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calculating dates in the ftiture that will tend to be highs. If you us a high as your begitming point, reverse these rules.

(6) If you use the date of an extreme low closing price as your beginning point, the "soft angles" will also typically come out as lows. The "soft angles" are

the 60°, 120°, 240°, 300° time angles. The "hard angles" will typically come out as highs. The "hard angles" are 45°, 90°, 135°, 180°, 225°, 270°, 315° time angles of the Square of Nine. The exception to the "hard angle" rule is the 270° time angle. This time angle will typically come out as a low if your beginning point was also a low. For future reference, "hard angles" are harmonics of 45° and "soft angles" are harmonics of 60°. If you use a high as your beginning point, reverse these rules.

(7) If a calculated ftiture date inverts, then you should invert the rest of the j-emaining future series of dates. That is to say, if a predicted high date tumed out to be the date of a low instead of the anticipated high, you should expect the remaining series to be subject to the same inversion. The remaining future dates that you originally calculated as highs will now be lows. The remaining ftiture dates that you originally calculated as lows will now be highs.

(8) Because highs and lows frequently come out on the same time angles as previous highs and lows, up-trends & downtrends tend to be the same in between the same time angles. For example, if there was a up-trend in the previous cycle preceding our current cycle between the 0° and 45° time angles, then we would anticipate or project an up cycle in between these same two angles for the current cycle. As mentioned in mle Ul, if the cycle inverts.

we would invert the remaining series. This rule (#7) applies to projecting uptrends and downtrends in between angles as well.

(9) Always maintain the daily chart from the most recent Bear Market Low. Always maintain the Daily, Weekly and Monthly charts from the first trade date. The all time low may also be useful and worth maintaining for your particular market. As shown earlier in the U.S. history examples, I prefer to use and maintain planetary longitudes as my time periods from the natal point.

A good site for free market data is

Periodic Number Cycles

Another that the Square of Nine served was for mathematical sequence.

Gann had always said that he based his calculations on cycle theory and mathemarical sequences. On page 75 of Tunnel Thru the Air. Gann says, "My ca)culations are based on the cycle theory and on mathematical sequences. History repeats itself That is what 1 have always contended, --that in order to know and predict the ftiture of anything you only have to look up what has happened in the past and get a correct base or starting point. My authority for stating that the ftiture is but a repetition of the past is found in the Bible".

By creating these Master Charts, Gann could look at periodic numerical sequences or number cycles on these geometric shapes to see if market tuming points had any mathematical relationship in Time or Price. Unlike ordinary cycles that are fixed in terms of size or length, periodic number cycles have a geometric growth that takes up successively larger units oftime or price in each new ring or cycle.

Another time technique that is based on Carl Futias work utilizes this very concept, i.e., using the time angles of the Square of Nine as a periodic number cycle. What you do is simply take the cardinal numbers, i.e. the numbers on the "+", and add these values to the dates of previous market tops and bottoms. Use these time periods as days, wieks, months, years or planetary longitude. What you do is build and maintain a list of dates of previous market tums and simply add the periodic time units that fall on the cardinal cross of the Square of Nine Chart (0°, 90", 180°, 270°). Because tops and bottoms tend to come out on the same time angles as previous tops and bottoms, you should select pairs of tops and pairs of bottoms for this technique. For example, lets take two recent lows in the stock market, October 23,1997 and September 1, 1998. On the Square of 9, we would add the number series of 2, 11,28, 53,86, 127, 176, 233,298 weeks for the 0° angle from each of these two dates to see if they had a common time period. Then we would do the same thing for the 90-degree, 180-degree and 270-degree angles (cardinal angles only). So we would run the series of 4, 15, 34, 61, 96, 139, 190, 249,316 weeks, 6, 19, 40, 69, 106, 151,204, 265, 334 weeks, and finally 8, 23, 46, 77, 116, 163, 218, 281, 352 weeks from both lows and circle all the time periods they have in common. Then, we would do this same procedure with months and circle all the months they have in common. Then do the days, etc. These common dates that we circled would be time periods that would require us to be on the lookout for reversals of trend. Using weeks, the only common time periods are the week of February 20\ 1999 and May 25 2012. Using months, the only common time periods are September 1999, March 2000. March 2001 and August 2013. Microsoft Excel can do these types of date calculations very quickly. You will be pleasantly surprised at the amount of accurate market turning

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