4-Handed Siteswap

See the following article: 4-Handed Siteswap II

Siteswap is a compact notation that describes some aspects of juggling patterns. It can also be used to describe certain passing patterns, as I will explain in this article.

How to use siteswap as notation for passing patterns

A siteswap tells you how many throws in the future a club should be thrown again. (In principle, siteswaps can be juggled with any objects, so whenever I write “club” you can imagine your favourite prop instead.) Consider the following example:

Let’s observe Alice and Bob while they pass 7 clubs in a waltz rhythm. They are standing opposite each other (and looking up slightly). The order in which their hands throw is
1) Alice right,
2) Bob right
3) Alice left
4) Bob left
and then again from the beginning.

Alice throws a floaty double cross pass with her right hand to Bob’s right hand. Before Bob throws this club again, he makes two other throws with the right hand. Fig. 1 shows how this is represented in a juggling diagram. (Note that in a juggling diagram you draw an arrow between two consecutive throws of a club. In a causal diagram, by contrast, the arrow only goes as far as the throwing beat on which the club is caught. Thus, causal diagrams are better for showing what the juggler does and sees, whereas juggling diagrams come closer to illustrating what siteswap tells us.)

Siteswap: 9 (Fig. 1)

The first number in the siteswap for this pattern is therefore a 9, as you can work out by counting the number of throws between two throws of the same club.
Now it’s Bob’s turn to do a single self, i.e. a throw from his right hand to his own left hand.

Siteswap: 9 6 (Fig. 2)

In two-handed siteswap a single self would be a 3, but this is a passing pattern, so here the number is 6. It is twice as big because Alice does a throw in between each two throws of Bob’s, and her throws are counted too.
Now Alice does her self…

Siteswap: 9 6 6 (Fig. 3)

…followed by a floaty double pass from Bob…

Siteswap: 9 6 6 9 (Fig. 4)

…which also leads to a point 9 throws ahead, this time from Bob’s left to Alice’s right hand. You will notice that you cannot tell simply from the number 9 whether it is a straight pass or a cross pass. In order to know that, you have to know who throws it. Next is a single self from Alice…

Siteswap 9 6 6 9 6 (Fig. 5)

…and another single self from Bob.

Siteswap: 9 6 6 9 6 6 (Fig. 6)

There seems to be a recurring pattern here: 966. And indeed, that’s exactly how it goes on.

Siteswap: 9 6 6 9 6 6 9 6 6 9 6 6 9… (Fig. 7)

OK, the juggling diagram starts to get confusing when the numbers are that high, but that is where causal diagrams come in.

How can you pass siteswaps?

The first thing you have to know about siteswap is that the number of clubs you need to throw a siteswap is equal to the average of the numbers in the siteswap. For example, in the 966 waltz you need (9+6+6)/3 = 7 clubs.

With the aid of a juggling diagram, or simply by counting the hands in the right order, you can translate the siteswap numbers into throws.
0: the hand stays empty
2: hand the club across to your own other hand (the handacross or zip)
4: strictly speaking, this is a quick throw to the same hand, but you could also do a flourish or simply hold onto the club for one beat (a hold)
6: a basic three-club cascade throw (a single self)
7: a floaty single pass, with Alice throwing straight but Bob throwing across (as in 7 club one count passing)
8: a double-spin throw into the same hand, as in the 4-club fountain (also known as a straight double self)
9: a floaty double pass, this time with Alice throwing across but Bob throwing straight
A=10: a triple to your own other hand (triple self)
B=11: a floaty triple pass in the direction of a 7

Floaty passes are slightly higher – and therefore stay in the air longer – than passes in synchronous patterns, in which the partners throw at the same time. What about the missing numbers, 1, 3 and 5? A 3 would be a very fast pass, and a 1 would be a very, very, very fast pass, but in practice they are virtually impossible to do if you and your partner are standing the normal passing distance apart. (But of course, you could stand in a different position, e.g. back to back, and hand the club across.) A 5 is a flat pass, and it also has to be pretty quick. (5s can be dangerous too. I have been given a black eye by a stray flat pass.)

From the point of view of the pattern as a whole, the throws are made in the order prescribed by the siteswap, but you have to remember that each individual juggler only does every other throw. To illustrate this point, you could think of the siteswap 86277 like this:
Alice: 8-2-7-6-7-8-2-7-6-7-
Bob: -6-7-8-2-7-6-7-8-2-7

You will notice that Alice always throws 82767. This juggler-specific sequence of numbers is called the local siteswap. Bob’s local siteswap is 67827. To distinguish it from local siteswaps, the siteswap of the pattern as a whole is called the global siteswap.

Here are three points to remember about local and global siteswaps:
1. If the period of the global siteswap is even, the local siteswaps are half as long as the global siteswap. For example, a global 777726 breaks down into a local 772 and a local 776.
2. Local siteswaps are not necessarily valid siteswaps! For example, the average of 776 is not a whole number, so 776 can’t be a siteswap.
3. Many jugglers divide the numbers of the local siteswap by two in order to make the self throws look the same as the selfs you are familiar with from interpreting siteswaps as two-handed patterns. In that case, the passing throws contain decimals, so there’s no danger of confusion.

Here is a (far from complete) list of interesting passing siteswaps:
- An amusing three-club pattern: 720
- 5 club 1 count: 744 (try to do a flourish on every 4)
- Programming: 777726
- The following patterns can be thrown unannounced into the previous pattern, allowing you to “program” your partner: 7777266, 77772 (but they can also be fun in their own right, especially 7777266)
- Why not: 86277 (see Kaskade No. 73, part 17 of this workshop series)
- Not why: 86772
- Maybe, also known as What the heck: 86727
- Two patterns related to 96677, as yet unnamed: 79662 and 96672
- Two 6-club patterns with long pauses to play around in: 79464 and 96474
- I found this siteswap on a number-plate in Sweden: 972
- 7 club 1 count: 7
- 7 club 3 count, also known as the waltz: 966
- French 3 count, also known as 3-count popcorn: 786
- The preceding two patterns can be combined to produce: 966867
- 7 club 3 count with triples against singles: 7B6666 (remember: A=10, B=11)
- A very fast, high popcorn-like pattern: 9A2 (can also be thrown as a trick in the waltz: …9669A6962966…)
- Two 7 club PPS variations: 777786 and 777966
- Two 7 club PPSPS variations: 77786 and 77966
- 7 club 5 count: 96686
- 5 count popcorn with triple-single: 7A666
- 5 count popcorn with columns (straight double selfs): 78686
- 7 count popcorn (according to Gandini’s definition) with columns: 7868686
- 7 count popcorn: 966A666
- Five patterns with zips: 88892, 99692, 89792, 97892 and 978972
- 8 club 1 count: 97 (can be thrown with either straight or cross passes)
- Three 8 club PPS variations: 996, 978 and A77
- Ollerup: 9969968
- 8 club 5 count popcorn: A6969
- Two 8 club patterns which contain the same throws: 9A678 and 97A86

You can construct more 7 club patterns out of 7, 86, 966, … For example: 9669667. Suitable building blocks for 8 club patterns are 8, 97 and 996. For example: 97978 and 97996, two variations on the 8 club PPPPS. Incidentally, I cannot do all of the patterns listed here.

If you understand causal diagrams, you can convert siteswaps into causals. As in the juggling diagram, the hands of the jugglers are represented schematically by R and L. Causal diagrams also include arrows, but here they go from the point in time when a hand throws a club to the point in time when it is caught again.

In order to draw a 9, you therefore count 9 (global) throws into the future and then jump back to the previous throw of the target hand that you have just identified by counting. This is where the 9 is caught, so this is where the arrow points to in the causal diagram. As a causal diagram, Bob and Alice’s 7 club waltz, the 966, looks like Fig. 8.

7 clubs waltz or 3-count (Fig. 8)

Can siteswaps handle more than two people?

In theory, yes. But there are practical difficulties. If you want to keep to so-called vanilla siteswaps, in which only one club (at the most) is thrown at each point in time, adding more people makes synchronisation increasingly difficult. And you have to be able to throw “four-thirds” passes, which are somewhere between a normal single pass and a floaty single pass.

In Ollerup, Ross successfully used vanilla siteswap to describe a three-person pattern called the Shamrock: 50673955. Suse, Flo and Jochen stood in a triangle, fairly close together, and almost took the clubs out of each other’s juggles. The hands throw in the following order:
1) Suse right,
2) Flo left,
3) Jochen right,
4) Suse left,
5) Flo right,
6) Jochen left

and back to the beginning. Using siteswap they succeeded in adding an extra club to the pattern. The new siteswap was 58673955. Needless to say, we tried to develop some more interesting patterns for three people. One promising candidate is 75355, known as the Birdsmash, but it still needs time to mature.

To be able to describe more – and above all synchronous – passing patterns, we need to be able to allow for more than one club to be thrown at a given point in time. There are various extensions of siteswap for dealing with these situations.

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