This guide started life as a handout for a workshop I taught at the 2001 Kingston Juggling Festival. My aim was to produce a concise summary rather than a complete tutorial; I hope I've succeeded. For your printing convenience the guide is also available as a one-page Adobe Acrobat file in either A4 or letter format. Thanks to Michael Ferguson and Todd Strong for comments on earlier drafts. — Greg

At any given beat rate, higher siteswap numbers mean higher throws. A faster beat means lower throws for all numbers. You can understand the numbers as meaning roughly:

• 0 — an empty hand
• 1 — a quick pass across, as in a shower
• 2 — a quick "throw to the same hand" (normally just a hold)
• 3 — a three-ball cascade throw
• 4 — a four-ball fountain throw
• 5 — a five-ball cascade throw... and so on up to 9, then
• a — a ten-ball fountain throw (write a instead of 10 so we don't confuse "ten" with "one-zero"; read a as "ten")
• b — an eleven-ball cascade throw... and so on

Many juggling patterns are based on alternating right and left-hand throws. We describe these using asynchronous siteswap.

Rules C2 and A1 together require that odd-numbered throws end up in the opposite hand, while even numbers stay in the same hand. Here are a few asynchronous siteswap examples:

• 3 — a three-ball cascade
• 42 — two balls juggled in one hand, a held ball in the other
• 330 — a three-ball cascade with a hole (two balls)
• 51 — a three-ball shower
• 53 — a four-ball half-shower
• 64 — three in one hand with one hand, two in one hand with the other (each at its regular height — this is hard)
• 73 — a five-ball half shower (the harder one!)
• 615150 — a three-ball shower with a "leak"

Some juggling patterns involve both hands throwing at the same time. We describe these using synchronous siteswap.

Rules C2 and S1 taken together demand that there be only even numbers in valid synchronous siteswaps. Can you see why? The x notation of rule S2 is required to distinguish patterns like (4,4) (synchronous fountain) from (4x,4x) (synchronous crossing). Unlike a 2, a 2x must always be thrown since it changes hands. Here are a few examples:

• (4,4)(4,0) — three-ball columns (a.k.a. Two Up, One Up)
• (4,2) — appears identical to 42 — The Fake, The Yo-yo, etc.
• (4,2x)(2x,4) — The Box
• (6x,4x) — the easier five-ball half shower
• (6,6)(6,6)(6,0) — Enrico Rastelli juggling five plates

In both alternating and synchronous patterns we can throw multiple objects from the same hand at the same time.

Applying C4 and M1 to the siteswap [33], we sum the throw numbers (3+3) and divide by the number of throws (one) to give six — so [33] is a six object pattern. Note that in multiplex patterns twos inside square brackets are almost always thrown rather than held. A few multiplex examples:

• [33] — six balls juggled in groups of two as a three-cascade
• 4[43]1 — a pleasant four ball variant of 441 , itself quite fun
• [32] — five-ball splits
• ([44],[44])(4,0) — Four Up, One Up

Here are a few reasonably easy but fun siteswap patterns:

501, 423, 441, 4413, 531, 5313, 534, 55244, 561, 633 (easier with bounced sixes), [33]33, [33][33]3, [33], [43]1421, 4[43]1, [32], (4,4)(4x,4x)

Training for five: 50500, 52512, 55500, 50505, 552, 55550

Siteswap notation doesn't show us how a throw is made; for example Mills Mess has a siteswap of 3, which completely ignores the sinuous arm crossing that makes it beautiful and fun to juggle. On the other hand it is useful to know that both Burke's Barrage and Windshield Wipers are juggled as 423, even if that doesn't tell the whole story. Happy juggling!

© Greg Phillips, 2001. This guide may be reproduced in any form provided the complete text, including this permission note, remains intact.