Siteswaps for the Masses

by Alan "Crunchy Frog" Morgan

  I read some of the articles on site swapping, but I still have no
  idea how the notation works. Could someone please explain it clearly
  to me? Thanks ..!

The perfect opportunity to present my own treatise on the subject...

I have heard people complain about how difficult site swaps are to
understand and with respect to the brainy people (Allen K, and Ed
Carstens being two of the most egregious offenders in the excessive
glial cell department) I think that some of the explanations are a
little opaque unless you already understand siteswap notation in the
first place.  I am a firm believer in explaining things by example, so
here is my attempt at demystifying site swaps:


        SITE SWAPS - INFORMATION FOR PEOPLE WHO DON'T UNDERSTAND
                THEM BY A JUGGLER WHO CAN'T DO THEM

There are 3 rules you need to remember about site swaps:

1. Each number says how high (and to which hand) you throw
   the ball.

2. Throws alternate hands.

3. A sequence of numbers is repeated indefinitely.

Lets take a very simple siteswap: 3  We start with the right hand
and repeat this pattern forever

	R L R L R L R L R L R L ...
	3 3 3 3 3 3 3 3 3 3 3 3 ...

What does this mean?  It means that first the right hand will throw
the ball it has just as it would if you were juggling 3 balls (i.e.
fairly low and to the other hand).  Then the left hand will throw the
ball it has just as it would if it were juggling 3 balls.  Then the
right hand, then the left.  This, not surprisingly, is a 3 ball
cascade.

Other simple patterns work in the same way.  A four ball fountain
would be: 4, or

	R L R L R L R L R L R L ...
	4 4 4 4 4 4 4 4 4 4 4 4 ...

One thing to note here, you must throw the four as you would if you
were doing an alternating fountain pattern.  i.e. the balls *must*
stay in the same hands and the throws *must* alternate.  It doesn't
matter if you ordinarily do four balls by using a crossing pattern, a
'4' must stay in the same hand for site-swaps.  In fact, all even
numbers stay in the same hands.  I'll repeat that: EVEN NUMBERS STAY
IN THE SAME HAND, ODD NUMBERS GO TO THE OTHER HAND.

It should be clear by now that all basic patterns are just a single
number ('5' is a 5 ball cascade, '8' an 8 ball fountain, etc).  Let's
try something a little harder: 5 5 5 0 0

	R L R L R L R L R L ...
	5 5 5 0 0 5 5 5 0 0 ...

What is this?  This happens to be a 3 ball pattern so start off with
two in your right and one in your left.  Throw the right hand as you
would for a 5 ball cascade, then the left, then the right.  At this
point it is time for the left hand but it doesn't have a ball.  A '0'
is the sign to pause, not make a throw, and that is what we do.
Likewise, the right hand pauses.  Next it is the left hands turn and
we have caught the first ball that was thrown so we throw it back as
we would for a 5 cascade, then right, then left, then two more pauses.
This you should recognize as 3 balls high or one of the first things
you are taught to do when learning 5 balls (it is sometimes called a
'flash' but this gets confused with making 'n' catches of 'n' objects
so I tend to avoid this).

Another pattern: 5 3

	R L R L R L R L R L ...
	5 3 5 3 5 3 5 3 5 3 ...

This is a four ball pattern.  The right hand throws high throws across
and the left hand throws lower throws across.  Sounds like a 4 ball
half shower, and for good reason.

The only other things that might be confusing are 1's and 2's.  A 1 is
a pass directly across and a 2 is similar to a 0, a pause.  The
difference is a 0 is a pause without a ball, a 2 is a pause with a
ball, a hold.  5 2 2 is thus a high 3 ball cascade.  7 2 2 2 2 is a
*very* high 3 ball cascade.

Now you know the basics, a couple of questions and answers and you
will be ready to go.

* How do I know how many balls it takes to do a 5 5 5 0 0?

Good question.  Add up all the numbers in the sequence and divide by
the length of the sequence, that is the number of balls.  5 + 5 + 5 +
0 + 0 = 15.  15/5 = 3 so it is a 3 ball pattern.  If you don't end up
with an integer when doing this then you don't have a valid pattern.

* I invented a pattern 5 4 3 but it doesn't seem to work.

Right, it doesn't.  Although 5 + 4 + 3 = 12 which would seem to imply
it is a 4 ball pattern you can't do it.  A throw of height 'n' will
land 'n' throws later.  The 5 and the 4 will land at the same time and
thus in the same hand (so will the 4 and the 3).  Try a 534 instead.
You will have a collision whenever you have two numbers that are 'n'
apart in the pattern and 'n' apart in value (larger number first).
Thus 9 ? ? 6 ? ? will never be a valid pattern no matter what you put
in place of the ?'s.  This can be rather tedious to figure out, so
either let a computer do it for you or use some of the sequences
suggested on the net which will have been debugged.

* What can't site swap notation do?

Rather a lot!  It doesn't distinguish between Mills Mess and a cascade
(for example) because in general it doesn't pay attention to hand
movements, just ball movements.  It also doesn't handle simultaneous
throws (at least the simple site swap notation doesn't) or
multiplexes.  Fortunately some jugglers with too much spare time worked
out some notations that work for these.  I can't deal with these
myself, I like to let a computer handle them.  Check out Ed Carstens'
JugglePro (hey Ed!  A plug!) for info on them.


One last thing to note is that usually the patterns are listed without
spaces so a 5 5 5 0 0 will be 55500.  For numbers above 9 use A, B,
etc.

That's it!  Of course, knowing the notation doesn't mean you will be
able to do the patterns, but it is certainly an important step.  Here
are some patterns to get you started.  You probably should get some
computer program (see moocow.cogsci.indiana.edu for info) so that you
can see what these look like before you try them.  Particularly since
I have stuck some *really* hard ones in here (heh).

3 object patterns
        3               (the cascade)
        5 5 5 0 0       (3 high throws)
        5 1             (shower)
        5 3 1           (toss one high and exchange the two in your hands)
        4 4 1           (the easiest pattern that no one knows.  Not a box)
        5 0 5 0 5       (3 ball chase)
        6 0             (3 in one hand)
        8 0 4 0         (3 in one hand the hard way >:-)
        6 1 2           (a decent approximation to a 3 ball box.  Since the
                         usual box has simultaneous throws it isn't quite
                         right, but it isn't bad.  You need to start this
			 with 2 balls in the *left* hand)

4 object patterns 
        4               (the fountain)
        5 3             (half shower)
        7 1             (shower)
        5 5 2           (4 ball chase)
	5 5 5 5 0	(4 in a 5 pattern)
        5 5 5 1
        5 3 4           (continually reversing half shower)
        10 1 6 1 2      (Dan Bennett's evil 4 ball pattern, a 4 ball box)

5 object patterns
        5
        6 4             (3 in one hand, 2 in the other)
        7 7 1
        6 6 6 6 1       (5 ball analogue of the 4 4 1 and 5 5 5 1)
	6 6 3		(supposedly Jason Garfield can do this with clubs)
        7 4 4           (out of 5, toss 1 high and juggle 4 briefly)
        7 7 7 3 1       (toss 3 high and exchange 2)
        14 1 10 1 6 1 2 (the logical extension of the 10 1 6 1 2)