The recipe
•Take any siteswap. I’m going to choose the five object pattern 78622.
•Subtract 4 from every number to give a derived siteswap. My derived siteswap is 342-2-2. (Despite the negative numbers, this is still theoretically a siteswap)!
•Number the beats in a causal diagram as follows:
•Now for the first beat, 1, add the first number in the derived siteswap, 3, and you get 1+3=4. So on the diagram draw a line from beat 1 to beat 4:
•For the second beat, 2, add the second number in the derived siteswap, 4, and you get 2+4=6. So on the diagram draw a line from beat 2 to beat 6:
•For the third beat, 3, add the third number in the derived siteswap, 2, and you get 3+2=5. So on the diagram draw a line from beat 3 to beat 5:
•For the fourth beat, 4, add the fourth number in the derived siteswap, -2, and you get 4-2=2. So on the diagram draw a line from beat 4 to beat 2:
•For the fifth beat, 5, add the fifth number in the derived siteswap, -2, and you get 5-2=3. So on the diagram draw a line from beat 5 to beat 3:
•As there is no sixth number in the derived siteswap, for the sixth beat, 6, we return to the beginning of the derived siteswap. When you add the first number, 3, you get 6+3=9. So on the diagram draw a line from beat 6 to beat 9:
•If you apply the same procedure for all the remaining beats you end up with the following pattern:
Five club why not?
This is the diagram for ‘five club why not?’ You can tell it’s a five club pattern from the diagram. There’s one continuous line running through the diagram, representing a club in the air at any given moment, and there are four hands juggling the pattern, which can each hold one club. It’s not surprising that it’s a five club pattern, given that we started with a five object siteswap!
Causal diagrams assume that each hand starts holding one club. In the diagram Adam’s first right hand beat has one arrow pointing away from it, but no arrow point to it, so he starts with two clubs in his right hand. Adam throws straight passes and his pattern is: pass self zip heff zip. A zip, or a hand-across, is where you hand a club from one hand to another. A heff is another name for a self-double throw. Brenda starts slightly after Adam and she throws crossing passes. Her pattern is: heff zip pass self zip. It’s essentially the same as Adam’s pattern, but Brenda starts with a heff.
In a four handed siteswap a 7 is a single pass. For one juggler it’s a straight pass and for the other it’s a crossing pass. A 6 is a single self throw, an 8 is a heff, and a 2 is a zip.
Why does this recipe work?
On any given beat, the number in a siteswap tells you how many beats later the same object will be thrown again. In a passing pattern with four hands, where one hand throws on each beat, an object is thrown four beats after it is caught. So when you subtract 4 from each number in a siteswap, the numbers in the derived siteswap tell you how many beats later an object will be caught in a four handed pattern. This is what the arrows in a causal diagram tell you, how many beats later an object will be caught.
Parsnip
In any siteswap you can swap any two numbers to get another siteswap. The number that moves right decreases by 1 with each step and the number that moves left increases by 1 with each step. I call this the downright rule, to help me remember that the number that moves right decreases.
If you swap the 8 and the 6 in the siteswap 78622 you get another siteswap: 77722. When you apply the recipe to this siteswap you get the following causal diagram:
This is the diagram for the five club pattern known as parsnip. Adam starts with two clubs in his right hand and one in his left hand. He throws straight passes and his pattern is: pass pass zip pass zip. Brenda starts slightly later holding one club in each hand. She throws crossing passes and her pattern is: pass zip pass pass zip.
Five club not why
If you swap the first two 7s in the siteswap 77722 you get another siteswap: 86722. Here’s the causal diagram for 86722:
This is the diagram for five club not why. Adam starts with two clubs in his right hand and one in his left hand. He throws straight passes and his pattern is: heff pass zip self zip. Brenda starts slightly later holding one club in each hand. She throws crossing passes and her pattern is: self zip heff pass zip.
Not why has the same throws as why not? but in a different order. Also these patterns fit together, so Adam can juggle why not? while Brenda does not why.
The siteswap for this hybrid pattern is: 7268278226. This is a period 10 siteswap. Whenever you juggle a siteswap with an even period as a four handed siteswap, each juggler has a different pattern.
Martin’s one count
You can add the period of a siteswap to any throw to get another siteswap with an extra object. If you add 5 to the first 2 in the five object siteswap 77722 you get the six object siteswap: 77772. Here’s the causal diagram for 77772:
This pattern is known as Martin’s one count and was discovered by Martin Frost. Both jugglers start with two clubs in their right hand and one in their left hand. Adam throws straight passes and his pattern is: pass pass zip pass pass. Brenda starts slightly later and throws crossing passes. Her pattern is: pass pass pass pass zip.
Parsnip is a good five club practice pattern for Martin’s one count.
Jim’s two count
If you swap the last two numbers in the siteswap 77772 you get another siteswap: 77736. To perform a 3 in a four handed siteswap, you would have to hand a club to your passing partner. In a normal face to face passing pattern this is not practical, so you can’t pass 77736 as a normal four handed siteswap. (You can’t pass siteswaps with 1s in them for the same reason)! You may be able to perform patterns like these side by side or back to back.
You can swap the third and fourth numbers in 77736 to get another siteswap: 77466. Here’s the causal diagram for 77466:
This pattern is known as Jim’s three count. Both jugglers start with two clubs in their right hand and one in their left hand. Adam throws straight passes and his pattern is: pass hold self pass self. Brenda starts slightly later and throws crossing passes. Her pattern is: pass self pass hold self.
Note that a 4 is a hold in four handed siteswap.
Why not?
If you swap the third and fifth numbers in the siteswap 77466 you get another siteswap: 77862. Here’s the causal diagram for 77862:
This pattern is known as why not? Both jugglers start with two clubs in their right hand and one in their left hand. Adam throws straight passes and his pattern is: pass heff zip pass self. Brenda starts slightly later and throws crossing passes. Her pattern is: pass self pass heff zip.
There is an alternative start for why not?
Adam starts with two clubs in each hand and Brenda starts with one club in each hand. Adam throws straight passes and his pattern is: pass self pass heff zip. Brenda starts slightly later and throws crossing passes. Her pattern is heff zip pass self pass.
When you’re trying to learn why not? you can throw it as a trick in Jim’s two count.
In Jim’s two count, Brenda replaces her normal pattern: pass self pass hold self, with: pass self pass heff zip, and then returns to passing Jim’s two count. Once you have learned this trick with both hands, you can try doing it continuously.
Not why
If you add 5 to the first 2 in the siteswap 86722 (five club not why) you get the six object siteswap: 86772. Here’s the causal diagram for 86772:
This pattern is known as not why. Both jugglers start with two clubs in their right hand and one in their left hand. Adam throws straight passes and his pattern is: heff pass zip self pass. Brenda starts slightly later and throws crossing passes. Her pattern is: self pass heff pass zip.
When you’re trying to learn not why you can throw it as a trick in Jim’s two count.
In Jim’s two count, Brenda replaces her normal pattern: pass self pass hold self, with: pass heff pass zip self, and then returns to passing Jim’s two count. Once you have learned this trick with both hands, you can try doing it continuously.
Not why has the same throws as why not? but in a different order. Also these patterns fit together, so Adam can juggle why not? while Brenda does not why.
The siteswap for this hybrid pattern is:7788277266. Both jugglers can switch between why not, not why? or Jim’s two count without changing their partner’s pattern.
Maybe
If you add 5 to the first 2 in the siteswap 78622 (five club why not?) you get the six object siteswap: 78672. Here’s the causal diagram for 78672:
This pattern is known as maybe. Both jugglers start with two clubs in their right hand and one in their left hand. Adam throws straight passes and his pattern is: pass self zip heff pass. Brenda starts slightly later and throws crossing passes. Her pattern is: heff pass pass self zip.
Maybe has the same throws as not why and why not? but in a different order. Despite this you can’t pass maybe when your partner is passing why not? or not why.
Seven club one count
If you add 5 to the 2 in the six object siteswap 77772 you get the seven object siteswap: 77777. Here’s the causal diagram for 77777:
This is seven club one count. Adam starts with two clubs in each hand and Brenda starts with two clubs in her right hand and one club in her left hand. Adam throws straight passes and Brenda starts slightly later and throws crossing passes. Strictly speaking this is a period 1 pattern, but arguably it’s also a period 5 pattern!
Martin’s one count is a good six club practice pattern for seven club one count.
Funky bookends
If you swap the last two 7s in the siteswap 77777 you get another siteswap: 77786. Here’s the causal diagram for 77786:
This pattern is known as funky bookends. Adam starts with two clubs in each hand and Brenda starts with two clubs in her right hand and one club in her left hand. Adam throws straight passes and his pattern is: pass pass self pass heff. Brenda starts slightly later and throws crossing passes. Her pattern is: pass heff pass pass self.
You can pass funky bookends with someone else who is passing parsnip!
This six club pattern is a good practice pattern for funky bookends. In this pattern both jugglers start with two clubs in their right hand and one in their left hand. Adam throws straight passes and his pattern is: pass pass zip pass zip. Brenda starts slightly later and throws crossing passes. Her pattern is: pass heff pass pass self. The siteswap for this pattern is: 7778277726.
This is essentially the same pattern. Adam starts with two clubs in each hand and Brenda starts with one club in each hand. Adam throws straight passes and his pattern is: pass pass self pass heff. Brenda starts slightly later and throws crossing passes. Her pattern is: pass zip pass pass zip.
Another bookends pattern
If you swap the third and fourth numbers in the siteswap 77786 you get another siteswap: 77966. Here’s the causal diagram for 77966:
This pattern is another seven club bookends pattern. Adam starts with two clubs in each hand and Brenda starts with two clubs in her right hand and one club in her left hand. Adam throws straight single passes and crossing double passes. His pattern is: single double self single self. Brenda starts slightly later and throws crossing single passes and straight double passes. Her pattern is: single self single double self.
Note that a 9 is a double pass in four handed siteswap. One juggler throws crossing doubles and the other juggler throws straight doubles.
Five count popcorn
If you swap the second and third numbers in the siteswap 77786 you get another siteswap: 78686. Here’s the causal diagram for 78686:
This pattern is known as five count popcorn. Adam starts with two clubs in each hand and Brenda starts with two clubs in her right hand and one club in her left hand. Adam throws straight passes and his pattern is: pass self self heff heff. Brenda starts slightly later and throws crossing passes. Her pattern is: heff heff pass self self.
You can pass five count popcorn with someone else who is passing five club why not?!
This six club pattern is a good practice pattern for five count popcorn. In this pattern both jugglers start with two clubs in their right hand and one in their left hand. Adam throws straight passes and his pattern is: pass self zip heff zip. Brenda starts slightly later and throws crossing passes. Her pattern is: heff heff pass self self. The siteswap for this pattern is: 7868278626.
This is essentially the same pattern. Adam starts with two clubs in each hand and Brenda starts with one club in each hand. Adam throws straight passes and his pattern is: pass self self heff heff. Brenda starts slightly later and throws crossing passes. Her pattern is: heff zip pass self zip.
Five count popcorn with triple-self throws
If you swap the second and fourth numbers in the siteswap 78686 you get another siteswap: 7a666. Here ‘a’ stands for 10. Here’s the causal diagram for 7a666:
Adam starts with two clubs in each hand and Brenda starts with two clubs in her right hand and one club in her left hand. Adam throws straight passes and his pattern is: pass self self triple-self self. Brenda starts slightly later and throws crossing passes. Her pattern is: triple-self self pass self self.
Note that ‘a’ is a triple-self in four handed siteswap.
Patterns with other periods
This article is about patterns whose siteswap is period 5, although we have seen some period 10 patterns. We can make four handed patterns with siteswaps with other periods. Here are some examples from the article on ‘tricks in three count/causal diagrams’.
The siteswap for five club three count is: 7446464.
The siteswap for Jim’s three count is: 7746666.
The siteswap for seven club three count is: 966.
The siteswap for French three count is 786.
Afterthoughts
As I was thinking about how to explain four handed siteswaps, it struck me that you could apply the same recipe to the causal diagram for synchronous passing patterns whose beats are numbered as follows:
For example here’s the causal diagram for the siteswap 756666:
This is the diagram for three count! When you think of four handed siteswaps like this the odd height throws have different meanings for each juggler. For Adam a 7 is a straight single pass and a 9 is a crossing double pass as before. But for Brenda a 5 is a straight single pass and a 7 is a crossing double pass. For both jugglers a 2 is a zip, a 4 is a hold, a 6 is a self, and an 8 is a heff as before.
Let’s try creating some tricks using the siteswap 756666756666. If you swap the fifth and seventh throws you get: 756696456666. Here’s the causal diagram for this pattern:
This is the causal diagram for an early double in three count.
If you swap the sixth and eighth throws you get: 756667746666. This is the same trick for Brenda.
If you swap the seventh and tenth throws you get: 756666956466. Here’s the causal diagram for this pattern:
This is a causal diagram for a late double in three count. Note that this creates a hold in Brenda’s pattern.
If you swap the eighth and ninth throws you get: 756666774666. This is the same trick for Brenda.
These are both tricks I already knew. However if you swap the seventh and ninth throws you get: 756666855666. Here’s the causal diagram for this pattern:
For this trick Adam throws a heff on the pass beat followed by a crossing zap on the next beat. A zap is a fast half spin pass. This is a new trick to me.
If you swap the eighth and tenth throws you get: 756666786366. This is the same trick for Brenda. Note in a synchronous pattern a 3 is a zap for Brenda.
* Animated gifs were created using JoePass. Here are the pattern files in zip format.
