symmetric passing patterns
Christophe Prechac
... . Feeds involving runarounds also enter this category.
Tired to show off in solo juggling, the passing partners engage in
friendly cooperation to create beautiful multihand patterns in which
improvisation, i.e. tricks and syncopations, is all the more interesting
since there is more than one brain involved.
Anyway, in the basic form of a symmetric passing pattern, all partners
do the same sequence of throws, either in phase or out of phase.
Apparently, there does not exist a comprehensive description of these
patterns, although digging the rec.juggling archive unearthed a somewhat
related and definitely beautiful article by Tarim (March 94, A new class
of passing patterns).
The purpose of this post is to describe all symmetric passing patterns
in terms of equivalent solo patterns. As an application, I list at the
end all 2 persons 7 objects 3 count patterns.
The analysis to follow makes heavy use of siteswaps. Causal diagrams are
also invoked for geometric intuition. It is also rather lengthy ... I
believe however that these theoretical considerations can be of
practical use, so many examples are provided.
* In phase patterns
This case is well-known. All jugglers pass and self together the same
throws, therefore when someone throws a pass, he is thrown a similar
pass so that everything happens as if all jugglers had not passed at all
and had instead thrown to themselves.
These passing patterns reduce to independent identical solo siteswaps.
For two people, the number of objects must be even.
Example : with two other waltzers, you can do a 4p 4p 1 PPS triangle
pattern.
* Out of phase patterns
- Let us look first at the case of 2-persons Waltz PSS'.
J2 begins his PSS' sequence 1.5 beats after J1. When J1 passes and gets
rid of a club, he is thrown back a P pass 1.5 beats later. Therefore
everything happens as if J1 had thrown a P+1.5 self and J2 had thrown a
P-1.5 self.
This is where causal diagrams provide intuition: translate J2's time
axis backwards by 1.5 beats. As a result, selves are unchanged, J1's
passes are shortened, J2's passes are lenghtened, and the two jugglers
are now passing in phase, swapping all passes then provides two
independent solo patterns.
If n denotes the number of clubs of the valid solo siteswap P-1.5 S
S' , the passing pattern PSS' must contain 2n+1 clubs, an odd number
of clubs. Conversely, starting from any length 3 , n clubs siteswap abc
, then a+1.5p bc will describe a valid 2-persons, 2n+1 clubs Waltz.
Examples:
222 --> 3.5p 2 2 : the slow 5 "ultimates" that Bruno and Hans
brilliantly demonstrated in Edinburg.
333 --> 4.5p 3 3 : 7 Waltz which Tarim and Martin Frost denote by 966
considering it as a 4 hands siteswap (I find this description slightly
akward and misleading as explained later).
- Similarly, for a two persons Pass Pass Self PP'S , P-1.5 P'-1.5 S
must be a valid n objects solo pattern and the PP'S passing pattern
will involve 2n + 2 objects, an even number. Sadly enough there is no 7
clubs symmetric PPS (for an asymmetric one, Martin Frost pointed out <4p
4p 3 / 3 4p 3p>).
Examples: 333 --> 4.5p 4.5p 3 , 423 --> 5.5p 3.5p 3 , two 8 clubs PPS
patterns.
- More generally, for 2 persons, if a(1) ... a(L) denotes the sequence
of throws, then b(1) ... b(L) must be a valid solo siteswap, where:
b(i) = a(i) if a(i) is a self,
b(i) = a(i) - L/2 if a(i) is a pass.
Conversely, given any n clubs solo pattern b(1)...b(L) , you may create
a 2 persons 2n+k clubs passing pattern with k passes.
Examples:
33 --> 4p 3 : 7-shower
531333 --> 534p333 : 7-popcorn,
13141 --> 3.5p 3 3.5p 4 1 : why not?
- With more than 2 persons, a general description becomes slightly more
complicated, though by no means impossible. Let L denote the length of
the pattern and P denote the number of passers. I assume that the set
of passers is connected through the passes (thus excluding the popular 4
count squares).
J0 starts first, J1 starts L/P beats later, ... , J(P-1) starts last,
i.e. (P-1)L/P beats after J0.
Let us denote the sequence of throws by a(1)pj(1) ... a(L)pj(L) : here
a(i) denotes the "height" (siteswap value) of the ith throw and pj(i)
means that when Juggler #k throws the ith throw, this throw will be a
pass to Juggler #(k+j(i)) [mod P] . Selves are therefore these throws
for which j(i) = 0 . This notation is essentially Ed Carstens' MHN
notation.
Let us now shift back by kL/P beats the time origin of Jk , for all k
, as explained earlier. Then, all passers are juggling in phase and the
ith throw of Juggler #k has become:
(a(i) - j(i)L/P) p j(i) if k+j(i) < P , i.e. if Jk is passing to
someone "after" him,
(a(i) + L - j(i)L/P) p j(i) if k+j(i) * P , i.e. if Jk is passing
to someone "before" him.
Now, swap all passes! I.e. have everyone throw selves that are identical
in height to the passes they are being thrown. This works because
everyone is passing in phase. The passing pattern is then reduced to P
independent solo patterns, in particular the pattern of the last juggler
is:
a(1) - j(1)L/P ... a(L) - j(L)L/P .
By the average rule the number of objects of this last pattern is equal
to (a(1) + ... a(L))/L - (j(1) + ... + j(L))/P
Conversely, starting from a solo siteswap with n objects, one may
contruct a symmetric P-passers passing pattern involving
Pn + (j(1) + ... + j(L)) objects, for any choice of the destination
mapping j( ).
Examples: (they all involve triangles, P = 3)
- { j(1) = 1 , j(2) = j(3) = 0 , 333 } --> 4p1 3 3 : a 10 clubs triangle
Waltz with passes always to the "next" partner.
- { j(1) = 2 , j(2) = j(3) = 0 , 333 or 144 } --> 5p2 3 3 or 3p2 4 4 :
two 11 clubs triangle Waltzes with passes always to the "preceding"
partner.
- Alternating passing partners in a triangle Waltz will require L = 6 ,
j(1) = 1 , j(2) = j(3) = 0 , j(4) = 2 , j(5) = j(6) = 0 , so that the
number of objects involved will be Pn + (j(1) + ... + j(L)) = 3n + 3
which is impossible for 10 or 11 clubs! Ok, with 12 : 344133 --> 5p1 4 4
5p2 3 3 . Kind of ugly but who wants to juggle this anyway? (Of course
passing in phase 4p44 is possible)
- { j(1) = 1 , 3 } --> 3.33p1 : 10 ultimates with passes to the next.
- { j(1) = 2 , 3 } --> 3.66p2 : 11 ultimates with passes the other way
round.
- What about ultimates with alternating partners ? As above we need a
multiple of 3 objects and there is nothing interesting apart from in
phase patterns.
Remarks:
* Symmetric patterns can be used to create asymmetric patterns by
shifting the time origins of one or more jugglers as explained above.
Examples: In phase 7 ultimates <4p / 3p> or Tarim's gallopped 7 shower
with crossing passes <4.5p 3 / 3.5p 3 (start 0.5 beats after J1)>
* The notation system used above, i.e. siteswap or mhn, does not say
which passes cross. For that matter, causal diagrams do not say it
either unless you have decided which hand each juggler uses first. So,
do it.
* The reasons why I do not like very much Tarim's notation, e.g. 966 for
the 7 clubs Waltz, are first that numbers in this system do not
immediately reflect heights of throws and which throws are passes, and
second that the sequence of numbers does not actually always denote what
the jugglers have to do : as an example 4.5p 1 5 will be denoted in
Tarim's system by 9 10 2 , so that dividing all numbers by 2 will yield
4.5 5 1 which is not the desired juggling sequence (and is also
impossible since 351 is not a valid siteswap). Also I am more familiar
with siteswaps involving 3 or 4 objects then 7 or more :)
List of 7 objects 3 count symmetric patterns: (max throw = 6, min pass =
3.5)
5.5p 5 0 , 5.5p 4 1 , 5.5p 2 3 , 5.5p 1 4 , 4.5p 6 0 , 4.5p 4 2 ,
4.5p 3 3 , 4.5p 1 5 , 4.5p 0 6 , 3.5p 6 1 , 3.5p 5 2 , 3.5p 3 4 ,
3.5p 2 5 .
Now, I only hope I will find partners to try a 10 clubs 3 count
triangle.
Good luck.
Christophe.
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Share what you know. Learn what you don't.
Wolfgang Westerboer
Hello Christophe, hello jugglers
First of all: thanks for the great article.
I just want to add some basic ideas for those of us, who are not that
familiar with mathematics and formulas, and I want to explain how I come
to the first pattern, the std. 7 club walz.
> * Out of phase patterns
> - Let us look first at the case of 2-persons Waltz PSS'.
> J2 begins his PSS' sequence 1.5 beats after J1. When J1 passes and gets
> rid of a club, he is thrown back a P pass 1.5 beats later. Therefore
> everything happens as if J1 had thrown a P+1.5 self and J2 had thrown a
> P-1.5 self.
> This is where causal diagrams provide intuition: translate J2's time
> axis backwards by 1.5 beats. As a result, selves are unchanged, J1's
> passes are shortened, J2's passes are lenghtened, and the two jugglers
> are now passing in phase, swapping all passes then provides two
> independent solo patterns.
> If n denotes the number of clubs of the valid solo siteswap P-1.5 S
> S' , the passing pattern PSS' must contain 2n+1 clubs, an odd number
> of clubs. Conversely, starting from any length 3 , n clubs siteswap abc
> , then a+1.5p bc will describe a valid 2-persons, 2n+1 clubs Waltz.
Siteswapping passing patterns:
Juggle:
Let´s start with 2 jugglers, one does 4 clubs and the other 3.
4 4 4
3 3 3
In total that is a 7 club pattern, of course.
Pass:
Both decide to pass. A has to pass one beat earlier than B, because of
his throws last one beat longer:
4 4p 4
3 3 3p
Late pass:
Things become interesting: B does a late pass,
and by that he forces A to change his rhythm:
4 4p 3
3 3 4p
Early pass:
A does an early pass by swapping his 4 4p to 5p 3. As in all early
passes, B´s rhythm is unaffected.
5p 3 3
3 3 4p
Now they have reached their desired patterns: all selfs are equal, the
height of their passes is as close as possible.
Delaying the pattern:
A and B do what I think is the usual thing jugglers do in such a
situation: they want to throw at the same height rather than at the same
time. A moves half a beat forward in time. His throws are reduced by
this amount of time, B´s throws have to go longer, i.e. higher.
4.5p 3 3
3 3 4.5p
Generalizing the idea:
A is throwing n+1
B is throwing n
the walz is
n+2 n n
n n n+1
and in the delayed pattern:
n+1.5 n n
n n n+1.5
Notation:
This notation for more than one juggler was sugested by Jack Boyce
first. I use it in JoePass!, a bit extended:
<"Pattern for A"|"Pattern for B">
Both patterns must have the same length.
The delayed 7-clubs walz can be written as:
#d1 0.5 <5p 3 3|3 3 4p>
--
Wolfgang Westerboer Sch...@smail.uni-koeln.de
"Kölnvention" Juggling Club http://www.koelnvention.de
Martin Frost me at stanford edu
> Many passing patterns are symmetric : 4 ct, Waltz, ultimates, triangles,
> ... . Feeds involving runarounds also enter this category.
Hi, Christophe. An interesting post. I'm still digesting it.
...
> Anyway, in the basic form of a symmetric passing pattern, all partners
> do the same sequence of throws, either in phase or out of phase.
...
> The purpose of this post is to describe all symmetric passing patterns
> in terms of equivalent solo patterns. As an application, I list at the
> end all 2 persons 7 objects 3 count patterns.
All such *symmetric* patterns, that is.
...
> 333 --> 4.5p 3 3 : 7 Waltz which Tarim and Martin Frost denote by 966
> considering it as a 4 hands siteswap (I find this description slightly
> akward and misleading as explained later).
I don't think it's misleading, as I'll explain later (;-)
...
> - More generally, for 2 persons, if a(1) ... a(L) denotes the sequence
> of throws, then b(1) ... b(L) must be a valid solo siteswap, where:
> b(i) = a(i) if a(i) is a self,
> b(i) = a(i) - L/2 if a(i) is a pass.
> Conversely, given any n clubs solo pattern b(1)...b(L) , you may create
> a 2 persons 2n+k clubs passing pattern with k passes.
I don't doubt your conclusion of 2n+k clubs, but I don't see the derivation
of that formula.
...
> 13141 --> 3.5p 3 3.5p 4 1 : why not?
Why not indeed. The 3.5's are slow, lofty singles (or else the pattern is
a bit fast, your choice). One person passes all straights and the other
passes all diags.
> Let us denote the sequence of throws by a(1)pj(1) ... a(L)pj(L) : here
> a(i) denotes the "height" (siteswap value) of the ith throw and pj(i)
> means that when Juggler #k throws the ith throw, this throw will be a
> pass to Juggler #(k+j(i)) [mod P] . Selves are therefore these throws
> for which j(i) = 0 . This notation is essentially Ed Carstens' MHN
> notation.
I like and have adopted the notation of indicating the person you're
passing to by a 'relative juggler' number, with 0 indicating selves. This
eliminates the need to use the "p" to indicate a pass! 30 is a self, 31 is
a single to the "next" juggler, 42 is a double to the second subsequent
juggler, etc. I've suggested this notation to Omri Barel for use in his
causal diagram editor.
> Examples: (they all involve triangles, P = 3)
> - { j(1) = 1 , j(2) = j(3) = 0 , 333 } --> 4p1 3 3 : a 10 clubs triangle
> Waltz with passes always to the "next" partner.
All dbls are diagonals if everyone starts with two in the right hand (all R
hands are in sync). If one person starts with two in the left hand, passes
to and from that person are straight doubles and other passes remain diags.
> - { j(1) = 2 , j(2) = j(3) = 0 , 333 or 144 } --> 5p2 3 3 or 3p2 4 4 :
> two 11 clubs triangle Waltzes with passes always to the "preceding"
> partner.
Straight triples (52 3 3), with all R hands in sync. Or straight singles
with self doubles (straight) (32 4 4).
> - { j(1) = 1 , 3 } --> 3.33p1 : 10 ultimates with passes to the next.
First two people throw straight, the third throws diags (starting R, all R
hands out of sync). High singles, or a slightly fast pattern.
> - { j(1) = 2 , 3 } --> 3.66p2 : 11 ultimates with passes the other way
> round.
First person throws straight, next two throws diags (starting R, all R
hands out of sync). I suggest fast-spinning low double passes, for a slow
pattern. Or high lofty singles and a fast pattern.
> * The notation system used above, i.e. siteswap or mhn, does not say
> which passes cross. For that matter, causal diagrams do not say it
> either unless you have decided which hand each juggler uses first. So,
> do it.
My causal diagrams have each hand listed explicitly with an R or an L.
Note, by the way, that R and L hands don't have to alternate (as in
patterns with hurries). So you can take an existing diagram for a pattern
with no hurries and change the pattern by swapping selected R's and L's,
creating hurries.
> * The reasons why I do not like very much Tarim's notation, e.g. 966 for
> the 7 clubs Waltz, are first that numbers in this system do not
> immediately reflect heights of throws and which throws are passes, and
Actually, they do indicate height (or really time). They indicate exactly
how much time later the same object is thrown again, which is exactly what
the numbers in solo site swap indicate. The reason I have described a
7-club 3-count as 966 instead of 4.5 3 3 is simply a matter of time
resolution. In this case, the resolution is twice what you're used to,
because all four hands throw at different times. If you count all
potential throwing times for all people and stick to integers, you get 966.
But there's no reason you can't call the same thing 4.5 3 3 with a
different time resolution.
I'm suggesting Omri use 4.5 3 3 for inputting a pattern like this in his
causal diagram editor, simply to avoid this confusion, even though it
results in non-integer siteswap numbers. But then a normal self will
always be a 3.
> second that the sequence of numbers does not actually always denote what
> the jugglers have to do : as an example 4.5p 1 5 will be denoted in
> Tarim's system by 9 10 2 , so that dividing all numbers by 2 will yield
> 4.5 5 1 which is not the desired juggling sequence (and is also
> impossible since 351 is not a valid siteswap). Also I am more familiar
> with siteswaps involving 3 or 4 objects then 7 or more :)
Actually, 9 2 10 (not 9 10 2) is what we would have called your 4.5p 1 5.
You simply multiply your numbers by two. Even numbers then are then selves
(2 is a handacross, like your 1) and odd numbers are passes in this setup
(because all four hands are throwing at different times).
> List of 7 objects 3 count symmetric patterns: (max throw = 6, min pass =
> 3.5)
> 5.5p 5 0 , 5.5p 4 1 , 5.5p 2 3 , 5.5p 1 4 , 4.5p 6 0 , 4.5p 4 2 ,
> 4.5p 3 3 , 4.5p 1 5 , 4.5p 0 6 , 3.5p 6 1 , 3.5p 5 2 , 3.5p 3 4 ,
> 3.5p 2 5 .
I'll have to try some of these. But the ones with 6's (quad selves) are
pretty much out, so that leaves these below, and all are "fast" because of
the .5 in the passes (or they're slower but harder if you add an extra
spin). Of course 4.5p 3 3 is the normal 7-club 3-count (my "pattern of the
90's").
With triple passes: 5.5p 5 0 , 5.5p 4 1 , 5.5p 2 3 , 5.5p 1 4 .
With double passes: 4.5p 4 2 , 4.5p 3 3 , 4.5p 1 5 .
With single passes: 3.5p 5 2 , 3.5p 3 4 , 3.5p 2 5 .
The easiest of these should be the ones without triple selves or triple
passes, namely:
With double passes: 4.5p 4 2 , 4.5p 3 3.
With single passes: 3.5p 3 4.
> Now, I only hope I will find partners to try a 10 clubs 3 count
> triangle.
It's not a fast pattern. Good luck.
Thanks for the suggestions.
Martin
Christophe Prechac
You wrote:
> I don't doubt your conclusion of 2n+k clubs, but I don't see the derivation
> of that formula.
This comes from the average rule, namely that for any multihand pattern
the sum of all throw values divided by the length of the pattern is
equal to the number of objects. Thus if the solo pattern b(1)...b(L)
contains n clubs, and you convince 2 jugglers to pass a(1) ... a(L)
(out of phase, with a(i) = b(i) if a(i) is a self and a(i) = b(i)
+ L/2 if a(i) is a pass), the number of clubs in the passing pattern
will be 2(b(1) + ... b(L) + kL/2)/L = 2n +k , where k denotes the
number of passes.
Also, about notation:
> Actually, 9 2 10 (not 9 10 2) is what we would have called your 4.5p 1 5.
As far as I understand Tarim's deep 94 article, the sequence of numbers
in his system is the sequence of throw values of a *four hands juggler*
alternating J1R J2R J1L J2L .
Therefore, if J1 is throwing 9 2 10 at even beats starting at t = 0
and J2 is throwing 10 9 2 at odd beats starting at t = 1 , the
resulting *four hands siteswap* will be 9 10 2 9 10 2 , or shortly 9
10 2 . This is why I find this notation slightly misleading : 9 10 2
is not the actual sequence of throws of each individual juggler.
Now, if is clear that the numbers you use refer to individual juggling,
ambiguity is removed and chosing 4.5 1 5 or 9 2 10 to denote a
pattern becomes essentially a matter of taste.
I hope that the non-technically minded jugglers will not get to bored by
this discussion, assuming some of them are still reading. I would like
to see more theoretical posts on r.j. Not only for intellectual
excitement but also for practical purposes. Btw, what about your book?
Cheers,
Christophe
Isaac Orr
>I hope that the non-technically minded jugglers will not get to bored by
>this discussion, assuming some of them are still reading. I would like
>to see more theoretical posts on r.j. Not only for intellectual
>excitement but also for practical purposes. Btw, what about your book?
I don't know whether I count as "technically minded" (I'm pretty sure most
those who know me would give a resounding "NO"), but I certainly wasn't
bored by this discussion, simply because I did not see it as theoretical at
all but rather as a source of great new patterns (albeit somewhat screened
by 2n+k noise...). 3 of the 7 club 3 count patterns you mentioned were new
to me, and I will implement them as causal diagrams and put them in my site
as soon as the current ("7 club passing") section will be ready, probably in
a few weeks time - all the causal diagrams are already prepared (over 80 of
them) and I'm currently working on the accompanying text. I'll post here
when it's ready, and in the meantime thanks for everything both you and
Martin have posted!
---------------------------------------------
Isaac Orr <o...@dynamica.net>
Club Passing and Juggling Simulator site -
http://members.xoom.com/IsaacOrr/
Johannes Waldmann
> I hope that the non-technically minded jugglers will not get to bored by
> this discussion, assuming some of them are still reading. I would like
> to see more theoretical posts on r.j. Not only for intellectual excitement
OK, can't resist that one. Those of you who are/were at university
should remember their formal language course, and recognize
the following reasoning used in Christophe's article:
We have a word (= a sequence of letters) w,
namely, the siteswap for the first juggler.
Since the pattern should be symmetric,
his partner has a word w' which is a shift s(w).
Again, since the pattern should be symmetric,
the pattern of the first juggler ist s(w') = s(s(w)).
Since w should be a prime pattern,
there are just two possibilities for the amount of the shift:
it is either (pattern length) or (pattern length)/2.
if we had a shift by a different amount,
we would get some overlap between w and s(s(w))
from which it follows that w is not prime
(i. e. it has the form w = u u .. u for some u)
> but also for practical purposes.
well...
--
-- Johannes Waldmann ---- http://www.informatik.uni-leipzig.de/~joe/ --
-- j...@informatik.uni-leipzig.de -- phone/fax (+49) 341 9732 204/209 --
Christophe Prechac
> Siteswapping passing patterns:
>
> Juggle:
> Let愀 start with 2 jugglers, one does 4 clubs and the other 3.
> 4 4 4
> 3 3 3
> In total that is a 7 club pattern, of course.
>
Hello Wolfgang,
In the transformation I described between passing patterns and solo
patterns, selves are unchanged, therefore I prefer a more direct route.
1/ Take the solo patterns:
6 3 3
3 3 3
2/ then swap the first throws:
3p 3 3
6p 3 3
3/ finally delay the second juggler by 1.5 beats:
4.5p 3 3
3 4.5p 3
This approach can be used to derive some transitions, e.g. from
right-handed to left-handed shower:
1/ Solo patterns:
5 3 4 5 3
3 3 3 3 3
2/ Swap all throws except the (future) selves:
3p 3 3p 3p 3
5p 3 4p 5p 3
3/ Delay J2 by 1 beat:
4p 3 4p 4p 3
3 4p 3 3p 4p
Here, the transition throws are simultaneous and therefore require
prearrangement.
As an alternative, in step 2/ there is no need to swap the transition
solo throws, thus also possible is:
4p 3 4 4p 3
3 4p 3 3 4p
Now, the double self of J1 clearly signals the transition to J2.
Finally, something more collision prone but flashier!
4p 4p 2 4p 3
3 4p 4p 3 4p
Here too the second double pass of J1 signals the transition ... or
crashes everything.
Yours,
Isaac Orr
>Hello Martin and thank you for your reply.
[slight snip of entire message content]
>Btw, what about your book?
Yes indeed, what about it? Martin, have you heard about Richard Dingman's
upcoming "Patterns: A Manual of Club Passing", which is supposed to be out
before the year (is out, that is). It boasts 500 diagrams, 200 pages, etc.
so you better hurry up if you want to catch the market while it's still
hungry...
Wolfgang Westerboer
> Sch...@pop.smail.uni-koeln.de (Wolfgang Westerboer) wrote:
>
> > Siteswapping passing patterns:
> >
> > Juggle:
> > Let´s start with 2 jugglers, one does 4 clubs and the other 3.
> > 4 4 4
> > 3 3 3
> > In total that is a 7 club pattern, of course.
> >
>
> Hello Wolfgang,
>
> In the transformation I described between passing patterns and solo
> patterns, selves are unchanged, therefore I prefer a more direct route.
Sh*t, I missed that:
>>------ quoted from the original post
>passes are shortened, J2's passes are lenghtened, and the two jugglers
>are now passing in phase, swapping all passes then provides two
>independent solo patterns.
>>------ end of quote
Other way round here. (Sometimes I feel like I´m sleeping. And very
deep, too.)
> 1/ Take the solo patterns:
> 6 3 3
> 3 3 3
>
> 2/ then swap the first throws:
> 3p 3 3
> 6p 3 3
>
> 3/ finally delay the second juggler by 1.5 beats:
Shouldn´t we name it "shift"?
(...quoted mail is continued with nice ideas for passing patterns...)
>>* The notation system used above, i.e. siteswap or mhn, does not say
>>which passes cross. For that matter, causal diagrams do not say it
>>either unless you have decided which hand each juggler uses first. So,
>>do it.
(In the following lines I will use some siteswap extensions from
JoePass! Hope you don´t mind, this is not a commercial. It´s just what
I´m used to and what I can check at once.)
I´m still wondering what kind of patterns can´t be written as pure
siteswap with some extra information about heigth, speed etc.
(As all patterns whith different speed for the jugglers: one does a
3-count, the other a 4-count etc. What other things are there which I
don´t know?)
You can shift one juggler in time and you get the patterns discussed in
this thread. You also can shift one hand in time and you get galopped
patterns. You can use different dwell ratios for every throw, see below.
But basically the structure of the patterns is defined by a
siteswap/mhn.
An example: The ultimalte triangle with 10 clubs can be written as
(using the JoePass!-notation)
#D+ ! calculating delay times in throws (4p-(0.666-0)=3.333p etc)
#d1 .333 ! delay for juggler 1
#d2 .666 ! delay for juggler 2
<3:2|4:3|3:1> !siteswap
_if_ you want every juggler to throw at the same height. The direction
follows the values of the passes. As a modification: if A switches
hands, i.e. starts with his left (and tells C about it, because he has
to know), every pass is a cross.
It´s just for the idea. Siteswap tells you when to throw and to what
juggler/hand. Everything else are additional informations that makes the
pattern more interesting, easier, whatsoever. In the siteswap above you
can clearly see that A and C are throwing tramline while B is throwing
cross . You can´t see it in the notation
3.333p1
This pattern can´t be read without extra information you have to write
explicite as in
#D- ! DO NOT calculate delay times in throws
#d1 .333 ! delay for juggler 1
#d2 .666 ! delay for juggler 2
<3.333:2|3.333:3x|3.333:1> !strange siteswap
(x for cross)
I heavily use non integer values to try out some patterns.
And I _like_ the idea posted by Christophe. This helps to develop a
whole group of patterns when we need them. I´m just wondering if an
additional classical siteswap notation will help to remember what to do:
"delay A by 0.5" for the timing
<4p|3p> for the structure
3.5p1 for the height and direction
I just wrote the siteswap for jim´s 3count, it looks really ugly:
<
4x 2x 3p% 3 3 3p |
3 3 3px 4x 2x 3px%
>
(% says: same hand again.)
Add some extra information about dwell ratio at the 4x 2x section of the
pattern and everything looks fine. Like this
<
4xo.7 2xo.2 3p% 3 3 3p |
3 3 3px 4xo.7 2xo.2 3px%
>
(o followed by dwell ratio fo the throw)
o .5 std dwell ratio
the 2xo 0.2 is the hurried bit.
(It would be even better if the extra information are not part of the
pattern.)
regards
Wolfgang
Tarim
> The purpose of this post is to describe all symmetric passing patterns
> in terms of equivalent solo patterns.
Firstly, Tarim would like to thank you for all the work you've
put into this, and for a most interesting and thought provoking
article. If, when you read Tarim's response, you find it a
little critical - don't worry - it is. Just don't take it
personally.
The first problem is - you don't actually describe ALL
symmetrical passing patterns (as is customary with this thread;
Tarim will explain why later.)
If Tarim could offer you only one tip on site-swaps in the
future:
Use Whole Numbers
Reason 1. It is easy to tell where the throws go.
Christophe writes:
> * The reasons why I do not like very much Tarim's notation, e.g. 966 for
> the 7 clubs Waltz, are first that numbers in this system do not
> immediately reflect heights of throws and which throws are passes
This is not entirely correct. In fact, apart from the
statement that you don't like Tarim's notation, it is entirely
incorrect. As Martin has pointed out - the time (height) of the
throw is related directly to the number - simply divide by 2 to
get the equivalent in 2 handed site-swap.
In a 4 hand site-swap:
Even number: Self
Odd number: Pass
In fact it is even more precise; for one juggler:
4n+0: Self to the same hand
4n+2: Self to the other hand
4n+1: Diagonal pass
4n+3: Straight pass
For the other juggler; simply reverse the straight and diagonal
passes. If a 9 (4n+1) is a diagonal pass, then a 7 (4n+3) will
be a straight pass. Tarim thinks it's much harder to tell this
kind of thing from throws which are labelled 3.5p or 4.5p.
Reason 2. It is easier to see how the individual parts fit.
Christophe writes:
> second that the sequence of numbers does not actually always denote what
> the jugglers have to do : as an example 4.5p 1 5 will be denoted in
> Tarim's system by 9 10 2 , so that dividing all numbers by 2 will yield
> 4.5 5 1 which is not the desired juggling sequence
9 10 2 is the _hand_ order. Try writing it like this:
Juggler A: 9 2 10
Juggler B: 10 9 2
Reading it in a kind of wavy up and down way gives the
site-swap 9 10 2 9 10 2. Reading just one line gives what each
juggler should do AND also shows when they should do it in
relation to each other.
Reason 3. So you don't miss any patterns.
Consider the pattern (in your notation):
4.5p 4.5p 4.5p 4.5p 1 3.5p 4.5p 1 3.5p
Chris writes:
> - More generally, for 2 persons, if a(1) ... a(L) denotes the sequence
> of throws, then b(1) ... b(L) must be a valid solo siteswap, where:
> b(i) = a(i) if a(i) is a self,
> b(i) = a(i) - L/2 if a(i) is a pass.
Applying this to the above pattern; the b(n) sequence is:
0 0 0 0 1 -1 0 1 -1
As the captain of the Belgrano nearly said, "This may be a
valid site-swap, but it's not one I've heard of." Conversely,
there is no valid site-swap which will produce the above pattern.
Tarim leaves the proof of this as an exercise for Martin.
If you don't want to write the causality diagram - consider the
4-handed site-swap 9 7 9 9 9 2 9 7 2.
Juggler 1: 9 9 9 9 2 7 9 2 7
Juggler 2: 7 9 2 7 9 9 9 9 2
Reason 4. It is easier to generate new patterns.
The juggling simulator Tarim uses most is Jack Boyce's J2
program. This wonderful program allows you to generate ALL the
site-swaps that exist within certain constraints. For example,
the latest one Tarim tried was:
J2 7 9 9 -x 0 1 3 4 5 8 -simple
Which says, generate all 7 object patterns with highest throw
9, of length 9, without any 0s, 1s, 3s, 4s, 5s or 8s in, which
cannot be decomposed into simpler site-swaps. This is where
Tarim got the site-swap 9 7 9 9 9 2 9 7 2. The reason you miss
out site-swaps like this is because they contain odd numbered
throws (passes) which are less than the pattern length. Your
method does not generate passes like this; you can see this much
more clearly if you use whole numbers. Think about how you only
add on L/2 (or in the whole number case, L.)
Reasons 5 to 17.
There are many other good reasons for using whole numbers.
Tarim will, doubtless, rant on about this again; especially if he
hasn't convinced you yet ;-) The only reason you (and you're not
alone) cling to fractional numbers in passing site-swaps is so
that you can compare the throw heights to the 2-handed site-swaps
you're used to. Feel the integers, Chris. One day, you too will
be equally at home in throwing, say, a 4-handed 9 as a, 2-handed
5.
Best wishes,
---__ __ o ___
/ (_// / / ) )
Christophe Prechac
Ta...@altern8.demon.co.uk wrote:
Hello Tarim, hello all,
I would like to thank Tarim for his nice response and no, I do not take
Tarim's critical points personally and I am most happy that this
discussion keeps going on.
> If Tarim could offer you only one tip on site-swaps in the
> future:
>
> Use Whole Numbers
I don't agree ael ;:)
> Reason 1. It is easy to tell where the throws go.
I seem to remember from Tarim's 94 article the ODDGODM and ODDGODR hand
patterns. Has Tarim definitely settled for ODDGODR?
Needless to say, with more than two passers there are even more
possibilities: see Wolfgang's last post, esp. the 10 ultimates triangle
example.
Anyway, what's the big deal with fractional passes?
For two passers, one throws according to the whole part of the throw,
the other does the contrary.
So, if you do not want to think, make the wrong choice and then try
again.
> Reason 2. It is easier to see how the individual parts fit.
Yesterday, I tried 3.5p 3 3.5p 4 1 . I told my partner we would do a 5
beats pattern which goes as: pass self pass double-self handacross, out
of phase with each other. I would begin and throw straight, he would
cross.
This, I think (apart from the direction of the throws), is exactly what
the notation says.
Otoh, 7 8 6 2 7 doesn't speak to me.
(The fact that we could not keep the pattern running is irrelevant to
the argument.)
> Reason 3. So you don't miss any patterns.
>
> Consider the pattern (in your notation):
>
> 4.5p 4.5p 4.5p 4.5p 1 3.5p 4.5p 1 3.5p
This one is a monster. I will not discuss it.
Consider rather the following exercice as a practical application of the
use of negative throw values: switching roles in 7 clubs Triple-Single
<5p 3 / 3p 3> .
This question was already investigated by Wolfgang 2 years ago ("New (?)
7 cl passing pattern/An unusual look to SiteSwaps").
I will depart here from Wofgang's assumption that all left throws must
be single selves, thus I am looking for a symmetric pattern of the form
5p 3 a b 3p 3 c d
where, say, passes are at least 3 and passes and selves are at most 5 .
The unknown throws a , b , c , d cannot all be selves or all passes,
otherwise swapping passes would result in two independent solo patterns
of 3.5 clubs each. In fact, for similar reasons, there must be 1 or 3
passes.
Let us assume 3 passes, the associated reduced 1 club solo siteswap (or
rather permutation) is then:
1 3 a' b' -1 3 c' d'
where the x' equal x - 4 if x is a pass, x' = x otherwise.
Since Tarim and the captain of the Belgrano (who is this one? another
r.j. guru?) cannot throw back in time, let us translate to get a 2 clubs
siteswap
2 4 a" b" 0 4 c" d"
where the x" equal x'+1 and lie between 0 and 6 .
We may forget about the orbit of the 4 throws to get a 1 club siteswap:
2 0 a" b" 0 0 c" d"
Now the solutions are easy to derive. One of them is:
2 0 1 4 0 0 0 1
which results in the nice transition pattern:
A: 5p 3 4p 3 3p 3 3p 4p
B: 3p 3 3p 4p 5p 3 4p 3
No prearrangement is necessary here: when the passer throwing triples
feels tired, he passes a double instead, thus clearly signalling to his
partner that it is time to switch roles.
> Reason 4. It is easier to generate new patterns.
In the funny (crazy?) exercice above, state transitions in 7 objects
siteswaps and perhaps also Martin's beloved diagrams are indeed easier.
More generally, what I am looking for is a way to find patterns that
follow a certain number of constraints, particularly in terms of rhythm
and individual juggling. The number of objects (and maybe also passers)
being not necessarily an issue.
As an example: in which (symmetric) patterns can you do Double Pass,
Double Pass, Triple Pass, Triple Pass followed by a few selves
continuously?
With six clubs and an 8 beats cycle, I proposed a solution previously in
another thread (it can be easily derived along the lines above). I
suspect that the pattern is well known but have never heard of it.
> Reasons 5 to 17.
>
> There are many other good reasons for using whole numbers.
> Tarim will, doubtless, rant on about this again; especially if he
> hasn't convinced you yet ;-) The only reason you (and you're not
> alone) cling to fractional numbers in passing site-swaps is so
> that you can compare the throw heights to the 2-handed site-swaps
> you're used to. Feel the integers, Chris. One day, you too will
> be equally at home in throwing, say, a 4-handed 9 as a, 2-handed
> 5.
Is it true? Is Tarim 4-handed?
Yours,
Christophe
Wolfgang Westerboer
As Christophe said: may this discussion keep on going. Once again, I
would like to add some short ideas, not an entierly new theory.
Christophe wrote:
> For two passers, one throws according to the whole part of the throw,
> the other does the contrary.
> So, if you do not want to think, make the wrong choice and then try
> again.
As you say: for 2 passers. With more than 2 people it might be a bit
difficult - you can´t try to what hand you have to pass to in the
discussed triangle, you have to know it. BTW, has someone done this
pattern once? Seems to me quite hard.
Martin wrote:
> I'm suggesting Omri use 4.5 3 3 for inputting a pattern like this in his
> causal diagram editor, simply to avoid this confusion, even though it
> results in non-integer siteswap numbers. But then a normal self will
> always be a 3.
Is that editor aviable somewhere? I would _love_ to check patterns that
way. Now I use a vector-graphics programm where I draw lines, mark one
end of the passing lines, group them and move the group. Pretty unhandy,
but it works.
I just realised that way, that the 7 club singles is a galloped
variation of the std. pattern
<4p 3|3 4p>
To get all throws at the same height, A delayes his left hand and B his
right hand, both by 0.5 beats.
And, if B switches hands, i.e. the staggered pattern, B has of course to
delay his left hand, too.
(JoePass! can do it in the new version, 1.7. I place it on
koelnvention.de/jp/ later this day. I guess everything is working fine,
but one never knows)
> In article <929519...@altern8.demon.co.uk>,
> Ta...@altern8.demon.co.uk wrote:
>
> Hello Tarim, hello all,
> I would like to thank Tarim for his nice response and no, I do not take
> Tarim's critical points personally and I am most happy that this
> discussion keeps going on.
The really great thing about this diskussion is that we are all are
right.
Tarim, because he gives us wonderful workshops with great patterns.
Christophe, because he comes with new ideas about juggling once a week.
Martin, because he always is right.
Me, because I write this lines and nobody can stop me now.
Now, as everything is that fine, I just want to explain why I prefer a
notation in which the values and their height doesn´t change with the
amout of jugglers who are involved in the pattern.
First of all, I´m from germany. In my country it is strictly forbidden
even to imagine 2 or more jugglers morphing to a 4 (6,8...) handed,
meta-tarimish creature. It´s part of the anti-drugs-law, I guess.
More serious: when does Tarim start to melt people together - when they
are in the same room, when they are looking at each other, when they try
to juggle in phase, when they pass?
Tarim wrote:
> If Tarim could offer you only one tip on site-swaps in the future:
>
> Use Whole Numbers
Every notation that helps us to find new patterns or to improve our
juggling skills is a good one. Personally, I want to copy and past
patterns together. I don´t want to think about a self in a 2 person
pattern as a 6 (or something else). I don´t want to change my numbers /
feeling for the numbers because someone stands in front of me.
I think about a 7 1-count like: two people doing 3.5 out of phase.
Fractional values can help people to find out what they are doing or
waht they can do next.
So we better should not say no. It´s great to see people playing wit new
ideas. Hey, someone once discovered sliced bread that way.