Harmonic charts are usually used to investigate minor aspects, including the infinite vibrations of Vibrational Astrology.
In this case, I will focus on the Square, which is the 4th vibration because it divides the circle into 4. We’ll work step by step to calculate the position of the planets of the square in the 4th Harmonic Chart.
Then, I’ll show you an actual example of how harmonic charts work at the end.
Aspects in astrology are based on particular divisions of the circle. For example, lines through the points of a square would divide the circle into 4 pieces. Each of these divisions would be 90 degrees (360 / 4).
Step 1
The first step is to calculate the position of the planets (and angles if you have some thing precise, like a lunation or ingress)
The position = the degrees between 0 Aries and the planet.
The first point of the square going counterclockwise is at 15 Taurus. So, you count 30 degrees for Aries plus the 15 degrees of Taurus. So the point is at 45 degrees.
The second point of the square is at 15 Leo. There are 4 signs before Leo at 30 degrees each, so 0 Leo is 120 degrees. Add the 15 to that and you have 135 degrees for the position of the second point.
The third point is 15 Scorpio. We have 7 signs before that, so 0 Scorpio is 210 degrees. Add 15 to that and it is 225 degrees.
I always double check that I get to 270 on the top, and we do.
There are 10 signs before Aquarius, so we start at 300 and add 15 for 315 degrees.
The computer calculates the position of every planet in the chart, but we’re going to stop there.
Step 2
Multiply by the number of the harmonic, in this case 4
Step 3
The answer you calculated in Step 2 is the new position of the planets in the harmonic chart.
Starting at 0 Aries, move counterclockwise by the number of degrees , 180 in this case.
45 degrees which is 15 Taurus x 4 which is the harmonic = 180 degrees
So that point of the square moves to 0 Libra
For the second point, we see that the answer is more than 360.
That means, we need to go around the circle in order to get to the right position.
When calculating, we subtract the multiple of 360 that we need to subtract in order to end up with a number below 360.
In this case, we just need to go around the circle one time, so we subtract 360 from our planetary position of 540 and end up with 180 degrees. 0 Libra
The other points work the same, but we need to go around the circle more times to get below 360, so we subtract higher multiples.
In the end, we see that all of them end up at 0 Libra.
The 4th harmonic divides the circle into 4 and the points of the square can divide the circle into 4, so this is an expected result.
The planets in a square (or grand cross in this case) will be in a conjunction in the 4th harmonic.
Another Way to Look at It
Math isn’t for everybody, so I wanted to add this here. Another way to visualize it is to say that the 4th harmonic is the same as putting 4 complete zodiacs in the circle. This is another way of thinking of going around the circle 4 times to place the point in the new position on the zodiac.
In this case, I left the purple squares exactly where they were and put a full zodiac in each quadrant. The circled numbers indicate which passage of the zodiac we are on.
In the bottom left quadrant, we are still on the 1st pass.
After we passed 0 Aries (360) and continued moving to 540, we ended up in the bottom right quadrant. This is the 2nd pass.
As you can see, All of the points end up at 0 Libra.
The number the harmonic you are calculating is the number of passes you need or the number of full zodiacs that need to fit in the zodiac.
This is why harmonic charts can be seen as a magnification of the chart. They focus in on a particular division of the circle so it can be seen more clearly.
A Real Example
Harmonic charts are not usually used for squares, because they are easy to see in the chart.
Natal Chart
Look at this chart
Which minor aspect is prominent in this chart?
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The Reveal
And when I change the aspect set to show quintiles, it becomes very clear.
Would you have even guessed?
5V chart
People who work with minor aspects, and people who work with the infinite divisions of the chart in Vibrational Astrology, use harmonic charts to magnify the chart and see what is going on in the harmonic they are interested in.
This person is the strongest 5V in the database, so what we mainly see is a large conjunction. Most people aren’t as concentrated in 5V as this person, so their chart will have other relationships or midpoints to analyze.
The planets that are in aspect to one another in the 5V chart are not pure 5V, but they are part of the 5V “family”
Trime
I can show what I mean with this trine he has here. Pluto trine Mars.
Note that Pluto is not part of the main conjunction here. The 4 planets are at 23 and Pluto is at 2.
A trine is a triangle which divides the circle into 3.
If we want to see the trine in the conjunction, we multiple 5V x 3 trine and get 15V.
Mars has joined Pluto in a conjunction in the 15V.
Just what we expected.
5V
Back to 5V
The Pluto is also square Jupiter
And the conjunction is in a 16ths relationship with Saturn. (dashed lines are 1/16)
Square
Let’s look at 20 V to bring Pluto and Jupiter together
In the 20th harmonic, Pluto and Jupiter are together and our dotted lines have become a square. (1/16 x 4 = 1/4 = square)
Notice how the magnification from the multiple trips around the circle moves the planets farther apart from each other.
That is normal.
Conclusion
In this explanation, I moved planets into a conjunction to help you understand how harmonic charts work. Often, we also learn more by doing the opposite.
For example, with a strong 44, you can see the interactions with the conjunction in 44.
But you will gain more understanding of the interactions between the planets if you look at the grand cross (or other square aspect) in 11.
The possibilities are endless!
Link up to Overview of Vibrational Astrology