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Universal and Natural Law:

Universal means it is applicable to everything in the universe including our personal lives (Gann applied it to his personal life as well as shown by notations in his personal ephemeris). Natural means how things exist and work in the nature. He also calls it Harmonic Law or the Law of Vibration because the application of the law involves using harmonics, wave lengths and amplitudes. So, Gann’s work is a master piece in observational science (as opposed to presently emphasized experimental science).

Simplicity:

Gann used basic level of mathematics, that is, just addition and subtraction of numbers or the faster way of doing so through division and multiplication. (For things to work, they have to be EXTREMELY simple. Since the universe is humungous (we don’t even know its size), it must work with 100% reliability – 99.999% reliability is a recipe for failure. Any good engineer knows that the less number of components a machine has the more reliable it is.)

Charts:

Gann used naked charts and price action trading. He built all indicators and charts of different time frames with the objective of identifying trends and change in trends. Decisions were made based on price action after taking certain time values into account.

Nothing was calculated from the prices and price action to arrive at fancy indicators (which are almost always lagging) or imaginary and arbitrary geometric shapes to make trading decisions and complicate things unnecessarily. Gann used various time interval charts such as daily, 2 day, 3 day, weekly, monthly, quarterly, yearly. He used daily charts for constructing minor trend indicator, 2 day trend indicator and 3 day trend indicator. 3 day indicator charts and weekly charts are main trend indicators.

Trend Following:

Gann’s system is a trend following system. Gann advises time and again to follow trend and let the market tell its own story. However, more people are attracted to his forecasting methods than trading methods because people want to know the future and it gives them comfort.

Planetary Motions:

Gann used planetary motions, both Geocentric and Heliocentric, extensively to arrive at extremely accurate price levels and times when they will occur. Gann's private letters, private ephemeris, soybean chart, Moon Signs Coffee chart are some examples of this. Gann was a 33rd degree mason (as per his advertisements) – a rare degree. 32 degree masons are also rare but more in number. A masonic lodge has astronomy everywhere and it’s natural to expect its application by free masons. So, it is wise to ignore those people who say Gann did not use planets. The main theme of Gann’s book, Tunnel Thru the Air or Looking Back from 1940, is that astrology and repetition of cycles works, and some other stuff such as clairvoyance does not. He refers to using transits and progressions. Planets rule the destinies of people and nations.

9 digits as method of calculations – Harmonics (Harmony)

Gann used the nine natural digits - 1, 2, 3, 4, 5, 6, 7, 8 and 9, as the basis of his calculations. He either divided or multiplied by the nine digits or multiplied the digits by themselves twice or three times.  A circle is commonly assigned 360 degrees. Its harmonics in degrees are calculated by dividing 360 by the nine digits. I say “commonly” because the circle can have any number of degrees assigned to it, for example, we assign the number of degrees equal to the high or low price to arrive at a stock’s price harmonics and its vibration. Additional harmonics are calculated by further dividing these harmonics, for example, 32nd harmonics are multiples of 11.25, 48th harmonics are multiples of 7.5 and 40th harmonics are multiples of 9, 15th harmonics are multiples of 24 and 30th harmonics are multiples of 12.

Astrologers call these harmonics aspects and use the names as shown below:

0 or 360 degrees - Conjunction

180 degrees - Opposition

120 and 240 degrees - Trine

90 and 270 degrees - Square

72, 144, 216, 288 degrees - Quintile

60 and 300 degrees - Sextile

51.43, 102.86, 154.29, 205.71, 257.14, and 308.57 degrees - Septile

45 and 315 degrees - Semi-Square, 135 and 225 degrees - Sesquiquadrate

40, 80, 160, 200, 280 and 320 degrees - Novile

When a number is multiplied by itself, we get the following:

Number   Square   Cube   Difference in Cubes

1                1              1             0

2                4              8             7

3                9              27          19

4                16           64           37       64 is also square of 8

5                25           125         61

6                36           216         91

7                49           343         127

8                64           512         169

9                81           729         217     729 is also square of 27

10             100         1000        271

11             121         1331        331

12             144         1728        397

13             169         2197        469

14             196         2744        547

15             225         3375        631

16             256         4096        721

17             289         4913        817

18             324         5832        919

19             361         6859        1027

The squares and cubes of higher numbers are also multiple squares and cubes of lower numbers or harmonics of the circle and repeat when whole circles or multiples of 360 are subtracted from them. For example if we continued the above table, 19 x 19 = 361, or 1, 20 x 20 = 400 or 40, 21 x 21 = 441 or 81, 23 x 23 = 529 or 169, 24 x 24 = 576 or 216 and so on. Therefore, when keeping track of time or planet movement in degrees, we should maintain BOTH full and net of circles distances travelled. They are extremely helpful in arriving at exact price levels.

Since each aspect or angle can be measured two ways, astrologers generally consider the smaller aspect. For example, they consider 225 degree aspect as 135 degree aspect. For our purposes 225 is 225 not any other number. Although both 135 and 225 degree angles form part of the fixed cross and are very powerful, 225 is more powerful because it is also square of 15. Note that 135 is square of 11.618, at golden ratio point in the circle but not square of a whole number. Similarly 71 is not a harmonic but 289 is square of 17. This distinction is very important when squaring and balancing price and time. We could stretch 71 to 72 but I don’t recommend doing.

These harmonic numbers are applicable to BOTH time and price cycles, represent important resistance levels and can be arranged beautifully in solids. This leads us to harmonic charts presented in the next section.

Angles (Angels) or simple ratios: Horizontal, vertical, diagonal

Horizontal Angles: These angles measure time as time is customarily represented on x-axis in the charts. It's measured in days, weeks, months, years and degrees. Time is kept by the Sun, the Moon and the planets. In our world of 4 dimensions of x, y, z axes and time, time itself is also multi-dimensional. Not all of time’s dimensions move forward simultaneously. Some of its dimensions can be moving backward at a given moment. This is very important concept to grasp because highs and lows in a market can and do come at the same time in one dimension although time has moved forward in other dimensions!

Vertical Angles: These angles measure price or harmonics of highs, lows and ranges.

Diagonal Angles: On a stock chart, these are measurements of rise over run, difference of ordinates over difference of abscissa, slope, dy/dx, or tangent etc. They simply measure the movement of price with respect to time. There is no need to calculate the exact angle using tangent inverse, ratios are sufficient. The prominent theme is to use the following angles and their inverses:  1 x 1, 2 x 1, 4 x 1, 8 x 1, 16 x 1 (Egyptian eye angles). Occasional use of other angles such as 3 x 1 is also seen. It does not mean you should ignore other harmonic angles such as 7, 9, 12, 14, 18 etc. For example, if dividing the circle into 12, year into 12 or the day into 24 works beautifully, there is no reason why it should be ignored in market analysis.

There are some important things to remember about Price-Time angles:

(i) 1 x 1 angle on a daily chart is different from the same angle on a weekly or monthly chart. Gann also used other chart frequencies. For example, on a weekly chart 1 x 1 angle would be 1 x 7 angle on a daily chart. If charts are plotted properly, leaving gaps for non-trading days ((a) time does not stop on manmade holidays; (b) price gaps are just a function of the chart time frame and hence arbitrary), you get a properly drawn, time-price balanced charts.

(ii) The perfectly balanced charts simply serve as a base to understand what we are doing. To obtain the required accuracy in calculations, we must consider all dimensions of time – there should be a Sun chart, Moon chart, Mars chart, Jupiter chart and so forth, BUT we are in the business of trading markets not making charts. When we understand what we are doing, the need to draw perfectly balanced charts disappears and the part of doing mathematical calculations with planets starts. This is analogous to physical masonry versus speculative masonry. The whole process is mental and mathematical. The limitations of the charts become apparent. Moreover, how do we go backwards on a chart when a planet turns retrograde and time is moving backwards only in that dimension?

Interesting Fact: The symbol for retrograde planets and prescription by a medical practitioner are identical. It is because at one time learning astrology was part of obtaining a medical degree. You can check how many times planets turned retrograde when you fell sick and recovered. The same happens to other aspects of life such a losing/gaining a job, missed opportunities coming back and so forth. Mirror image unfoldings in the markets are no exceptions. There's lot of information in the diagram above. It shows Gann angles. It also shows some of the divisions of the square and is the basis of Gann calculators - Square of 90, Square of 144, Square of 52. An important thing to remember is that the square can be any number, not just the harmonics of the circle or squares of natural numbers. So, this can be a square of a high, low or range. The measurements made using the circle particularly when dealing with area, volume, division and multiplication etc. are approximation. The only way to tackle this issue is to use degrees. However, square is very different. It is exact and we can divide it, multiply it, expand by its side, diagonal or corner and do many other things. Using cubes adds the third dimension to this. Gann used various squares to calculate important time and price points.

Factors to consider in analysis

Price – Price is the only reality. You cannot argue with it.

Volume – Volume is the driving force that moves the markets.

Time – Time is the most important factor and master. We can't change it or do anything about it.

…and

There is a relationship between price and time. In other words, a stock trades at a specific price at a given time. More importantly, at important turning points, time and price are in ratio to each other. That ratio can be any number but more common numbers are 1, 2, 3, 4, 8, 16. These are commonly known as Gann fans or angles of 1 x 1, 2 x 1, 3 x 1, 4 x 1, 8 x 1, 16 x 1 or their inverses such as 1 x 2, 1 x 3, 1 x 4, 1 x 8, and 1 x 16.

A very important point to keep in mind is that when the time-price ratio is exact, the price does not have to change its trend, the trend can accelerate or decelerate, that is, add or subtract energy from the system.

This analysis of price and time relationship is what makes Gann analysis unique. To trade, all you need is charts and ephemeris.

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