These harmonic numbers are applicable to BOTH time and price cycles, represent important resistance levels and can be arranged beautifully in solids.

1. 1st Harmonic - Square of the circle or 360 degree circle chart. (Please note that if this chart is started at zero, it ends at 360. Also note that that square root of 360 is 18.97 - very close to 19)

Example: All time high of Intel (INTC) stock in early September 2000 was $75.83 (split adjusted actual trading price) when Jupiter was opposite Pluto. When the planets formed aspect again in September 2001 after the 9/11 attacks, the low of the stock was $18.96 or exactly 1/4th. These seemingly weird numbers are not random at all.

Gann Square of the Circle Chart.JPG

2. 2nd, 3rd, 4th, 6th and 8th Harmonic – Square of 90

Square of 90 encompasses 5 harmonics. ½ of 90 is 45 or 8th harmonic and double of 90 is 180 or 2nd harmonic. 1/3rd of 90 is 30 or 12th harmonic, 2/3rd of 90 is 60 or 6th harmonic. 120 is simply double of 60. 

3. 5th Harmonic – Square of 72 or 144

72 is the 5th harmonic chart and square of 144 is 2 squares of 72. Treating 144 as a complete circle and dividing it by 12 and 8 (≡ 30° and 45° in a 360 circle respectively), we get 12 and 18. Using 12, we arrive at the Master 12 Chart. 18 ties into the 6 squares of 9 that follow. Similarly 10th harmonic is simply ½ of 72.


It can be said that square of 144 is Jupiter cycles of 12 years expressed in months. It is also equal to 2/3rd of the Uranus cycle in days (84 x 365 x 0.666 = 20420 and 144 x 144 is 20736 with a difference of 316 days). Square of 104 is the Mars cycle of 23 months in weeks. 4 squares of 52 are Saturn cycle (29.45772 x 365.25 = 10759 and 52 x 52 x 4 = 10816, a difference of 57 days). Square of 90 is the Mercury cycle and also 4 squares of 90 are the annual Sun cycle. However, all of this is just an attempt to linearize the natural cycles so that they can be measured in days and difference from actual cycles can be significant and hence not usable for precise trading purposes. Time measured in days, weeks, months and years works better than these linearized cycles. Master 12 chart is simply 30th harmonic chart. Although Gann mentions its use in months, it works well with all planets not just Jupiter. Given below is Gann square of 12.

Gann Square of 12.JPG

4. 7th Harmonic – Square of 52

DJIA high on September 3, 1929 was 386, that is, 7.5 times 51.43. NASDAQ Composite all time high in March 2000 was 5132.


5. 9th Harmonic – 6 squares of 9 (40°) Chart. This chart also has the error of 1 when used as the 9th harmonic chart. Additionally, the chart is cube of 9 chart because each side has 9 numbers. Numbers in these 6 squares cover only the faces of the cube and don’t cover the inside of the cube. To do so would require 729 (9 x 9 x 9) numbers, that is, additional 243 hidden numbers. 729 days are also two years in days tying beautifully into the square of 52 or 104 weeks.

DJIA low in July 1932 was 40.5, exactly half of 81.

Gann 6 Squares of Nine.JPG

In the materials available in the public domain, the squares of 52, 144 and 90 were used as calculators only. However, numbers can be inserted into them to arrive at important vibration points. These 3 calculators combined cover the harmonics created by dividing the circle by the first eight digits. This is very important and must be borne in mind at all times.


Platonic Solids and Master (universal, fixed, cannot be changed) Charts

Tetrahedron (4 faces), Octahedron (8 faces), Cube or Hexahedron (6 faces), Dodecahedron (12 faces), Icosahedron (20 faces) are the five solids described in Plato’s Timaeus in reference to classical elements. When you are thinking of creation, God and elements, it is natural to have this line of thought. The five elements are Fire, Earth, Air, Water and Sky.

Platonic Solids.JPG

Ideally, the solids should be arranged in the order of the natural signs of the natural horoscope, that is, Fire, Earth, Air and Water. However, doing so brings the cubes of natural numbers before their squares. The Universe could be substituted with ether to complete the five elements. Needless to say, one way or another, everything in our world is made up of these five elements. 


Gann took this a step further and added numbers to the solids as follows which leads to #6:


6. Squares of natural numbers to Tetrahedron (see Gann’s Coffee Rio Low 300 October 2, 1936 chart). This is my favourite chart because it includes squares both odd and even natural numbers. Some people call it triangle or helix chart. For Price-Time harmonic chart, that is, for us to run the planets around this, here is the view with one edge in the centre.

Gann Helix or Square of Numbers Chart.JP

7. Square of odd natural numbers to half of Octahedron, that is, 4 faces only (Square of 9), square of even natural numbers to the other half of Octahedron (Square of 4) - both charts are presented in the same order below;

Gann Square of 9.JPG

As is evident from the square of 9 chart above, important harmonics of 360 can be expressed as squares of natural numbers or square of harmonics points between the natural numbers. For example: 60 is 7.75 x 7.75, 80 is 9 x 9, 120 is 11 x 11, 144 is 12 x 12, 150 is 12.25 x 12.25, 210 is 14.5 x 14.5, 225 is 15 x 15, 240 is 15.5 x 15.5, 288 is 17 x 17, 300 is 17.33 x 17.33, 315 is 17.75 x 17.75 etc. Gann mentions error of 1 where he describes this chart because some numbers work fine with the chart starting at 1 while others work fine with the starting at 0. To achieve more accurate results, avoid this error of 1 in this and all other charts, I advise calculating the exact numbers algebraically when using these charts and calculators. 135 is 11.618 x 11.618, 180 is 13.414 x 13.414 (see other important ratios section) and so forth. This is same as squaring the circle in degrees and the error of 1 as Gann mentions while explaining the square of 9. However, we should continue with the squares beyond 19 and use BOTH exact numbers and numbers reduced by circles of 360. These numbers represent very powerful mathematical points of force in the universe. It can also be said that the chart is a square root calculator.

Personal Examples: I got married when Jupiter was 196 degree to my natal Jupiter. I lost my job in Vancouver when Jupiter was 1089 (33 x 33) degree (also 9 degree after full cycle reduction) and I got another job in Toronto when Jupiter was back at 1089! Yes, change of both job and place… and many more examples including the one in January 2019 when Jupiter was 1483 degrees (38.5 x 38.5). Intel (INTC) stock high/lows tie into the squares of natural numbers particularly when measured by the movement of Saturn. 

Gann Square of 4.JPG

Among the Egyptian pyramids, there is a pyramid with flat surface. Most people think that it is an incomplete pyramid and Egyptian universities teach as such. However, it is a COMPLETE pyramid. Here is why: When we connect diagonals of the square of 9, they intersect in the middle of the box containing number 1, that is, only one box (or stone, or tile) is required to form the top. When we connect the diagonals of the square of 4, they intersect where squares containing numbers 1, 2, 3 and 4 join. So, four boxes are required to form the top. Therefore, the top has to be a flat surface. A corollary to this is that when we are measuring the flat top pyramid, we should take one side of the top and divide it into two to get the proper unit of measurement used by the builders to build the monument.

Interesting Fact: A few years ago, on the advice of a renowned archeologist, a decision was made to celebrate the glory of ancient Egypt. Part of ceremonies was to complete the "incomplete pyramid" by installing the “missing piece”. It was cancelled at the last moment on intervention by free masons. Had the process gone ahead, it would have shown the wisdom of ancient Egyptians and ignorance of the present day Egyptians. 

8. Difference of cubes of natural numbers to cube - Cube Chart or Hexagon Chart

Gann Hexgaon Chart.jpg

Gann, Golden Mean (Phi), Square root of 2, Square root of 10, e, and pi

There are certain other important ratios found to exist in the nature, namely, 1.618 (φ), 1.414 (√2), 3.162 (√10), 2.718 (e), and 3.142 (Pi or ∏). However, there is no mention of any of these in the Gann literature anywhere. This begs the question: Did a serious student of natural law such as Gann miss these important numbers? Let’s examine them one by one.


Fibonacci ratio or Golden Mean or Phi or 1.618 is an important natural number and people have built market trading systems based on it alone. It is found in the pentagonal symmetry; many things existing in nature are found to have this ratio present including the human body and its beauty appeals to the human eye. Its inverse removes 1 before the decimal leaving 0.618. The ratio works on ANY TWO numbers as long as both numbers are not zero, not just on popularly believed 0, 1 sequence. Its square (0.618 x 0.618 = 0.382) of 0.382 is also important. When viewed in terms of cycles (circles) the other square (1.618 x 1.618 = 2.618) does not change its position. 8th division of the natural circle is 45 degrees angle. 3/8th is 135 degrees and 5/8th is 225 degrees. 3/8 of 1 is 0.375 and 5/8 is 0.625. Difference between these numbers and Fibonacci numbers is a meagre 0.007 (0.625 – 0.618 = 0.007, 0.382 – 0.375 = 0.007). Square root of 1.618 is 1.272. It is also the ratio of diameter of the moon to that of the earth and the human gestation period in days is close to this number. 100 or 10 x 10 is an important resistance level and 100/360 is 0.277. The difference between the two numbers is 0.005.


Square root of 2 is 1.4142. 150 degrees is five signs in a horoscope and an important angle. 150 divided by 360 gives us a value of 0.416. So, the difference between 0.414 and 0.416 is just 0.002.


Square root of 10 is 3.162. 60 degree is 6th harmonics. 1/6th of 1 is 0.166. The difference between the two numbers is 0.004.


Value of e is 2.718. 5/7th of the circle is 257.14 degrees and that of 1 is 0.714. The difference between 0.718 and 0.714 is just 0.004.


Pi or 3.1415 is the most commonly known approximate value. It is used in relation to the circle generally as 22/7 or more accurately as 355/113. An easy way to remember this number is 13,14,15 without 1 in the beginning. 51.43 degree is 1/7th of the circle. 1/7th of 1 is 0.142. The difference between the two numbers is negligible.


By now it should be clear why people relying solely on these ratios are missing most of the Gann’s system. It does not mean we should ignore these numbers. When they occur, they occur very precisely.

Then the next question is: Is this number to be ignored in favour of 8th harmonics. I don’t know, you be the judge by looking at the following examples:

(i) Nasdaq Composite High on March 10, 2000 was 5132.52. This number divided by Composite’s natal Sun and Uranus’ position at the time of high of 318.6 or 8.6 degree Aquarius gives 16.109 or 1.611 with decimal adjustment;

(ii) Nasdaq Composite Low in April 2001 was 1619.59;

(iii) Low in October 2002 was 1109.64 - (a) Multiply 1.618 by itself 5 times, that is, calculate its 5th power and see what you get.  (b) Divide the low by the Composite’s Pluto’s natal position of 179.34 or 29.34 degree Virgo, Yup! you get our favourite number again.

(iv) December 24. 2018 low was 6190.17.

Astrologers say the horoscope promises of the things to come. The above examples are mathematical proof that natal positions indeed provide price levels very precisely at appropriate time. This ties into Gann’s concept of active angles.

Please get used to decimal adjustment and transposition (in Gematria there is no difference between them) of numbers when dealing with markets. This is how nature expresses herself. Example:

March 10, 2000: Nasdaq Composite High was 5132.52

March 12, 2003: Nasdaq Composite Low was 1253.22

There was a difference of just 2 days. Both dates and levels were extremely important in the history of the index.

…and then on July 20, 2015: Nasdaq Composite High was 5231.94

When setting up these charts, please make sure to run the numbers and planets in the same direction. My preference here in Canada is anti-clockwise. Residents of Southern Hemisphere could do it clockwise. Of course, the real position is to hold the paper parallel to the floor with the horoscope facing upwards. 


Note: If you study the Bible, please make sure you use the version containing information in cubit. Because numbers have meaning (there is a full chapter dedicated to numbers and is generally ignored instead of being studied), their meaning gets lost when cubit get converted into foot/inch (Foot, Pound, Second or FPS system) or metre (Metre, Kilogram, Second or MKS system or the modern SI system). Also note that units are always singular although in our daily use we incorrectly use plurals such as inches, feet, miles, kilometres, litres, gallons etc. Most unit symbols are written in small letters.