Siteswap

Siteswap is a notation used in juggling to describe and analyze juggling patterns, particularly toss juggling patterns. It represents a sequence of throws made by the juggler, using numbers to indicate the number of beats until a ball is next thrown from the same hand.

A siteswap pattern consists of a sequence of numbers, typically presented as a string of digits, representing the throws made in a repeating cycle. Each number in the sequence indicates the relative height of a throw, measured in the number of hand positions it takes for the ball to be caught. A "3" represents a throw that will be caught by the opposite hand after three hand positions (one cycle), a "4" represents a throw that will be caught by the same hand after four hand positions, and so on. A "0" represents an empty hand position, meaning no ball is thrown.

The notation provides a concise and unambiguous way to communicate juggling patterns. It allows jugglers to easily describe patterns, to analyze their properties, and to discover new patterns. The height of a throw is directly related to the time the ball spends in the air. Higher numbers correspond to higher throws and thus longer air time.

Siteswap notation is typically used for synchronous patterns, where both hands throw at the same rate. Asynchronous siteswap, sometimes called multiplex or Mills Mess notation, exists to describe patterns where throws from the two hands are not evenly spaced in time. Variations also exist to describe passing patterns and other complex juggling arrangements.

The validity of a siteswap sequence can be determined mathematically. The average of the numbers in the sequence must equal the number of balls being juggled. This rule provides a quick check for whether a sequence is physically possible to perform. However, even a valid sequence may be difficult or impossible for a given juggler to execute due to physical limitations or coordination requirements.