4 Handed Siteswaps

OK, so you're probably at least vaguely familiar with 2-handed
siteswap.  No?  Then go and get at least vaguely familiar with it.
OK?  Good.  So, the basic idea of this article is to explain how any
siteswap which can be done with 2 hands can also be done (in theory)
with 4 hands - specifically in a passing pattern for 2 people.

So, from 2-handed siteswap, you should know the following facts:
1. The hands alternate in throwing.

2. Even numbered throws go to the same hand.

3. Odd numbered throws go to the opposite hand.

You may also think you know this fact:

The height of the throws are as if you were juggling that many balls.
So a 5 is as high as a throw of a 5 ball cascade

Forget that particular fact.  It has its uses, particularly when
trying to work out how to juggle a new siteswap, but it's not very
helpful when generalising siteswap.  In fact, if you haven't already
done so, replace it with this fact:

The number states how many beats it will be until the thrown object is
dealt with again.

If that's new to you, have a play with it.  Do some siteswaps and
convince yourself that it's true.  Even the siteswap 3 is a good
example, so really you've got no excuse not to try it.

So, what we really want to know is a similar set of rules for 4-handed
siteswap.  What to pass, what to self, and where to do both.  So
let's see where we get the 2-handed rules from:

1. The hands alternate in throwing.

This is just a rule of siteswap that we define.  But what's the
equivalent with 4-hands?  It's that all 4 hands take it in turns to
throw.  The usual way to define this is one person's right, the other
person's right, the first person's left, the other person's left.  Or,
labelling the people A and B, and the hands L and R - AR BR AL BL.

You could do it differently, but that's just complicating issues, so
we're sticking to that order.

On to the next rule:

2. Even numbered throws go to the same hand.

OK, so this comes from rule 1.  In 2-handed siteswap, the hand order
is RLRLRL..., and so all throws from the right hand will go to the
right.  Same with the left.  For 4 handed siteswap, the throwing order
is AR BR AL BL AR BR AL BL..., or just considering *who* is throwing:
ABABAB...  So it should hopefully be clear that all even numbered
throws go to the same person.  So if it's even, it's a self.

The question now is: What hand does it go to?  Well, we know it's an
even throw, and it's going to be a self.  If it's a 2, it'll go to the
other hand.  A 4 will go back to the same hand.  A 6 goes to the other
hand.  And so on.  The way I like to think of it is to divide any even
numbered throws by 2, and think about them as if they were just 2
handed siteswap values.  So a 2 in 4 handed siteswap is very much like
a 1 in 2 handed siteswap - i.e. a zip.  Like this:

4H 2 --> 2H 1
4H 4 --> 2H 2
4H 6 --> 2H 3
4H 8 --> 2H 4

The next rule in 2 handed siteswap:

3. Odd numbered throws go to the opposite hand.

Should now be pretty easy to translate to 4 handed siteswap.  Since
we've already established that even numbered throws go to yourself,
it's not a giant leap to say that odd numbered throws go to the other
person.  Again, the question is which hand do they go to?  Let's
consider the siteswap 5 to demonstrate:

Ball: a  b  c  d  e  a  b  c  d  e  a  b  c  d  e  a  b
Hand: AR BR AL BL AR BR AL BL AR BR AL BL AR BR AL BL AR

So in this diagram, the balls, labelled a-e are being thrown by the
hand indicated.  If we follow ball a, it goes from AR to BR, to AL, to
BL.  It's then going to go back to AR again (everything thrown from BL
goes to AR if you check it).  That means that the 5s are thrown by
person A as crossed passes (R-R, L-L) and by person B as tramline
passes (R-L, L-R).

If we went up to the siteswap 7, we'd see that A would be throwing
them as tramline passes, and B would be throwing them as crossed
passes.  So, for 4 handed siteswap, person A throws 5s, 9s, ds etc. as
crosses, and throws 3s, 7s, bs etc. as tramlines, with person B doing
the opposite.  In many patterns, there is only one type of throw, and
so usually you just need to decide who passes crossed and who passes
straight.

And that's pretty much it.  If it's a valid 2 handed siteswap, it's
also a valid 4 handed siteswap.  The rules are:

1. All 4 hands take it in turns, and both people also take it in
turns.

2. Even numbered throws are selfs.

3. Even numbered thows divided by 2 are selfs which are equivalent to
  the 2 handed version.

4. Odd numbered throws are passes.

5. When one person throws a pass crossed, the other person will be
  throwing the same type of throw straight.

One other thing to consider is how you look at the siteswap.  For a 4
handed siteswap, we have 2 different ways of looking at it - the
global siteswap and the local siteswap.  The global siteswap is the
one we've been talking about so far, where all 4 hands take it in
turns to throw.  The local siteswap is what one person throws, and is
useful when you're trying to figure out what your end is doing.  To
get the local siteswap, you simply pick a starting point and skip
every other number until you get back to where you started from.

So, for example, if we think of the siteswap 77722, it goes like this:

7 7 7 2 2 7 7 7 2 2 7 7 7 2 2 7 7 7 2 2 ... 
A B A B A B A B A B A B A B A B A B A B ... 

7  7  2  7  2  7  7  2  7  2  ... 
A  A  A  A  A  A  A  A  A  A  ... 

  7  2  7  7  2  7  2  7  7  2 ... 
  B  B  B  B  B  B  B  B  B  B ... 

So person A is throwing 77272, and B is throwing 72772.  If you halve
all of the numbers, you will get a pattern which has half-integer
throws in - those are the passes (because they've come from the odd
numbers).  The other numbers are equivalent to the 2 handed siteswap.

So A will then be doing 3.5 3.5 1 3.5 1.  Or Pass-Pass-Zip-Pass-Zip,
as it tends to be said.  It's a 5 object, 2 person passing pattern
known as "Parsnip", and it's quite nice.  It's not a technically
difficult pattern, but it can take a bit of getting used to.

This tends to be the way I transform a 4 handed siteswap into
something I can think about when I'm actually juggling it.  So, in
summary, and with examples, this is my method:

1. First of all you need to know what your end is doing, so you want
  the local siteswap.  Start at the beginning and pick every other
  number to get that.  Examples:

74464 -> 74446
86277 -> 82767
86772 -> 87267

2. Halve the digits. Anything which is a non-integer is a pass. 3.5s
  are usually singles, 4.5s are doubles, 5.5s are triples etc. So
  with the above transformed siteswaps (and with spaces between
  digits for clarity):

74464 -> 74446 -> 3.5 2 2 2 3
86277 -> 82767 -> 4 1 3.5 3 3.5
86772 -> 87267 -> 4 3.5 1 3 3.5

3. I usually then transform the resulting siteswaps into words where:
"Single" is a single pass
"Double" is a double pass
"Triple" is a triple pass
"Zip" is a zip (obviously)
"Hold" is a 2 (almost always a hold)
"Self" is a self 3
"Heff" is a self 4
"SelfTriple" is a self 5 (and said quickly enough to not be confused
with "Self. Triple"

We now have:
74464 -> 74446 -> 3.5 2 2 2 3 -> Pass Hold Hold Hold Self (Never
actually done this one, but there's potential with the holds)
86277 -> 82767 -> 4 1 3.5 3 3.5 -> Heff Zip Pass Self Pass (This is
usually called Why Not)
86772 -> 87267 -> 4 3.5 1 3 3.5 -> Heff Pass Zip Self Pass (Usually
called Not Why because of it's similarity with the last one)

If you throw the passes as vertical flats, it's quite interesting to try
the 3 and 4 object siteswaps 522 (with one of the zips behind the back)
and 552.

Siteswaps to avoid are those involving 1s and 3s, mostly because
they involve hurling a club very quickly to your partner.  And if
there's an odd number of digits in the siteswap, then it's guaranteed
that at some point they're going to hurl it back at you.

So, if that all made sense, then here's some other things to try:

1. Change the order in which the hands throw to AR AL BR BL.  It's a
  weird rhythm, but certainly doable with some easy siteswaps.

2. Break a close (juggling) friend's hand, and persuade them to learn
  3 handed siteswaps.

3. Try converting synch siteswaps to 4 hands.  I started to think
  about this recently, and there's certainly room for some
  interesting stuff (probably).