Decans and Duads: The Math Behind it All

Quick Information:

Decans and duads were used by ancient astrologers as a way to more accurately interpret the influence, or impact, of a planetary placement based on where it lies in it's "parent" sign (the sign in which inhabits a given decan and duad). The main difference between the two, are that decans form 3 equal subdivisions while duads form 12. Both decans and duads are utilized for the same purposes and information.

Decans are subdivisions that split each sign into thirds; with each decan taking up 10* of it's "parent" sign (approximately 10 days). In decans, the element must be the same inside each sign. So if the sign is Sagittarius (fire element), for instance, then the decans inside that sign must all be fire signs. The first decan will always be the same sign as it's "parent" and will take up the degrees from 0*00'00" through 9*59'59". So sticking with the Sagittarius example, our first decan would be in Sagittarius. Now just like a zodiac wheel, decans have a specific order that they must go in. After Sagittarius, the following fire sign in the zodiac would be Aries. So the second decan in this example falls in Aries and would take up the degrees 10*0'0" through 19*59'59". Following the second decan, the third decan would fall into Leo -- as this is not only the next fire sign along the zodiac wheel, but is also the only remaining fire sign left in the zodiac. The third decan would take up the degrees 20*0'0" through 29*59'59". 

Below, I have created a table for easy reference to the decan placements of each sign. I've also included the planetary rulers of each of these and well as energy associations in regards to decan influences.

Again, the big difference between decans and duads, are the amount of subdivisions. Duads create 12 subdivisions in a sign, each one taking up only 2.5* (approximately 2.5 days). This is a dramatic change versus the 10* subdivisions in decans. Because there are 12 subdivisions, each sign in the zodiac are used. Just like with decans, the first subdivision belongs to the "parent" sign and the each next sign will follow the order of the zodiac. (We're going to go ahead a use Sagittarius as our "helper" for the rest of this blog post) So if the "parent" sign is in Sagittarius, that means that the first duad would have to be in Sagittarius, as well. Following Sagittarius, the second decan would fall in Capricorn, and so-forth.

Below, you'll see that I've also created a reference table to use with finding the duad placements in each sign, just as I did for the decans.

The Math No One Talks About:

Now, it's time to have some fun;

This part is going to be sort of the classic "math book" style of teaching -- containing mainly example equations and a little bit of reading material. But if you don't get it or don't think I did a great job at explaining, feel free to reach out to me and I will absolutely help answer any of your questions.

Okay, so it's important to know:
1* = 60' = 3600"

1' = (1/60)* = 0.01666667

1" = (1/3600)* = 2.77778e-4* = 0.000277778*

In order to do this, we have to do two conversions. First, we need to convert our angle degrees into decimal degrees; and then at the end, we will convert it all back.

For angle with d integer degrees, m minutes, and s seconds:

d*m's"

For converting integer degrees into decimal degrees, you will need the following formula:

dd = d + m/60 + s/3600

Ex.) We'll do a quick equation with a degree that's at 15*30'45"

15*30'45"

[Remember; (dd) = d + m/60 + s/3600]

dd = 15 + 30/60 + 45/3600 = 15.5125

So, our decimal degree after converting the angular degree is; 15.5125*

Ex.) We're going to pretend that we have a sun placement at that same 15*30'45" that we would like to find the decan and duad for. And (why not?) let's pretend that this placement is in the sign of Sagittarius:

DECAN SOLUTION:

So, if you reference the decan table, you will see that the degree coordinates of 15*30'45" in Sagittarius fall into the second decan in Aries. We have to now subtract the lower limit of the decan, that it falls into, from the angular degree that the placement has.

15*30'45" - 10*00'00" = 5*30'45"

So we now know that our Sagittarius sun is located in the second decan of Aries at 5*30'45". Now we can get to work...

1) Separate your decan angular degree components

5*30'45"

d=5

m=30

s=45

2) Remember our equation; (dd = d + m/60 + s/3600)

dd = 5 + 30/60 + 45/3600 

dd = 5.5125

3) Now, we need to multiply by 3 (this is because we have three subdivisions, or decans, in our "parent" sign):

5.5125 x 3 = 16.5375

4) Now that we have solved for our decimal degree, we need to convert back to an angular degree:

16.5375 = 16 + (.5375)

5) Multiply only the decimal portion for minutes (.5375) by (60)

m = integer((dd) - d) x 60

16 + (.5375) (60) =

16 + (32/60)

6) Multiply for seconds (.5375 - 32/60) 3600 = 15

s = integer((dd) - d - m/60) x 3600 

7) Plug it in:

d=16

m=32

s=15

8) ANS) 16*32'15"

9)  ANS) Sagittarius sun locatied at 16*32'15" in the second decan in Aries

DUAD SOLUTION:

Everything is the exact same for duads as it is for decans aside from the same difference we've been talking about this whole time -- there are 12 duards versus 3 decans. So where we multiplied our (dd) by 3 before, we will be multiplying by 12 instead. (**See step 3**)

So a Sagittarius sun at 15*30'45" would fall into the seventh duad in Gemini. The lower limit of the seventh duad is 15*, so we will subtract 15*00'00" from 15*30'45" to get our duad angular degree:

15*30'45" - 15*00'00" = 0*30'45"

Now, once again, we go through all of our steps:

1) Separate your angular degree components:

0*30'45"

d=0

m=30

s=45

2) Remember our equation; (dd = d + m/60 + s/3600)

dd = 0 + 30/60 + 45/3600 

dd = 0.5125

3) Now, we need to multiply by 12 (this is because we have twelve subdivisions, or duads, in our "parent" sign):

(.5125) (12) = 6.15

4) Now that we have solved for our decimal degree, we need to convert back to an angular degree:

6.15 = 6 + (.15)

5)  Multiply only the decimal portion for minutes (.15) by (60) 

m = integer((dd) - d) x 60

6 + (.15) (60) =

6 + (9/60)

6) Multiply for seconds (.15 - 9/60) 3600 = 0

s = integer((dd) - d - m/60) x 3600 

7) Plug it in:

d=6

m=09

s=00

8) ANS) 6*09'00"

9) ANS) Sagittarius sun located at 6*09'00" in the seventh duad in Gemini

FINAL EXACT DEGREE PLACEMENTS:

Sun located at 15*30'45" in the sign of Sagittarius.

Sun located at 16*32'15" in Sagittarius in the 2nd decan of Aries.

Sun located at 6*09'00" in Sagittarius in the 7th duad of Gemini

I hope that this was able to teach a couple of people something new. Maybe some people never realized how much math actually goes into astrology. If you have any questions or suggestions on what I should write about next, please let me know on twitter (@BSinLeo).

Thank you,

Brendon S.