Multi-handed Pattern Notation

by Ed Carstens

I just wanted to share the process which I am currently using to come
up with multi-handed patterns.  I have already outlined this process
in theory.  Here's an example of how you can come up with a new
pattern on your own.  No computer program is necessary for this.  The
hardest calculations you make are addition and subtraction!

Let's start by permuting the zero-perm. matrix for L=4,H=3:
|(1,1)  (1,2)  (1,3)  (1,4)|     |(2,1)  (1,2)  (3,3)  (2,3)|
|(2,1)  (2,2)  (2,3)  (2,4)| --> |(3,1)  (2,2)  (2,4)  (3,4)|
|(3,1)  (3,2)  (3,3)  (3,4)|     |(1,1)  (3,2)  (1,3)  (1,4)|

Now we find the relative (throw) matrix by subtracting the 0-perm.:
i.e. (2,1)-(1,1)=(1,0), (1,2)-(1,2)=(0,0), etc.

|(1,0)  (0,0)  (2,0)  (1,-1)|
|(1,0)  (0,0)  (0,1)  (1,0) |
|(-2,0) (0,0)  (-2,0) (-2,0)|

Now add 3 objects to each hand by adding (0,3) to each element:
|(1,3)  (0,3)  (2,3)  (1,2) |
|(1,3)  (0,3)  (0,4)  (1,3) |
|(-2,3) (0,3)  (-2,3) (-2,3)|

We could stop here but the (1,2) indicates a hold which is being
passed which can't happen so we have to add a (0,4) to this because
L=4.  Doing this adds one more object to the pattern so we may want to
subtract (0,4) from another element.  The only candidate for this is
the (0,4) in the 3rd row,3rd col.

Rob   |(1,3)  (0,3)  (2,3)  (1,6) |        Rob: S3,R3,G3,S6
Steve |(1,3)  (0,3)  (0,0)  (1,3) |   or   Steve: G3,S3,S0,G3
Greg  |(-2,3) (0,3)  (-2,3) (-2,3)|        Greg: R3,G3,R3,R3

This is it!  Now let me explain what these numbers mean: Each row
indicates the succession of throws made by one hand.  For standard
passing patterns one hand can be thought of as one passer since he
normally only throws with one hand at a time.  Let's say Rob has the
top row, Steve has the 2nd and Greg the 3rd.  Rob's first instruction
(1,3) tells him to pass a single to Steve.  Greg's first instruction
(-2,3) tells him to pass a single to Rob.  Steve passes a single to
Greg.  (This is a triangle.)  (0,3) indicates a left-right self or
vamp.  (0,0) indicates no catch which will occur once a pattern is
underway.  (Startup discussed later.)  (1,6) indicates that Rob must
throw a quad to Steve out of his left hand.  You can convert to an
easier notation for the pattern as shown on the right.

Starting a pattern can be a problem.  In this case we have not altered
the object number since we subtracted (0,4) and added (0,4).  If we
had changed it, one person would have to start with an extra club or
something and I have no idea how it would startup.  For this
particular pattern, the relative startup


will be sufficient.  The quad that Steve throws himself takes the
place of the quad being thrown a beat earlier from Rob.

Multi-handed Pattern Notation / Juggling Information Service /
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