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Siteswap notation is used by jugglers to define different juggling patterns. Each pattern is characterized by a string of numbers, for example '51' or '234'.

Imagine you are juggling to a metronome. On odd beats you throw and catch a ball from the right hand, and on even beats you throw and catch a ball from the left hand. The numbers correspond to the number of beats later that the ball just thrown will land.

It follows that odd numbers represent throws to the opposite hand and even numbers represent throws to the same hand. A '1' corresponds to a quick pass from one hand to another, and a '2' corresponds to pausing. A '0' corresponds to having an empty hand. The string is repeated ad infinitum, so '53' really corresponds '5353...'.

Take the example of the two ball juggling pattern '31'. Start with a ball in each hand.
  • '3' - Throw a ball from the right hand so it will land in the left, three beats later.
  • '1' - Pass a ball from the left hand to the right.
  • '3' - Throw the ball that was just passed so it will land in the left, three beats later.
  • '1' - Catch the ball that is about to land in the left hand, and pass it to the right hand.
  • Repeat the last two steps.
Many juggling patterns can be written using Siteswap. The Three ball cascade is written simply as '3', and the Three ball shower is written as '51'. There are many other more complicated patterns like '441' and '5551', '504', and '51713151'.

Siteswap has some interesting mathematical properties too. The average of the numbers in the string tells you how many balls are in the pattern: for example '5551' is for four balls. It follows that the average of the numbers must be an integer to define a valid pattern. Even if the average is an integer, a sequence may not be valid: for example '432' is invalid, as it involves catching three balls at the same time.

Siteswap doesn't make any attempt to describe any complicated motion of the arms found in advanced patterns like Burke's Barrage, but it can be extended to allow for multiplexing.

If you wish to find out more, there are many freeware programs available on the internet which demonstrate Siteswap very well.

So, you want to learn to do this crazy thing? Chris' writeup excellently explains the concepts involved, but there is a wide gulf between theory and practice. To juggle a particular pattern, let's say 5-3-1 (my current favorite siteswap, although I'm improving at 7-1-1 and 7-3-1-3-1) you first have to realize that all of these heights that we are referring to are relative. That is, I might juggle a 5 at head height and you might want to throw it three feet above your head. This means that in order to get into the math nerd zen that is siteswap juggling you'll have to know how high you throw a 1, 2, 3, 4, 5, 6, and 7. I can tell you how high they are for me, but that is all supposition for you. If you have trouble with the higher numbers, then you should realize that you are probably not throwing them high enough. A 7 is really REALLY high.

Also, a good minimum level of skill is the ability to do a four ball fountain (siteswap of 4) and a three ball shower (siteswap 5-1). Being able to flash five balls would be even better. Having a little bit of a numbers juggler in you will help immensely. The skill involved in juggling large amounts of numbers will help here, and vice versa. But on to some actual practice!

First we'll do 4-4-1. This might be considered the canonical siteswap pattern. It was discovered by the guys who invented this notation. They noticed that this was a valid pattern, and tried it; then they found out that nobody had ever done it before. So the pattern is 4-4-1, which translates into "throw like I'm juggling two in one hand, do that again with the other hand, then hand across". The pattern that this generates is, initially, pretty indescribably wierd. I know I couldn't handle it. I just had to trust the numbers. I would simply say "four, four, one" over and over again as I did each corresponding throw. As time went on I started to understand what was going on, but part of the beauty of the system is that you don't need to. All you need to do is follow the instructions. Try talking aloud - it helps, even if people look at you funny.

Now we'll try 5-3-1. This is a pretty cool pattern, but it will either become arches or boring to look at if you don't keep the height ratios in sync. First of all, if you can flash five balls, just try this pattern. Say it out loud and try it. It might just work for you. If you aren't a five ball juggler, then here's some tips. That five should, initially, probably be about a meter above your head. This is not because that is the height people juggle five at, far from it. That is simply because you won't be very fast on the 3-1 step so you need to buy yourself extra time. Okay, now throw a high ball for right to left, and then quickly do a low shower (3-1) from left to right. If you don't drop, then congratulate yourself, you just did it! Now learn it the other way. After that, say the pattern out loud and do it continuously. You should be juggling 5-3-1 in short order.

To learn how high a 5 should be, learn to juggle 5-3-1. To learn how high a 6 should be, either learn three in one hand, or learn 6-3-3 (a four ball pattern). 7-3-1-3-1 will teach you about 7 throws, and 8-3-3-3-3, and 9-3-1-3-1-3-1, and so on.

Give it a try, it's pretty fun!

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