siteswaps

Siteswaps are a notation system used to describe juggling patterns. A siteswap is a sequence of numbers, each representing a throw. The number indicates the time in beats that the thrown object will be held before it is caught. For example, a '3' means the object will be caught exactly three beats after it is thrown. A '0' represents an object that is immediately passed from one hand to another, or juggled without being thrown into the air.

Siteswaps are typically written as a series of numbers separated by commas. The sequence repeats indefinitely. For a pattern to be valid, the average throw height of all the numbers in the sequence must be equal to the number of objects being juggled. This is known as the "average rule". For instance, a siteswap of '3 1' with two objects means the throws are of height 3 and 1. The average is (3+1)/2 = 2, which matches the number of objects being juggled.

The number of objects in the juggling pattern is equal to the number of throws in the sequence if the sequence is a "proper" siteswap, meaning the average throw height equals the number of objects. If the average throw height is not an integer, it indicates that the sequence is not a proper siteswap, but the same calculation still holds for the number of objects. Siteswaps can be used to represent patterns with any number of objects, and are a powerful tool for understanding and creating new juggling routines.