The main limitation of the notation used here is that it ignores all information concerning throwing and catching positions, as well as any characteristics about the objects being juggled (number of spins on clubs, etc.). When an object is thrown, the ONLY things this notation tells you are which hand to throw to, and the amount of time until the object is caught and thrown again. You have complete freedom in choosing how these should come about: Make a standard throw, throw behind the back, bounce off the floor, do a helicopter spin on your head, or whatever, so long as the object winds up at the right place in the right amount of time. The notation's ignorance of these throwing styles means that tricks like the 3 ball cascade and Mills Mess are lumped together, but if you apply some creativity to the output of the program you can get most tricks that people do, and many that have never been done before.
'3', for example. Note that our notation doesn't
need to specify the destination hand, since odd numbers always go to the
opposite hand, even numbers to the same hand (a result of constraining
ourselves to a R-L-R-L throwing rhythm). Another way of thinking about
it is this: When you do a throw 'n' (n is the throw number), throw just
as you would if you were doing a cascade or fountain with n objects, at
the same handspeed. A 3 is a short toss across, a 4
is higher and into the same hand, and so on.The patterns that the program generates are just sequences of these numbers -- the first number describes the first throw made, the second number the second throw (opposite hand as the first), and so on. At the end of the pattern you loop back to the beginning and continue.
Valid 3 ball tricks include:
3 = standard cascade
51 = shower (that's 5 and 1, not fifty-one)
42 = two in one hand, hold with the other
441 = an interesting box-like pattern
531
55500 = a 3-high flash
The '0', '1', and '2' throws need some
explanation. A '2' throw is
thrown again 2 throws in the future, in other words the next throw out of
the same hand. Since the hand does nothing before throwing the
object again, we are free to interpret a '2' as just a hold for one count.
A '1' is a fast zip across from hand to hand, as in the shower. Finally,
a '0' is no throw at all; the hand is empty (the pattern
60 is 3 in one hand, the other hand empty).
Notice that if you average the throws in each of the above patterns you
always get 3, the number of objects being juggled. This is one of the
ways you can tell whether or not a string of throw numbers comprises a
valid pattern. '76' doesn't work, but '75' is a
valid 6 ball pattern
(commonly known as the 6 ball half-shower). Not all strings of numbers
with integer averages are valid patterns, however.
51, the shower. To switch
from the cascade into the shower you have to go through a series of
intermediate throws in order to avoid getting two balls in a hand at once.
For the shower, a valid starting sequence of throws is '52' (note that this
is not a valid repeatable pattern, by the average rule). Switching from
the cascade to the shower and back again we could go:
...33333333 52 515151...5151 2 3333333...
We say that '52' is a valid starting sequence for the excited state
siteswap 51, and '2' is a valid ending sequence (gets you back
into cascade). The starting and ending sequences are in general not unique.
24[54]. From the middle of a cascade (no starting
sequence is needed, since this is a ground state pattern), we first do a hold
with our right hand, throw a shorter toss from the left hand to itself, and
then simultaneously throw a 5 and 4 with the right (the
hand had 2 balls in
it, since it did the hold first). Then we can either switch back into the
cascade, or repeat the trick with a left-handed hold, etc. (since the
pattern is of odd length it switches hands each repetition). [This, by the
way, is a trick that Anthony Gatto did in his act, except that he did it
all while juggling over his head. He can also do 26[76] with 7 balls.]
'x' after any throw that crosses
over into the other hand (a throw without the 'x' is assumed to be directed
to the same hand that threw it). A '2' is still a hold, but a '2x'
is similar to the '1' in the siteswap notation above: a short pass from hand
to hand. A '0' is still no throw, and a '0x' is not allowed.
ALL throw numbers now must be even.Examples of synchronous patterns:
(4,4) = 4 ball synchronous fountain
(4x,4x) = a common crossing version of the 4 ball fountain
(4x,2x) = 3 ball shower with simultaneous throws
(4,2x)(2x,4) = the 3 ball "box" or "see-saw" pattern
(6,6)(6x,2x) = a 5 ball trick
(6x,6x)(2x,2x) = a 4 ball trick
(4,4)(4,0) = 3 balls in 4 ball fountain (1 missing)
You are free to choose which hand corresponds to which slot in the
parenthesis, but your choice must remain consistent throughout a given
pattern. Multiplexing can also be notated, exactly as above; for example
the 4 ball pattern (4,2)(2x,[44x]) has a multiplexed '4'
and '4x'. Lastly, the concepts of ground state/excited state patterns
and starting/ending sequences are valid here as well, but now for instance the patterns
(4,4) and (4x,4x) play the role that the cascade/fountain
did, since these are the 4 ball synchronous patterns of length 1.
2 is a hold,
a 3 is a toss to the other hand, etc.). Append a 'p' to a number to
represent a passed throw. To figure out which of your partner's hands to
pass to, use this rule: If without the 'p' the throw would go to your left
hand, throw at your partner's left, and so on.
Some example patterns should help clarify this. (Note the version of the average rule
here: Add up the numbers within each <|>, and average to get the number
of objects.)
<3p|3p><3|3> = ordinary 6 object passing. Notice how the
instructions for each person are sectioned off.
Each person starts throwing with his right.
<3p|3p> = "ultimate" passing, where all throws are passes.
<3|3> = two people doing 3 ball cascades (boring).
<4p|3><2|3p> = a left-handed double, if done once from the
middle of a "cascade" (in this case
<3p|3p><3|3> qualifies). This is a ground
state trick, so no starting sequence is needed.
<2|3p><2p|3><[3p2]|3p>
= a multiplexed pattern, the left-handed single
(a good way to fake out your partner). Do the
first hold with your right hand, since that is
when your partner is doing a '3p'. The '2p' is
from your left to his left, and then you
resume.
The discussion so far is actually too restrictive. In particular, we don't need to
assume that the two jugglers' right hands throw at the same time. This is explicitly
not the case in two-count, 7 club passing -- there the right hand of juggler #1
throws at the same time as the left hand of juggler #2 (making the passes alternate).
But we can write 7 club, two-count passing as <4p|3><3|4p>, if we now
identify the first juggler as starting with her right (a pass), and the
second as starting with her left (a self). The sharp reader will notice that our
rule above for figuring out which hand a pass goes to is now reversed: A '4p'
from your right goes to your partner's left.
It may be conceptually simpler to
imagine turning one of the jugglers around 180 degrees, keeping the appearance of the
pattern the same -- essentially swapping her right and left hands.
The jugglers now have synchronized right hands, so our original
passing rule holds and a '4p' from your right hand goes to your partner's
right. But now turn your partner back around -- you will be throwing at her left hand.
At any rate, keep in mind that every passing pattern in this notation can be interpreted in two ways:
One with the right hands together, one with them staggered. You might consider what the
7 club, two-count <4p|3><3|4p> would be in the former point of view.