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.