Siteswap
Siteswap is a mathematical model to calculate possible juggling patterns and also notation to write down juggling patterns as a series of numbers.
Central Description
Siteswap assumes that each throw happens on a beat.
- Each number in siteswap represents the number of beats between throws for one object
Vanilla Siteswap
Siteswap that describes "normal" juggling patterns of the type of the 3 ball cascade or 4 ball fountain are called vanilla siteswap.
Because we only describe these patterns, vanilla siteswap has some some additional rules:
- only one object can land on the same beat (= no multiplexes)
- each hand throws on a separate beat (= only one object is thrown on each beat = no synchronous patterns)
There are extensions to the notation that allow siteswap to handle multiplex and synchronous patterns.
Example: 3-object cascade
This is the normal 3 ball cascade with two hands. Each arrow points to the next throwing event with the same object 3 beats later.
Numbers and arrows are colored with the color of the object involved:
- ball A: red
- ball B: blue
- ball C: black
Height of the curved arrows is also chosen differently for each object to make it easier to follow the path of one object - this is not meant to indicate a difference between throws, just to make reading the diagram easier.
Right and left hand are written underneath the numbers as R and L . As expected, all throws cross to the other hand.
The last three dashes represent throws that have not been made yet.
Notation: The throw sequence is 3333333333. One shortens a pattern to the shortest non-repeating part of the sequence, so siteswap for the 3-ball cascade is written as "3".
Throw Heights
The siteswap numbers roughly represent the time between throws and hence higher numbers mean higher throws.
The distance that an accelerated object travels is quadratic with time, and the same is true here. A throw with siteswap "5" would be about 25 times as high as one with siteswap "1".
In general, you can roughly imagine the heights of a siteswap "n" as that of the n-object cascade. With the addition, that mixing high throws and low throws does tend to make the high throws higher and the low throws lower compared to patterns with just one type of throw.
