Six handed siteswaps

The recipe

Take any siteswap. I’m going to choose the nine object pattern b9aab939abb6a69.

Subtract 6 from every number to give a derived siteswap. In my example the derived siteswap is 534453-334550403. (Despite the negative numbers, this is still theoretically a siteswap)!

Number the beats in a causal diagram as follows:numbered three person causal diagramNow for the first beat, 1, add the first number in the derived siteswap, 5, and you get 1+5=6. So on the diagram draw a line from beat 1 to beat 6:first throw of patternNote that 5 is the derived siteswap on beats 5, 10, and 11. So we can draw a similar line starting at each of these beats. Also the pattern repeats, so we can draw a similar line from beats 16, 20, 25, and 26:similar throws to the first throw

For the second beat, 2, add the second number in the derived siteswap, 3, and you get 2+3=5. So on the diagram draw a line from beat 2 to beat 5:second throw of the patternNote that 3 is the derived siteswap on beats 6, 8, and 15. So we can draw a similar line starting at each of these beats. Also the pattern repeats, so we can draw a similar line from beats 17, 21, 23, and 30:similar throws to the second throwFor the third beat, 3, add the third number in the derived siteswap, 4, and you get 3+4=7. So on the diagram draw a line from beat 3 to beat 7:third throw of the patternNote that 4 is the derived siteswap on beats 4, 9, and 13. So we can draw a similar line starting at each of these beats. Also the pattern repeats, so we can draw a similar line from beats 18, 19, 24, and 28:similar throws to the third throw

For the seventh beat, 7, add the seventh number in the derived siteswap, -3, and you get 7-3=4. So on the diagram draw a line from beat 7 to beat 4:the fourth throw of the patternAlso the pattern repeats, so we can draw a similar line from beat 22:similar throws to the fourth throwFor the twelfth beat, 12, add the twelfth number in the derived siteswap, 0, and you get 12+0=12. So on the diagram draw a line from beat 12 to beat 12 (or leave it out).

Note that 0 is the derived siteswap on beat 14. So we can draw a similar line starting at that beat. Also the pattern repeats, so we can draw a similar line from beats 27, and 29.

The result is the following pattern:

Martin’s one count feeding Jim’s two count

Brenda feeds on Martin’s one count. Her pattern is Adam Chris zip Adam Chris. In the diagram, Brenda throws straight passes to Adam and crossing passes to Chris. Chris and Adam pass to Brenda on Jim’s two count. Chris starts a third of a beat after Brenda and his pattern is self pass self pass hold. Chris throws straight passes to Brenda. Adam starts two thirds of a beat after Brenda and his pattern is pass self pass hold self. Adam throws crossing passes to Brenda.

If we relabel the throws in Chris’s pattern, then all Brenda’s passes are straight and Adam and Chris throw crossing passes to Brenda:martin's one count feeding jim's two countSo the siteswap for this feed is: b9aab939abb6a69. In six handed siteswap ‘b’ (or 11) is a straight pass to the person on your left, ‘a’ (or 10) is a crossing pass to the person on your right, 9 is a self, 6 is a hold, and 3 is a zip.animation of martin's one count feedCompare this pattern with Martin’s one count feed #3 from the article on period five feeds. In that feed, Adam and Chris start half a beat after Brenda (also they pass why not? instead of Jim’s two count). It’s probably easier to get the timing right if Adam and Chris start half a beat after Brenda. All of the period five feeds in that article can be described by six handed siteswap!

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 six hands, where one hand throws on each beat, an object is thrown six beats after it is caught. So when you subtract 6 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 six handed pattern. This is what the arrows in a causal diagram tell you: how many beats later an object will be caught.

Martin’s one count triangle

It’s possible for all three jugglers to feed Martin’s one count as a six handed siteswap. The siteswap for this pattern is aabb3.martin's one count triangleAdam starts with four clubs. His pattern is Brenda Chris Brenda zip Chris, with crossing passes to Brenda and straight passes to Chris. Brenda starts with two clubs a third of a beat later. Her first throw is left handed and her pattern is Chris zip Adam Chris Adam, with crossing passes to Chris and straight passes to Adam. Chris starts with three clubs a third of a beat after Brenda. His pattern is Brenda Adam Brenda Adam zip, with straight passes to Brenda and crossing passes to Chris.animation of martin's one count triangleIn the animation for this pattern there are four red clubs which are always thrown as crossing passes to the person on the right.

It’s natural to ask whether we can perform triangle patterns with any other period five patterns!

Parsnip triangle

In this parsnip triangle everyone passes straight doubles to the person on their right. The siteswap for this pattern is ddd33. In six handed siteswap a ‘d’ is a straight double to the person on your right.parsnip triangleChris starts with three clubs in his right hand and one club in his left hand. His pattern is double double zip double zip, with straight double passes to Adam. Adam starts with two clubs, one and a third beats after Chris. His pattern is double zip double double zip, with straight double passes to Brenda. Brenda starts with two clubs in her left hand and one club in her right hand, a third of a beat after Adam. Her first throw is left handed and her pattern is double double zip double zip, with straight double passes to Chris.animation of parsnip triangleMaybe triangle

In this maybe triangle everyone feeds on maybe, throwing straight passes to the person on their right, and crossing passes to the person on their left. The siteswap for this pattern is b9ca3. In six handed siteswap a ‘c’ is a heff.maybe triangleChris starts with three clubs and his pattern is Adam self zip heff Brenda, with crossing passes to Adam and straight passes to Brenda. Brenda starts with four clubs, two thirds of a beat after Chris. Her pattern is Adam Chris self zip heff, with straight passes to Adam and crossing passes to Chris. Adam starts with two clubs, two thirds of a beat after Brenda. His pattern is heff Chris Brenda self zip, with straight passes to Chris and crossing passes to Brenda.animation of maybe triangleIn the animation for this pattern there are two red clubs, which are always crossing passes to the person on the right, two green clubs, which are right hand straight passes to the person on the left and left hand self throws, two blue clubs, which are left hand straight passes to the person on the left and right hand self throws, and three white clubs, which are heffs and zips. Compare this with the colour coding for the anticlockwise pass pass self runaround and the pass pass self feast in the article on three person runarounds.

There are two anagrams of this siteswap: ac9b3 and abc39, the second of which was discovered by Bernard, Christoph, and Evl from Germany, and is known as pentagram.

Why not? triangle

In four handed siteswap the anagrams of maybe are not why and why not? This is not the case in six handed siteswap! However we can make a why not? triangle, where everyone’s pattern is not exactly the same. The siteswap for this pattern is bbbcc933aaac993.why not? triangleEveryone starts with three clubs. Adam’s pattern is Chris heff zip Brenda self, with straight passes to Chris and crossing passes to Brenda. Brenda starts a third of a beat later with her left hand. Her pattern is Adam heff zip Chris self, with straight passes to Adam and crossing passes to Chris. Chris starts a third of a beat after Brenda. His pattern is Brenda self Adam heff zip, with straight passes to Brenda and crossing passes to Adam.animation of why not? triangleIn the animation the pattern is colour-coded so that Adam and Brenda pass green clubs, Adam and Chris pass red clubs, and Brenda and Chris pass blue clubs.

Menno’s triangle

In six handed siteswap there are many period five patterns that you don’t get with four handed siteswap. The anagrams of the maybe triangle are two examples, Menno’s triangle is another. (I call this pattern Menno’s triangle because Menno taught it to me. I don’t know if he created it!) The siteswap for Menno’s triangle is 9e9a3. In six handed siteswap an ‘e’ is a crossing double to the person on the left.menno's triangleChris starts with three clubs in his right hand and one club in his left hand. His pattern is Adam double to Brenda zip self self. Brenda starts with three clubs, two thirds of a beat after Chris. Her pattern is self Chris double to Adam zip self. Adam starts with two clubs, two thirds of a beat after Brenda. His pattern is self self Brenda double to Chris zip. All the passes cross.animation of menno's triangleIn the animation for this pattern, there are two red clubs which are always passed to the person on the right.

There are two anagrams of this siteswap: e99a3 and 99ea3.

Pass pass zip feed

You can create other feeds with six handed siteswap. One interesting feed is pass pass zip feeding three count. The siteswap for this feed is: b9aab9399.pass pass zip feedEveryone starts with three clubs. Brenda’s pattern is Adam Chris zip with straight passes. Adam and Chris pass to Brenda on three count with crossing passes. Chris starts a third of a beat after Brenda and his pattern is self pass self. Adam starts a third of a beat after Chris and his pattern is pass self self. Note that I have relabelled the beats in Chris’s pattern so that all of Brenda’s passes are straight.animation of pass pass zip feedMild madness feeds

Another interesting six handed siteswap feed is mild madness feeding Jim’s three count. This feed was created by Martin Frost. The siteswap for this feed is: b9aab939999abb6a69999.martin's mildness feedEveryone starts with three clubs. Brenda’s pattern is Adam Chris zip self Adam Chris self with straight passes. Adam and Chris pass to Brenda on Jim’s three count with crossing passes. Chris starts a third of a beat after Brenda and his pattern is self pass self self pass hold self. Adam starts a third of a beat after Chris and his pattern is pass self self pass hold self self. Note that I have relabelled the beats in Chris’s pattern so that all of Brenda’s passes are straight. This pattern is known as Martin’s mildness.animation of martin's mildness feedIn the animation for this pattern Brenda passes green clubs with Adam and red clubs with Chris.

If you take the causal diagram for Martin’s mildness and relabel the beats in Brenda’s pattern, then Brenda throws crossing passes and Adam and Chris throw straight passes. This pattern is known as Martin’s madness.martin's madness feedMild madness triangle

It’s possible for all three jugglers to feed mild madness as a six handed siteswap. The siteswap for this pattern is ab9b9a3. When I feed mild madness I always throw the first of each pair of passes to the person on the left. To ensure that this happens in this triangular pattern I had to turn the causal diagram for the pattern upside down. So in this pattern ‘a’ is a crossing pass to the person on the left and ‘b’ is a straight pass to the person on the right! I understand that some people like to throw the first of the two passes to the person on the right.mild madness triangleEveryone starts with three clubs. The pattern for Chris is Brenda Adam zip self Brenda Adam self, with crossing passes to Brenda and straight passes to Adam. Brenda starts a third of a beat later with her left hand. Her pattern is Chris self Adam Chris zip self Adam, with straight passes to Chris and crossing passes to Adam. Adam starts a third of a beat after Brenda. His pattern is self Chris Brenda self Chris Brenda zip, with crossing passes to Chris and straight passes to Brenda.animation of mild madness triangleIn the animation the pattern is colour-coded so that Adam and Brenda pass green clubs, Adam and Chris pass red clubs, and Brenda and Chris pass blue clubs.

If you relabel the beats in Chris’s pattern then Adam feeds Martin’s mildness, Brenda feeds Martin’s madness, and Chris’s pattern is unchanged.mild madness triangle variationThere are several anagrams of the siteswap ab9b9a3.

Jim’s two count feast

This is another period seven six handed siteswap. Everyone passes on Jim’s two count and passes to everyone else including themselves. They throw straight passes to the person on their left and crossing passes to the person on their left. The siteswap for this pattern is: ab96999.jim's two count feastEveryone starts with three clubs. The pattern for Adam is Brenda hold self self self Chris self, with crossing passes to Brenda and straight passes to Chris. Brenda starts with her left hand, a third of a beat after Adam. Her pattern is Adam self Chris hold self self self, with straight passes to Adam and crossing passes to Chris. Chris starts a third of a beat after Brenda. His pattern is self self Brenda self Adam hold self, with straight passes to Brenda and crossing passes to Adam.animation of jim's two count feastIn the animation the pattern is colour-coded so that Adam and Brenda pass green clubs, Adam and Chris pass red clubs, and Brenda and Chris pass blue clubs.

If you relabel the beats in Brenda’s pattern, then all Adam’s passes are straight, and all Chris’s passes are crossed. Brenda’s pattern is unchanged, except now she starts right handed.jim's two count feast variationYou can create similar feasts for other Jim’s patterns.


* Animated gifs were created using JoePass. Here are the pattern files in zip format.

 

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