**Lesson 3 – How to Use
W.D. Gann’s Square of Twelve (144), the Pythagorean Theorem, and the Ancient
Geometry of the Square to Project and then Confirm Important Highs and Lows**

** **

I have found Bradley Cowan’s Price-Time Vector (PTV) a useful tool. PTVs often relate to the Square of Twelve, its octaves and harmonics. The PTV uses the Pythagorean Theorem to combine both Price and Time into a single value.

The usefulness
of the PTV was discovered by and written about by Bradley Cowan. ** The PTV exposes incredibly useful
information that otherwise would go unnoticed.** In real time I have found it to be a
very useful tool

**Cowan’s Price-Time Vector (PTV)**

The Price-Time Vector is a unique tool that combines both price and time calculations into a single value. Similar PTV values repeatedly unfold in the markets. It is the knowledge of these similar PTV values that allow a trader to project the time and price of future turning points.

In order to understand the significance of geometry in many markets it is also meaningful to understand the significance of certain numbers. The following discussion of the Square of Twelve uses the soybean market as the tool for analysis but the same analysis is applicable to most markets.

W.D. Gann and Brad Cowan both wrote about the Square of Twelve. W.D. Gann sold plastic overlays with 0 to144 on both the horizontal and vertical axes. 144 is the First Square of Twelve.

Gann hand charted commodity prices. On a hand chart of November 1948 Soybeans Gann numbered the weeks along the top of the chart. When he came to 288 weeks he marked a large arrow on the chart and then quit numbering. It is obvious Gann recognized that the Square of Twelve was an important analysis tool.

Cowan’s book on the Square of Twelve uses soybeans as his subject. He uses his Price-Time Vector (PTV) as a major tool for his analysis. Much of the data in this section is based on Cowan’s writings and analysis.

** **

**Examples of the ****Square**** of ****Twelve**** **

**in the Soybean Market from 1976 to 1987**

__This
chart of May soybeans shows repeated examples of the price level of significant
highs and lows aligning with multiples of the ____Square____ of ____Twelve____. __

The data also shows two examples of when the differences between important swing highs and lows aligned with the square of twelve. May beans declined $1.41 ½ (144) between March 31 and July 21, 1978. May beans rallied $4.37 ½ (144 x 3 = 432) between October 4, 1982 and September 16, 1983.

** **** **** **

**More Examples of the ****Square**** of ****Twelve**** **

**in the Soybean Market of 1976 to 1987**

__This
chart of May soybeans shows repeated examples of when the differences between
important swing highs and lows were the ____Second Square____ of Twelve or 288. __

May beans declined $2.89 ½ between June 22, 1979 and April 3, 1980. May beans declined $2.86 ½ between November 21, 1980 and March 6, 1981. The difference in price between September 16, 1983 and February 17, 1984 is $2.90. The difference in price between July 21, 1978 and May 25, 1984 is $2.88. The difference in price between March 19, 1982 and May 25, 1984 is $2.88 ½.

__This
data indicates that keeping track of price differences is practical and useful.
__

** **

**An Example of Price-Time Vectors (PTVs) and the ****Square**** of ****Twelve**** in the Soybean Market of
1976 to 1987**

__The
declining PTV from ____November 21, 1980____ to ____October 4, 1982____ has a value of 648.96. This value is 0.96 different from
an ideal value of 144 x 4.5 = 648. __

__ __

__The
value of the rising PTV from ____October 4, 1982____ to ____September 16, 1983____ has a value of 497.57. This PTV does
not have a direct relationship to the ____Square____ of ____Twelve____. __

__ __

__One can
add PTVs FJ (648.96) and JK (497.57). The sum is 1146.53. This sum is the
Eighth ____Square____ of ____Twelve____ (1152). __

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**Three Recent Examples of the ****Square**** of ****Twelve**** **

**in the Soybean Market**

__From ____August 1, 2003____ to ____March 26, 2004____ cash soybeans at central ____Illinois____ rallied from $5.33 ½ to $10.40 ½ or
$5.07. This rally of $5.07 equals 3.5 times 144 (504). __

__ __

__The
Price-Time Vector from ____March 26, 2004____ to ____October 15, 2004____ has a value of 575.54 which equals 144
x 4 (576). It is interesting to note that October 2004 is the beginning of the
current 27-28 Year Cycle of Volatility. Twenty-seven years earlier this exact
same Price-Time Vector (576.4) from ____April 22, 1977____ to ____October 20, 1977____ preceded the beginning of the 27-28
Year Cycle of Volatility. __

__ __

__From
April to ____June
24, 2005____
cash beans rallied from $5.89 ½ to $7.33 ½ or exactly $1.44. __

**I emphasize again that this lesson uses soybeans as its tool for
analysis but the same methodology is applicable to most markets. **

** **

**Price-Time Vectors and the Harmonic Web of 144 at the High of ****December 1, 2006**** In Cash Soybeans at ****Central Illinois****. **

Our newsletters
advised subscribers of a 27-Month Interval of the 36-Year Cycle with a Cycle
Turn Window that extended from November 10 through December 3, 2006. Beans traced out a high on December 1, 2006. The following chart appeared in my December
newsletter and shows the Price, Time, and Price-Time values that aligned with
the high of December 1^{st} and signaled that a cyclic high was in
place. History shows this cyclic high marked the beginning of the first
consolidation in cash beans since the low of September 12, 2006.

** **

__Take
some time to study this chart.__** **The Price-Time Vector from the low of October 13, 2004 to the high of June
24, 2005 has a value of
308.06. The Price Time Vector from the high of June 24, 2005 to the low of October
10, 2005 has a value of
230.69. The PTV from October
10, 2005 to the high of December 1, 2006 has a value of 322.24. If one sums these PTVs they equal
860.99. The sixth Square of Twelve is 864. The difference in
price between the low of October
10, 2005 and the high of December 1, 2006 is $1.45, the Square of Twelve.

The difference in price between the high of July 8, 2004 and December 1, 2006 is $2.87, the Second Square of Twelve.

The Price-Time Vectors can be summed another way. If one adds the PTV’s from October 13, 2004 to June 24, 2005; from June 24, 2005 to October 10, 2005; from October 10, 2005 to September 12, 2006; and from September 12, 2006 to December 1, 2006 the sum is 935.80. 144 x 6.5 = 936.00. In addition, there are exactly 288 trading days from October 10, 2005 to December 1, 2006.

This data
confirmed that Gann’s 27-Month Interval of the 36-Year Cycle with a Cycle Turn
Window projected for November 10 through December 3^{, }2006 had reached its crest. As stated above,
history shows the high of December 1^{st} marked the beginning of the
first consolidation in cash beans since the low of September 12, 2006.

**Summary and Conclusions**

This lesson shows soybeans (and other markets as well) regularly make highs and lows at prices that are directly related to the Square of Twelve. In addition, the lesson shows the price at many highs and lows are directly related to other highs and lows by the Square of Twelve.

Besides these relationships of price to the Square of Twelve, this lesson shows the practical use of Bradley Cowan’s Price-Time Vector (PTV). The lesson shows that without the use of the PTV many relationships to the Square of Twelve would go unnoticed.

The relationships of Price, Time, and Price-Time to the Square of Twelve can be a useful tool in market analysis. While a few other services may use the Square of Twelve, I am not aware of any other service that uses Cowan’s Price-Time Vectors (PTV’s) in their analysis.

This lesson shows the importance of the Square of Twelve in market analysis.

I hope you find these lessons beneficial. As I said at the beginning if you have any questions or comments please don’t hesitate to email me at office@HarmonicTiming.com I can typically respond within forty-eight hours.

Thanks for your interest.

Ernie

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future turning points can reap large profits.” **