedean spiral.

It appears that ancient civilizations, believed to have had no contact with one another, built pyramids all over the world in order to enshrine the ‘X’ and ‘Y’ coordinates onto them.

Readers interested in an Excel Spreadsheets of the Square-of-9 (3000 & 10000) are welcome to contact the author here:

About the Author

Pauline Novak-Reich is the former manager research-foreign exchange at the ANZ’s (Australian & New Zealand Banking Corp.) dealing room from 1980 -1993.