Author: Christophe Pr?chac

Many passing patterns are symmetric : 4 ct, Waltz, ultimate, triangles, ... . 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, therefore 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 themselfs.

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, selfs 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 "ultimate" 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 3p 4p>).

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:

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] . selfs 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:

Now, swap all passes! I.e. have everyone throw selfs 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:

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 ultimate with passes to the next.

- { j(1) = 2 , 3 } --> 3.66p2 : 11 ultimate with passes the other way round.

- What about ultimate 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 ultimate < 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:

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

Author: Christophe Pr?chac

Notes : For clarity, in the causal diagrams below, short and long holds 1x and 2 are not depicted

In all causal diagrams, the causal chains may be distinguished from each other by their different colors. This allows us to represent passing patterns where the jugglers make sync throws: follow the colored paths to understand which hands throw to which.

7 clubs 3 count in doubles

7 clubs 3 count in singles

10 technofeed

8 technofeed

6+1 ultimate

This pattern is based on 6 sync ultimate. The rest beats of the base pattern offer room to add a seventh club which is passed diagonally to avoid collisions. The version below is way easier for the second passer but it is possible to change roles on the fly.

5+2 ultimate

7 sync shower

7 PPS

7 PPS in singles!

Mild madness

PPHSPPS

Martin's ultimate

PPPPH

10-1 ultimate

For ball bouncers only!

Author: Christophe Pr?chac

1. Introduction

Multi-hand notation

Multi-hand notation has been developed by Ed Carstens for use with his juggling program JugglePro. It is an analytical notation system that extends the siteswap construction to an arbitrary number of hands and to an arbitrary juggling rhythm.

Once the juggling hands are allowed to throw at any given beat, one can describe transitions between async patterns and sync patterns or even more bizarre rhythms. Note that in the original mhn system no attention is paid to catching beats, only throwing beats are taken into account.

Multi hand notation, much like standard siteswap notation, is useful both to provide short descriptions of patterns and to simulate them on juggling softwares.

Causal diagrams

Causal diagrams were invented by Martin Frost. They offer appealing geometric pictures of juggling patterns, particularly passing patterns.
Let f denote the permutation on (a subset of) HxZ defining a juggling pattern, where H is the set of hands and Z is the set of integers. Then, essentially, the causal diagram of the pattern is the ladder diagram of f-2 (that is: f translated 2 beats in the past).

Now, why is this mapping f-2 so interesting?
While the original permutation describes the paths in HxZ of the objects juggled, the new one f-2 describes the paths, or the timetable, of the problems encountered by the jugglers, which is often all we are interested in: we do not care which clubs we juggle, we merely want to sustain the pattern as a whole.

This construction works fine both for async patterns and sync patterns. It needs to be adapted however in order to allow for more general patterns: transitions between different rhythms, galloped patterns, etc ...

Causal diagrams are often much easier to use than siteswap/mhn descriptions when one tries to work out syncopations in passing patterns. They are also a powerful tool to discover (i.e., most often, rediscover :)) new patterns.

This page

In this page and its complement, the hurries page, the mhn system and the causal diagram construction are adapted so as to obtain a complete correspondence beween the two notation systems.

The main novelty in the mhn system used here is that it explicitely takes into account the "catching beats", henceforth refered to as dwell beats.

The causal diagram construction is also slightly modified: this concerns essentially the representation of an empty hand 0 and a short hold 1x .

2. Relaxed juggling

Common juggling wisdom as well as practise suggest that in normal situations, the same hand cannot throw twice in a row (unless hurried throws are allowed). Between two throwing beats, there must be one beat where the hand catches a new object and prepares for the next throw.

Let s be the siteswap value of a throw, s >= 2 , s tells us how many beats in the future the object will be rethrown (or maybe held further for a while), it does not tell us however how many beats the object spends in the air.
The usual implicit assumption is that the airtime value will lie somewhere strictly between s-2 and s , depending on the style of the juggler, or in technical terms on his choice of dwell ratio.

Here we will adopt a "relaxed" style of juggling, assuming an airtime value strictly less than s-1 which means that once an object is caught, it will spend at least one beat in the hand before being rethrown. This assumption is necessary if we want to allow the possibility to violate it later in the hurries page! Anyway, in this page it will be maintained throughout:

Assumption

To a throw of siteswap value s corresponds an airtime value
strictly less than s-1

After an object has landed, it will be prepared for the next throw:

Definition

For an object thrown with siteswap value s , the juggling action that takes place in the target hand s-1 beats later, i.e. one beat before it is rethrown, is refered to as a dwell hold

Exceptions for some "small throws":

The "relaxed juggling" assumption does not apply when s=0 - an empty hand - or s=1x - a short hold. There will be no corresponding dwell hold.

When s=2 - a "throw" usually interpreted as a long hold - it does apply if this 2 is indeed thrown.

When s=1 - a fast handacross - the relaxed juggling assumption is difficult to meet: the club should land in the past! We will maintain it however, obviously an idealization, and the dwell hold takes place immediately in the target hand.

3. Notations

Throws are denoted as in JoePass!
However, for "inactive" hands, it is essential to differentiate between the two following cases:

The hand is empty.
The hand has just caught an object and is doing a dwell hold.

Note that this distinction makes no sense in the original mhn system since both cases correspond to an absence of throw and pure mhn, as well as genuine siteswap theory, only cares about throws.

For a given hand, a dwell hold will be denoted by a dash: - .

4. Causal arrows

For an object thrown at beat t with a siteswap value s>=2 , landing will occur between beats t+s-2 and t+s-1 , according to the previous assumption. Therefore the target hand must empty itself or be already empty s-2 beats in the future.
Hence the causal arrow representing the throw will be of length s-2 .
In particular, a 2 throw will be depicted by a closed loop and a 2x throw by a vertical arrow.

A fast handacross 1 requires the target hand to be ready for catch immediately, i.e., it must have emptied itself previously. Hence a 1 beat crossing backwards arrow.

A short hold 1x is a problem only for this very hand that is currently doing the short hold. We will depict this by a big point.

An empty hand 0 can only occur if this hand has thrown or was already empty one beat before. Hence a 1 beat horizontal backwards arrow.

A dwell hold - is not really a throw. It will not be depicted

Actually, short holds 1x and long holds 2 do not really need to be depicted. They offer no additional information to reconstruct a mhn pattern from a causal diagram (unless one wants to emphasize if a 2 is thrown or held). For clarity, and particularly in passing patterns, they will often not be depicted.

5. Summary of assumptions and notations

• is empty
• "dwell holds" an object that has just been caught
• "holds" an object
• throws an object

6. Examples

Solo juggling

1

slow 1

1x1

async to sync shower

51 to (2x,4x)

sync to async shower

(2x,4x) to 51

3 cascade at height 5

1x5

3 shower to high 3 switch

5151 5x1 51x51x...

2 at height 3!

3x1x

4x throw

4x flash

from 4 sync to 4 async

from 4 async to 4 sync

Passing patterns

3 ultimate

There is only one backwards going causal chain. Passes are drawn in red for emphasis.
See the oddpatterns page for more interesting passing patterns where the jugglers throw sync throws.

4 ultimate

With flat vertical passes as in Marc and Benji's beautiful number.

5 ultimate, 2 beats version

(holds are not represented)

Gandini's patterns from hell

Take any symmetric passing pattern where the jugglers throw singles in phase and choose any number k (preferably prime with the period of the pattern). Then replace every kth single by a double.

E.g. PPS with k=5:

A 36 beats cycle! Hopefully, the causal is of no particular interest :)

Kickups

Kickups may be seen as particular cases of multiplex throws. The analysis developed in this page extends easily to multiplex patterns. I skip however a formal mhn description of the patterns for simplicity. Also, in the causal diagrams below, I omit the backwards going arrows that indicate that the foot is empty after the kickup.

6 to 7 Shower

J2 throws a straight double pass on his pass beat, this is a signal for J1 to switch into the 7 clubs version of the pattern.

6 to 7 Waltz

J2 throws a straight double pass (of siteswap value 4.5) on his pass beat, thus signalling to J1 to switch into the 7 clubs PSS pattern with double passes.

6 to 7 PPS

J2 throws crossing double passes on his pass beats, this again is a signal for J1 to start doing his part of the 7 clubs version of the pattern.

Author: Christophe Pr?chac

1. Introduction

The concept of hurry was first developed by Martin Frost in an excellent article of the Fall '97 issue of Juggler's World.
More recent treatments of the subject, with special emphasis on 3 count passing, were given by Isaac Orr in Juggle, 2000 and Wolfgang Westerboer in Kaskade, 2000.

Here, all 3 clubs are thrown at single height. Two clubs are always thrown to the same hand the remaining club crosses back and forth. The crossing club, although thrown at height 3 , is always rethrown after 2 beats, the non-crossing clubs however are thrown every 4 beats.

2. A new definition

We feel that the traditional definition is a little bit unprecise, for instance the following pattern

is not a hurried pattern although it follows the hand pattern RRLL. Here, 3 clubs are juggled at height 5, on triples if you wish, but they are rethrown every 6 beats, making the pattern very relaxed indeed.

Moreover, one may encounter hurries even under the regular RL hand pattern, e.g. :

that is: juggling 3 clubs in doubles in frenzy circus style. The clubs are thrown at height 4 but rethrown every 3 beats, i.e. 1 beat earlier than normal.

We will therefore adopt the following:

Definition

A hurry occurs whenever, skipping the dwell hold,
a club is rethrown 1 beat too early

3. Sync interpretation of hurries

Here, we develop a simple method to translate any hurried pattern in the familiar language of sync siteswap theory.

The method is based on the following simple observation: when we watch someone doing a slow 3 clubs cascade, there is no way to decide whether he is doing the async siteswap 3 with a high dwell ratio or the sync siteswap (2 , 4x)(4x , 2).
Indeed, the ladder diagrams of 3 with a dwell ratio d > 0.5 , and (2 , 4x)(4x , 2) with a dwell ratio of 2d-1 are the same.

This simple observation holds for any juggling pattern, hurried or unhurried. Given our assumption of a dwell ratio greater than 0.5 , any mhn juggling pattern, hurried or unhurried, can be reinterpreted as a unhurried sync siteswap juggling pattern.
Essentially it amounts to reinterpret all dwell holds - as short holds 1x , and to double the time scale.

For example, the 3 patterns above can be written in sync notation as:

This way to denote hurried patterns is useful to emulate hurried, and other non-standard rhythm patterns such as 1x5 , on juggling simulation softwares.
You might need to adjust heights and/or number of spins to get a reasonable animation. Also the animated juggler will move his hands during the numerous 2 holds appearing in the sync representation

Hurried passing patterns can be written in sync notation as well (and therefore be animated), e.g. Mild Madness:

can be written in sync form as:

The following section proposes a lighter and more direct way to represent hurried patterns.

4. Hurried mhn* notation and a glossary

Hurried mhn*

Starting from mhn notation, we now allow for the possibility to throw one beat earlier than normaly implied by the throw (siteswap) sequence.
Following common usage, a hurried throw will be identified by a star: * .

To say that a throw of siteswap value s >= 2 leads to a hurried throw t*, means that the club will be rethrown with a throw value of t after only s-1 beats instead of s beats, i.e. skipping the usual dwell beat.

Not of much practical use, but in theory a fast handacross 1 can lead to a hurried throw as well: the club is then rethrown immediately.

Examples

The hurried patterns presented previously can be written as:

which is much more understandable at first glance than in the sync notation:

The sequence (- , 3x)(1x , 3*)(3x , -)(3* , 1x) clearly indicates what is going on in 3x3* : self R , followed by crossing R , then self L and crossing L , all in singles. The * on the crossing throws point out that the crossing throws are the difficult throws of the pattern. The short holds 1x are additional information that may or may not be used.

(0 , 4x*)(4x* , 0) is also quite clear: fast crossing doubles.

Finally, in Mild Madness, the sequence

Validity of mhn* patterns

Checking the validity of a hurried mhn* pattern is essentially the same as for a regular mhn pattern: follow the numbers and make sure that they define a valid permutation.
Now, however, when one traces the path of an object, one has to make sure at each rethrowing beat that the object has not already been rethrown one beat before as a hurried throw. With some practise it is not really difficult.

The average rule

From a pure mathematical point of view, a hurried throw is equivalent to a normal throw combined with a throw one beat later that goes one beat in the past: * = -1x one beat later. This observation does not seem to be very useful except for the following:

The average rule still holds:

Count each hurried pointer * as an additional -1 throw, then the average of the throws over time, multiplied by the number of hands, must equal the number of clubs

A glossary

Since mhn* and sync are analytical representations of the same patterns, it is possible to translate from one language to the other. The glossary goes as follows:

Notes:

The causal diagrams of the patterns, written in mhn* or sync are of course the same, up to the doubling of the time scale and to the representations of the various holds 2 , 1x , - which are anyway redundant and can be omitted if one wishes.

Whether a throw is hurried or not has no influence on its sync translation.

Translating back from sync to mhn is also possible, although the three mhn "throws" - , 1x , 2 correspond to the same sync throw 2 . Precise description is left to the reader :).
Anyway, the hurried throws are the throws that are immediately preceded by an empty hand or another throw from the same hand that is not a 1x .

5. Examples

Solo juggling

Alternating two clubs singles in one hand

Throws are drawn in green for emphasis.

4 doubles/singles switch

1 up 2 up

Starting from the pattern 3x3* , the rest beats are suppressed and used for additional (hurried) selfs. This trick can be applied in many hurried passing patterns, e.g. Jim's 3 count.

Alternating shuffle

A nice trick

Two versions:

A 4 objects 4 count tennis

Passing patterns

A nice 3 count trick

With the handacross behind the back

A PPS trick

J1 throws his second pass in advance as a straight double. Follow the colored causal paths to understand which hands throw to which.

async/sync ultimate

J1 forces the rhythm to change without throwing doubles.

Martin's ultimate

Oddities

0 sync shower!

See (0x,0x).txt for more on this nice pattern.

Akward 1 shower

Fast 2 shower

Author: Christophe Pr?chac

(As posted on rec.juggling, February 2001)

This article presents a simple way to deduce (k+1)-people (3k+n)-clubs feed passing patterns from n-clubs solo siteswaps. A non-exhaustive series of feed passing patterns is constructed by this method as an application: included are many popular feeds, such as the shower and ultimate feeds, as well as some lesser known exotic patterns of the hurried and slow-fast variety. The only essential restriction is that the selfs of the feedees have to be ordinary singles of siteswap value 3 : you better bring your own popcorn then, if you wish to proceed (and perhaps some aspirin too :)).

Start with everyone juggling solo (but perhaps not in phase): one juggler, the feeder, is juggling a n clubs solo siteswap, while the other jugglers, the feedees, juggle ordinary 3 clubs cascades. Now, at some point, the feeder can choose not to do a particular solo throw of siteswap value s but to do a pass instead of siteswap value a to some feedee ; the feedee will then reply by a pass of siteswap value b after a delay of d beats. To keep the patterns going without trouble (i.e. drops) it must be that b+d = s and a-d = 3. If passes are done to the same height (an assumption that can be relaxed at will later on, see the 10 clubs PPS feeds below), we get

That's about it basically. The main interest of this method is that it reduces the search of patterns that follow a specific rhythm for the feeder - say PPS - to the examination of simple solo siteswaps - ss'3 in the previous case. Therefore the patterns to follow will be classified according to the feeder's rhythm: shower, ultimate, etc ...

All passing patterns are written in the siteswap syntax of Wolfgang's irrelevant :) juggling simulator JoePass! available at : http://www.koelnvention.de/software/joepass/index.html (hey, Wolfie I haven't received your check yet, are you sure it's in the mail??). If you can't juggle them, you can at least watch them!

A remark about the directions of the passes (straight or crossing): they depend on which hands are used first by the jugglers. The default hand pattern in JoePass! has everybody starting from the right hand but you can change this by using the #jugglerStartLeft n switch (n: number of juggler you wish to change). A similar remark holds for outside passes versus inside passes (see e.g. the 10 clubs ultimate feed below).

Let us start with the most popular feeds:

Shower feeds

3333 and passing on the first and third throws --> a = 3 , d = 0

Similarly 5353 --> a = 4 , d = 1

(Add #jugglerStartLeft 2,3 to make the feedees pass from the right hand as usual)

etc ... you get the picture: 7373 --> a = 5 , d = 2

ultimate feeds

33 and passing on all beats --> a = 3 , d = 0

44 --> a = 3.5 , d = 0.5

(Since juggler 2 is on the left of juggler 1 in the default position, you may wish to add #jugglerStartLeft 1 to have the feeder make outside passes as usual)

55 --> a = 4, d = 1

PPS feeds

Since there is no 4 clubs siteswap of the form ss'3 with s=s', it is clear that there can be no symmetric 10 clubs PPS feed. Many assymetric patterns are possible however.

453 and passing on the first two beats would yield a = 3.5 , d = 0.5 for one feedee and a = 4, d = 1 for the other feedee, resulting in:

This pattern might feel a bit strange to the feeder: the passes are very close to each other but different nevertheless, it is therefore perhaps safer (more stable) to change the delay of one feedee. There are four possibilities:

The 4 clubs siteswap 633 provides yet another completely different pattern:

The symmetric 11 clubs PPS feed is well known:

663 -->a = 4.5 , d = 1.5

More exotic patterns

(the feeder is on the middle line in the causal diagrams) Start with the feeder doing sync crossing (!) 4 clubs in singles which I denote by (3* , 3*), see http://pogo5.free.fr/juggling/hurries.html for details on hurried mhn* notation, then let him pass all right hand throws --> a = 3 , d = 0

One can add a club to the previous pattern (well, at least theoretically) by starting from the 5 clubs hurried half shower (3* , 4x*) --> a = 3.5 , d = 0.5

Similarly, starting from the hurried 4 clubs sync solo pattern (3* , 4)(- , 3*)(4 , 3*)(3* , -) and passing the high throws --> a = 3.5 , d = 0.5

Getting weirder. Now the feeder is juggling 4 in singles the usual async fountain way and still 2 times faster than the feedees. This pattern can be denoted by 3x* keeping in mind that throws occur every half beat (the tempo is given by the feedees). Passing all throws we get a = 3 , d = 0 and a pattern that can be denoted as:

Still crazier and a special dedication to some one-bearded multi-handed British passing guru. To get the usual 9 clubs version of Alan's Anguish, we need the feeder to juggle a 3 clubs cascade 2 times faster than the feedees. Let us (or at least let me!) denote this pattern by 2.5x*, still remembering that throws occur every half beat (2.5 throws should "normally" be rethrown after 2.5 beats, but due to the hurry pointers '*' everywhere, all throws are actually rethrown 1 beat earlier, i.e. after 1.5 beats). Passing all throws we get a = 2.75 (!), d = - 0.25 and:

Author: Christophe Pr?chac
Credits: Kaskade 62 & 63

As in Kaskade 59, we are just the three of us ... and the song remains the same: what can we do with approximately 9 clubs?

This passing workshop is devoted to a few feed passing patterns with 8, 9 and 10 objects. They are all derived from actual regular practice sessions down here in Paris, in some dark and - this being written in winter - poorly heated room. Although these patterns are relatively rarely seen in the gyms, I believe them to be both interesting and useful for practising more standard patterns.
You will perhaps appreciate that all the proposed patterns can be juggled under a fairly low ceiling as they contain only single-spin throws (syncopations notwithstanding).

About the description of patterns:

In all the patterns, the jugglers are denoted by J1, J2, J3. The feeder is J2 and the feedees are J1 and J3 .
In the triangle feed position, feedee J1 is the feedee on the right, from the feeder's viewpoint..

All patterns are illustrated (and summed up) by causal diagrams. The feeder J2 stands on the middle line, feedee J1 is above on the first line, and feedee J3 is below on the third line. The causal diagram also contains implicitely the starting position: each hand at the beginning of the diagram starts the pattern with 2 clubs, the other hands start the pattern with 1 club.
 

Eight-clubs feeds

Say you are three passing partners but you only have eight clubs. Do you desperately need to borrow an additional club?? No! Just as it is possible for two passers to have fun with 5 clubs, see the article on 5-clubs ultimate in Kaskade 56, there exist 8-clubs feeds that are both interesting and enjoyable. Alternatively, you may consider practicing these patterns as warm-up exercises before more serious stuff, or ... as chill-out sessions after some furious number passing.

Eight clubs fast/slow ultimate/ultimate feed

Everybody juggles an ultimate pattern: no selfs, only passes. But the feeder and the feedees follow different rhythms.

The feeder - on the middle line, in the diagram above - is on the fast side: he (or she, of course) juggles on a standard ultimate rhythm and makes only outside passes along the sequence: Cross, Cross, Straight, Straight, or in other words: R to J1R, L to J3L, R to J1L, L to J3R.

The feedees are on the slow side: they juggle twice slower than the feeder, as if doing one side of the 2-passers 5-clubs ultimate pattern on a rather quiet pace. This huge amount of time for the feedees between the passes can (must?) be put to good use to insert and improvise fancy variations: flourishes, pirouettes, additional throws such as Self+Handacross between passes, box variations: passing with the "wrong" hand while simultaneaously freeing the "correct" hand with a handacross, ...

Starting position: The feeder has 2 clubs in each hand, the feedees have 1 club in each hand.

Siteswap description: < (- , -) (2 , 3p2x) (- , -) (3p2 , 2) | (- , 3p1x) (3p3x , -) (- , 3p1) (3p3 , -) | (2 , 3p2) (- , -) (3p2x , 2) (- , -) >

Eight-clubs slow/fast ultimate/4-count feed

A reasonably simple pattern and a very nice one to watch. In this pattern, the usual triangle position of the jugglers is stretched to a straight line, the feeder J2 stands in the middle with J1 on his right.

The first feedee J1 is doing 4-count right-handed while the second feedee J3 is doing 4-count left-handed out of phase with J1, meaning that J3 will start throwing passes 2 beats after J1.

The feeder is now on the slow side of the pattern and he makes only passes on a very slow pace, but he will do them behind the back or under the arms for more fun and visual effect.

(Don't be abashed by the backwards going arrows, they simply mean that the feeder's hands remain empty for one beat after he has passed.)

The sequence of passes for the feeder is as follows: 1. throw behind the back with left and catch with the right, 2. pause, 3. throw behind the back with right and catch with the left, 4. pause.

Notice that the rest beats of the feeder allow him to indulge in fancy swinging movements between the catching and throwing positions. Also, the feeder might turn a half-pirouette now and then, resulting in normal outside passes and catches (try it, it really isn't difficult).

Needless to say, the feedees can try to throw all their usual 4-count tricks ...

Starting position: The feeder has 1 club in each hand, feedee J1 has 2 clubs in the right and 1 in the left, feedee J3 has 2 clubs in the left hand and 1 in the right.

Variation: Both feedees pass with the right hand making life for the feeder (slightly) more difficult.

Siteswap description: < (- , 3p2) (3 , -) (- , 3) (3 , -) | (3p1x, -) (0 , 1x) (- , 3p3x) (1x , 0) | (3 , -) (- , 3) (3p2 , -) (- , 3) >

Nine-clubs feeds

The nine-clubs shower feed is certainly the most popular passing pattern for 3 jugglers, be they beginners or advanced. And for good reasons: it really is a wonderful pattern! The only drawback of the shower feed is that it is strictly right-handed ... In my opinion, a passing session cannot be complete and really fulfilling without a few ambidextrous patterns. Come on: bring some relief to your left shoulder and give them a try!

Changing roles in the Nine-clubs PPS feed

The nine-clubs PPS feed has been already addressed in Kaskade 59. Here I would only like to mention that it is both feasible and entertaining to change roles on the fly in this pattern now and then.

One feedee wants to move to the feeder's side, making the other feedee the new feeder. How does it work?

One solution goes like this:
Assume that J3 , the feedee on the left of the feeder J2 , is also the "second" feedee, i.e. the feedee who receives the _second_ pass of the feeder. Now, J3 wants to move to J2's side, making J1 the new feeder, he will do this as follows: on his right hand pass beat, J3 begins to walk towards his new position on the (left) side of J2, catches the incoming club in the left hand, while still walking and turning leftwards in order to face J1, and throws the club back to J1 on his normal left hand pass beat.

So the entire move lasts for 3 beats. During this period J3 can either stop throwing selfs (and therefore manage 2 clubs in the left hand for a short while) or keep on juggling normally, throwing his two selfs (I find it easier this way).
Naturally, the ex-feeder J2 will have to stop passing to J3 : he will shift from PPS to PSS without transition.
While J1, the new feeder, will have to convert his first self into a pass to J3, shifting from PSS to PPS without transition.

The sequence of throws is summed up in the causal diagram:

Try it! Hilarity and drops guaranteed on first tries!

Remarks:
With every switch the hand order of the feeder's passes is exchanged: in the example
above from (RO = right outside, etc ...) RO LO LI RI   to   RI LI LO RO .
Oddly enough, if the "first" feedee wants to move, the transition is less natural. See by yourself!

Siteswap description: < 3p2 3 3 3p2 3 3 3p2 3p3 3 3p2 3p3 3 |
3p1 3p3 3 3p1 3p3 3 3p1 3 3 3p1 3 3 |
3 3p2 3 3 3p2 3 3 3p1 3 3 3p1 3 >

Nine-clubs PPH/3-count feed

An advanced 9-clubs pattern perhaps, since it is a little bit fast. What happens here is that the feeder will do Pass Pass Handacross while the feedees will follow a 3-count rhythm Pass Self Self. What? Pass Pass Handacross instead of Pass Pass Self!? How can it be?? Let us look at the causal diagram:

(the backwards going arrows represent the handacrosses)

Notice three points from the causal diagram:
- from the throw positions, one sees that the pattern is staggered: the feedees' passes are done half a beat after the feeder's
- from the lenghts of the arrows, the (single spin) passes must he higher than the selfs
- finally, note that the feeder's passes are straight while the feedees make crossing passes.

Starting position: The feeder and feedee J1 have 2 clubs in the right hand and 1 in the left, feedee J3 has 2 clubs in the left hand and 1 in the right. Each feedee waits for the feeder's pass to be thrown to him before replying by a pass.

Variation: The feeder makes crossing passes and the feedees make straight passes.

Siteswap description: feedees J1 and J3 delayed by half a beat
< 3.5p2x 3 3 | 3.5p1 3.5p3 1 | 3 3.5p2x 3 >

Nine clubs ultimate feed

A nice pattern, and quite doable if the feeder feels comfortable with 6 clubs ultimate. The feeder always makes inside straight passes. J1 showers left-handed and J3 showers right-handed.

Starting position: The feeder and feedee J3 have 2 clubs in the right hand and 1 in the left, feedee J1 has 2 clubs in the left hand and 1 in the right.

Variation 1: The feeder makes outside passes.
Variation 2: Both feedees pass with the right hand.

Siteswap description: < 3 3p2 | 3p3 3p1 | 3p2 3 >

Nine clubs Alan's Anguish

This pattern is similar to the Eight clubs fast/slow ultimate/ultimate feed examined previously: everybody juggles an ultimate pattern: no selfs, only passes ; but the feeder and the feedees follow different rhythms.
The feeder - on the middle line, in the diagram above - is on the fast side: he juggles on a standard ultimate rhythm and makes only inside passes along the sequence: Cross, Cross, Straight, Straight, starting with J3 on the left, in other words: R to J3R, L to J1L, R to J3L, L to J1R.
The feedees are on the slow side: they juggle twice slower than the feeder, as if doing one side of the 2-passers 5-clubs ultimate pattern on a rather quiet pace. Once you manage to get a reasonably stable pattern, the feedees can try to use the huge amount of time between the passes to insert and improvise fancy variations as in the 8 clubs version. Note that the feedees always pass to the closest feeder's hand, namely J2R for J1 and J2L for J3 .

The pattern differs from the 8 clubs versions in two respects however: the pattern is now staggered and the single spin passes should be higher than usual (say, as in 7 shower in singles). Also ... it is much more difficult!

Starting position: The feeder has 3 clubs in the right hand and 2 clubs in the left, the feedees have 1 club in each hand. Each feedee waits as long as possible before passing back to the feeder.

Siteswap description: feedees J1 and J3 delayed by half a beat
< (2 , 3.5p2x) (- , -) (3.5p2 , 2) (- , -) | (- , 3.5p3x) (3.5p1x , -) (- , 3.5p3) (3.5p1 , -) |
(- , -) (2 , 3.5p2) (- , -) (3.5p2x , 2) >

Ten clubs feeds

A few (low-ceiling) 10-clubs patterns to finish off this passing session.

Ten clubs ultimate feed

A logical follow-up of the 9-clubs ultimate feed ... but actually a completely different pattern! (and also a much more difficult one)

The feeder juggles a (relatively fast) ultimate pattern with outside straight passes. J1 showers right-handed while J3 showers leftt-handed. Both feedees throw crossing passes. The passes of all the jugglers should be high and lofty, and in any case, they should be higher than the selfs of the feedees.

Notice that the causal diagram is divided in 2 independent parts: each hand of the feeder passes 5 clubs with a different feedee (so that each feedee passes back to the hand that feeds him). You can also readily see that the pattern is staggered: the passes of the jugglers alternate along the sequence J2 J1 J2 J3 . The relative lenghts of the arrows clearly indicate that all passes should be higher than the selfs of the feedees.

Starting position: The feeder has 2 clubs in each hand, feedee J1 has 2 clubs in the right hand and 1 club in the left hand, feedee J3 has 2 clubs in the left and 1 in the right. Each feedee waits for the feeder's pass to be thrown to him before replying by a pass.

Remark: This pattern is also know as the gorilla pattern. Guess why!
Tip for the feeder: practice each hand separately (i.e. with only one feedee).
Variation 1: The feeder's hands pass simultaneously. This is what sometimes happens naturally after a while anyway.
Variation 2: The feeder makes outside crossing passes (and the feedees pass straight). I personnaly find this version easier than the true "gorilla".
Variation 3: Both feedees pass with the right hand

Siteswap description: feedees J1 and J3 delayed by half a beat
< 3.5p2x 3 | 3.5p1 3.5p3 | 3 3.5p2x >

Ten clubs shower singles feed

The ten clubs shower feed in doubles is very popular. Surprisingly, the single spin version is almost never seen.

The feeder will essentially do one side of 7-clubs shower in singles ... but with two partners instead of only one. This means that he will juggle on a slightly galopped rhythm, the selfs following quickly the passes, with selfs higher than usual and actually as high as the passes. For the feedees, they have to make lofty single passes to the same height as the feeder's, and certainly higher than the selfs ; moreover the feedees might be slightly galopped as well, the first self quickly following the pass.
The pattern is staggered: the feeder passes first to J1 who will wait as long as possible before passing back, then the feeder passes to J3 who in turn waits before replying.

A remark about the rhythm: in actual practice, the pattern is not as much galopped as the causal diagram suggests ; in order to even the rhythm, most jugglers will keep the clubs in their left hands for a longer time than they keep them in their right hands.

There is a collision problem here between the feeder's pass to J3 (on the left) and the incoming pass of J1: make sure that J1's passes are long and high enough.

Starting position: The feeder has 2 clubs in each hand, each feedee has 2 clubs in the right hand and 1 club in the left. Each feedee waits for the feeder's pass to be thrown to him before replying by a pass.

Variation: Switch back and forth from the the standard double spin version of the pattern to this single spin version.

Remark: In case of a drop, the pattern will rapidly settle down to a standard 9-clubs shower feed. It is possible to kick up the dropped club back into the pattern as follows: move the club on your right foot, then, on your (last - if you are a feedee) self beat, throw a lofty single pass with the left hand while simultaneously kicking up the dropped club to your right hand. Everybody will feel quite hurried for a few throws. Good luck!

Siteswap description: too tedious ;-)

Ten clubs sync shower feed

The last pattern is really advanced for the feeder. Essentially, he will do one side of 8-clubs shower in singles, passing a lofty single with the right hand while simultaneously throwing a same height single self from the left hand.

Both feedees juggle a right-handed shower pattern with passes and selfs as high as the feeder's (they should try to juggle as sloooow as possible ...).

Starting position: The feeder has 2 clubs in each hand, the feedees both have 2 clubs in the right hand and 1 club in the left hand.

Siteswap description: < (- , 3p2) (3 , -) | (3* , 3p1*) (3* , 3p3*) | (3 , -) (- , 3p2) >

Author: JiBe

introduction: remembering 6 clubs passing

With 6 clubs, the base of most passing patterns is two jugglers juggling a solo 3 club cascade synchronously. They're doing some singles and alternate right and left hand throws. Let's write that as: - RH self: S - LH self: S - RH self: S        etc... so each juggler's sequence is SSSSSS....

J1: SSSSS J2: SSSSS

So what happens when J1 decides to throw a pass to J2? For instance, J1 throws a single pass from his RH to J2's LH. Then: J1 now has one less club in his pattern. He now needs to get another club back, and J2 is the only supplier available at the moment. J2 sees a 4th club arriving in his cascade. He has to get rid of a club by passing it to J1 in order to keep going. In fact, J1's pass arrives in his LH at the same time than his RH self. Thus he needs to pass instead doing this RH left, which is at the same time than J1's pass.

J1 passes to J2 --> problems

Solution: J2 passes at the same time

J1 and J2 throw synchronously (as passes or selfs) with their RH and LH alternatively.
Selfs (noted S) are crossing singles (RH -> LH or LH -> RH)
Passes (noted P) are tramline singles (RH -> LH or LH -> RH)
The rhythms are symetric (symetric passing patterns) and synchronous: if J1 does S, then J2 does S -- if J1 does P, then J2 does P.

What happens with 8 clubs?

We're going to do exactly the same thing. The base is now 2 jugglers juggling a solo 4 club fountain in doubles. We can juggle exactly the same patterns than with 6 clubs, but some of the rules change:

Selfs (noted by S) are straight doubles (RH -> RH or LH -> LH)
Passes (noted by P) are crossing doubles (RH -> RH or LH -> LH)

There is no more single-pass or single-self !

Example 1 - basic patterns

Once the theory is known, there is not much more to say, except:

These patterns are collision prone because both jugglers are passing crossing passes at the same time. See the collision page for assistance!.
In 4-count (PSSS), you pass and receive from the same hand. Each club you receive is the one you're going to throw back. In usual 6 and 7 club patterns, this happens in a 3-count.

Here are a few patterns you can try:

4-count (PSSS)

3-count or PSS (and the 6-count) are detailed here.

1-count or ultimate (P). Also worth trying in singles.

PPS (to be mastered before example 2)

and the chocolate bar (PPSS) !

Example 2 - Mild Madness

I haven't tried this yet, however JoePass! can do it perfectly :-) , and I think it might be possible to do 1 or 2 cycles if you can already do the above PPS and have understood well 6 club Mild Madness.

Here's how it goes:
J1 (top line in the diagram) throws crossing passes, J2 throws straight passes
We don't have (as in mild madness) a pass-zip, rather a double-zip (the double being a self).
In fact, it's worse than that; because when you receive a pass at the 'wrong' end, you have to throw a crossing self double followed by a zip (or at the same time as the zip).
The full cycle is in fact: PPS PPScZ, which means:
Pass, Pass, Double Self - Pass, Pass, Crossing Double Self, Zip
The causal diagram for a full cycle shows all this.

8 clubs Mild Madness

Author: JiBe
Credits: original idea by Brendan Brolly

Thanks to Tarim for clarifying some things for us on this matter in Rotterdam.  Also, feel free to take a look at the articles posted on this subject at rec.juggling in 1994 (there's one in particular by Tarim that is interesting because it expands the theory to include other rhythms and feeds, which I will do here one day).

This theory, whose application lies essentially in 6- and 7-club ultimate, says the following:

To pass 6 (or 7) clubs in ultimate is somewhat like juggling 4 (or 5, respectively) alone, horizontally, from the point of view of one of the two jugglers.

Thus one could try to derive traditional siteswap figures using the following rules.  The numbers can be written in BN (Brendan notation), since the pattern doesn't follow the classic rules of siteswap. With 4- and 5-ball solo patterns as a starting point, one may be inspired to find corresponding passing patterns.

So that's from the passer's point of view. 

For the one who's catching the passes, just one tip:  throw only when you have to.  To clarify, wait until a pass arrives (in the case of doubles and triples) to empty your hand (by throwing).  

Classic examples in 6 ultimate

The corresponding passes are in red.  Note that the top juggler, who receives the passes, waits each time until the last possible moment to throw, the pauses shown by blue arrows.  

 

BN : 53 siteswap : <3p 3p 2 3p 3p ...| 3p 4p 3 3p 3p ...> Written out : double-self

BN : 534 (continuous) siteswap : <3p 2 3p| 4p 3 3p> Written out : double, self, pass, double, self, pass,... Note : this becomes almost  PPS

BN : 552 siteswap : <3p 3p 2 3p 3p ...| 3p 4p 4p 2 3p...> Written out : double, double, pause

BN : 5551 siteswap : <3p 3p 2 3p 3p 3p...| 3p 4p 4p 4p 1 3p...> Written out : double, double, double, hand-across

BN : 55550 siteswap : <3p 3p 2 3p 3p 3p...| 3p 4p 4p 4p 4p 0 ...> written out : double, double, double, double, empty hand

BN : 633 siteswap : <3p 3p 2 2 3p ...| 3p 5p 3 3 3p...> Written out : triple, self, self

Try also 6451, 64514 (continuous) and all siteswaps that come to mind.

---

Classic examples in 7 ultimate

BN : 64 Written out : double pass, double self

BN : 663 Written out : double pass, double pass, self

BN : 744 Written out : triple pass, self, self

Try also 6662, 66661, 97531 (???), 66771661 (or the continuous version: 66{771}661, you'll see) and all siteswaps that come to mind.

Author: JiBe
Credits: causal diagrams were invented by Martin Frost

Introduction

Siteswaps for passing

A passing siteswap consists of two sets of numbers (N for one side, M for the other) between brackets: '<...>' and separated by ' | '.

Each of the sequences describes the throws of one juggler.  By default, these are integers, as in a solo siteswap (but you will see that this is not always true).  A throw that is a pass will be indicated by a p after the number (ex.:  3p for a normal single self). When you get to the end of the sequence, go back to the beginning as in solo siteswaps (instead of writing "a b c a b c a b c a b c ..." we settle for "a b c").
  If the sequence is especially long, it may be separated into 2 (or more) parts in the following format:
<N1 N2 | M1 M2>
<N3 N4 | M3 M4>

When the two jugglers do exactly the same thing (at the same time or staggered), the rhythm is called symmetrical (Christophe's "symmetrical passing patterns").  Thus sometimes we only need to write one sequence.
  Ex.: 5p 3 3 3 instead of <5p 3 3 3 | 3 3 5p 3>

For those who know nothing about solo siteswaps, take a look at the recommended sites posted on the links page.

Causal diagrams

A two-person causal diagram is made up of two lines.  Each line represents one of the jugglers.  On these lines are written the letters R and L, which represent the two hands of each juggler:

• R = Right hand
• L = Left hand

Next, we add arrows between the letters (hands), which represent a throw, whether a self (staying on the same line) or a pass (crossing lines).

Time progresses from left to right, from which it follows that the arrows point toward the right:  first one throws and then one catches.  That explains the alternation of L's and R's on each line; in a normal juggling pattern, one's hands throw one after the other.

For each circle (letter), there will be an arrow coming in and another arrow going out, i.e. one incoming pass and one outgoing pass (cf. the examples below; the first explanatory diagram don't show this because it is not a complete diagram).  This illustrates the fact that one must throw a club in order to be able to receive another.  The incoming club is the cause of the next throw.

Different types of arrows and what the numbers mean

The explanations given here follow (for now) the normal rules of siteswap, which state:

• an odd throw (1, 3, 5..., i.e. handacross, singles, triples) go from Right Hand to Left Hand (or RH to LH). This is shown by R->L or L->R (pass or self) arrows.
• an even throw (2, 4, 6..., i.e. doubles, quadruples, etc.) go from Right Hand to Right Hand (or LH to LH).  This is shown by R->R or L->L arrows.

Beware however, contrary to the ladder diagrams, the arrows do not lead to the time when the same club will be thrown again.  The arrow points at the moment when the club is caught (if it had been thrown there), combined with the moment when another club is thrown to take its place.

Passes

<3p .....| .....>	A single pass (single spin) that goes straight across (R to L)
<4p .....| .....>	Double pass
<5p .....| .....>	Triple pass (it's easy to imagine what quadruple passes would look like...)

Classic selfs (3, 4, 5...)

<3 .....| .....>	Normal single self.
<4 .....| .....>	A double (which then comes back to the hand that threw it).
<5 .....| .....>	A triple self (changing hands)

Bizarre selfs (0, 1, 2)

<3p 2 .....| 4p .....>	Keep one club in hand (the arrow won't always be drawn). When no club arrives for a given hand, one may hold the club for another beat.  That's a chance to do a flourish, thumb twirl...
<3p 1 .....| 3p .....>	A handacross.  The arrow goes backward (back in time)!!!  That's because this handacross is the cause of the previous throw: you have to free the right hand for catching it.
<3p 3p 3 0 | ..... >	An empty hand (no need to throw).  Again, the arrow goes back in time: in order for the hand to be empty, one must have made an earlier throw with the same hand.  That's the cause that makes it possible to catch the incoming club.

Some examples

4-count or every other

<3p 3 3 3 | 3p 3 3 3>

This is the most common pattern (every other).  The jugglers pass at the same time and always with the right hand.  There are 3 selfs between each pass.

3-count with a 441

<3p 3 3 3p 4 4p 1| 3p 3 3 3p 3 3>

Waltz:  jugglers pass at the same time and alternate between right and left hands.

Here one of the jugglers, upon receiving a pass does:  - self double (4) - crossing double pass (4p) - handacross (1, the arrow pointing left)

2-count with doubles and triples

<3p 3 3p 2 3p 3 3p 3| 3p 3 4 4 5 3 0 3>

 

Here, the bottom juggler does the traditional right-left-triple in 2-count.

The first double, thrown at the same time as a regular pass, arrives late (a double takes longer to get there than a single).  The top juggler therefore has a pause (a 2) with his left hand (which otherwise would have received a regular pass).

When someone throws a triple, there is no pass coming to the right hand, which will then be empty two counts later (at which point the arrow goes backward: a 0).

Standard 7 clubs in 2-count

<4p 3 | 3 4p>

Here you will begin to grumble, and with good reason: why are 4's (doubles, all the passes) not made as crossing passes (R to R or L to L, as before)?

It's because the two jugglers are no longer doing exactly the same thing at the same time.  The R's of the top juggler correspond to the bottom juggler's L's.  There is a staggered start, which is not indicated by siteswap notation (on Joepass! you would enter it as "#jugglerStartLeft 2").

Crossing 7 clubs in 2-count

<4p 3 | 3 4p>

This is crossing 7 clubs in 2-count which follows the rules stated above.  The jugglers throw with the same hand at the same time, but one of them must make left-handed passes.

Staggered starts

You have seen in the previous examples that the two jugglers don't always throw with the same hand at the same time.  According to the time delay between both their right (or left) hands, I categorize rhythms into three families (not counting hurries or 'galloped patterns').

Siteswap does not take staggered starts into account.  Therefore, sometimes there are several ways to juggle certain sequences (cf. <4p 3 | 3 4p> in the examples above).
Be also aware that the new rules stated under are valid only for passes. Selfs throws will always follow the usual rules.

Family 1 : Delay=0

This includes 4-count, 3-count, 2-count, 1-count with 6 clubs, 4-count or crossing 2-count with 7 clubs...

 
In this family, the standard siteswap rules apply:
- even passes (4, 6... i.e. doubles, quadruples...) cross:  R->R or L->L
- odd passes (3, 5... i.e. singles, triples) go straight across:  R->L or L->R.

Family 2 : Delay=1 count

For example, 2-count or compressed mesopotamia with 7 clubs.

 
Note that the 1-count delay means that when A throws with the RH, B throws with the LH.  In this family, the standard siteswap rules are reversed:
- even passes (4, 6... i.e. doubles, quadruples...) go straight across: R->L or L->R
- odd passes (3, 5... i.e. singles, triples...) cross: R->R or L->L

Family 3 : Delay=0.5 count

These are essentially 7-club patterns-- 3-count, ultimate--but also some with 6 clubs--whynot?--as well as 8 and more.

 
In this family, the rules change completely; since the delay is no longer a whole number, neither are the passes.  The passes are now written as 3.5p, 4.5p, 5.5p...
In practice, you may choose to do either doubles or singles for 3.5p (which is between 3 and 4 - I know, you could've figured that out on your own).

A second new element is that in this case, one juggler makes all crossing passes, while the other makes all straight passes (without changing the numbers).  Thus we have: If N (=3.5p for example) is a crossing pass for J1, it is straight for J2.  And N+1 (4.5p in this case) is therefore a straight pass for J1.

A special siteswap notation may be applied to these patterns: 4-handed siteswaps.

I know that some people won't agree with this classification system.  However, if the diagrams are new for you, this may be less confusing.
FYI, some points to consider:

Properties

Siteswap : properties

The total number of clubs equals:
(average of the numbers in the two sequences)*(number of jugglers).

For example, for <3p 4 4 1 | 3p 3 3 3 > :
average = (3+4+4+1+3+3+3+3)/8 = 3 (24/8)
and the number of clubs = 6 (3*2, i.e. 3 clubs per juggler).

One could also calculate the number of clubs juggled by each juggler (with his corresponding sequence) as in normal siteswaps.  When doing this, one often ends up with numbers like 3.5 clubs per juggler (for regular 7 clubs).

Causal diagrams : properties

In order to calculate the number of clubs in a causal diagram, we must first find (and define this notion) the number of causal lines present in the diagram.  In the example below, the three causal lines are clearly shown (one blue, one green, one red).  This should be enough to understand the concept of causal lines.  One may also make a vertical line and count the number of arrows that it crosses, but in this case arrows that go from right to left (hand-across and empty hand) should be counted as negative.

So we have:  number of clubs = ( number of lines ) + ( total number of hands).
In the case of 2-person passing patterns, there are 4 hands.

Here: number of clubs = 3 + 4 = 7 (it's a popcorn with 7 clubs).

In short, the lines represent the number of objects in the air at a given time, as opposed to those which jugglers hold in their hands (which is how we get the formula).

Moving on

Hurries

A hurry is often defined as throwing twice in a row with the same hand.  This often happens because someone catches the club in the "wrong" hand.

Here I've shown the hurries in green, breaking the alternation of RLRLRL... by sometimes having 2 R or 2 L in a row.

Multiplexes

Here I've tried to represent a duplex in a 2-count pattern (6 clubs).  The bottom juggler catches two clubs in his right hand and throws them back two counts later.  

The diagram's ambiguity comes from the fact that one line (the red one) is broken. We should agree on a way of dealing with this, perhaps by introducing a new arrow (like the dotted one) in the diagrams.  

Various self patterns

If desired, one may add an extra line to show self patterns which necessitate, for example (as is the case here for columns) synchronous throws.  Note that the line (red loop) thus created does not intervene in the calculation of the number of clubs in the pattern (we have simply created a problem for ourselfs by throwing a club even though nothing forced us to do so). 

Note: Most jugglers do this pattern by throwing synchronous doubles, handacross, pass (not synchronous doubles, hand-across, self, pass).  When making a clear diagram, you can see that theoretically that triples should be thrown, but by taking some liberties in throw height, it still works with doubles.

Kickups

A kickup is the action of picking up and "throwing" (in a self or a pass) a club with one's foot.  A circle with an F (for Foot) suffices for this type of diagram.  In this case, you create a new line since you add another club to the pattern.

Thus you can play with the diagrams, doing what you want with them.  Feel free to take some initiative!

More jugglers

Adding jugglers is simple, both for the diagrams and for siteswaps.  In the diagrams, all you have to do is add a line for each new juggler.

For siteswap, you add a sequence of numbers for each juggler (still using a '|' (pipe) to separate each juggler).  On the other hand, you must identify which juggler should receive which passes, so we write 3p1 to note a pass thrown to juggler number 1 (The jugglers need to be numbered first).

Classic feed

<3 3 3p2 3 | 3p3 3 3p1 3| 3p2 3 3 3>

Line with a turn

<3p2 3 5p3 2 2 3 ...| 3p3 3 3 4p1 2 3 ...| 3p1 3 3 3 3p2 3 ...>

Author: JiBe

Diagonal collisions: RH->RH and RH->RH (or LH->LH and LH->LH)

Diagonal collisions 2: RH->RH and LH->LH

		To avoid this, you have to agree that the person who throws with the right hand (R to R) will throw their pass from the outside (from as far right as possible) and the one who throws left-handed passes will throw from the inside (from the centre).  The diagrams on the left will give you an idea.  An example of a such a pattern is Brendan's Folly.
With collision	Without collision

Head-on collision: RH->LH and LH->RH

		This type of problem is rather difficult to resolve and is only relevant to certain barbaric patterns (e.g. compressed Mesopotamia).  In theory, one must create imaginary corridors, the two jugglers slightly offset from one another (see diagrams); in practice, it's still hard to do!
With collision	Without collision

Author: JiBe

Reminder:
The context is that of patterns that can be put into classic siteswap notation, in which one's hands throw one after the other.

Consequences, examples, and other aspects of the problem:

• The simplest example (in solo juggling) is the following:
  In a 3-club cascade, throw a single from the RH to the RH (in other words, go into a round of two in one hand, in singles).  In classic siteswap notation, you would throw a double (3333 423 33).  Throwing a single makes the club come down one count sooner and forces you to throw one count sooner.
• Often (but not always), it's because a club arrives one count sooner (coming as a pass or a self) that one must throw one count sooner.
• Often (but not always), this means someone will have to throw twice in a row from the same hand.  Right-Right-Left-Left-Right... This property (which applies quite often) is sometimes given as a definition; however, it is neither necessary nor sufficient.
• There exists a notation in which you simply add a star after the number which signifies a hurry throw.  Going back to the first example: when the double is changed to a single, 333 423 333 becomes: 33 3x 3* 333.
    The 2 gets skipped, and the 4 is replaced by a 3x (a 3 followed by an x to specify that it doesn't cross).  The star indicates that there is a hurry, and therefore that it's the same hand that threw the 3x.

All that was to give you an idea of the principle; to be able to go on to discover your own passing patterns.
In passing, to create a hurry (we will later see how to get out of them using various passes), one throws a crossing pass which otherwise should have been straight pass (or vice versa).

Let's take a classic 4-count, for example:

	Classic 4-count: < 3p 3 3 3 | 3p 3 3 3>
	With a hurry on the last pass: < 3px 3 3 3 | 3p 3* 3 3 >

The bottom juggler makes their last pass a crossing single (in blue, R to R).  The hurry (in red) comes from the fact that the top juggler makes a pass with their right hand at the same time.  They must free their right hand right afterward in order to receive the crossing pass.  It's easy to see that the alternation between Right and Left (RLRLRL) is broken--we have RLRL RR LRLR.

Thus we can create new patterns based upon most classic patterns; all that needs to happen is for one juggler to cross all his passes that he previously threw straight across.  The two jugglers can then continue on with the same rhythm.  In the example above, the top juggler starts a 4-count left-handed cycle after the hurry.

Continuous 4-count with a hurry: <3px 3 3 3 3px 3* 3 3 | 3p 3* 3 3 3p 3 3 3>

 
Thus we get a pattern with one juggler who crosses all their passes (in blue).  The two jugglers alternate 2 cycles of left-handed 4-count and then 2 cycles of right-handed 4-count.  The hurry (in red) switches from one juggler to the other.

3-count with a hurry (Jim's 3-count): <3px 3 3 3px 3* 3 | 3p 3* 3 3p 3 3 >

So that's how we get new patterns!  Consult the hurry section on the rhythms page to see more.
See also Martin's Madness, which uses a hand-across to alter the basic pattern.

This is only a modest introduction.  Those who would like more in-depth explanations of hurries (definition, mathematical aspect, etc.) can look at Christophe's article on the subject.  For applications, see also the following pages: self hurries, pass hurries.

Author: JiBe

What's the aim of this page?

1. I'm waiting to catch a pass inmy right hand.
2. Bad luck. My partner has decided to throw to my left hand!
3. What can I do?

Different, new patterns can be deduced from this (depending on how I react) if my partner keeps on making their passes this way (always crossing instead of the usual staight).

I've identified 3 ways to react. I wanted to make diagrams for other patterns than the 4-count, but I think you'll get it anyway.

4-count

4-count hurry 1:

React as in Jim's 3-count (this is the easiest way)

You keep on juggling a 4-count, whatever hand the club arrives in. I sometimes call it the "no-zips" version.

<(-,3p)(-,3)(3,-)(-,3) (3p,-)(-,3)(3,-)(-,3)% | (-,3px)(3,-)(-,3)(3,-) (-,3px)(-,3)(3,-)(-,3) %>

4-count hurry 2:

Pretty hard. You keep juggling a right handed 4-count. A short zip allows you to throw as if the club had arrived in the right hand.

<(-,3p)(3,0x)(-,3)(3,-) | (-,3px)(3,-)(-,3)(3,-)>

4-count hurry 3:

As in Mild Madness

There is a zip as previously, but this one is easier since you allow yourself to throw twice from the same hand (using a straight self single in the case of a 4-count).

<(-,3px)(3,-)(-,3)(3,-) (-,3px)(3x,2x)(3,-)(-,3) % | (-,3p)(3x,2x)(3,-)(-,3) (3p,-)(-,3)(3,-)(-,3)%>

Author: JiBe

• sending a pass to the wrong hand
• sending a self to the wrong end

I deal with passes here. This page deals with the selfs and we will assume that we're using a rhythm which is not a 1-count.

Let's take any passing rhythm and see what we can do with the selfs:

• SSS with the 4-count (PSSS)
• S with the  2-count (PS), or PPS ...
• SS with the 3-count (PSS),  and also chocolate bar (PPSS)
• ..

Throws of value 3:

• 3: normal self (crossing single)
• 3x: straight single (RH to RH, or LH to LH).

Examples with a 3-count:

• (3x, -) (3*,  -) (- , 3px)
• (3x, -) (3x*, -) (3p*, -)
• (3x, -) (1*, 3x) (- , 3px*)
• (3x, -) (1*, 3) (3p*, -)

Examples with a 4-count:

• (3x, -) (3*, -) (-, 3) (3px, -) : L L R L (crossing pass)
• (3x, -) (3*, -) (-, 3x) (-, 3p*) : L L R R (normal pass)
• (3x, -) (3x*, -) (3*, -) (- , 3p) : L L L D (normal pass)
• (3x, -) (3x*, -) (3x*, -) (3px*, -) : L L L L (crossing pass)
• (3, -) (- , 3x) (-, 3*) (3px, -) : L R R L (crossing pass)
• (3, -) (- , 3x) (-, 3x*) (-, 3p*) : L R R R (normal pass)

• (3x, -) (1*, 3x) (3x* , 1*) (1*, 3p*): the box
• (1, 3*) (1*, 3*) (1*, 3*) (1*, 3p*): shower

Throws of value 4:

• 4: normal straight double
• 4x: crossing double. Now you can do backcrosses in doubles.

Examples with a 4-count:

• (-, 4x) (2, -) (3*, -) (-, 3px) : Crossing double, self, crossing pass
• (-, 4x) (4x, -) (-, 4p) : Crossing double, crossing double, double pass (with backcrosses!)
• (-, 4x) (4x, -) (-, 4x) (- , 3p) : Crossing double, crossing double, crossing double, pass

Author: JiBe
Credits: based on Christophe Pr?chac ideas

7 club popcorn (a definition): a passing pattern in which one juggler lifts 4 clubs, leaving the other one juggling 3 clubs, before he throws back a club and reverse the situation. Similarly, you can define some 8 and 9 club popcorns.

Thanks to Christophe (this pages owes a lot to Christophe and to Hans Gault who discovered these patterns), I understood what were the mathematics (siteswap formulas) behind all these patterns.

You can find some other kind of popcorns (with more than one pass per cycle for instance), but I won't describe them here.

Theoretical part

s s s ... (n times) = {s}n.
Example : {4}3 = 4 4 4

Then it's very short, we simply have the following popcorn families:

You see very well from these formulas there is a 4 clubs part, a pass, and a 3 clubs part.

Remark: All these pattern are symetric, meaning that both jugglers do the same thing (but staggered). We thus only write the sequence of one juggler.

Practical part

When you replace n by some reasonable values, you get quite a few patterns. What is also amazing is to discover here some classical patterns such as the 2-count or the 1-count.

In 2n-count popcorns, the passes are tramline and always made by the same hand.
In (2n+1)-count popcorns, one juggler does crossing passes, the other does straight passes. Juggler 2 starts half a beat after juggler 1, and passes are made from both hands.

Note also that all sequences of 4's can be replaced by an equivalent 4 club siteswap (44 can be replaced by 53, 4444 by 5551, ...). You can do that at any time without warning your partner since it's not going to change anything on their side of the pattern. The same applies to the 3's (333 replaced by 441 or 531).

I've added some stars to indicate the very good ones.

Author: JiBe

This notation is used in certain specific cases:

• It only describes patterns for 2 jugglers (which is where we get 4 hands), referred to here as J1 and J2.
• The patterns in question must be asynchronous.  As per the explanation of causal diagrams page, these are patterns with a delay of 0.5 (with passes like 3.5p, 4.5p... in normal siteswap). This means that J1 and J2 never throw at the same time.

Since J1 and J2 don't throw at the same time, one might think of it as nothing more than a single imaginary juggler with 4 hands throwing the clubs one after another in the following order:  RH-J1 (J1's right hand), RH-J2, LH-J1, LH-J2. 

Thus we can assign numbers to each throw as we did in normal siteswap and obtain the following table showing the correspondence between the two:

Remarks :

• All normal siteswaps are valid 4-hands siteswaps. And that was actually the primary goal of this notation: finding an interpretation for passing of nomal one person siteswaps. You can take a siteswap generator, tell him not to use 1, 3 or 5's, and generate all possible asynchronous rhythms for 5 to 9 clubs.
• Divide by 2 to obtain the equivalent in normal siteswap.
• All even numbers are selfs, while odd numbers are passes.
• You will notice that I did not specify whether the passes are crossed or not.  That's OK- if J1 does 7 and 11 crossed, then J2 does 7 and 9 straight across, with 9 being straight for J1 and crossed for J2.
• I marked certain passes as being impossible.  This is true in a normal configuration, but it could, however, be possible to do them as a hand-across in back-to-back, for example (for 3 and 5).
• Note that if 10 can easily be confused with a 1 followed by a 0, 1's are almost non-existent in 4-handed siteswaps.  So 10, 11, 12, etc. are always read as ten, eleven, twelve, etc. in this type of siteswap, unless specified explicitly.  They are sometimes replaced by a,b,c...
• You can find some more advanced stuff on the subject in Norihide Tokushige's article: passing siteswap.
  

How to use it and examples

When faced with a 4-handed siteswap, first we have to know to whom the sequence applies--the 4-handed juggler, J1, J2?

Normally, there's a sequence for the virtual juggler: S1 S2 S 3 S4 S5 ...
and it is specified: where J1 does S1 S 3 S5 ... and J2 does S2 S4 ...

You can draw a table to associate each number with the hands of each juggler if you still need to convince yourself:

example 1 : 966 (3-count with 7 clubs)

The pattern is 966 in which J1 and J2 do 966 (lofty double pass, self, self).

example 2 : 96677 (asynchronous bookends)

The 4-handed siteswap is 9 6 6 7 7 9 6 6 7 7 ...
J1 does 96767, J2 does 67967 (identical to 96767).

The pattern is 96677 in which J1 and J2 do 96767 (lofty double pass, self, lofty single pass, self, lofty single pass).

example 3 : 9629669669969929 (Copenhagen countdown)

The 4-handed siteswap is 9 6 2 9 6 6 9 6 6 9 9 6 9 9 2 9
... J1 does 92696992, J2 does 69669699.

The pattern is 9629669669969929 in which J1 does 92696992 and J2 do 69669699. Don't feel obligated to try it, it's just to have an example where J1 and J2 don't do the same thing (this is because the length of the sequence is an even number).

Author: JiBe

The theory behind this is not very complicated at first glance. A slow-fast pattern (for 2 jugglers) is actually a pattern in which each juggler has to juggle at a faster pace than the other. For example: if J1 makes 3 selfs between each pass (4-count), J2 would make only 2 selfs (3-count) or 1 (2-count).

The 2 jugglers then have to agree on a few necessary modifications. Since J2 is doing a 3-count, J1 will have to throw the passes to the left then to the right alternatively whatever their rhythm (ambidextrous or not). Thus, sometimes they will have to cross their passes (and sometimes not).

There is a slow side and a fast side to this pattern. Usually people say that the slow side is the side where the juggling is slower.
For example: if J1 makes a 4-count and J2 a 2-count then J1 has the fast side and J2 the slow side.

If you would like to pursue this further, don't miss Johannes Waldmann article in issue number 61 of Kaskade: Hobo Zwiefacher
You can also have a look at a few examples (which are not all that easy):
technofeeds, Alan's Anguish and the feed 3-count/ultimate.

Author: JiBe

When doing a "feed", there is somebody (the feeder) who's passing to 2 other jugglers (the feedees), facing them at the same time. F passes to F1 and F2 in a pattern which has to be defined. F1 and F2 only pass to F. F1 and F2 usually juggle the same pattern, but staggered since we assume that F is not going to catch 2 clubs at the same time (this assumption is broken with synchronous patterns).

As a consequence, F passes twice as often as F1 or F2, since they have to throw as many passes as the F1 and F2 together. If F does an n-count, F1 and F2 do a 2n-count (no matter how many clubs there are). We're assuming here that F1 and F2 are doing the same pattern.

Example:
In the most classical feed, the feeder F is doing a 2-count alternating between the 2 feedess, who do a 4-count. While a pass is made between F and F1, F2 is doing a right hand self. The causal diagram (for 9 clubs) shows that very well, F being the middle line.	If you can't read this, check the page about "causal diagrams".

Once the feeder's rhythm is known, it is easy to find what rhythm the feedees are doing (slow-fasts not allowed here).

Now you can go back to the feed section to try out a few patterns.

Author: JiBe
Credits: Kaskade 64

We carry on with "just the three of us" (see previous articles), but this time we will get more interested on moving and swapping places than on rhythms. The basic pattern is a normal feed, with the feeder in a 2-count (but tips will be given for a 3-count or PPS feeder).
Keep also in mind that if most of the patterns can (and should) be done continuously, it is good practise to learn step by step and to make breaks (no, keep juggling, break here just means you don't move anymore) after each change of feeder/feedee.

About the drawings :
Most patterns are illustrated with drawings featuring three jugglers called A, B and C, seen from the sky. There is a nose for the direction which they should be looking at (normally the direction where the passes come from).
Plain arrows indicate passes, and you should be able to distinguish between left and right passes. Dotted arrows indicate movement.
The drawings are made only when a pass happen (every 2-counts for a 2-count).

Simple Outs & Ins

At the moment of receiving (and sending) a pass, a feedee, for instance B, can decide to leave the pattern (Out). He just has to make it clear for the others jugglers, by either saying it or moving out of the pattern. The two remaining jugglers carry on with a 4-count (2-count is also possible), the other feedee changes nothing and the feeder does now right-hand selfs instead of passes to B. Now B can come back (In) at four different places (see fig.), including his previous position. At that moment, a feed can resume. The new feeder, by making it obvious to B (either by looking at him or making an obvious pass gesture or both) will start passing to B instead of doing right hand selfs. B has to react by starting passing to him at the same moment.

If you want to go from one position to another in the shorter possible time, you are doing "Quick Outs & Ins". The sequence goes like this if you go next to the current feeder: (1) throw your last pass from your position, (2) start moving while placing the club in your left hand in the right (where there is 2 clubs now), (3) catch the incoming pass from the feeder while moving to your new position, (4) turn quickly while the two other jugglers pass, (5) pass to the new feeder while doing a last backward step, this first pass in your new position happens 4 counts after the last one.
Only steps (1) and (5) are pass beats (for the moving juggler). You can also keep juggling while doing it but it's more difficult as you have to quickly turn while juggling.
You can try "Quick Outs & Ins" to go the 3 available positions you see in the drawing, going through the passing being the more challenging one. Try also moving to another place after each pass.

If you want to do the same thing with the feeder in PPS, just bear in mind the following points (assuming that if you are B, you move toward position 1, if you are C, you move to position 2) :
If you are the left feedee (from the feeder's point of vue) and you leave with a right pass, you come back on the other side with a right pass 4 counts after (same with left).
If you are the right feedee, and you leave with a right pass, you come back with a left pass 5 counts later (but you could also agree to come back 3 counts later).
If the juggler on your right starts moving, you become the new feeder by doing (just after his pass) : pass (old feeder), self, self (do a pass instead if you agreed on 3 counts), pass (old feeder), pass (moved juggler, 5th count).
If the juggler on your right starts moving, you do : self, pass (old feeder), self, pass (moved juggler, 4th count).
If you're the old feeder, you carry on with a 3-counts with the un-moved juggler, making selfs instead of passes to the moved one.

Tornado

Here, you just have the two feedees swapping places. The feeder does not move at all, he just has to follow what's going on so that he can adjust his passes.
How B moves first is important because it will be of use in all the following patterns (this one being the easiest). B, at the moment of throwing a pass, decides to move so that he already has made a small step to the front when the corresponding pass comes to him (Fig.1). He then keeps on moving to the left and to the front so that he is ready to step in front of C (and to pass, Fig.3) just after A and C next passes (Fig.2), which should be just on his left side. As B moves now to the back, he frees place for A and C passes (Fig.5).
While B moves to the left as described, A should also move slightly to the right to ease B's task.
That's it, B and A have changed places, A is now ready to do the same thing (Fig. 5&6). If you do so continuously, it just looks like B and A are turning around each other.

Bruno's Nightmare

In this pattern, and in the following ones, the principle is the same : you should consider a giant, using three human jugglers as props, and juggling a 3 ball cascade with them. The path followed by the jugglers is a figure of 8.

If we describe one movement, we will see how B (Fig. 1) can go through the passing to come next to C, without stopping juggling and passing.
If you look closely, the first 3 steps are exactly the same than in the tornado. But after that, instead of moving back (next to A), B will now come next to C. He will keep moving to the left, but will also start turning so that he can do a last pass to C (Fig. 5), and will be ready for the next pass to A (after Fig. 6). It's now C's turn to go to the other side (Fig. 6).
The pattern has a 30-pass cycle. You should also be aware that going from right-feedee to right-feedee (B's described movement) doesn't feel exactly the same than going from left to left (C's following movement).

This version of Bruno's nightmare (with the feeder in a 2-count) is the easiest to learn and is the original one (invented by Bruno Saxer and corrected by Martin Frost). Now if you find this one too slow, you can try faster variations by shortening the number of passes made by each feeder (the following turbo is one of the very fast variations) or changing the rhythm (a 3-count variation is described later but you can try PPS or ultimate).

3-count Bruno's Nightmare

In this nightmare, the feeder does a 3-count, one feedee a right handed 6-count and the other a left handed 6-count. What makes it difficult is more the changes between rhythms than the movement itself.
As the 3-count is slower than the previous 2-count, we use here fewer passes for one change of feeder. The feeder will do only 3 passes (C in Fig.1, 2, 3) before he becomes a feedee (C in Fig. 4). What happens is when B (as a feedee) tries to change side, he will only make two passes to C before starting passing to A (new feeder).
There is nothing really new if the previous version is understood. What could be clarified is the change of rhythm. For every juggler (if done continuously), it goes like this :
3-count (3 passes)
right-handed 6-count (3 passes)
3-count (3 passes)
left-handed 3-count (3 passes)

Turbo

Turbo follows the principle of Bruno's nightmare, but with a much shorter cycle (the shorter you can find with a 2-count).
If you carefully look at B, he has already turned 180° by the time he makes his second pass which is a pass to A (and not C as previously). Having said that, the drawings should be self-explanatory.
In this pattern, there is not much time left to think about what to do, just do it.

For all these patterns, each juggler should pay attention to where the juggler he passes to is moving. Therefore, he can do his passes so that when the juggler has moved, the pass is not too far from him nor aimed at his face.

Author: Johannes Waldmann
Credits: Kaskade 61

You know the polka, you know the waltz - now it's time to learn the Zwiefacher. The Zwiefacher is a dance in which three-four time alternates with four-four. Let's just listen in to what Erlenmeyer and Keulenheier have to say on the subject…

Erlenmeyer: Wanna pass?
Keulenheier: Sure thing. Which pattern?
Erlenmeyer: Let's start with ordinary passing.
Keulenheier: You mean the waltz!
(Editor's Note: The waltz is the basic 3-count pattern - self-self-pass. See part 2 of the passing workshop series in Kaskade 57.)
Erlenmeyer: Well actually I'd rather just do right-handed passing.
Keulenheier: Shame on you! But I've got just the pattern for us: you can do your boring old 4-count and I can do the waltz.
Erlenmeyer: At the same time? But then three of your throws have to take the same amount of time as my four, otherwise the passes would arrive at the wrong time.
Keulenheier (KH): Exactly. And your passes have to alternate between straight and across because I'm passing left and right, so I expect your passes to come in left and right too.
Erlenmeyer (EM): But you always pass to my left hand, even though your rhythm is the waltz. So you also throw alternately straight and across, straight with the right and across with the left. (See fig. 1)

Grafik 1: slow fast 34.ps

EM: OK, you've had your rest now. It's my turn to do the slow side of the pattern.
KH: But I want to carry on doing my waltz!
EM: And I want to carry on catching left and passing right... Hey, it IS possible! You carry on doing your waltz, but now I'm going to switch to a 2-count: every right-hand throw is a pass, every left throw is a self. Otherwise it's the same as before - I alternate between straight passes and cross passes to you. Great, now I can relax. (Fig. 2)

Grafik 2: slow fast 23.ps

KH: OK, I've had enough of that! From now on I'm doing a 1-count. Every throw is a pass. You carry on with your 2-count if you want.
EM: But then I have to juggle twice as fast, you lazy sod! (Fig. 3)

Grafik 3: slow fast 12.pass

EM: Phew, this is getting a bit strenuous. Let's go back to 3- and 4-count. Let me try your side of the pattern for a change.
KH: Go ahead. But just to make it interesting, lets swap roles after every pass: On the first beat you do the waltz and I do the 4-count, then on the next beat you do the 4-count and I do the waltz.
EM: That sounds reasonable. So where should I throw to? Before, when I was doing the 4-count, I had to keep changing my target, throwing straight to the left hand, then across to the right…
KH: …and I always had to aim at your left shoulder while I was doing the waltz. That was alternating straight and across too, because I was constantly switching my passing hand.
EM: So now it goes like this: I do (straight pass, self, self, cross pass, self, self, self)…
KH: …and I do (straight pass, self, self, self, cross pass, self, self) (Fig. 4)

Grafik 4: slow fast fast slow 34.ps

EM: This is getting complicated. I pass with the right hand, the left hand, across and straight - everything combined with everything else.
KH: Yes, and the change of pace each time also makes it very - er - instructive, don't you agree?
EM: You're not kidding. "Instructive", eh? I suppose that's one way of putting it. What you really mean is that we aren't going to be able to keep it up for very long.
KH: Hmm. Let's cheat a bit. The main thing is to make sure that the pass after the waltz doesn't arrive too early, otherwise the one who's doing the 4-count has to hurry too much.
EM: Exactly! So why don't we throw the pass after the waltz as a double so that it stays in the air for longer.
KH: That's just what I was thinking. But then the thrower of the double-spin pass has to insert a short pause, otherwise he'll find himself waiting for a pass that doesn't come.
EM: So let's recap. I have to go: (straight pass, self, self, double cross pass, wait, self, self, self)…
KH: …and I have to go: (wait, self, self, self, cross pass, self, self, double straight pass).
EM: OK, that might even work. But how do we start?
KH: Let's think. Your last throw on the first beat is a double cross pass.
EM: That looks exactly the same as an early double in the normal 4-count.
KH: Right, so let's both start with a 4-count, and at some point you can throw an early double, to which I respond by throwing a single cross pass. (Fig. 5)

Grafik 5: 3443

KH: So this pattern not only includes both right and left passes that go either straight or across; it also includes singles and doubles. That's why my mates call it the "Leipzig Allsorts", after a special kind of vegetable stew that's supposed to be popular in our home town.
EM: I say, have you noticed that we always throw the double pass with the same club. It's always up high - from me across to you, from you straight to me, then from me across again to your other hand, then from you straight back to me.
KH: That's why you could look at this pattern as a preliminary exercise on the way to doing the waltz with seven clubs. In the 7-club waltz, three of the clubs are doing precisely that.
EM: Seven minus three ... so where are the other four, then?
KH: Two stay with me as selfs, and the two others stay with you. (Fig. 6)


Grafik 6: walz7.ps

EM: But let's get back to 6 clubs. We were doing waltz versus 2-count a while ago.
KH: You can also turn that into an Allsorts-type pattern. You go: (straight pass, self, double cross pass, wait, self, self) and I go (wait, self, self, cross pass, self, double straight pass) (Fig. 7)

Grafik 7: allerlei 2332.ps

KH: Now we're both doing the low pass always with the same club.
EM: Wait a minute, here in the causal diagram the arrows are pointing in different directions!
KH: But the arrows are not the paths of the clubs. If you draw those, you get a ladder diagram.
EM: So why don't we do that?
KH: Because there aren't so many arrows in the causal diagram, and it's easier to interpret them.
EM: I bet a One-count/Two-count Allsorts is also possible.
KH: Of course. You do (straight pass, double cross pass, wait, self) and I do (wait, self, cross pass, double straight pass)
EM: And we can start into that like we did before, with an early double pass out of a simple 2-count. (Fig. 8)

Grafik 8: allerlei 1221.ps

KH: That's pretty heavy stuff!
EM: Now that I look at it, this is a Pass-Pass-Self.
KH: Which is why it can also be used as a way of practising for the 7-club PPS. (Fig. 9)

Grafik 9: pps7.ps

EM: Oh look, here comes old Stürenburg from the National Convention Date Coordination Authority. I bet he'd like to hear about our new patterns after a hard day's work.
KH: Not only that, he'd probably like to try them out.
Stürenburg: Good day, gentlemen. Yes indeed, I could do with a bit of a waltz right now...
KH: ... and you'd probably like me to do a 4-count. All right. But it would be a shame if Mr. Erlenmeyer had to stand around doing nothing. Perhaps I could have you both doing the same pattern.
EM: Good grief, but that means that you'd be feeding, so you'd have to do a 2-count instead of a 4-count.
KH: Quite right. I pass first to Mr Erlenmeyer's right shoulder, then to Stürenburg's right, then Erlenmeyer's left, then Stürenburg's left.
Stürenburg: Whereas we always waltz-pass to your left shoulder.
KH: Could I ask you both to keep the pace fairly slow - otherwise it'll be hard for me to juggle fast enough. (Fig. 10)

Grafik 10: slow fast feed 323.ps

Stürenburg: I think you've earned a rest, Mr Keulenheier. We should swap sides now.
EM: Not sides, but numbers! If we both do 4-count and Mr Keulenheier does a 3-count…
KH: Well, it is possible. But instead of doing a proper waltz, like you were doing just now, I think I'd rather do a Pass-Pass-Self. If you would be so kind, would you please aim your 4-count passes alternately to my left and right shoulders. (Fig. 11)

Grafik 11: slow fast 4pps4.ps

EM: That was fun. But it's time for bed now. Before we next get together, perhaps you could try and think of a way to do a three-person Leipzig Allsorts.
Stürenburg (exits, mumbling to himself): I must try that out at the business lunch tomorrow with the ladies and gentlemen of the Passing-Pattern-Naming-and-Administration Authority…

Author: Jon Skjerning-Rasmussen
Credits: Kaskade 65

Introduction

If you are reading this article you probably know the feeling: time slows down, the outside world has finally lost all its importance, you are thinking about nothing in particular, yet your mind is not wandering, there is simply no necessity for you to use your imagination or your capacity for abstract thought - all that matters is that you are alive - Alive and Passing. Magically every throw is perfect - every catch requires absolutely no effort, two (or more) minds are tuning in to the same frequency. And then comes the moment that is the beginning of the end: you become conscious of what is happening, a small river of chills (and adrenaline) is running up your spine - and 'Bang' it all falls apart and you both let out a small 'yeehaa' or a 'wow'.
The three articles in this series are about some of the weird and wonderful patterns that I and other nerds have come up with during moments of great inspiration. Hopefully they will bring you as much enjoyment as they have brought me.
Before I get started with the patterns I would like to thank Wolfgang for inventing the marvellous tool: JoePass!, without which several of the patterns here wouldn't have been invented yet (by me at least). I will also advertise the usefulness of 'causal diagrams'. Knowing how to use them can be a major factor in enhancing the output of one's sessions of creative inspiration.
In these articles I take as my basic presumption that the reader has at least some knowledge of causal diagrams. For the ones who want to groove on these patterns in actual 3-dimensional space, however, I find it essential to be able to juggle the pattern that I find to be the doorway these types of patterns: the 7-club 3-count. So I start with explaining that pattern. But enough talk. Let's get to the patterns.

Patterns

I have divided the funky 7-club patterns into different categories (not something I have given a lot of thought to so it mightn't be the most efficient way):
7-club 3-count (if you can call one pattern a category - maybe 7-club 1-count should also go in this category, see kaskade 57).
Pass-Pass-Selfs (pps)
Bookends (ppsps - or pspsp if you like)
Countdowns
Popcorns
Other Patterns (whatever doesn't fit into the other categories, so far I have at least one pattern here)
This first article deals with the three first categories, but fear not, the other categories will be carefully dealt with in the following issues. And, by the way, sometimes I have added a few 3 people feed patterns derived from the 7-club pattern, but hey…

To start a pattern, simply follow the causal diagram, beginning at its left side. Every juggler holds one club in every hand, plus one club for every arrow that reaches the hand from the left side of the pattern. In the first pattern, J2 will start with 4 clubs, and J1 has 3 clubs.

1. 7-club 3-count

This is, as I said, the basic ambidextrous 7-club pattern. I always warm up with this one before moving on to other patterns.
If you have done no ambidextrous juggling before, learn the 6-club 3-count (pss), and do that until you have the throwing rhythm totally automatic. Practice throwing 'late doubles' in this patterns (i.e., a crossing double pass on the pass beat). This trick is likely to make your partner fuck up the pattern as she gets a 'hold', and thus won't be passing back the same club as she receives (which is what you normally do in a 6-club 3-count). To avoid this, count out loud: "right, two, three, left, two, three, right, …". When you both can throw continuous 'late doubles' you are definitely ready to do try the 7-club version.
In this pattern you are both throwing double passes. However one of you, 'juggler 1' (J1), will be crossing your passes while the other, 'juggler 2' (J2), goes straight. The passes will also need to be slightly floatier than normal doubles (for mathematical and practical reason). J2 (the one that passes straight) starts with 4 clubs doing: floaty straight double pass, self, self, … J1 waits 1 1/2 beats (or 'as long as possible') before starting, doing: floaty crossing pass, self, self, … (or he can wait only half a beat and starts with a left self).
Pat. 1:

The four handed siteswap for this one is 966 (if you don't understand why and can't wait another page, see footnote 2).
If you have problems with the rhythm you can 'colour code' the pattern. To do that, take 3 clubs of a different colour, and hold them so that they will be the passes. J1 has one coloured club and holds it as the first one in the right hand. J2 (the one who starts) holds one coloured club in the right had as the first one and one coloured club as the second one in the left hand. This way you will always be passing the coloured clubs, while the 'normal' clubs always are selfs.
All the tricks that can be thrown in a 6-club 3-count can also be thrown in the 7-club version, only they have to have one more spin - doubles become triples, triples become quads, etc. J1 will have to make her triples straight and his quads crossing, while J2 will do the opposite. Keep in mind that all the passes have to be done floaty here.
If you just want some great patterns to groove on, move straight on and leave the tricks till you are juggling with someone not as nerdy (or zen) as you.

2. Pass-Pass-Selfs

A great passing rhythm whose basic pattern is pretty well known among ambidextrous passers. However, also another variation exists. The result is at least as spine tingling.

The basic pps

J1 does crossing doubles and J2 does a straight single followed by a crossing double. J2 starts with 4 clubs, and both jugglers start simultaneously:
Pat. 2:

This pattern can also be done with reversing the passes so that the double passes are straight, and the single is crossing - a nice variation that feels quite different. To do this one juggler starts with the left hand. (Just imagine that all the 'R's are 'L's and vice versa in J2's line in the causal diagram).

'Singles versus doubles'

Here is a pps where J1 does everything on singles. J2 does all doubles (also the selfs, which makes this side it a bit harder and groovier to juggle). J1 has 4 clubs.
Pat. 3:

Also here can it be interesting to reverse the passes so the singles are crossing and the doubles are straight (the self double stays straight!).

Feeds

As pps has twice as many passes as 3-count (pss) it is the perfect pattern for feeding two 3-counts. There are probably heaps of ways to do this. Here are two, one with 11 clubs and a funkier one with only 10.

11-club 3-count feed

This one is fairly simple, as all the passes are floaty doubles. The 'feeder' (FF) has 5 clubs and throws inside, inside, self, outside, outside, self. 'feedee 1' (F1) stands on the right side of 'feedee 2' (F2) and starts 1 1/2 beats after FF (when FF's first right pass is arriving), doing the crossing side of a 7-club 3-count starting with the right hand. F2 does the same, but waits 2 1/2 beats after FF and starts from the left hand.
Pat 4:

10-club funky 3-count feed

In this pattern everybody starts at the same time from the right. F1 stands to the right of F2. FF has 4 clubs and does: crossing double to F1, straight single to F2, self, cross doub (F2), straight single (F1), self. All the feedees' passes are straight and both start with a self before doing their 3-count sequences. F1 does: left single pass, self, self, right trip pass, self, self. F2 does: left trip pass, self, self, right single pass, self, self.
Pat. 5:

But let's now go back to 2 people and 7 clubs…

3. Bookends

Now we get into 7-club versions of the 'old' 6-club pattern 'bookends', a 5-count with 3 passes and 2 selfs. The selfs always have min. one pass in between (got that?) . (see footnote 1).

Basic Bookends

The basic pattern in this section is another great fusion of technology, creative inspiration and skill (thanx for your patience, Mandy), but it isn't actually that hard, you just add another pass and another self to the basic pps. J2 starts with 4 clubs.
Pat. 6:

Don't forget to try both ends and to reverse the passes like in the other patterns.

Asynchronous Bookends

Here is a version where both jugglers do (almost) the same. J1 does floaty crossing singles and straight floaty doubles and J2 does the opposite - is that clear?!?. J2 has 4 clubs, and J1 starts immediately (half a beat) after.
Pat. 7:

As this pattern is asynchronous (none of the four hands throw at the same time) it can be written down as a fourhanded siteswap: 96677 (see footnote 2). Each juggler throws 96767.

Funky Bookends

For an even weirder bookends (as if it needs to get any weirder!) try 86777, where each juggler juggles 87767 in turn. J1 has 4 clubs, and J2 starts half a beat later.
Pat. 8:

Sdnekoob

For a 'reverse' bookends (sspsp) try this one - it even has a triple in it - oooohhh. J1 starts with 4 clubs (at the same time as J2).
Pat. 9:

This one cannot be written in a fourhanded site swap as it is a synchronous pattern, which also means that the passes don't need to be floaty, and that you can try making the crossing passes straight and vice versa.
"And I'm spent…"

Footnotes:

1. There are (at least) two different ways to think about bookends patterns. One is to just do ppsps, the other is to pspsp (i.e., three right hand shower passes in a row followed immediately - no self in between! - by three left hand passes). Try to do the same pattern with both "feelings" - it doesn't feel like the same pattern even though your body is doing exactly the same (trippy, huh). I also discovered that this pattern is exactly the same as one that Wolfgang describes in Kaskade 57 as
<4p 3 4p 3 3p|3 4p 3 4p 4p>, but never mind…
2. Brief explanation of fourhanded siteswap
- 6s are normal selfs (the same as 3 in "normal" siteswap)
- 7s are floaty single passes (or 3.5s)
- 8s normal self doubles (to the same hand - like normal 4s)
- 9s are floaty double passes (4.5s)
- 10s are crossing self triples (5) (please note that 10 can easily be confused with a 1 followed by a 0, however 1s almost never appear in fourhanded siteswap, so a 10, 11, 12, etc are always to be read as ten, eleven, twelve, etc. in this type of siteswap here, unless otherwise specified)
- 11s are floaty triple passes (5.5)
So all even numbers are selfs while odds are passes - a 5 would be a very fast pass, a 4 is a hold, a 2 is a zip and a 0 is an empty hand. I don't think I believe in 1s and 3s, definitely not with clubs.
Important about the passes (but not about the selfs): if "juggler 1" does 7s, and 11s straight and 9s crossing, then "juggler 2" will have to do her 7s and 11s crossing and the 9s straight.

Author: Jon Skjerning-Rasmussen
Credits: Kaskade 66

Introduction

This is the second article in a series of (at least three) articles on wild 7-club passing. All the patterns are ambidextrous so if you are not used to passing 7 clubs using both hands I advise you to learn some of the patterns described in the last issue of Kaskade (65), where I went into '7-club three count', different versions of 'pass, pass, selfs', a few 'bookends' (or ppsps) and a couple of 3-person feeds based on some of the patterns.
This time the focus is on one of the branches of wild 7-club patterns we didn't get a chance to look into last time namely 'Countdowns'. And there is also a 'bonus pattern' that doesn't seem to be closely related to the other patterns, but that just makes it even more interesting.

Countdowns

This is a branch of passing that has existed for a while in 6-club passing, but hasn't (as far as I'm concerned) been introduced into the vast world of 7-club passing. But fear not! Here it comes. There is at least one Really Nice Pattern in this category - invented by Trevor Lewis and me here in my back yard in Copenhagen - hence the name.

The Copenhagen Countdown.

This pattern is a countdown from 3 - (that is, one round of three-count, then a two-count, a one-count, a two-count and then all over again). As you can see, the name 'countdown' is actually not really appropriate as there is as much counting up as there is down, but what the heck. The countdown from 3 is the shortest of the patterns worth denoting with the dubious term (a countdown from 2 would be a pps). It actually only has 8 throws before it repeats itself, which makes it one-sided (as 8 is an even number). The entire throwing sequence is then psspspps. Some people (myself included) find it easier to remember the entire sequence rather than counting down (and up). I normally think of it as one round of a three-count (that is 'pssp') followed immediately by the reverse (that is 'spps').
To do this pattern warm up by doing it with 6 clubs. When that feels comfortable pick up that extra club and proceed to the Copenhagen Countdown.
In this pattern 'Juggler 1' (let this be the best of you if you are not at the same level - the reason for this will become clear in a moment) starts with two clubs in each hand throwing the countdown sequence like in the 6-club version but making his passes crossing floaty doubles. If 'Juggler 1' (J1) starts from the left hand it will be easier for 'Juggler 2' (J2), (so J1 actually does the left-handed version of the countdown, while 'J2 does it right-handed. You could practice the left-handed version with 6 clubs first if you are sure this won't mess up your partner's head even more as he will then have to learn it left-handed. The terms 'left-handed' and 'right-handed' are not totally appropriate in this context as the pattern has two right passes and two left passes, no matter what hand you start from. However, the pattern is still one-sided since it repeats every eight beats, and it actually feels a bit different doing the 'left-handed' version.).
J2 has two clubs in his right and one in his left and does exactly what he was doing in 6-club version (starting right-handed), only his passes are (straight) floaty doubles (this will be fairly easy if you have the 6-club version solid). J2 starts one and a half beats after J1, so the timing of the start is exactly like in a 7-club three-count, (for more info on the 7-club three-count see Kaskade 65).
But wait! There is more! Because to get this to work J1, gets two 'zips' (aka 'handacrosses' or '1s' in normal siteswap) instead of two selfs. The zips are in the diagram represented by the back pointing arrows. So her entire throwing sequence is pzspsppz (Note: The first zip in the first round should be thrown as a normal self, meaning that the first actual zip is throw number 8). This might all sound very complicated but it is a lot easier than it sounds, as the zips come natural (if you are used to doing zips, that is). It might also be helpful to know that the two zips are both from right to left so J1's right hand will be doing no normal selfs (except for its very first throw) so the her right hand will be starting with a self and then doing pass, pass, zip, zip, pass, pass, zip, etc.
Pat 10:

In case anyone is interested, the (fourhanded) site swap for the Copenhagen Countdown would is 9629669669969929. J1 does 92696992 and J2 starts one and a half beats later and does 96696996 (Note: For - for a brief explanation of fourhanded siteswap see Footnote 2 in the article in Cascade 65).
OK, enough explanations. Enjoy and remember that this pattern is not so difficult - so if you are an ambidextrous 7-club passer and this seems impossible you are probably doing something wrong. If, however, this beauty seems easy - try the way more challenging versions of the 'Oslo Countdown', or get another mad passer and try one of the versions of the JaSoN's Countdown which is a pattern where the feedees do the easy end of the Copenhagen Countdown. If, on the other hand, you don't feel quite up for that but still want to do some more 'funky 7-club passing', then go directly to the 'Bonus Pattern' at the end of the article.

Oslo Countdown

This one is a real bastard as the sequence is 15 beats long (from each side, that is), and furthermore because of collision danger. If you are planning on just a little bit of success with this pattern do yourself the favour to learn the 6-club version. Just do one round of four-count, one of three-count, one of two-count, a one-count, a two count, a three-count, and then all over starting with the other hand. The throwing sequence is pssspsspsppspss.
The original version of the Oslo Countdown is a synchronous pattern where both jugglers do straight (!) passes - either on triples or doubles (mathematically it is supposed to be triples, but doubles may - or may not - be easier to control). It was courageously invented and attempted last summer with Magnus in the centre of Oslo). Especially around the one-count the pattern gets a bit weird for J1 as the sequence goes (starting from throw number 8) … pass, hold, pass, pass, zip, pass, empty hand, zip, pass, hold … Anyway - here it is. Good luck. J1 starts with 4 clubs.
Pat 11:

If you can't get it work, don't worry - I have only managed to do three quarters of it so far, but since that is counting down, up and down again it means that it by no means is impossible. When we tried it in doubles we found that making the four-count very fast (try to do a 7-club four-count in doubles in stead of triples to warm up). The one-count, on the other hand, should be nice and slooooow.
Once you have tried your luck with this one you can try a version that is (possibly) a bit easier. (I say 'possibly' because I have actually never done this one as the only decent passing partner here in Copenhagen is JoePass!) there is an asynchronous version that might be a bit easier, as all the passes are floaty doubles (definitely doubles!), and as it contains no holds or empty hands. However there is a self double, but hey - if you have gotten this far that shouldn't be a problem. J1 starts with 4 clubs, and J2 starts one and a half beats later.
Pat 12:


The monster siteswap for that one would be
966966869669669669969929962966
where each juggler juggles the following:
1: 9668 966 96 9 92 926
2: 9666 966 96 9 96 966
(The underlined sequence is a mirror image of the Copenhagen Countdown!).
OK enough of these weirdies - there are still loads of possibilities of coming up with other countdowns. I know that Tarim has come up with a few - but in his versions J2 doesn't juggle anything like a countdown - therefore I have left them out. Let's just finish off the countdown section with a pattern for three people. Presenting: 'JaSoN's Countdown Feed' (little fanfare in the readers mind).

JaSoN's Countdown Feed

This pattern I invented in Rotterdam last year with Simon and Nick, but unfortunately they live in Germany and England, so I haven't had the chance to get it really solid. The pattern has both an 11-club version and a 12-club version (I don't remember which one we did in Rotterdam - but we had it working for a while so it was there were probably only 11 pieces of plastic in the air).
Anyway, warm up by juggling it with 9 clubs. 'Feedee 1' (F1) does pssp-spps while 'Feedee 2' (F2) starts four beats later thus doing spps-pssp (don't get confused by the hyphen - it, doesn't mean anything, is for the people that choose to think of the countdown from 3 as a pssp followed by the reverse: spps). The feeder (FF) does ultimate starting with two inside passes then going into the sequence which is four outside passes, four inside passes etc. This is a nice pattern and can be extended to the n-feed, the w-feed etc. In these cases only the two jugglers on the end do the countdown - all the others are feeding. Well, back to The Real Stuff.
To do the 11-club version have have the two feedees do the easy end of the Copenhagen Countdown (that is straight double passes and no zips). F1 starts with 4 clubs and does pssp-spps. F2 has 3 clubs and starts at the same time as F1 doing spps-pssp. Both start with the right hand. FF starts at the same time as the feedees but from the left hand and he does ultimate. He does one inside pass before going into the real sequence which is four outside passes (starting from the right) followed by four inside passes (also starting right, of course). All the passes are normal (not floaty) straight doubles as this pattern is synchronous.
Pat 13:


FF is the centre line and F1 is the top line, and F2 is the bottom line. If you don't understand the difference between inside and outside passes imagine that you are walking along the middle line of the causal diagram passing in the direction of the arrow (with the appropriate hand) each time you walk over one of the letters.

12-Club JaSoN's Countdown feed

In the 12-club version all the passes are floaty doubles and F2 (this time equipped with 4 clubs) starts with a left hand pass half a beat before the feeder and a whole beat before F1. FF and F1 both start with the right hand. F2 starts one throw earlier in the throwing sequence thus doing pspps before going into the Copenhagen Countdown sequence. To get this to work FF will be crossing and the feedees doing straight passes (as in the diagram), but it can also be done with FF going straight, and the feedees doing crossing passes. Have fun!
Pat 14:

A Bonus Pattern

This last pattern has got its own chapter, not because it is better than the others, but simply because it doesn't seem to be related to any of the other patterns described here. It is a pppss and it is not too hard to juggle, but lots of fun. J1 starts with 4 clubs and throws three crossing double passes (not floaty) followed by two normal selfs. J2 starts at the same time as the other and throws a self before starting the pppss sequence which goes: straight single pass, straight single pass, straight triple pass, self, self. As this pattern has odd length cycle it takes 10 beats before it repeats. This pattern is a real jewel. Groove on this.
Pat 15:

OK, enough of this - next time it is popcorn time - 'groovy baby'.

Author: Jon Skjerning-Rasmussen
Credits: Kaskade 68

Introduction

And so it came to pass: new patterns were discovered and questions were asked, and in due time this article, the fourth of its kind, took form. Aiming to lure its readers into the vast regions of club passing anno 2002 this article explains, clarifies and elaborates on patterns, notations and diagrams, in a way that opens up these areas to beginners as well as more advanced passers. In other words: if you want to learn how to read causal diagrams and develop your own variations, read this. If you already know this and just want some of the new wild 7-club patterns go straight to the second part. In the article I try to stay as simple as possible. Therefore I have moved much additional stuff and www links into the notes at the end of the article.

Part 1: Causal Diagrams explained

After writing three articles on 7-club passing I was told that a lot of people had read them but didn't understand the diagrams, so here I explain what you need to know to read and use these diagrams. Let's start by looking at what I consider the basic 6-club passing pattern: the 3-count (right pass, self, self, left pass, self, self…) (see footnote 1).
Diagram 1:

To read the diagram it is enough to know that the first line represents one juggler (J1) and the second line the other juggler (J2), R means 'right', L means 'left', time goes from left to right and the distance from the first throw (the first R) to the second throw (the first L) is one beat. The numbers are not normally included but represent the normal two-handed siteswap values of the throws, and will probably prove helpful to those who understand them - if you don't understand siteswap, don't worry (see footnote 2), the diagrams explain the patterns perfectly and much more visually. The diagram reads in the direction of time (from left to right), and the arrows that stay in the same line (e.g., with J1) represent self throws while the arrows that go from one line to the other are passes (e.g., from J1 to J2).
To find out what you have to do you can imagine that you are walking along your line and doing what it says on each grey tile. In this pattern both jugglers start at the same time with a right hand single pass to the other's left hand (a straight pass), then one beat later, they throw a single left hand self (a 3) and then a right hand self, then a left hand single straight pass, a right self and a left self, and then back to the beginning of the diagram. Normally only one round of the pattern is shown, but some places I have put in two or more to get a better feel of the continuity and the tricks.
When you get to the end of the diagram you simply go back to the beginning, and if you have the diagram on paper you can actually cut it out and make a loop of the strip.

The throws

"Causal Diagrams are very easy for a club juggler to read because an arrow that travels one beat along the chart happens, by a lucky chance, to be a Single. Similarly a two beat arrow is a Double, three beats for a Triple and so on" (The Compendium of Club Juggling p. 20).

In relation to siteswap you can say that the length of the arrow = x-2 where x is the normal two-handed siteswap value of the throw. So a 5 is (usually) a triple as 5-2 = arrow length 3.
Here is the 4-club solo pattern 534, (or cross triple, cross single, self double).
Diagram 2:


Especially in 7-club passing a lot of patterns are asynchronous (i.e., no hands throw at the same time), When that is the case the passes (but not the selfs) are half a beat longer and are normally thrown as floaty singles, doubles, triples, etc. In the diagram this is represented by two shifted lines of L's and R's, as in diagrams 3 and 9-12.
Here are two rounds of 7-club 3-count with floaty double passes.
Diagram 3:


If you study the diagram you will notice that you can connect the arrows to form three long lines (causal lines), going from the start to the end of the pattern - that means that this is a 6-club pattern. Why? Because the number of object = the number of causal lines (in this case 3) + the number of hands in use (in this case 4, as I here am only dealing with patterns where each juggler uses both hands to juggle, but it works for any number of hands). A 6-club, 2-person pattern has 2 causal lines (as for example in diagram 3), an 8-club pattern has 4, and so on. This has to do with that the arrows don't represent objects, but causes (in the sense that each club is thrown because another club is arriving - see footnote 3), hence the name 'causal diagram'. Charley Dancey explains:
"Each line in the Causal Diagram leads from one throw to the throw that is caused by it" (The Compendium of Club Juggling p. 18).
So to find out how many objects there are in a given causal diagram, simply draw a vertical line and see how many arrows it crosses and then add the number of hands.

Back pointing arrows

Now we come to a thing that is a bit tricky about causal diagrams: backwards pointing arrows. That an arrow is pointing backwards in time doesn't, however, mean that the objects are travelling backwards in time (sorry!), but it is because the arrows don't represent objects but causes (if this sounds weird to you, don't worry, as I said, you don't need to know it, just accept it - see footnote 4).
An arrow pointing back one beat is a 1 (or a zip or handacross), and an arrow pointing back two beats is a 0 or an empty hand. An arrow pointing back to the same spot is a 2 (normally a hold). Let Charlie explain again:

The 2's are shown as causal arrows that cause themselfs. This is not quite as crazy as it sounds, the plain English translation of this mathematical oddity is that you are holding an object because you are holding it.
The 1 … produces a causal arrow moving one beat to the left. It seems to be illogical but it actually means: to place a club into that hand you had to empty it first!
The 0, or empty hand, produces a highly unlikely looking arrow that moves two beats to the left. The meaning of this is: for the hand to be empty you must have made a throw from it [two beats] beforehand" (The Compendium of Club Juggling p. 21).

Here is one round of two-club shower (31), two out of three clubs in a 3-club cascade (330), and then a hold (2). Notice that the zip and the empty hand are in the hand where the arrow starts. Note also that in counting causal lines backwards pointing arrows count negative, so actually there are 0 causal lines going from the beginning to the end of the pattern, hence there are the same amount of objects as there are hands (here two).
Diagram 4:


Here are the diagrams for J1 passing one club back and forth between her two hands, while J2 has no clubs. As the arrows are pointing backwards here it means that there are -3 causal lines (see footnote 5), with four hands that makes one club.
Diagram 5:


An early double by J1 and an early triple by J2 in a 4-count looks like this:
Diagram 6:

How can I see who starts with how many clubs and in which hands?

The answer to this is fairly simple. Each hand starts with 1+a clubs - a represents the number of arrow pointing to the hand from beyond the start of the diagram. In diagram 7 you see that there is one arrow pointing to J1's first L, one to his first R and one to J2's first R. This means that J1 has two clubs in each hand while J2 has two in the right and one in the left. If she wants to start with a pass, she just waits one beat and has two clubs in the left hand. This rule is easily applicable to most diagrams, but as faith will have it, the one of the next patterns (diagram 9) is an exception where J1 has three in the right and one in the left. This is because the left hand needs to be empty to receive the first zip from the right hand. (A way to avoid this is to do a hold instead of the first zip, but only in the first round).

Designer dru… eer patterns

Inventing new patterns using causal diagrams is very easy (except that often the patterns you invent are not new), just draw a line of R L R L R L R L R Ls for each juggler on a piece of paper and connect them all with each other, if all letters are connected with one incoming and one outgoing arrow, it is juggleable (in theory). If you have a computer you can use Wolfgang's wonderful program JoePass! (see the links) which makes it even easier to play with causal diagrams - and playing with them is the easiest way to learn to understand them. You find the link at the end of this article.
In designing new patterns it is important to remember that each letter (L or R) must have exactly one arrow starting and one ending there for the pattern to be valid. When adding people to the pattern just add lines in this feed, where feeder does pass, pass, self and the feedees do a 3-count, all on singles. Note that the feeder is in the middle, that way the arrows don't have to go from the top line to the bottom line. If you do pattern where everyone passes with everyone (like triangles or feasts) you need arrows from each line to each other line.
Diagram 7:


In this pattern all three jugglers start simultaneously from the right hand, the feeder and the top feedee with a pass, the bottom feedee with a self and then a left pass.
It is also possible that the jugglers start at different times, like in the normal 7-club three-count (diagram 3), where J2 starts one and half beats later, or in the 7-club two count where J2 start one beat later (provided J2 wants to start with a pass). Here is the causal diagram for that one - (it is shown left handed just to annoy all them right handed passers!).
Diagram 8:


Here I show three rounds of the pattern, as one round consists of only two beats.

Part 2: New wild 7-club patterns

And now it's time to use your newly acquired knowledge about causal diagrams to learn some new 7-club patterns invented during the winter and spring on JoePass!. As I don't have anyone to do serious passing with here in Copenhagen, I had to wait until EJC in Bremen to try them out with Iñaki some late night - and to tell you the truth, I was positively surprised, as I found them more interesting than I had expected. Well let's start where we started that long night with two 7-club 3-counts.

Two 'new' 3-counts

This first pattern we found quite difficult to juggle, but we managed to get 5 rounds of it, so it is definitely possible. The fourhanded siteswap (see footnote 6) for this pattern is 1029 (see footnote 7). The causal diagram should now explain the rest.
Diagram 9:


To start this pattern J1 has 3 clubs in her right hand and 1 in the left. She starts at the beginning of the diagram, throwing self crossing triples, left straight pass, zip, and then the same starting from the left. J2 has 2 clubs in his right hand and 1 in the left. He starts one and a half beats later doing the same sequence as J1, except that his passes are crossing. As this pattern is a 3-count it can be juggled by J1 while J2 does a normal 3-count (or a French 3-count - see Kaskade 67 for this pattern explained). To go into it from a normal 3-count do pass, self, self crossing triple, pass, zip, self crossing triple, etc. It is of course also possible to throw only one round of this like a trick in a normal (or French) 3-count (this is probably easier than doing it continuously, but I wouldn't know, as I just thought of it now).
The next pattern is 948 in fourhanded siteswap and has a very nice causal diagram.
Diagram 10:


Actually this pattern is a normal 3-count with a 42 (see footnote 8) (self double, hold) instead of the two normal selfs. This we first discovered after having learned the pattern, and it actually feels very different from the normal 3-count - especially if the 2 is thrown instead of held.
The start is like in a normal 7-club 3-count, with each juggler just doing 42 instead of 33.

Some 'new' 5-counts

When I was asked to write this fourth article I of course tried to come up with some new patterns for it. However, I ran into one problem, I kept inventing 'old' patterns, or very slight variations of them, but I think I managed to come up with two new patterns. The first one is a bookends with a hold and the second one I don't know how to classify, but is somehow related to the French 3-count, but also a little popcornish.
The bookends is 97647.
Diagram 11:


To juggle it J1 has 4 clubs and starts at the beginning of the diagram cross double, self, straight single, cross double, hold (or little funky 2-throw). J2 starts half a beat later (almost at the same time) and does straight double, hold (or 2-throw), straight double, self, cross single. This pattern is very nice to juggle, since the hold gives it a funny and refreshing rhythm. I don't think Iñaki and I managed to get it solid enough to throw the 2s every time, so I don't know how that is, but I kinda like having holds in passing patterns, it somehow gives them new potential, as you suddenly can put a whole range of tricks in there.
The other 5-count I managed to come up with is more simple, it is 96686 and looks like this (see footnote 9):
Diagram 12:


J1 has 4 clubs and does straight double pass, self, self, self, straight self double. J2 starts one and a half beats later and does straight self double, cross double pass, self, self, self.
This pattern is really nice as it has three selfs left to play with. Siteswapwise you can do 441, 531, 522, 423 or 342 as very nice variations. I really recommend to try out trying all variations in a continuous pattern, as they are lovely patterns in their own right. Actually we learned some of them as patterns before we realised that they were variations of 96686, and it was almost disappointing to realise what they were.
Well, I think that was all for me, and if all goes after the plan Sean Gandini will write about popcorn feeds or something like that, next time.

Footnotes:

1. Many people still consider the 4-count to be the basic pattern, but as that is a very one-sided pattern, that limits the left hand to the odd early double, I strongly recommend practicing all tricks from a 3-count, as this will enable you to be able to do all tricks from both sides and as it is a much more balanced pattern. If you want to get into more complex patterns, being used to do left hand passes makes it possible to do more than ten times as many patterns (just imagine if in solo juggling the left hand always did selfs - 3's - how boring).
2. If, however, you do worry and want to learn about siteswap check out the Internet.
3. This is not important to understand either, but basically causal diagrams only deal with 'problems' (two hands and two clubs = no problem; two hands and three clubs = one problem; four hands and seven clubs = three problems; etc.).
4. But if you are interested, check out
http://www.free-dome.org/orr/PassingPage/ClubPassing/Help.htm (Itzik Orr).
and an article about mhn & causals (Christophe Préchac)
5. That there is negative one causal lines makes sense when you consider that there is nothing that causes the club to be passed to the other hand (except, of course, the mind of the juggler). In 'normal' juggling an object is thrown when another object approaches the hand, in that way the approaching object can be said to be the cause of the following throw.
6. For explanation of fourhanded siteswap see Kaskade 65. Briefly can be said that to get 'normal' siteswap simply divide by two. Odd numbers are floaty passes and even numbers are selfs. Note that in fourhanded siteswap the two jugglers share the throws, so that in the sequence 'abcde' J1 does 'acebd', while J2 does 'bdace'.
7. 10 reads ten and not one zero, which is quite logical as 1s are virtually impossible to throw in fourhanded siteswaps, as they would be very fast handacrosses from one juggler to the other.
8. When I write about what one juggler does I often use normal twohanded siteswap - I hope this it is n't too confusing.
9. Actually this pattern is a 5-count popcorn with an early double, if the popcorn is 86867, not that it really matters, but that just shows how all the patterns are related. For more on this see the last issue of Kaskade (67).

Author: Jon Skjerning-Rasmussen
Credits: Kaskade 67

This third article in my series on 7-club passing is about one of my favourite branches of patterns: 'Popcorns', and I must confess that most of these patterns are not my inventions. It is mainly thanks to Sean Gandini that I can present this section. I have, however, taken some of the patterns a bit further to funk up some already very funky patterns. Before we get into the patterns just a few words on what popcorns are.
As I will mainly be dealing with 7 club popcorns, I won't need to get into Gandini's technical definitions here. In this section it is sufficient to say that a 7-club popcorn is one where one juggler juggles 4 clubs for a few beats while the other does 3 at the same speed (or maybe at a different speed?). Normally the 4 clubs are juggled as triple-single, but they might as well be in the 4-club fountain style. Some people prefer the term Twin Towers for this variation, but I don't know about that…

6-count Popcorn

The classic popcorn is a 6-count (which makes it one-sided), and both jugglers do normal selfs from the left while the right hand does: crossing triple self, straight double pass, single self. I normally start with the triple, and the other juggler waits three beats and then starts with her triple. The timing in the start is the same as in normal boring right-handed 7-club shower (that is, wait until the double is half way and then start - but with a self triple!).
Pat 16:


This is a great pattern and it has heaps of variations. Try for instance to throw the triples as backcrosses or do one round of the Twin Towers, in stead of the triple-single (that is 44 instead of 53). As each juggler throws three single selfs in a row after the pass, starting with the left hand. Try to substitute this for one round of left-handed 441 or 531 (each of which has its own body variations). 531 is particularly spectacular as the 5 is thrown at the same time as the other juggler's normal self triple. Another variation that I just thought of now is to throw the double pass as a straight self double, followed by a left crossing single pass (which then arrives on time). The possibilities are infinite once you start using a pattern like this as a base pattern for tricks and syncopations.
As this popcorn is a 6-count it is incredibly easy to pick up when you drop - once you know how to (picking up that is, we all know how to drop). To practice this, put 1 club at each juggler's feet and do very slow asynchronous shower on doubles with the remaining 5 clubs while 'holding through the gap' (that is, never pass when you are just holding two clubs). In causal diagram it looks like this:
Pat 17:

Whenever you want, pick up your extra club just after your pass and then start with your self triple as your partner's pass is half way. Once you can pick up in this pattern you can keep it going almost forever.
The only drawback about this pattern is that it is one-sided… But fear not here comes a both-sided version. Presenting the 7-count Popcorn:

7-count Popcorn

To juggle this pattern all you have to do is:
add an extra self,
make your passes a bit more floaty,
convince your partner that this won't work unless she crosses her passes.
This pattern is a real beauty and can actually be even more relaxed than the 6-count as you don't have to concentrate on keeping your passes lowish.
Pat 18:


Try the same variations as in the 6-count version. Now you can chose where to put the 441 or the 531 as you have 4 selfs to play with. Or you can do 3-club site swaps with a sequence of 4, like the ultra funky 5340. If done continually you can actually add an extra club and do a floaty single pass instead of the 0 (See pat. 26 below).
Making the double pass a straight self (a normal 4), followed by a floaty single pass (crossing if you were doing straights and vice versa), makes a fantastic pattern (10666867 in fourhanded siteswap - each juggler does 10687666 - see footnote 1). If you can both juggle 534 solo you have a bigger chance of success, as you throw a right-handed 534 followed by a floaty single pass and three selfs and then the same but left-handed.
Pat 19:


For bigger chance of success in this pattern let J1 start like in the normal 7-count popcorn, as it can be quite hard otherwise to get the timing right for J2. As you probably normally tend to time your triples after the incoming double passes it will probably take a few attempts to get used to receiving single passes (not to mention throwing them while looking up at your triple!) - but if you take the time to learn it you will be rewarded by extra thrill, and you will be able to go on to the next pattern… If, however, you give up here then move on to pattern 21, which is quite a lot easier.
OK, you are still here! For extra funk you can put all the variations of the 6-count popcorn into it, as there are still three selfs left to play with. Here it is shown with J1 doing a popcorn with a 531 (106871062) while J2 does the Twin Towers version with a 441 (8887882).
Pat 20:


Obviously this is quite difficult, and I recommend using pat. 19 as base pattern, and then putting in the siteswaps (and body moves) once you have it running smoothly.

5-count Popcorn

A both-handed popcorn can also be done on a 5-count where each juggler does crossing self triple, self, floaty single pass, self, self (J1 straight, J2 crossing). This pattern is not actually that difficult, though still lovely.
Pat 21:


The siteswap, for those who need that kind of information: 106667 (each juggler does 106766). As a self triple is thrown every 5 beats it will be the same club that does all the triples = very easy to remember.
For syncopations there are not that many possibilities, as there are only two selfs, there not so many obvious site swap variations. However 42 is nice, especially if you throw the 2 as a low self single - or whatever you can come up with. (51 unfortunately doesn't work - 'clash'). Try also throwing an extra self triple on the beat right before the normal triple, this means that you get a zip instead of self after the second triple (got that? Well basically you just throw 551 before the pass instead of 353.
Reversing the logic of before (where we changed the 7-count so that we passed a single one beat later) we can likewise throw what would be an early double followed by a hold - which again opens new possibilities, as you now have a hold and your two selfs (that is a 233) to play with. Try, for instance, to throw a 530, a 440 or a 413 there, or even a 512 (with or without actually throwing the 2). Here you can see these four variations with J1 doing 413 and 512 and J2 doing 440 and 530.
Pat 22:

4-count Popcorn

Now we have had 5-, 6- and 7-count popcorns, but also 4-count and 3-count are possible.
To do a 4-count (one-sided) popcorn, reverse the throwing rhythm of the well known 7 club 4-count passing pattern 'triple-self', so that the triples are selfs and the right hand singles are passes (the left hand still only throws single selfs). This mightn't be so interesting in itself, but it can be thrown towards a 'triple-self' or as a trick in it. I haven't bothered working out tricks and syncopations for this as it's a right-handed pattern, and I prefer to use both halves of my brain!

3-count Popcorn

More interesting (for me) is the 3-count versions of popcorn. Following the logic of the previous patterns the basic 3-count version of popcorn would be throwing a self triple followed by a single self and then a very quick pass (a low flat):
Pat 23:


This pattern is almost impossible to do nicely (or even not nicely) - it might even be dangerous to attempt this with clubs, as the pass is a 5, (or what would be a 2,5 in solo juggling). However I've been told that it is possible (though still stupidly difficult) to do it with rings. To make it juggleable with clubs it is, however, possible to throw every pass one beat earlier and as a single or to throw every pass on the same beat as normal but as a single (the passes are in both cases straight if you were crossing and vice versa). Both emerging patterns will have a hold (or a funky little 2-throw, if you want) the siteswaps are 1047 and 1074. (For 8 clubs try 'triple self, pass, pass': 1077).
Pat 24:


Pat 25:

French 3-count

Let's have a pattern that has been around for a few years, a pattern that may or may not be a popcorn, namely the French 3-count, or the 867 - a real beauty once you crack it.
Pat 26:


J1 starts with a self double and then a floaty straight single pass followed by a self single. J2 starts one and a half beats later with a left self double, then a right floaty single crossing pass and a left self.

8 Clubs wild popcorn

And for the ones who still haven't had enough I present a last minute wild 8-club popcornish thing that I invented with Dani in Barcelona a few days ago - it is a 7-count, and it rocks, what more can I say. We have almost done a whole round of it, but it feels very right. J1 passes straight singles and crossing doubles, J2 vice versa. To start let J2 start with a left hand self triple immediately followed by a self triple by J1. as I'm running out of article space I'll let this siteswap (101066897 - each juggler does 106910687) and the casual diagram speak for itself.
Pat: 27


Pop 'til you drop!

Footnote:
1 For a brief explanation of this see Kaskade 65. If you don't have that then just remember that odd numbers are passes and even are selfs and if you want the "normal" siteswap numbers just divide by 2.

Author: Norihide Tokushige

Original PDF version available at: http://www.cc.u-ryukyu.ac.jp/~hide/siteswap.pdf

1. Introduction

There are a couple of variations of siteswap notation for passing. For example, Buhler–Graham–Wright introduced a notion of juggling poset. Any passing siteswap can be represented by using a juggling poset, but it is not so handy. On the other hand, we are familiar with the usual siteswap, i.e., siteswap for two hands. Why not interpret the usual siteswap as a siteswap for passing? In this note, we propose several ways of interpretation from the usual siteswap to the passing siteswap. We can not obtain all passing patterns in this way, but we can still find infinitely many new, interesting passing siteswaps. One of the good points of our method is the simplicity of the notation. For example, 7 club 3-count is “966,” Jim’s 3-count is “7746666,” or Flurry is “726” in our notation.

2. Basic idea

Remember how 77722 goes in the usual siteswap. We associate the right hand and the left hand alternately to the sequence in the following

7	7	7	2	2	7	7	7	2	2	...
R	L	R	L	R	L	R	L	R	L	...

Now two jugglers, say Hide and Tomoko, juggle this sequence as a passing pattern. So they associate H and T instead of R and L.

7	7	7	2	2	7	7	7	2	2	...
H	T	H	T	H	T	H	T	H	T	...

But both Hide and Tomoko have two hands, they actually juggle as follows:

number	:	7	7	7	2	2	7	7	7	2	2	...
Hide/Tomoko	:	H	T	H	T	H	T	H	T	H	T	...
hand	:	R	R	L	L	R	R	L	L	R	R	...
club	:	1	2	3	4	5	4	5	1	2	3	...

Then this is a 5 clubs passing pattern, and it looks like 7 club 1-count with some hand acrosses. Hide’s sequence is 77272 and Tomoko’s sequence is 72772. Looking at the sequence more carefully, we find that Hide’s 7 is straight pass, while Tomoko’s 7 is cross pass. (We assume that they are passing in the face to face position.) In the usual siteswap 2 means holding a prop, but in our case 2 means the (self) hand across.
Next, imagine Hide and Tomoko are doing 77722 in the above sense. If we identify Hide’s right and left hands with a big Right hand, and identify Tomoko’s right and left hands with a big Left hand, then we get a picture of the usual 77722 siteswap by this imaginary big juggler — let’s call him Ninja. This is the basic idea of how to connect the usual siteswap and our passing siteswap.

3. Asynchronous patterns

Ninja’s asynchronous siteswap such as 77722 is interpreted as an asynchronous passing siteswap for Hide and Tomoko. The rule of the interpretation is the following:

Hide starts first with his right hand, and then Tomoko’s right hand follows. Hide takes Ninja’s right hand, and Tomoko takes Ninja’s left hand. This implies that even numbers are self, and odd numbers are pass. As for even numbers, multiple of 4 (0,4,8,...) is straight self, and even but not multiple of 4 (2,6,10,...) is cross self.
More practically,

number	self throw
0	empty hand
2	hand across
4	holding a club or flourish
6	cross single spin
8	straight double spin
10	cross triple spin

Odd numbers are a little bit tricky. The same number for Hide and for Tomoko means different type of pass.

number	Hide's pass	Tomoko's pass	spin
5	cross	straight	half? (fast)
7	straight	cross	single (slow)
9	cross	straight	double
11	straight	cross	triple

Let us see an example. 7777266 is a 6 club passing pattern known as Mild Madness.

number

:

7

7

7

7

2

6

6

7

7

7

7

2

6

6

7

7

7

7

2

6

6

Hide/Tomoko

:

H

T

H

T

H

T

H

T

H

T

H

T

H

T

H

T

H

T

H

T

H

hand

:

R

R

L

L

R

R

L

L

R

R

L

L

R

R

L

L

R

R

L

L

R

pass / self

:

p

p

p

p

s

s

s

p

p

p

p

s

s

s

p

p

p

p

s

s

s

cross / straight

:

s

c

s

c

c

c

c

c

s

c

s

c

c

c

s

c

s

c

c

c

c

club

:

1

2

3

4

5

6

5

1

2

3

4

6

5

6

1

2

3

4

5

6

5

Hide’s sequence is 7726776, that is pass, pass, hand across, self, pass, pass, self, and all passes are straight. Tomoko’s sequence is 7767726, that is pass, pass, self, pass, pass, hand across, self, and all passes are cross.

4. Synchronized patterns

Ninja’s synchronized siteswap is translated into a synchronized passing siteswap for Hide and Tomoko. Synchronized passing means that at each time two hands (not necessarily two hands of one juggler) are position of throwing clubs. There are three different translations — HT, RR, RL.

4.1. Type HT

Hide and Tomoko take Ninja’s sequence alternately. The rule is as follows.

Ninja’s right corresponds to Hide’s right and Tomoko’s left. Ninja’s left corresponds to Hide’s left and Tomoko’s right. A multiple of 4 (0,4,8,...) is self, and pass is otherwise (2,6,10...). A number with “x” is cross, and a number without “x” is straight.

2, 6, 10, ...	:	straight pass
2x, 6x, 10x, ...	:	cross pass
0, 4, 8, ...	:	straight self
4x, 8x, 12x, ...	:	cross self

For example, (6,6) is the 6 club synchronized 1-count. Let us see another example. (6,4)(6x,4)(4,6)(4,6x) is a 5 club pattern. If you do 4 as a single straight self, this pattern looks like 5 club 1-count with extra single selves.

number	:	(6,4)	(6x,4)	(4,6)	(4,6x)	(6,4)	(6x,4)	(4,6)	(4,6x)
H / T	:	H H	T T	H H	T T	H H	T T	H H	T T
R / L	:	R L	L R	R L	L R	R L	L R	R L	L R
p / s	:	p s	p s	s p	s p	p s	p s	s p	s p
c / s	:	s s	c s	s s	s c	s s	c s	s s	s c
club	:	1 2	3 4	5 2	1 4	5 3	1 2	4 3	5 2

Hide’s sequence is (6,4)(4,6), that is (straight pass, straight self) (straight self, straight pass). Tomoko’s sequence is (4,6x)(6x,4) if we write numbers in (right, left) order and this is (straight self, cross pass)(cross pass, straight self).

4.2. Type RR

Hide’s right and Tomoko’s right are synchronized, and so both their left hands as well. The rule is as follows.

Hide takes Ninja’s right and Tomoko takes Ninja’s left. A number with “x” is pass, and a number without “x” is self. For self, a multiple of 4 is straight. For pass, a multiple of 4 is cross.

2, 6, 10, ...	:	cross self
2x, 6x, 10x, ...	:	straight pass
0, 4, 8, ...	:	straight self
4x, 8x, 12x, ...	:	cross pass

For example, (6x,6x) is the 6 club asynchronous 1-count, (6x,6x)(6,6) is the 6 club 2-count. Let us see another 6 club passing pattern (8x,6)(6,8)(2,6x). This is a neat variation of 3-count passing.

number	:	(8x,6)	(6,8)	(2,6x)	(8x,6)	(6,8)	(2,6x)	(8x,6)	(6,8)	(2,6x)
H / T	:	H T	H T	H T	H T	H T	H T	H T	H T	H T
R / L	:	R R	L L	R R	L L	R R	L L	R R	L L	R R
p / s	:	p s	s s	s p	p s	s s	s p	p s	s s	s p
c / s	:	c c	c s	c s	c c	c s	c s	c c	c s	c s
club	:	1 2	3 4	5 6	5 2	3 1	6 4	6 2	3 5	4 1

Hide’s sequence is 8x,6,2 that is pass, self, self (all cross). Tomoko’s sequence is 6,8,6x that is self, self, pass (cross, straight, straight).

4.3. Type RL

Hide’s right and Tomoko’s left are synchronized. The rule is as follows.

Hide takes Ninja’s left and Tomoko takes Ninja’s right. A number with “x” is pass, and a number without “x” is self. A multiple of 4 is straight for both pass and self.

2, 6, 10, ...	:	cross self
2x, 6x, 10x, ...	:	cross pass
0, 4, 8, ...	:	straight self
4x, 8x, 12x, ...	:	straight pass

For example, (8x,6)(6,8x) is the 7 club 2-count, (10,6)(6,6)(8x,6)(6,10)(6,6)(6,8x) is the 7 club popcorn.

5. Conversion from async to sync

An asynchronous pattern can be transformed to a synchronized pattern by shifting one beat on one side of ladder diagram. The rule is the following:

For this conversion, we need to divide an asynchronous sequence into two digits segments. For example, 77722 is transformed as follows.

77 72 27 77 22 --> (6x,8x)(6x,2)(2,8x)(6x,8x)(2,2)

5.1 From async to type RR sync

In this case, the only change is the length of pass. Hide’s pass decreases one beat, while Tomoko’s pass increases one beat. (No changes for self, no changes for the
direction(cross/straight) of pass.)

sequence

:

77

72

27

77

22

-->

(6x,8x)

(6x,2)

(2,8x)

(6x,8x)

(2,2)

Hide/Tomoko

:

HT

HT

HT

HT

HT

H T

H T

H T

H T

H T

hand

:

RR

LL

RR

LL

RR

R R

L L

R R

L L

R R

5.2 From async to type RL sync

In this case, the only change is the length of pass. Hide’s pass increases one beat, while Tomoko’s pass decreases one beat. (No changes for self, no changes for the direction(cross/straight) of pass.)

sequence

:

27

77

22

77

22

-->

(2,8x)

(6x,8x)

(2,2)

(6x,8x)

(6x,2)

Hide/Tomoko

:

TH

TH

TH

TH

TH

T H

T H

T H

T H

T H

hand

:

LR

RL

LR

RL

LR

L R

R L

L R

R L

L R

For practical convenience for doing RL pattern, Tomoko can start the same sequence as asynchronous pattern after one beat pause.

sequence

:

-7

77

22

77

22

-->

(-,8x)

(6x,8x)

(2,2)

(6x,8x)

(6x,2)

Hide/Tomoko

:

TH

TH

TH

TH

TH

T H

T H

T H

T H

T H

hand

:

-R

RL

LR

RL

LR

- R

R L

L R

R L

L R

6. 3-count, PPS examples

There are many variations of 3-count and PPS passing patterns for RR, RL type coming from ground state siteswaps.
Notation: Hide takes a sequence from the left part, and Tomoko takes a sequence from the right part.

{8x62,86x2} * {68x6,686x,a8x2,ax82}

For example, Hide takes 8x62, and Tomoko takes 686x. Then, (8x,6)(6,8)(2,6x) is a 3-count pattern for RR and RL. In the above case, there are 2 * 4 = 8 different 3-count patterns for RR (and 8 for RL, too). (Remember 2 means hand across, 6 means single, 8 means double, a means triple. Numbers with x means pass, numbers without x means self. For self, 2,6,a are cross, 8 is straight. For RR type, 6x, ax are straight pass, 8x is cross pass. For RL type, 6x, ax are cross pass, 8x is straight pass.)

6.1. 6 club

3-count
{88x2,ax62,666x} * {88x2,ax62,666x}
{8x82,66x6,a6x2} * {8x82,66x6,a6x2}
{6x62} * {88x6,886x,ax66,a66x}
{6x82} * {86x6,8x66}
{8x62,86x2} * {68x6,686x,a8x2,ax82}

PPS
{8x8x2,ax6x2,66x6x}
{6x6x2} * {8x8x6,8x86x,a6x6x,ax6x6}
{6x8x2} * {86x6x,8x66x}

6.2. 7 club

3-count
{6x68,6xa4,668x,6ax4,848x,8ax2} * {886x,88x6,a8x4,ax66,ax84,a66x}
{8xa4,86x8} * {68x6,a46x,a8x2,ax46,ax82}
{6x88,688x,6ax6,8x68,a48x,aax2} * {8x66,8x84,a6x4}
{6xa6,6ax6,a48x,aax2} * {86x6,8x66,8x84,a6x4}
{68xa,8a6x,axa4,88x8,ax68} * {666x,68x4,846x,88x2,ax44,ax62}
{aa6x,ax88,a8x8,axa6} * {66x4,86x2,8x44,8x62}
{8xa6,a6x8,8x88} * {8x46,8x82,a6x2}

PPS
{6x66x,6x8x4} * {88x8x,8ax6x,axax4,ax68x,6x8xa}
{6x6x4} * {a8x8x,aax6x,ax88x,axax6}
{6x6x8,8xax2} * {8x8x6,ax6x6,8x86x,a6x6x}
{6x86x,6x8x6} * {86x8x,8xax4,8x68x,6x6ax}
{6x8x8,6xa6x,axax2,68x8x,6ax6x,ax48x,axax2} * {86x6x,8x66x,8x8x4,ax6x4}
{8x66x} * {axax2}
{8x8x8} * {8x8x2,ax6x2}
{8xa6x,ax6x8} * {8x46x,8x8x2,ax6x2}

1-count
{6x6x6x} * {8x8x8x,8xax6x}

Norihide Tokushige
College of Education, Ryukyu University
Nishihara, Okinawa, 901-0213 JAPAN
hide@edu.u-ryukyu.ac.jp

Author: Sean Gandini
Credits: Kaskade 69

See the following part, Popcorns II: asymmetry, synchronicity and more people
Download a ZIP archive with popcorn patterns for JoePass!.

This article is an abbreviated version of extensive exploration of popcorns that we have undertaken over the last couple of years. Although the first popcorns where distinctively club patterns, the patterns described here are worth trying with all the other classic juggling props, and indeed any other that you can think of.

We have taken for granted a basic understanding of siteswaps and less importantly for this article causal diagrams. Causal Diagrams where explained in the last issue of Kaskade (68). If you are unfamiliar with siteswaps I urge you to spend the couple of hours it takes to gain an understanding of them, for they are an invaluable tool in understanding a myriad of wonderfull juggling patterns.

The passing notation we use is Jack Boyce's extension of classical siteswaps. All patterns are given from the perspective of a 2 handed juggler.

Because of lack of space I haven't included most of the charts. I have put them up on our Internet site where you can also find for sale the laminated versions.

Definition of popcorns.

For the purpose of this article we will define popcorn passing patterns as jugglers taking turns at popping. Popping in this context means lifting into an amount of objects higher than the one they previously had and then throwing the extra things back out. We shall return and be more specific with this definition but for now it should serve us well.

Classic popcorn

As already thoroughly defined in this column the classic popcorn is <5 3 4p 3 3 3 | 3 3 3 5 3 4p > which since it is symmetrical we can call 5 3 4p 3 3 3

Now for our purposes we want to change the 53 to 44 so as to go from the most simple 4 object pattern to the most simple 3 object pattern. So we get 4 4 4p 3 3 3

Ok so that's a popcorn in its basic state, in this case you juggle 4 for a bit, throw a pass and then juggle 3 for a bit.

Expanding Popcorns

So now what we want to do is find all the symmetric patterns of the above form that go from 3 to 4 objects. By Symmetric I mean patterns where both jugglers do the same thing, in this case out of time with each other.

The chart below is the expansion:

	Horizontally we expand by adding a 3 on one side of the pass and a 4 on the other. This means that each step along the chart gives each juggler an extra throw of the 2 solo patterns.
	Vertically we expand by adding and removing 3s by increasing and decreasing the pass by half a beat. So for example in club juggling decreasing the pass from a 4 to a 3.5 means doing a floaty single instead of a normal double.

7 objects popcorn chart

The chart expands to infinity upwards and to the right

There are a lot of fun patterns here! Over the last year we have juggled most of them. The lower extremities tend to be the hardest. Our problems started with the 2.5 passes. In principle these are faster than an ordinary 3. We got round it by really slowing down our 4s. I initially included the 1ps,1.5ps and 2ps for aesthetic reasons but have realised that one can turn them into interesting patterns by giving the club, as opposed to passing it.

Notice interestingly that the patterns on the column furthest to the left, 3.5p, 4p3, 4.5p33, 5p333, 5.5p3333 are the usual 7 objects 1-count, 2-count, 3-count, 4-count and 5-count respectively. Here we encounter our first dilemma since each juggler lifts into the new amount of objects for 0 beats. Are they popcorns?

For a more thorough understanding of the popcorn progression it might help to look at the causal diagram chart for the seven object chart. Sometimes diagrams can speak more than words or numbers.

More Objects

So now lets look at 8 object popcorns.

There is a chart where both jugglers do the same thing in time with each other, patterns like 46p33, however for now we will concentrate on patterns where the jugglers are symmetrically staggered in time. This means both jugglers do the same thing at different times.

So the staggered chart has 2 passes, each juggler lifting from 3 objects to 5 objects.

We started learning the patterns above with rings so as not to have to deal with spin. The ones we found easiest to start with where the longer versions of ……4p4p….. With these you have time to steady your 5 object pattern before having to throw out. However if you find five difficult perhaps the shorter patterns are easier. With clubs we started with 54p4p3 with the 5 a triple and the 4s doubles. We also do the above long pass with the fives as doubles.

So back to the charts, here are the two 9 object charts In the first chart each juggler alternates between 4 and 5 object patterns while in the second it is between 3 and 6 object patterns.

9 objects 1 pass

9 objects 3 passes

We haven't yet managed the 3 pass versions with clubs. I would love to see them!

Notice that for now we are just listing popcorns where the lowest amount of objects juggled is 3. There are however popcorns which go from 2 objects to 4 objects, from 0 to 6 or indeed any combination that you care to think of!

Siteswap syncopations

Earlier we changed the classic popcorn from 53 to 44. We can now do the opposite and replace any series of throws by their siteswap equivalent. So for example classic popcorn has 3 selfs (siteswap 3) throws which we can replace by any period 3 siteswap. Ie 522, 441, 531, 342…

The other fun thing one can do is synchopate the passes as well. So for example 334p4p55 can become 335p3p55!

And last but not least you can apply the principle of late and early passes that one does in 4 count passing. So in classic popcorn 444p333 one of the jugglers can do 45p3333. In club passing this could be a crossing triple pass.

In Conclusion

Up to now we have only considered patterns that leave ground state and return to ground state. There are off course a whole family of patterns where this is not the case. For example one can draw up the chart of popcorns that go from 3 shower to 4 shower. The problem is that we cannot do this without transition throws. The resulting patterns are very interesting but lack the qualities that I would call popcorn. To clarify I would redefine popcorns as going from ground state to ground state. This implies that contrary to what one might think not all passing patterns are popcorns. Next article we will look more in detail at what we mean as ground state as well as all kinds of hybrid popcorns.

I hope that you will find some interesting patterns to play with in the ideas above.

Thanks for Wolfgang Westerboer, JiBe and Jon Skjerning-Rasmussen for their help writing this article.

See the following part, Popcorns II: asymmetry, synchronicity and more people
Download a ZIP archive with popcorn patterns for JoePass!.

Bibliography

An extended version of this article including all the charts can be found at www.gandinijuggling.com
Jack Boyce's passing notation http://juggleanim.sourceforge.net/doc/notation.html
Christophe Prechac's extremely technical but very interesting pages, See particularly his article on generating all symmetric passing patterns from 2 handed siteswaps. http://pogo5.free.fr/juggling/mhn&causal.html
Wolfgang Westerboers fantastic passing animator http://www.koelnvention.de/software/index.html

Author: Sean Gandini
Credits: Kaskade 52

These are a group of fun 3-object two-person patterns. I will describe them as ball patterns but obviously they work for all the standard objects. The basic concept behind take-away patterns is the replacement of hands within a juggling pattern. That's it. One person juggles, the other takes some or all of the pattern away. Hence the name "take-away".
The first bunch of patterns are just cyclic replacements. By this, I mean patterns that repeat in nice concise loops, like pop music. You juggle for three beats, I juggle for three beats, then we start all over again.
In traditional group juggling these cycles tended to be quite straightforward. Cycles of 2, 3 or 4 throws. We have pushed it further by generalising. Our generalisation is that on any given beat there can be a replacement; so the replacing need not happen as neatly or as regularly as described above. But more of that later.
A word on positions: Contrary to the Kama Sutra and for simplicity's sake we will limit ourselfs to a simple number of positions. Obviously you can extrapolate at will.
In an idealised scenario the balls stay in place and the hands weave around them. This is easier said than done. There is a tendency to give the balls to the taker. In this respect a clarity of counts is very useful. One of the most common drops on take-aways is not being sure if the other person is taking or not, "the hovering hands". Help your partner by being as clear as you can.

Side by side.

Let's assume that the two jugglers are standing (sitting, lying) side by side. Illustration 1. Our jugglers are called Rachid and Shamira. In the simplest possible scenario Rachid juggles 3 objects. At any point Shamira can replace either of Rachid's hands. If one thinks of the 3 balls as independent from the hands, then any landing ball can be caught by any of the free hands. Think for a moment of a juggling pattern as floating in space. There are two points where the hands meet the balls, it is at those points that the replacing can happen. For simplicity's sake we shall begin by replacing right with right and left with left. By this I mean that a ball thrown from a left hand will always be caught by a right hand and vice versa. Whether this hand is mine, yours, the pope's or a zebra's is unimportant. This restriction is purely for simplicity and to provisionally limit the amount of patterns involved. As we shall see later we can lift the restriction to generate a whole other family of patterns.

3/3 Out
Let's start by learning 3/3. The notation 3/3 means that each juggler catches three times. So we get a 6 beat cycle that goes:

For simplicity's sake we will also refer to the two closest hands as inside hands and the two further-away hands as outside hands. (Illustration 1).
Rachid starts with 2 Balls in the Right Hand and 1 Ball in the Left Hand. He throws the first ball from his right hand to Shamira's outside hand. (Illustration 2). She then takes the second ball with her inside hand (Illustration 3) followed by the third ball with her the outside hand (Illustration 4). Three catches in all.
Rachid then does the same, his outside hand followed by his inside hand followed by his outside hand (Illustrations 5,6,7). And so on ad infinitum (or not).
This pattern is quite instinctive to most westerners. Remember that you always take away from the outside hand first. If you colour code the balls you will always end up with the same balls in the same hands in the same order. So if you start by taking a mauve ball with your outside hand, both of you will take the mauve ball as your first ball with your outside hand. Now what could be easier? You take the balls and you give them straight back.
Although this pattern is easy to do without counting I would encourage you to start by counting it. The more you count now the easier it will be not to count later.

3/3 In
Same idea only the inside hands take first. This is a lot harder. You have to reach right across your partner. The colour coding works as well. As you learn this pattern you will find that there is a pleasant weaving that begins to happen between the inside hands. (Illustrations 8, 9, 10)

5/5 Out
This is very similar to the above but one waits longer between takings. The extra wait is what makes this pattern slightly tricky for most people. On the other hand one has longer to steady the pattern. This is a very useful pattern for learning odd counts. Needless to say the initial colour coding is no longer valid.

5/5 In
Included for thoroughness. Same as 3/3 in but with two extra juggling beats.

2/2
Now things start to get interesting but tricky. What is odd about this one is that once the pattern gets going you end up catching your own first ball. It really helps to slow this down as much as you can. Take each throw one at a time and count it out loud. Note that both jugglers do slightly different things. One does Inside Hand followed by Outside Hand whilst the other does Outside Hand followed by Inside Hand. This pattern is not symmetrical. By this I mean that you get a different pattern if Shamira starts from the one you would get if Rachid started. (Illustrations 11-15)

1/1 Out
Outside hand to outside hand is what is usually called a share. It is simply a shared 3 ball cascade. This is one of the most common 2 person juggling patterns. (Illustration 16)

1/1 In
The other 1/1 pattern, Inside hand to inside Hand, is wonderfully different and seldom seen. (Illustration 17)

4/4
I think by this point it becomes self-explanatory. This is more of the same. The two jugglers do different things. The second version reverses the jugglers' roles.

11/11
Medicine for the counting ill.

Asymmetry
We've been doing patterns of the a/a variety. Needless to say we could go on forever although perhaps this would be pointless. I would nonetheless recommend playing with some different counts: 6/6, 7/7, 8/8… 134/134 great for taking turns at cooking the evening meal. But needless to say the two numbers don't need to be the same, so:

3/2
Rachid catches twice followed by Shamira catching three times. If you practised 2/2 and 3/3 then this pattern is a cut and paste between the two. Contrary to all the other previously encountered patterns this pattern cycles through its 2 states. By this I mean that the second time you go and grab the balls you will begin with a different hand. It takes ten throws(or catches) to get back to the beginning.
So for example Rachid alternates between Right, Left and Left, Right, between Inside/Outside and Outside/Inside. Shamira alternates between R L R and L R L, O I O and I O I.
I think that by now you can work these things out, but here are some other fun combinations:

2/1
One version of this pattern is a real standard although it is usually done one juggler behind the other. The juggler juggling the 1 ends up throwing it back and forth to herself.
The other version is rather delightfully unexpected and gives some interesting hand weaving.

4/3
Straightforward.

5/3, 4/2, 11/3 and so on ad infinitum.

More Complexity
Let's go further by adding one more segment.

3/3/2
Rachid does 3 catches, Shamira does 3 catches, Rachid does 2 catches and it starts all over again with the roles reversed, Shamira does 3 catches, Rachid does 3 catches Shamira does 2 catches and we are right back to where we started. The pattern has three segments and two jugglers so each juggler will end up doing every part of the pattern. This pattern can hurt the mind.

3/2/1
I found this particularly difficult to learn.

2/2/1 and 2/1/1
These are total brain melters, monitor how long it is before you can have a conversation at the same time.

5/3/1, 2/3/1, 11/2/124 or 2/1/2/3 or 4/17/2/124
Needless to say you can add as many segments as you desire.

Different Positions (Illustration 18)
Some of these positions are illegal in some countries.

The above is an extract from the leaflet for the Patterns video which contains all of the above plus a lot more and is available from Gandini Video Productions at £17.50 + £2,50 p&p.

Author: Sean Gandini
Credits: Kaskade 70

See the previous part, Popcorns I
Download a ZIP archive with popcorn patterns for JoePass!.

For this article we shall assume that you have read last issues' article. Last time we looked at 2 person symmetric popcorns. This time round lets look at some different kinds of popcorns and how one expands the popcorn idea to more people. Again even though the article is very notation heavy and slightly theoretical it is very much rooted in real world juggling patterns. I highly recommend downloading Joe pass and the files for a lot of these patterns. Ok so here we go:

Semi-Asymmetric popcorns

Up to now we have assumed that both jugglers lift into the same amount of objects. This is not always necessarily the case. We can build popcorns where both jugglers lift into different amounts. Lets imagine for example that you want juggler one to lift into 5 objects and juggler two to lift into 4 objects. This would be a 1 pass 8 object popcorn. We obviously won't do the charts for all of the possible asymmetric patterns but for reference below is part of the 8 object asymmetric 4/5 popcorn.

554p444|4444p33

Note that we now need to show both passers roles since the pattern is asymmetric. Note also that the pattern 554p444|4444p33 illustrated above should strickly speaking be written as 554p444|4p333444; that is the second part of the pattern starts on the pass. We find that for the purposes of this article and to illustrate the particularities of popcorns the notation we have chosen is clearer.

There is also a whole family of patterns which have the jugglers lifting into the same amount of objects but holding their patterns for different amounts of time. So there is a further expansion of each pattern in the original symmetric charts which involves elongating the numbers on one side whilst shortening the numbers on the other side. So for example below is the expansion of the classic popcorn into its 3 mutations.

444p333

44p3333|4444p33

4p33333|44444p3

Every pattern can be mutated this way. In fact we can combine the two procedures above to generate a third family, popcorns of different lengths and different amount of objects. Lets look at the mutations of 554p444|4444p33 a pattern which we met before:

Progressive popcorns

It is also possible to progressively lift into a given pattern. For example if we take the 8 object 2 pass popcorn: 554p4p33, the jugglers take turns at lifting from 3 to 5 objects. We can stagger the lifting by separating the passes. So lets look at the pattern 554p4p33 which we met in the 8 object 2 pass chart last issue. So by inserting some 4s the pattern becomes:

554p44p334,
the bold 4s are the inserted 4s.

then 554p444p3344 and so on and so forth. So essentially any popcorn pattern with more than 1 pass can be progressive!

Needless to say we can use the staggering procedure that we met above to make the patterns asymmetrical.

More People

Ok so what happens if there are more jugglers involved. Once again we shall only look at patterns where all jugglers do the same thing at different times. Spatially the jugglers can stand wherever they want, for practical reasons however the easiest way to juggle these patterns in a triangle or a line formation.

So lets look at 3 jugglers with 10 objects. Here each juggler will take turns at lifting from 3 objects to 4 objects.
Below is the chart expanded in the same way as the 2 person chart.

Here the chart increases Horizontally by adding a 4 on the left side of the pass and 2 x 3 on the other side.
It increases Vertically by adding 0.3 to the pass.

Again note that the column on the left side of the chart has the 1-count, 2-count, 3-count, 4-count…patterns.

Lets now look at 11 object 3 person popcorns. There are 1 pass and 2 pass versions of this. Below is the 1 pass version.

For fun lets look at a small selection from the 4 person charts:

Below is the 13 object 1 pass charts. The chart increases vertically by adding 0.25 to the pass and horizontally by adding one 4 on one side and 3 x 3 on the other.

The 14 object chart for 4 jugglers, is the same as the 7 object chart for 2 juggler so it has not been included.
All the 2 person charts can be transformed into 4 person charts by doubling the jugglers and the amount of objects.

If you have got this far with me then you can imagine how to construct charts for more jugglers.

Synchronous popcorns

Essentially one can draw the same kind of charts as the asynchronous popcorns. However things get slightly complicated. We mentioned in the last article that we defined popcorns as jugglers juggling a certain amount of objects in ground state and lifting/descending into a different amount of objects still in ground state.

If a lone juggler jugglers 4 objects asynchronously there is only one way of staying in ground state, that is throwing 4s. This is not the case for synchronous 4. One can throw (4,4) or (4x,4x), two different ways of staying ground state. For odd numbers of balls there are 4 different ways of staying ground state.

What this basically means is that every pattern has numerous equivalent versions.
However bearing this in mind the chart process still works. Below are examples of the various charts.

7 Objects:

(4,5p)(4x,2x)(4x,2x)	(4,4)(4,4p)(4x,2x)(4x,2x)	(4,4)(4,4)(4,4p)(4x,2x)(4x,2x)(4x,2x)	(4,4)(4,4)(4,4)(4,4p)(4x,2x)(4x,2x)(4x,2x)(4x,2x)
(4,4p)(4x,2x)	(4,4)(4,4p)(4x,2x)(4x,2x)	(4,4)(4,4)(4,4p)(4x,2x)(4x,2x)(4x,2x)	(4,4)(4,4)(4,4)(4,4p)(4x,2x)(4x,2x)(4x,2x)(4x,2x)
(4,3p)	(4,4)(4,3p)(4x,2x)	(4,4)(4,4)(4,3p)(4x,2x)(4x,2x)	(4,4)(4,4)(4,4)(4,3p)(4x,2x)(4x,2x)(4x,2x)

And for fun:

9 Objects:

(7p,4)(4,4)(4,4)	(4x,6x)(7p,4)(4,4)(4,4)(4,4)	(4x,6x)(7p,4)(4,4)(4,4)(4,4)
(6p,4)(4,4)	(4,6x)(6p,4)(4,4)(4,4)	(6x,4)(4,6x)(6p,4)(4,4)(4,4)(4,4)
(5p,4x)	(4,6x)(5p,4x)(4,4)	(4,6x)(5p,4x)(4,4)
	(4,6x) (4p,4x)	(4,6x) (4p,4)(4,4)

More People synchronous

So needless to say we can make the synchronous charts for more jugglers.

Below is the chart for 3 jugglers and 10 objects.

Generalising

One can of course combine the above ideas. So you can use the above as a cookbook and make your own recipes. For example you might enjoy making 3 person progressive synchronous asymmetric popcorns. One can combine synchronous and asynchronous patterns.

So too finish an 3 person asymmetric 11 object popcorn with one juggler lifting from 3 to 4, one juggler lifting form 4 to 5 and one juggler lifting synchronously from 3 to 4.

So that's the end of our exploration of popcorn patterns. I would like once again to stress that these patterns are a lot of fun to juggle. Getting confortable with the notation and the diagrams takes a while but the juggling rewards are huge. I lookforwards to any feedback you might have on these ideas and I hope that you get something out of them.

See the previous part, Popcorns I
Download a ZIP archive with popcorn patterns for JoePass!.

Addendum

As an addendum to the last article we would like to add that a 2 person pattern can be done in several different different ways, depending on the hand throwing order. So for example the classic 7 object 2 count 4p3 in 4 different ways:
- Both jugglers starting with their rights.
- Both Jugglers starting with their lefts.
- Juggler one starts right and Juggler 2 starts left.
- Juggler one starts left and Juggler 2 starts right.

This is the same for patterns of an even period. Patterns of an odd period have just 2 versions.

Now whereas the 2 person popcorn charts have either 2 or 4 different hand arrangements, the 3 person patterns have 4 or 8 different possibilities. So choosing the easiest or most convenient way of juggling a particular patterns will not always be easy. I suggest trying different possibilities using intuition to guide you.

Bibliography

An extended version of this articles including all the charts and files for joe pass can be found at http://www.gandinijuggling.com/popcorns.htm
New Passing site on the internet www.passingdb.com has many films of patterns relevant to this article.
Wolfgang Westerboers fantastic passing animator http://www.koelnvention.de/software/index.html
For an understanding of states: Mark Thomas http://www.markthomasonline.co.uk/state.html

Author: Wolfgang Westerboer
Credits: Kaskade 56

The illustrations are taken from Charlie Dancey's great book, the Compendium of Club Juggling, and the title is the first of his three "Golden Rules of Club Passing" (by kind permission of the author).

What is more important when passing: throwing or catching? Think about this before reading on.

For me, both are equally important. Somebody has to catch my throw - either my partner or myself. If the throw is sloppy, it will be difficult to catch, which means that the pattern will get shaky and may collapse altogether. I reckon jugglers in general don't pay enough attention to their passing throws and just accept that their partner is going to have to work hard to catch them. Who cares, they think, as long as the pattern keeps going somehow. Which is OK as far as it goes, I suppose, but it looks terrible.

Pattern 1 (P 1): 5 club 1 count (single spin)

Let's kick off with a pattern that's simple yet interesting and offers lots of scope for variations. And one that not everybody thinks they can already do easily.

2 jugglers throw 5 clubs,
A always throws across (cross throws)
B always throws straight ("tramlines"),
Every club is passed, i.e. all left and right throws are passes, not self-throws (1-count or "ultimate" passing)
Start:
A holds 2 clubs in the right hand, 1 club in the left,
B holds 1 club in the right hand, 1 club in the left
Both throw with the right hand first
A and B throw alternately: B throws exactly between A's throws.
The rhythm is perfectly even: throw, catch, throw, catch,...

This pattern is relatively easy to follow, so both partners have time to concentrate on everything: Am I getting the rhythm, the direction and the spin right? How is my throwing technique? Is my body posture OK? etc.
We've made a habit of starting our passing sessions with this pattern to get used to each other's styles. And it's a really good exercise for right-and-left passing (see P 6).

Note:
Be careful not to go too slow. You shouldn't have the feeling that there's a pause in the pattern. Try throwing flats (throws with no spins) - that will speed things up automatically.

P 2: 5 clubs 1 count (double spin)

The rhythm here is similar to the single-spin version (P 1), except that everything gets higher and slower.

The sequence is totally even: throw, pause,...
Everything else is as in P 1

This pause gives you time to do things like pirouettes and somersaults, or let someone else take over your clubs and your position...

P 3: 5 clubs 1 count (double spin, variation)

After you've been experimenting for a while, you'll probably notice that there are other ways of throwing doubles. One is to delay the throw, which feels like this:

Throw, pause, pause,...
Otherwise, everything stays as in P 1

Your own pass just about slips past the incoming club from your partner.
The two pauses can now be filled in with whatever moves you have time for (see above). However, the difficulty with this pattern is that you tend to fall back into P 2. To counteract this tendency, you can juggle a 2-club shower while waiting for your partner's pass to arrive: double pass, single self, hand across. The pass from your partner lands in the hand that does not catch the self. You could both do this at the same time, though at first it's probably better if you take it in turns. Important: practise the shower on both sides, not just one - the pattern is much easier if the juggling is continuous.
The pattern only works if both partners maintain the right rhythm. The partner throwing across should make sure that the throws don't fly like propellers, a typical mistake when passing diagonally (watch out for this on P 5 and P 6 too).
If you can keep the rhythm going without the mini-shower, you have time for other things. For example, you could do a couple of flourishes (twirling the club in your hand). The problem here is that to do a flourish you have to catch the pass with the club the other way up. In other words, the thumb of your catching hand should be pointing down and your elbow out to the side. The cross pass is easier to catch like this than the tramline pass.
Note:
If you throw at "normal" speed, the pass throws go much higher than a normal single pass or the self when you squeeze in the 2-club shower. To be precise, they should be the same height as the throws in 7 clubs 1 count.
Alternatively, one of the partners could throw singles and the other doubles. In this case, both partners start at the same time (more difficult).

Note on P 1, P 2 and P 3

These patterns are great for throwing "at random", meaning that you don't always have to stick to your role as a tramline or cross passer, but can choose to throw to your partner's "wrong" hand for a change. This is great fun, but both partners have to be wide awake.

P 4: 5 club 1 count box

Most people know the box pattern with balls: throw straight up on the right, simultaneously hand across from left to right, straight up on the left, simultaneously hand across from right to left.
Here is a 5-club passing pattern based on this technique:

Both partners throw straight ("tramlines")
A throws doubles, B throws singles
A juggles the box, B juggles in the same rhythm as in P 2
Start:
A: 2 clubs in the right hand, 1 in the left
B: 1 club in the right, 1 in the left
Start out of synch, i.e. B passes around the incoming club
A always hands the same club across between passes.

Notes:
B can incorporate a mini-shower or something similar (see Pattern 3). A's rhythm is too tight for that.
Both jugglers can throw to the same height if B starts a bit earlier than usual (but still later than A). In that case, both throw high singles or low doubles.
You don't have to throw tramlines: both can throw either always cross passes or always tramlines, but you can't mix, sometimes cross passes, sometimes tramlines.

P 5: 7 clubs 1 count

With this pattern it's particularly important to keep cool, juggle slowly and throw accurately.

2 jugglers with 7 clubs,
A throws every club straight (tramlines)
B throws every club across
Start:
A: 2 clubs in the right hand, 2 in the left,
B: 1 club in the right hand, 2 in the left
A and B both start with a throw from the right.

A typical problem with this pattern is that people try to throw "normal" singles. It is possible, but it's incredibly fast. If you prefer things to be more relaxed, try throwing the clubs at a height somewhere between double and single, i.e. roughly head height.
Reread the note on Patterns 2 and 3, and especially try Pattern 3 to get a feeling for the height. Take a look ahead to Pattern 6 too.

P 6 6 clubs, Pass Pass Self Variation

This 6-club pattern is an excellent exercise to prepare for 7 clubs 1 count.

2 jugglers pass 6 clubs
A always passes across, B always passes straight (tramlines)
Both throw in a pass pass self rhythm
A throws a passing box: pass, pass, hand across
Start:
A: 1 club in the right hand, 2 in the left
B: 1 club in the right hand, 2 in the left

To start with, A can pass doubles and B singles. The start sequence is then as follows: A goes pass, pass, hand across; B goes self, pass, pass. Both throw with the right hand first.
However, it's easier if both partners throw to the same height. A throws lower, B throws higher, both roughly to head height (see notes on Pattern 3). As B now has to start earlier, she might as well start with pass, pass, self with the left hand as soon as the first pass from A is in the air. The result is a calm passing pattern in which the passes go to exactly the same height as in 7 clubs 1 count, except that this time both partners do a self, which makes things easier to control.

Theory:

Some of you might want to point out that some of the patterns presented here cannot be true 1 counts - and you would be right. Even though we talk about 1 counts throughout, in fact we've been describing patterns that range from 1 count to 3 count, as you might have noticed when we varied Pattern 2 to make Pattern 3. The background: many of the patterns described here contain "throws" that are in fact pauses - the club is not released but held. Often you don't notice it while juggling, which is why a pattern appears to have fewer self-throws, or none at all. But if you know about the hidden (non-thrown) self, you can easily construct patterns in which, for example, one partner throws twice while the other throws 3 times.
Here's a quote from Charlie's book on the Seven Club One Count: This is a very unusual Passing Pattern - one of the very few in the Compendium of Club Juggling that uses half beats. All of the patterns presented here (except P 2) involve both partners throwing passes that can be the same height or they can be at different heights. In P 1 A passes a 2 and B passes a 3, or both passes are equivalent to 2.5. In all of the other patterns, one partner passes a 3 and the other a 4, or both pass a 3.5. To throw to the same height, one partner must throw slightly early - to be precise, one half-beat early.

Author: Wolfgang Westerboer
Credits: Kaskade 58

(Illustration from: Charlie Dancey's Compendium of Club Juggling, p. 90, "Golden Rules of Club Passing", by kind permission of the author.)

Usually when you juggle you throw alternately, first with the right hand, then with the left hand, or vice versa. Occasionally you might even throw with both hands simultaneously. There are not many patterns in which the same hand throws several times in succession. Yet those patterns can really add a touch of spice to your juggling. The term "hurries" has come to be generally accepted for these moves, for reasons which will become obvious when you first try them. After a while, though, you can learn to calm things down a bit. And for most hurries there is also a variation that involves both hands throwing alternately as usual. More about that in the Theory section, which also contains some notes on the site swaps. But let's begin with the practical side. I've described the tricks in considerable detail and drawn causal diagrams to make it easier for you to get into the patterns and the causal diagrams.
To enable the same hand to throw twice in succession, it has to catch two clubs in succession. In all of the patterns described in this series so far, that doesn't happen. Why not? Because both jugglers dutifully throw to the hand whose turn it is to catch next. But what if this order is broken? Take P7 from Part 2 of the series, for example: the 6 club 3-count. Most of you will have tried this out in the meantime. It helps a lot to use a different colour for the clubs that get passed to distinguish them from the self-clubs. It's always the same club that gets passed diagonally, and always the same club that gets passed straight.

P13 6 Club 3-Count, 1 Single Cross Pass

<3px 3* 3|3px 3* 3>

Here is a variation on that pattern: Juggler A passes with the right hand - but for the sake of devilment, she doesn't pass straight to B's left hand but diagonally to B's right hand. For A, nothing has changed so far, but B now has a problem. This shows up clearly in the causal diagram: the first pass from A (top line) goes from right to right and forces B to throw twice with his right hand - first a pass and then immediately afterwards a self. As a consequence, each juggler now throws with opposite hands: A left, B right, etc. The revenge for A's deed comes a few throws later, when she suddenly gets a club thrown back at her wrong hand (see Fig. 13)
If you're superstitious, you'll find the numbering of this trick highly appropriate: it just refuses to work, because both throw the following pass on the same side of the pattern, A with the left, B with the right, increasing the likelihood of collisions.

P14 6 Club 3-Count, 2 Single Cross Passes

<3p 3 3 3px 3 3 3px 3* 3|3p 3 3 3p 3* 3 3p 3 3>

To make life easier for both of you, A decides to throw another diagonal pass, this time left to left. That gets you back into the normal 3-count.
As you can see from the causal diagram, the Hurries are equally divided between the two jugglers after the two passes: the first is B's problem, the second is A's. After that, both can throw in the normal 3-count pattern. This ends our first (successful?) expedition to the world of the Hurries.

P15 Jim's 3-Count

<3px 3 3 3px 3* 3 | 3p 3* 3 3p 3 3>

This is surely the most famous pattern of the outgoing 20th century. It is nothing other than P14, but without a break. This is a real right-left pattern with Hurries for both. Try it, it's really not as difficult as you think. (The other day we managed it during a "right-left passing for beginners" workshop.)
After the first diagonal pass from A the passes are always thrown twice in succession from the same hand, i.e.: right pass, left pass, left pass, right pass. Of course, there are also a number selfs in between, but they would only have got in the way if I'd included them here.
The diagram (Fig. 15) shows only the first half of the pattern. As the hands are swapped around at the end of P14, the second part of the pattern is simply a mirror image of the first half.

P16 6 Club 3-Count, 2 Single Cross Passes

<3px 3 3 3p 3 3 | 3p 3* 3 3px 3* 3>

Another way of getting out of the problem you've created for yourselfs in P13: A and B always pass diagonally in alternation. Then all the Hurries are at B's end. A passes with both hands to B's right hand. B only passes with his right hand, alternating between straight and diagonal throws.

P17 6 Club 3-Count, Self Double Hurry

<4x* 2* 3px | 3 3 3p>

This is another pattern in which one juggler is lumbered with all the Hurries. B "forces himself" to throw a Hurry (unlike P13, in which it was A who forced her partner into the Hurry). B begins with a double from the right, immediately after a pass. Doubles normally go to the same hand, but he throws this one to his left hand, causing the problem for himself - in a few moments this club is going to land in his wrong hand. Before that happens, B simply waits. In the causal diagram you'll notice that the arrow from the left hand points back to the same hand, which simply means: keep hold of the club. But then the double from the right has to be caught - with the left hand. And that is also where the pass from A is about to land. So B has to empty that left hand as quickly as possible. He can't pass straight ahead (because the pass from A is winging its way in, see P13), so he has to pass diagonally (see P14). Again, this pattern can be repeated continually without a break.

P18 7 Club 3-Count, Diagonal

<4p 3 3 4p 3* 3 4p 3 3| 3 5px 3 3 5px 3 3 5px 3*>

In the normal 7-club 3-count one juggler passes straight and the other passes diagonally. However, now B, who should be passing straight, decides to throw all passes diagonally. This naturally creates Hurries, which are equally distributed between the two partners. Even so, the pattern is somewhat unbalanced in the sense that one hand passes more often than the other. Which hand does more passing depends, of course, on how you start. What better way of exercising your weaker hand? As in P15, the causal diagram shows only the first half of the pattern.

Notes on the diagrams:
In part 2 of this workshop series the causal diagrams did not indicate which hand is throwing. This is now essential, however, whereas there is no longer any need to indicate whether a throw is a single, a double, or a whateverelse - that naturally follows from the length of the arrow (see part 2, A Causal Puzzle).
Following Martin Frost's suggestion (in Jugglers World, Summer 1994) I have marked the Hurries with an asterisk *.

Theory:

Mathematicians reading this article will probably have torn out all their hair by now. Each of the so-called site swaps contains a few special characters to denote whether the same hand throws again (indicated by *) or whether a pass should be diagonal instead of straight (x). This doesn't have much to do with the good old site swap notation in its classic form. Instead, I have noted down what you think you're throwing. I'd be happy to answer any questions on this subject by e-mail (see address at the end of this article). If enough readers would be interested, I could go into the background in more detail in the next Kaskade.

For many Hurries there are variations which do without Hurries. You simply insert a hold (a 2 in site swap) between the Hurries and adjust the length of the other throws accordingly. Thus, a Hurry with the right hand disappears in a hold with the left and a throw from the right. As a consequence, diagonal passes have even site swap numbers. Take a look at P15. A throws diagonally, her passes are therefore 4p; B throws straight, which is 3p. If the holds are now inserted and the Hurries removed, the pattern becomes:
<4p 3 3 4p 2 3 3 | 3p 2 3 3 3p 3 3>
To ensure that both partners throw to the same height, A delays her throws by half a beat (see part 1 of this workshop series), and both pass to a height of 3.5. This pattern is only half as much fun, though, because the Hurries are missing.
Here's a question to wrestle over: In which of the patterns can you not get rid of the Hurry using this method?

On the Causal Puzzle:

Lay the pattern onto the basic puzzle framework you kept from part 2 of this workshop. Note in pencil which hand is throwing. I'm not going to recommend using a ball-point pen because I don't get a cut from the sales of Kaskade or the revenues of your copy shop.

References:
Charley Dancey, Compendium of Club Juggling, ISBN 1898591 14 8
Jugglers World, Summer 1994
Jugglers World, Fall 1997

Author: Wolfgang Westerboer
Credits: Kaskade 59

The illustrations are taken from Charlie Dancey's Compendium of Club Juggling, p. 187, by kind permission of the author.

So far this workshop series has covered passing patterns for two jugglers only. Now it's time to add some variety by looking at patterns involving more than two. More people mean more choices of where to pass to.
This article is divided into two parts. First of all, I list the most common formations for deciding who passes to whom, and where to stand. To keep it simple, these descriptions all involve 3 people juggling a total of 9 clubs.
The second part gives an overview of various patterns using these basic formations. As always, there's a causal diagram to go with each pattern.

1. Formations

If there's a feeder (see below), that juggler's throws are always noted in the middle line. In the diagrams, the feeder is always juggler B. The person who dictates the rhythm is printed bolder in the diagrams, causals and siteswaps.

Feed

The classic pattern for 3 jugglers is the Feed. In a feed, one juggler, the feeder, distributes passes to 2 partners, the feedees, whereas both feedees pass only to the feeder. As a rule, that means that the feeder passes twice as often as the feedees. As the feedees cannot see each other, their best bet for keeping the rhythm is to keep pace with the feeder. The typical feeding configuration is shown in Figure 1.

Triangle

See Figure 2. In contrast to the feed, all the jugglers in a Triangle pass at the same time, e.g. they could all throw to the partner on their right, along the "outside lane" of the triangle. Or they could pass "inside" to the partner on the left (this feels very confusing at first, because somebody else's clubs suddenly pop up in front of your nose). Or they could alternate right and left - ouch! The pattern starts with everyone doing the old "up-down-pass" ritual in synch. What makes triangles a bit tricky is that you receive a club from one side while you're passing to the other side. I've trained myself to look first in the direction of the incoming club and then to look where my own pass went. Maybe then at least next time I can manage not to throw straight at my partner's head. If you're doing a 3-count in a triangle, the clubs that are passed always stay on the same path: a club passed on the outside always comes back on the same outside lane.

Line

Looking at Figure 3, you might get the impression that the Line isn't much different from a triangle. And indeed, the jugglers have "only" positioned themselfs differently. But it's not quite that simple. The juggler in the middle finds it very hard to catch passes from the partner standing behind - trying can be painful, but succeeding looks great! The juggler in the middle passes blind, throwing the clubs back over his shoulder. The partner at the back has to tell the one in the middle where to throw to. Whether the club goes over to the left or the right of the middle juggler's head is almost irrelevant - it's primarily a matter of taste. A nice variation is where the middle juggler turns round to pass to the other partner - but it's not easy and has to be announced in advance as both of the other jugglers have to adjust their passes accordingly. Again, the juggler who dictates the rhythm is printed bold.

More

The other day at a convention, somewhat spaced out after the usual nocturnal, insomniactivities, I was wandering around the gym at 12 in the morning when a thought came to me: Why do jugglers always throw clubs, but clubs never throw jugglers? Here's an idea: how about a passing sequence in which you switch from one formation to another, without stopping of course. A few throws in the feed position, then into a triangle, then transition to a line, then back to a triangle, then you all throw one club high, carry the others to your partner's position and catch the club that your partner threw. In other words, passing jugglers instead of clubs. Alternatively, you could put the clubs on the floor and swap places, or carry them and hand them over to a partner on the way to your new position. There are some simple patterns involving jugglers moving around and changing places while passing - and also some hellishly complex patterns. There isn't the space to describe them here - instead, I suggest you check them out at your next convention.

2. The Patterns

I'll confine my descriptions to feeds and triangles, leaving out the line (only because of lack of space). For a detailed descriptions of lines, see Charlie Dancey's Compendium of Club Juggling.

P19: 9 Club Feed 2-count / 4-count, <3:2 3 3 3| 3:1 3 3:3 3|3 3 3:2 3 >

This is the best known feeding pattern. The feeder passes a 2-count, the feedees pass 4-count. All start at the same time. The feeder (B) and juggler A begin with a pass, C begins with a self.
As the feedees have quite a lot of spare time between passes, they can rescue the pattern if they see that the feeder is in trouble. If he's not in trouble, they can get him into trouble by doing chops or triples (instead of the right self). How about one feedee doing only chops, the other doing only triples?!

P20: 10 Club Feed 2-count / 4-count, < 3 4:1 3 3 | 4:1 3 4:3 3|3 3 3 4:2 >

Again, all start at the same time. However, in contrast to P19 the feedees start with a self from the left hand. All passes are thrown as doubles. The feeder throws a "normal" 7 club 2-count, but as a feed, passing first to A, then to C, etc. The feedees pass whenever they see the feeder's pass in mid-air coming towards them - in other words, they respond to the feeder's pass. Remember, the feedees pass doubles too.
A common problem with this pattern is that the passes from the feeder to the left feedee (from B's point of view) collide with the incoming passes from the right feedee. This is simply due to limited airspace. If the right feedee throws a bit higher than usual, the feeder has room to throw his passes underneath. The title illustration shows what it can look like.

P21: 9 Club Feed - Pass Pass Self / 3-count, <3:2 3 3 | 3:1 3:3 3 | 3:3 3:2 3 >

The feedees juggle a waltz, the feeder does a pass-pass-self rhythm. The jugglers always pass simultaneously: the feeder receives a club from the feedee he's just passing to. It helps to remember that the clubs are passed back to the juggler who passed them to you. For the feedees, the pattern is pretty simple, but the feeder has his work cut out for him. Many feeders find it easier to start with the feedee on the right. He then throws: outside (pass right), outside (pass left), self (right), inside (pass left), inside (pass right), self (left). At the beginning the clubs seem to come fairly chaotically (and painfully) from all directions, raining down on the poor feeder. After a while, though, you get a feel for what's going on. It helps to juggle slowly and pass with long swinging movements.

P22: 9 Club Triangle 3-count, <3:3 3 3 3:2 3 3|3:1 3 3 3:3 3 3 |3:2 3 3 3:1 3 3>

As mentioned above, the triangle is often thrown as a 3-count. All the passes go alternately to the right partner then to the left partner. Consequently, each juggler passes to both of the others. To put it another way, all three of you are feeders! If you start with the right partner, the sequence is: outside (pass right), self, self, outside (pass left), self, self. Note that you pass in one direction and receive from the other. You can't see both clubs at the same time, so take care of yourself and your partners. For a change you could also try passing only to your right (or only to your left) partner.

P23: 9 Club Triangle - Pass Pass Self, <3:2 3:3 3|3:1 3 3:3|3 3:1 3:2 >

Now we're getting down to business! This pattern is a mixture of P21 and P22: each juggler is feeding a pass-pass-self. Note that each of the jugglers has a different rhythm: one goes pass-pass-self, one goes pass-self-pass, and one goes self-pass-pass. Theoretically you could all throw outside, outside, self, inside, inside, self. But then the passes can easily collide. Don't be put off by the diagram. The pattern looks complex, but it isn't really all that difficult.

Theory

The theoretical part of our workshop this time is fairly concrete - it's about a feeding pattern and a problem. Let's start with the pattern.
Imagine you're doing P19 when along comes a fourth juggler (D) who wants to join in. No problem - you reposition yourselfs as shown in Figure 4.
B and C feed - B with C and A, C with B and D. A and D do a 4-count. You soon get the hang of it. It's easiest if the two feeders start with the pass they throw to each other, and then pass to their respective feedees: B passes first to C, then to A; C passes first to B, then to D.
Now the problem - again a feeding pattern: The basic pattern is P20, the 10-club feed, and along comes juggler D again. He grabs three clubs and you position yourself as described above. B and C start, but this time B starts with a pass and C with a self (see description of P20). It works OK for about three throws, then D starts complaining that something's going wrong. A doesn't agree. As far as she's concerned, everything's fine.
In situations like this, D usually gets told to stop moaning - it's his fault, he must be doing something wrong. After all, if A can do it, why can't D? After a lot of arguing and more failed attempts, you decide to switch positions, and now you discover that whoever stands in D's position has a genuine problem. If D juggles the normal 10-club feedee rhythm, the pattern simply cannot work.
What's wrong?
In a 10-club feed, the feeder always passes first, and the feedee always responds with a pass of her own (see P20). You can't simply turn things around and have the feeder responding to the passes of the feedees, as passes and selfs would then collide. Or, to be more precise: It is possible, but the feedees have to change their rhythm. More on that later.
When D joins the group, he passes to C, one of B's feedees. We've just established, however, that C responds to B's passes, i.e. C passes later than B. In order for D to fit into the pattern, he has to pass in such a way that C can respond to his passes too, i.e. D always has to pass before C. That can't be done with a normal 4-count, so D has to "overtake" C.
Here's how he does it. B sets the rhythm and starts with a pass to C; D starts in with a pass to C at the same time as B throws his first pass to A. Then... D waits. He simply holds two clubs until the moment when he has to empty his left hand to catch the incoming pass from C. To do so, he throws a left self and then a pass to C. (See Charlie Dancey, p. 33: "Double Return".) That takes quite a long time - if he gets bored, he could do a 2-club shower instead: left self, right hand-across, left self, right pass. This gives D's pattern a clear rhythm (see Part 1 of this workshop series in Kaskade 56). It's a pity that D can't start the pattern with all the others, but has to wait, as described above. Here's the siteswap for this one:
< 3 3 3 4:2| 4:3 3 4:1 3 | 3 4:2 3 4:4| 1 3 4:3 3 >
Back to the pattern I promised you, in which the feedees pass ahead of the feeder. After what I've just described, it's quite easy: Take 9 (!) clubs. Both feedees throw a Double Return, the feeder responds to the incoming passes. <1 3 4:2 3 | 3 4:3 3 4:1| 4:2 3 1 3 >
And to finish off, here is the same thing for 2 jugglers: both pass 4-count, with double spins. B throws a "normal" 4-count, A overtakes him with a 2-club shower. < 4:2 3 1 3| 3 4:1 3 3>
It only remains to mention that instead of handing the club across, you could also throw it as a triple (substitute a 5 for the 1 in the siteswaps). For each substitution, add one club.

References:
Charley Dancey, Compendium of Club Juggling, ISBN 1898591 14 8
Check out the rec.juggling discussion forum. The participants often discuss new patterns and ideas. Go to conventions. Meet other jugglers. Have fun. ;-)

Author: Wolfgang Westerboer
Credits: Kaskade 60

The illustrations are taken from Charlie Dancey's Compendium of Club Juggling, p. 187, by kind permission of the author.

This time we're going to take another look at feeds patterns that involve more than 2 jugglers. Don't know what I'm talking about? Then take another look at the last issue of Kaskade.
Last time I mentioned the possibility of combining passing with moving around. It's especially easy to do that while feeding: two of the partners keep the juggle going, while the third gathers in his clubs, runs to his new position and re-joins the pattern from there. He could also continue juggling as he runs it's all a question of keeping up the rhythm.
But whether juggling or not, you should still be counting as you move to a new position. Otherwise you might be in for a nasty surprise, as the title of this workshop suggests in some patterns you'll be walking right through the line of flying clubs, so please be careful! Reading this article is fairly safe, but actually juggling the patterns is not. I, for my part, am not taking any responsibility for injuries sustained while trying them out.
This time I'm going to stick to the 2-count variants of the patterns. If you prefer to throw with both hands, you can try the patterns with a left 2-count. I'll save runarounds with combined left and right passes for later editions.

R1: Runaround 1 6 clubs, 2-count, singles

Let's start with something easy. A, B and C are standing in the positions shown in Fig. 1 a-c.
A and B are passing 6 clubs in a 2-count rhythm. C already raises his open left hand that will make things easier for B in a few moments.
Without advance warning, B now starts passing to C. As C is already holding up his catching hand, B can see exactly where she has to throw to. A continues throwing to B, which means that after a while, A no longer has any clubs, and B and C are passing together.
When everyone has calmed down again, A can move to the position shown in Fig. 1b, next to B. C turns slightly so that he's looking at A, and the 2nd round can begin. Try the pattern in all positions. I've shown the first 3 positions in Fig. 1. After that the pattern repeats itself, except that you're standing in slightly different places.

R2: Runaround 2 6 clubs 2-count, singles

Try to keep the pattern going without a break: you never pass back to the partner you received from, but always to the third juggler. At the beginning that means: as soon as A has passed his last club to B he runs to his new position. Just before he gets there he receives his first club from C, for whom the rule also applies: never throw back to B.
While running, always keep your eye on the pattern. You move around anti-clockwise, while the pattern rotates clockwise. Don't rush and panic. You have two whole beats with nothing in your hands. And if you already take your first step as you're passing your last club, and take your last step (backwards) as you catch your first club from the other partner, you'll find you have plenty of time.
The idea is not to first get to the new position and only then turn round. If you do that, you'll probably have to catch the pass with your teeth. Running and turning is all one movement.

R3: Runaround 3 7 clubs 2-count, singles

To add some spice to the proceedings, you can add an extra club. At the start, B has 3 clubs, A has 3 clubs, and C already has 1 club. Each of you will always throw to the same partner: B always to C, A always to B, C always to A.
A and B start together. As C already has one club, he starts to throw to A's new position one beat earlier than in R2. Take your time, throw slowly, calm the pattern down. It won't work if you get hectic. I've drawn you a causal diagram for the pattern. The diagram shows you that there's enough time to pass and run across it's not necessary to carry the extra club across, though you can if you want to. When you only have one club remaining in your left hand, you go across, handing it from left to right as you go. That slows the pattern down and makes it easier.

Variations:

More clubs: R1 and R2 can also be done with more than 6 clubs. Using 7 clubs, the rhythm is alternating and you pass doubles, as in a normal 2-person 7-club pattern. The same can also be done with 8 clubs, and it's easier than you might think.
Fewer clubs: The fewer clubs you use, the easier the juggling. The main difficulty here is not to lose the rhythm. Take a look on the Internet. I've written the basic patterns for 3-7 clubs and 3 jugglers for JoePass! (but only the pattern with 7 clubs contains a description of the movement).
Other patterns, more jugglers: This is the subject of a separate section.

R4: Runround 2 6 clubs 2-count, singles

Runaround the other way around. Instead of running to the right of the pattern to stand at your opposite number's left side, the idea is now to stand on his/her right. Of course, you could run all the way around both partners. But it's more exciting to go straight through the middle. At first sight, you might think that this is not so very different from R2, but you'd be wrong. As you have to run through the pattern, you have to pay very close attention to the passing rhythm, otherwise it could hurt.
When only one juggler is running, you don't move around in a circle, as in R1 R3, but move sideways along a straight line (Fig. 2). Alternatively, when your partner has just run away, you could step across into his/her vacated position, in which case the pattern rotates on the spot (Fig. 3). This is more suitable for conventions and other places where space is limited.
As A makes his last pass, he gets ready to run, waits until B and C have passed, then goes through the pattern, turning so that he backs into his new position while receiving from C. The interesting thing is that instead of passing to the person on the right of the pair standing opposite you, you now pass to the person on the left. That means that the flight paths of the passes now cross each other, and there is a danger of mid-air collisions. For this reason, the passers should not pass at the same heights. We have made it a rule that the passes to the juggler who's just arrived at a new position fly slightly higher and are therefore in the air slightly longer. In Figs. 2b and 3b that means: C passes slightly higher than B.

R5: Shooting Star:

Find yourselfs another juggler and a total of 9 clubs. Imagine (or draw) a pentagon on the floor. A juggler is now standing at 4 of the 5 corners of the pentagon, leaving one corner empty (Fig. 4).
The rules are the same as before: When you have no more clubs, you run. But in a curve to the left, as in R4, not to the right, as in R1-3. Yes, you go through the pattern.
When you only have one club left, start to move with the pass. You have to go into the middle of the pattern before the pass from your left neighbour. Now three clubs fly around you (you hope!) in all different directions.
The first time you try this, you should interrupt the move at this point. The others should stop passing. When everyone has calmed down again, you can try the full sequence. Start as before, but this time don't stop in the middle, continue forward as soon as the clubs have gone past. This should be a fluid movement, and not too fast. If you go too fast, you just run right into the passes. So please, BE CAREFUL!
You can do the Shooting Star with one extra club. That makes it slightly faster, and you begin to understand where the name came from.

Author: Wolfgang Westerboer / Christian Holl?nder
Credits: Kaskade 57

(Illustration from: Charlie Dancey's Compendium of Club Juggling, p. 90, "Golden Rules of Club Passing", by kind permission of the author.)

This time we present the basic pattern of left-right passing: the 3-count. In this pattern, every third throw is a pass, followed by two selfs. The passes come from the left and right hand alternately. Passing with both hands is a lot of fun, and can help you to improve your posture and your juggling in general.

Passing Pattern 7 (P7)

6 Club 3-Count Singles Siteswap: <3p 3 3|3p 3 3>

This is a relatively simple pattern that leaves lots of scope for variations. There are enough self-throws to allow you to incorporate solo tricks, and enough passes for both partners to practise passing tricks.
2 jugglers throw 6 clubs, A and B both throw straight. Every third club is passed: Pass, Self, Self, Pass, Self, Self... Look at the illustration. The white part in the middle represents the repeating pattern.
Start:
A holds 2 clubs in the right hand, 1 club in the left
B holds 2 clubs in the right, 1 club in the left
Both A and B start at the same time with a right-hand pass
(Grafik Muster 7)

Passing with the left hand will feel strange to start with, but don't worry, you'll soon get used to it. Even so, for most people it takes time and practice before they're able to pass as accurately with their left hand as they do with their right. At the beginning it helps to make a conscious effort to pass from the inside to the outside.

441 Variations

441 variations are all based on a pattern that you're probably familiar with from solo juggling: after throwing 2 doubles (D), you hand (or "feed") one across (F). Try it out. Notice that the pattern alternates from side to side: the first cycle starts with the right hand, the second with the left, etc.
Start for P8 to P11:
As in P7 or
straight out of an ongoing 3-count
In the following descriptions the "normal" passing beat is underlined. That should make it easier to get into the following patterns, starting from the basic P7.
Two basic principles that apply to all throws:
Singles (S) are thrown to the other hand, i.e. from right to left or from left to right. Doubles (D) go to the same hand, i.e. from right to right or from left to left.
Single passes (SP) are thrown straight, from right to left or from left to right. Double passes (DP) go diagonally, from right to right or from left to left.
That might sound trivial, but it's an important point - regardless of whether you're throwing a self or a pass: singles go to the other hand, doubles to the same hand.

P8 6 Club 3-Count 441 <4 4p 1|3 3 3p>

Underneath the incoming pass you throw a double, followed by a diagonal double pass to your partner, then hand the remaining club across, the "feed" (F). Now you can either repeat the same pattern on the other side or go back to the normal 3-count pattern. A quote from Charley Dancey on the feed (p. 21): "...this produced a causal arrow moving one beat to the left. It seems illogical but it actually means: to place a club into the hand you had to empty it first."
(Grafik Muster 8)

P9 6 Club 3-Count 441 <4p 4 1|3 3p 3>

A throws the double self not underneath the incoming pass but at the same time as B throws her pass. Just before that, A has thrown a double pass to B. The double self is followed by the feed. At the beginning you'll probably find it quite difficult to keep P8 and P9 apart - especially when you're trying to juggle them.
(Grafik Muster 9)

P10 6 Club 3-Count 441 <4p 3 3|3p 4 1>

With this variation the 4 4 1 combination is divided between the two jugglers. Juggler A passes a double instead of the usual single. B could now simply hold on to one club for a moment (H) and throw a self with the other hand, but of course that would be a dead boring thing to do. Instead, she can throw a double and feed a club across. It's great fun: you have to really watch for the moment when your partner throws the double pass and then immediately throw the double and do the feed.
(Grafik Muster 10)

Notes on P8 - P10:

A and B should take it turns to practise P8 - P10. If both of you try to throw these patterns simultaneously, the clubs are likely to collide. If you throw P8 - P10 solid, i.e. without reverting to the normal pattern in between cycles, you can also throw the passes as high singles. The selfs stay as normal singles and doubles. (See the Theory section in Part 1 of this workshop series.)

Try P8 to P11 in permanent alternation:
P8.1: <4 4p 1 3 3 3p | 3 3 3p 4 4p 1 > P9.1: <4p 4 1 3 3p 3 | 3 3p 3 4p 4 1 >
P10.1: <4p 3 3 3p 4 1 | 3p 4 1 4p 3 3> P11.1: <4p 3 1 3 4p 3| 3 4p 3 4p 3 1

P11 6 Club 3-Count 441 <4p 3 1| 3 4p 3>

Here's a mean trick to round off this series: A throws a double pass, as in P9. However, B does not respond in the "normal" way, i.e. with a single pass, but instead goes straight into P10 and throws a double pass too. A can now throw a single rather than a double, followed by a feed, and the pattern is rescued. Alternatively, A could pause for 2 beats, holding onto his clubs.
(Grafik Muster 11)

P12 7 Club 5-Count <3p 3 3 4 4 | 4 4 4 3p 3>

We've chosen a really smart pattern to finish with: the 5-count with 7 clubs. This is likely to make life slightly difficult even for experienced passers.
Start:
A: 2 clubs in the right hand, 2 in the left
B: 2 clubs in the right hand, 1 in the left
(Grafik Muster 12)


As with the 3-count, the second cycle starts with a throw from the other hand. The difficult thing about this pattern is not so much the passes, although at the beginning you'll probably tend to throw them too high. No, it's the double selfs that cause the real headaches. Make sure that you're throwing the doubles to roughly the same height as your partner, otherwise you'll lose the rhythm. And don't throw the doubles too low or you'll get more mid-air collisions.

Here are a few more variations on the 7 Club 5-Count (roughly in increasing order of difficulty):
<6p 3 3 3 3|3 3 3 5p 3> <3p 3 3 4 4|4 4 4p 3 3> <4p 3 5p 3 3|3 4p 3 3 4p>
<4p 3 4p 3 3p|3 4p 3 4p 4p> <4p 4p 4p 4p 3 | 3 3p 3p 3p 4p >

And if you still haven't had enough, you can try to throw all of these variations in succession without a break in between.

A Causal Jigsaw:

Don't be put off by the amount of text that follows. This section contains more patterns than the whole of the rest of this workshop article - you just have to piece them together for yourselfs.

Causal Diagrams were developed in the early 90s by Martin Frost. In the summer 1994 issue of Jugglers World he wrote:
"Each arrow represents a throw. This causal notation not only displays the sequence of throws that each juggler has to execute in a pattern, but it shows which clubs force other clubs to be thrown."
Our thanks to Martin for having this idea and allowing us to use it in this workshop.

Causal Diagrams make it easy to write down and read juggling patterns.
The pattern is read from left to right. Each throw is represented by an arrow.
The hands always throw alternately, starting with the right (for now!)
The length of the arrow tells us how long a club is in the air, and also how many times the club spins - under normal circumstances. The spin is indicated by a letter: S = single, D = double, H = hold. (There's nothing to stop you putting lots of wrist into a single to make it a triple. But please warn your partner before you try it.)
First, take another look at the diagrams in the first part of this workshop.

Now, here comes the puzzle which you can use to build simple passing patterns for 2 jugglers and 6 clubs. The basic pattern (grey background) consists of two jugglers each throwing singles on their own. In other words, both of them are juggling a cascade.
If you now lay the jigsaw pieces onto the base plan, you automatically get a passing pattern.

(Grafik Puzzle)

How about a 6-club 5-count, i.e. a 6 club pattern with cycles that are 5 throws long? Or a 3-count in which one of you passes only doubles and the other only singles? Oh yes, and don't forget to actually juggle the patterns you've made! I hope you enjoy playing with this.
Don't throw the plan away - you're going to need it again later on.

Author: Christophe Pr?chac

Many passing patterns are symmetric : 4 ct, Waltz, ultimate, triangles, ... . 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, therefore 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 themselfs.

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, selfs 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 "ultimate" 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 3p 4p>).

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:

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] . selfs 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:

Now, swap all passes! I.e. have everyone throw selfs 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:

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 ultimate with passes to the next.

- { j(1) = 2 , 3 } --> 3.66p2 : 11 ultimate with passes the other way round.

- What about ultimate 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 ultimate < 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:

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

Author: Christophe Pr?chac

Notes : For clarity, in the causal diagrams below, short and long holds 1x and 2 are not depicted

In all causal diagrams, the causal chains may be distinguished from each other by their different colors. This allows us to represent passing patterns where the jugglers make sync throws: follow the colored paths to understand which hands throw to which.

7 clubs 3 count in doubles

7 clubs 3 count in singles

10 technofeed

8 technofeed

6+1 ultimate

This pattern is based on 6 sync ultimate. The rest beats of the base pattern offer room to add a seventh club which is passed diagonally to avoid collisions. The version below is way easier for the second passer but it is possible to change roles on the fly.

5+2 ultimate

7 sync shower

7 PPS

7 PPS in singles!

Mild madness

PPHSPPS

Martin's ultimate

PPPPH

10-1 ultimate

For ball bouncers only!

Author: Christophe Pr?chac

1. Introduction

Multi-hand notation

Multi-hand notation has been developed by Ed Carstens for use with his juggling program JugglePro. It is an analytical notation system that extends the siteswap construction to an arbitrary number of hands and to an arbitrary juggling rhythm.

Once the juggling hands are allowed to throw at any given beat, one can describe transitions between async patterns and sync patterns or even more bizarre rhythms. Note that in the original mhn system no attention is paid to catching beats, only throwing beats are taken into account.

Multi hand notation, much like standard siteswap notation, is useful both to provide short descriptions of patterns and to simulate them on juggling softwares.

Causal diagrams

Causal diagrams were invented by Martin Frost. They offer appealing geometric pictures of juggling patterns, particularly passing patterns.
Let f denote the permutation on (a subset of) HxZ defining a juggling pattern, where H is the set of hands and Z is the set of integers. Then, essentially, the causal diagram of the pattern is the ladder diagram of f-2 (that is: f translated 2 beats in the past).

Now, why is this mapping f-2 so interesting?
While the original permutation describes the paths in HxZ of the objects juggled, the new one f-2 describes the paths, or the timetable, of the problems encountered by the jugglers, which is often all we are interested in: we do not care which clubs we juggle, we merely want to sustain the pattern as a whole.

This construction works fine both for async patterns and sync patterns. It needs to be adapted however in order to allow for more general patterns: transitions between different rhythms, galloped patterns, etc ...

Causal diagrams are often much easier to use than siteswap/mhn descriptions when one tries to work out syncopations in passing patterns. They are also a powerful tool to discover (i.e., most often, rediscover :)) new patterns.

This page

In this page and its complement, the hurries page, the mhn system and the causal diagram construction are adapted so as to obtain a complete correspondence beween the two notation systems.

The main novelty in the mhn system used here is that it explicitely takes into account the "catching beats", henceforth refered to as dwell beats.

The causal diagram construction is also slightly modified: this concerns essentially the representation of an empty hand 0 and a short hold 1x .

2. Relaxed juggling

Common juggling wisdom as well as practise suggest that in normal situations, the same hand cannot throw twice in a row (unless hurried throws are allowed). Between two throwing beats, there must be one beat where the hand catches a new object and prepares for the next throw.

Let s be the siteswap value of a throw, s >= 2 , s tells us how many beats in the future the object will be rethrown (or maybe held further for a while), it does not tell us however how many beats the object spends in the air.
The usual implicit assumption is that the airtime value will lie somewhere strictly between s-2 and s , depending on the style of the juggler, or in technical terms on his choice of dwell ratio.

Here we will adopt a "relaxed" style of juggling, assuming an airtime value strictly less than s-1 which means that once an object is caught, it will spend at least one beat in the hand before being rethrown. This assumption is necessary if we want to allow the possibility to violate it later in the hurries page! Anyway, in this page it will be maintained throughout:

Assumption

To a throw of siteswap value s corresponds an airtime value
strictly less than s-1

After an object has landed, it will be prepared for the next throw:

Definition

For an object thrown with siteswap value s , the juggling action that takes place in the target hand s-1 beats later, i.e. one beat before it is rethrown, is refered to as a dwell hold

Exceptions for some "small throws":

The "relaxed juggling" assumption does not apply when s=0 - an empty hand - or s=1x - a short hold. There will be no corresponding dwell hold.

When s=2 - a "throw" usually interpreted as a long hold - it does apply if this 2 is indeed thrown.

When s=1 - a fast handacross - the relaxed juggling assumption is difficult to meet: the club should land in the past! We will maintain it however, obviously an idealization, and the dwell hold takes place immediately in the target hand.

3. Notations

Throws are denoted as in JoePass!
However, for "inactive" hands, it is essential to differentiate between the two following cases:

The hand is empty.
The hand has just caught an object and is doing a dwell hold.

Note that this distinction makes no sense in the original mhn system since both cases correspond to an absence of throw and pure mhn, as well as genuine siteswap theory, only cares about throws.

For a given hand, a dwell hold will be denoted by a dash: - .

4. Causal arrows

For an object thrown at beat t with a siteswap value s>=2 , landing will occur between beats t+s-2 and t+s-1 , according to the previous assumption. Therefore the target hand must empty itself or be already empty s-2 beats in the future.
Hence the causal arrow representing the throw will be of length s-2 .
In particular, a 2 throw will be depicted by a closed loop and a 2x throw by a vertical arrow.

A fast handacross 1 requires the target hand to be ready for catch immediately, i.e., it must have emptied itself previously. Hence a 1 beat crossing backwards arrow.

A short hold 1x is a problem only for this very hand that is currently doing the short hold. We will depict this by a big point.

An empty hand 0 can only occur if this hand has thrown or was already empty one beat before. Hence a 1 beat horizontal backwards arrow.

A dwell hold - is not really a throw. It will not be depicted

Actually, short holds 1x and long holds 2 do not really need to be depicted. They offer no additional information to reconstruct a mhn pattern from a causal diagram (unless one wants to emphasize if a 2 is thrown or held). For clarity, and particularly in passing patterns, they will often not be depicted.

5. Summary of assumptions and notations

• is empty
• "dwell holds" an object that has just been caught
• "holds" an object
• throws an object

6. Examples

Solo juggling

1

slow 1

1x1

async to sync shower

51 to (2x,4x)

sync to async shower

(2x,4x) to 51

3 cascade at height 5

1x5

3 shower to high 3 switch

5151 5x1 51x51x...

2 at height 3!

3x1x

4x throw

4x flash

from 4 sync to 4 async

from 4 async to 4 sync

Passing patterns

3 ultimate

There is only one backwards going causal chain. Passes are drawn in red for emphasis.
See the oddpatterns page for more interesting passing patterns where the jugglers throw sync throws.

4 ultimate

With flat vertical passes as in Marc and Benji's beautiful number.

5 ultimate, 2 beats version

(holds are not represented)

Gandini's patterns from hell

Take any symmetric passing pattern where the jugglers throw singles in phase and choose any number k (preferably prime with the period of the pattern). Then replace every kth single by a double.

E.g. PPS with k=5:

A 36 beats cycle! Hopefully, the causal is of no particular interest :)

Kickups

Kickups may be seen as particular cases of multiplex throws. The analysis developed in this page extends easily to multiplex patterns. I skip however a formal mhn description of the patterns for simplicity. Also, in the causal diagrams below, I omit the backwards going arrows that indicate that the foot is empty after the kickup.

6 to 7 Shower

J2 throws a straight double pass on his pass beat, this is a signal for J1 to switch into the 7 clubs version of the pattern.

6 to 7 Waltz

J2 throws a straight double pass (of siteswap value 4.5) on his pass beat, thus signalling to J1 to switch into the 7 clubs PSS pattern with double passes.

6 to 7 PPS

J2 throws crossing double passes on his pass beats, this again is a signal for J1 to start doing his part of the 7 clubs version of the pattern.

Author: Christophe Pr?chac

1. Introduction

The concept of hurry was first developed by Martin Frost in an excellent article of the Fall '97 issue of Juggler's World.
More recent treatments of the subject, with special emphasis on 3 count passing, were given by Isaac Orr in Juggle, 2000 and Wolfgang Westerboer in Kaskade, 2000.

Here, all 3 clubs are thrown at single height. Two clubs are always thrown to the same hand the remaining club crosses back and forth. The crossing club, although thrown at height 3 , is always rethrown after 2 beats, the non-crossing clubs however are thrown every 4 beats.

2. A new definition

We feel that the traditional definition is a little bit unprecise, for instance the following pattern

is not a hurried pattern although it follows the hand pattern RRLL. Here, 3 clubs are juggled at height 5, on triples if you wish, but they are rethrown every 6 beats, making the pattern very relaxed indeed.

Moreover, one may encounter hurries even under the regular RL hand pattern, e.g. :

that is: juggling 3 clubs in doubles in frenzy circus style. The clubs are thrown at height 4 but rethrown every 3 beats, i.e. 1 beat earlier than normal.

We will therefore adopt the following:

Definition

A hurry occurs whenever, skipping the dwell hold,
a club is rethrown 1 beat too early

3. Sync interpretation of hurries

Here, we develop a simple method to translate any hurried pattern in the familiar language of sync siteswap theory.

The method is based on the following simple observation: when we watch someone doing a slow 3 clubs cascade, there is no way to decide whether he is doing the async siteswap 3 with a high dwell ratio or the sync siteswap (2 , 4x)(4x , 2).
Indeed, the ladder diagrams of 3 with a dwell ratio d > 0.5 , and (2 , 4x)(4x , 2) with a dwell ratio of 2d-1 are the same.

This simple observation holds for any juggling pattern, hurried or unhurried. Given our assumption of a dwell ratio greater than 0.5 , any mhn juggling pattern, hurried or unhurried, can be reinterpreted as a unhurried sync siteswap juggling pattern.
Essentially it amounts to reinterpret all dwell holds - as short holds 1x , and to double the time scale.

For example, the 3 patterns above can be written in sync notation as:

This way to denote hurried patterns is useful to emulate hurried, and other non-standard rhythm patterns such as 1x5 , on juggling simulation softwares.
You might need to adjust heights and/or number of spins to get a reasonable animation. Also the animated juggler will move his hands during the numerous 2 holds appearing in the sync representation

Hurried passing patterns can be written in sync notation as well (and therefore be animated), e.g. Mild Madness:

can be written in sync form as:

The following section proposes a lighter and more direct way to represent hurried patterns.

4. Hurried mhn* notation and a glossary

Hurried mhn*

Starting from mhn notation, we now allow for the possibility to throw one beat earlier than normaly implied by the throw (siteswap) sequence.
Following common usage, a hurried throw will be identified by a star: * .

To say that a throw of siteswap value s >= 2 leads to a hurried throw t*, means that the club will be rethrown with a throw value of t after only s-1 beats instead of s beats, i.e. skipping the usual dwell beat.

Not of much practical use, but in theory a fast handacross 1 can lead to a hurried throw as well: the club is then rethrown immediately.

Examples

The hurried patterns presented previously can be written as:

which is much more understandable at first glance than in the sync notation:

The sequence (- , 3x)(1x , 3*)(3x , -)(3* , 1x) clearly indicates what is going on in 3x3* : self R , followed by crossing R , then self L and crossing L , all in singles. The * on the crossing throws point out that the crossing throws are the difficult throws of the pattern. The short holds 1x are additional information that may or may not be used.

(0 , 4x*)(4x* , 0) is also quite clear: fast crossing doubles.

Finally, in Mild Madness, the sequence

Validity of mhn* patterns

Checking the validity of a hurried mhn* pattern is essentially the same as for a regular mhn pattern: follow the numbers and make sure that they define a valid permutation.
Now, however, when one traces the path of an object, one has to make sure at each rethrowing beat that the object has not already been rethrown one beat before as a hurried throw. With some practise it is not really difficult.

The average rule

From a pure mathematical point of view, a hurried throw is equivalent to a normal throw combined with a throw one beat later that goes one beat in the past: * = -1x one beat later. This observation does not seem to be very useful except for the following:

The average rule still holds:

Count each hurried pointer * as an additional -1 throw, then the average of the throws over time, multiplied by the number of hands, must equal the number of clubs

A glossary

Since mhn* and sync are analytical representations of the same patterns, it is possible to translate from one language to the other. The glossary goes as follows:

Notes:

The causal diagrams of the patterns, written in mhn* or sync are of course the same, up to the doubling of the time scale and to the representations of the various holds 2 , 1x , - which are anyway redundant and can be omitted if one wishes.

Whether a throw is hurried or not has no influence on its sync translation.

Translating back from sync to mhn is also possible, although the three mhn "throws" - , 1x , 2 correspond to the same sync throw 2 . Precise description is left to the reader :).
Anyway, the hurried throws are the throws that are immediately preceded by an empty hand or another throw from the same hand that is not a 1x .

5. Examples

Solo juggling

Alternating two clubs singles in one hand

Throws are drawn in green for emphasis.

4 doubles/singles switch

1 up 2 up

Starting from the pattern 3x3* , the rest beats are suppressed and used for additional (hurried) selfs. This trick can be applied in many hurried passing patterns, e.g. Jim's 3 count.

Alternating shuffle

A nice trick

Two versions:

A 4 objects 4 count tennis

Passing patterns

A nice 3 count trick

With the handacross behind the back

A PPS trick

J1 throws his second pass in advance as a straight double. Follow the colored causal paths to understand which hands throw to which.

async/sync ultimate

J1 forces the rhythm to change without throwing doubles.

Martin's ultimate

Oddities

0 sync shower!

See (0x,0x).txt for more on this nice pattern.

Akward 1 shower

Fast 2 shower

Author: Christophe Pr?chac

(As posted on rec.juggling, February 2001)

This article presents a simple way to deduce (k+1)-people (3k+n)-clubs feed passing patterns from n-clubs solo siteswaps. A non-exhaustive series of feed passing patterns is constructed by this method as an application: included are many popular feeds, such as the shower and ultimate feeds, as well as some lesser known exotic patterns of the hurried and slow-fast variety. The only essential restriction is that the selfs of the feedees have to be ordinary singles of siteswap value 3 : you better bring your own popcorn then, if you wish to proceed (and perhaps some aspirin too :)).

Start with everyone juggling solo (but perhaps not in phase): one juggler, the feeder, is juggling a n clubs solo siteswap, while the other jugglers, the feedees, juggle ordinary 3 clubs cascades. Now, at some point, the feeder can choose not to do a particular solo throw of siteswap value s but to do a pass instead of siteswap value a to some feedee ; the feedee will then reply by a pass of siteswap value b after a delay of d beats. To keep the patterns going without trouble (i.e. drops) it must be that b+d = s and a-d = 3. If passes are done to the same height (an assumption that can be relaxed at will later on, see the 10 clubs PPS feeds below), we get

That's about it basically. The main interest of this method is that it reduces the search of patterns that follow a specific rhythm for the feeder - say PPS - to the examination of simple solo siteswaps - ss'3 in the previous case. Therefore the patterns to follow will be classified according to the feeder's rhythm: shower, ultimate, etc ...

All passing patterns are written in the siteswap syntax of Wolfgang's irrelevant :) juggling simulator JoePass! available at : http://www.koelnvention.de/software/joepass/index.html (hey, Wolfie I haven't received your check yet, are you sure it's in the mail??). If you can't juggle them, you can at least watch them!

A remark about the directions of the passes (straight or crossing): they depend on which hands are used first by the jugglers. The default hand pattern in JoePass! has everybody starting from the right hand but you can change this by using the #jugglerStartLeft n switch (n: number of juggler you wish to change). A similar remark holds for outside passes versus inside passes (see e.g. the 10 clubs ultimate feed below).

Let us start with the most popular feeds:

Shower feeds

3333 and passing on the first and third throws --> a = 3 , d = 0

Similarly 5353 --> a = 4 , d = 1

(Add #jugglerStartLeft 2,3 to make the feedees pass from the right hand as usual)

etc ... you get the picture: 7373 --> a = 5 , d = 2

ultimate feeds

33 and passing on all beats --> a = 3 , d = 0

44 --> a = 3.5 , d = 0.5

(Since juggler 2 is on the left of juggler 1 in the default position, you may wish to add #jugglerStartLeft 1 to have the feeder make outside passes as usual)

55 --> a = 4, d = 1

PPS feeds

Since there is no 4 clubs siteswap of the form ss'3 with s=s', it is clear that there can be no symmetric 10 clubs PPS feed. Many assymetric patterns are possible however.

453 and passing on the first two beats would yield a = 3.5 , d = 0.5 for one feedee and a = 4, d = 1 for the other feedee, resulting in:

This pattern might feel a bit strange to the feeder: the passes are very close to each other but different nevertheless, it is therefore perhaps safer (more stable) to change the delay of one feedee. There are four possibilities:

The 4 clubs siteswap 633 provides yet another completely different pattern:

The symmetric 11 clubs PPS feed is well known:

663 -->a = 4.5 , d = 1.5

More exotic patterns

(the feeder is on the middle line in the causal diagrams) Start with the feeder doing sync crossing (!) 4 clubs in singles which I denote by (3* , 3*), see http://pogo5.free.fr/juggling/hurries.html for details on hurried mhn* notation, then let him pass all right hand throws --> a = 3 , d = 0

One can add a club to the previous pattern (well, at least theoretically) by starting from the 5 clubs hurried half shower (3* , 4x*) --> a = 3.5 , d = 0.5

Similarly, starting from the hurried 4 clubs sync solo pattern (3* , 4)(- , 3*)(4 , 3*)(3* , -) and passing the high throws --> a = 3.5 , d = 0.5

Getting weirder. Now the feeder is juggling 4 in singles the usual async fountain way and still 2 times faster than the feedees. This pattern can be denoted by 3x* keeping in mind that throws occur every half beat (the tempo is given by the feedees). Passing all throws we get a = 3 , d = 0 and a pattern that can be denoted as:

Still crazier and a special dedication to some one-bearded multi-handed British passing guru. To get the usual 9 clubs version of Alan's Anguish, we need the feeder to juggle a 3 clubs cascade 2 times faster than the feedees. Let us (or at least let me!) denote this pattern by 2.5x*, still remembering that throws occur every half beat (2.5 throws should "normally" be rethrown after 2.5 beats, but due to the hurry pointers '*' everywhere, all throws are actually rethrown 1 beat earlier, i.e. after 1.5 beats). Passing all throws we get a = 2.75 (!), d = - 0.25 and:

Author: Christophe Pr?chac
Credits: Kaskade 62 & 63

As in Kaskade 59, we are just the three of us ... and the song remains the same: what can we do with approximately 9 clubs?

This passing workshop is devoted to a few feed passing patterns with 8, 9 and 10 objects. They are all derived from actual regular practice sessions down here in Paris, in some dark and - this being written in winter - poorly heated room. Although these patterns are relatively rarely seen in the gyms, I believe them to be both interesting and useful for practising more standard patterns.
You will perhaps appreciate that all the proposed patterns can be juggled under a fairly low ceiling as they contain only single-spin throws (syncopations notwithstanding).

About the description of patterns:

In all the patterns, the jugglers are denoted by J1, J2, J3. The feeder is J2 and the feedees are J1 and J3 .
In the triangle feed position, feedee J1 is the feedee on the right, from the feeder's viewpoint..

All patterns are illustrated (and summed up) by causal diagrams. The feeder J2 stands on the middle line, feedee J1 is above on the first line, and feedee J3 is below on the third line. The causal diagram also contains implicitely the starting position: each hand at the beginning of the diagram starts the pattern with 2 clubs, the other hands start the pattern with 1 club.
 

Eight-clubs feeds

Say you are three passing partners but you only have eight clubs. Do you desperately need to borrow an additional club?? No! Just as it is possible for two passers to have fun with 5 clubs, see the article on 5-clubs ultimate in Kaskade 56, there exist 8-clubs feeds that are both interesting and enjoyable. Alternatively, you may consider practicing these patterns as warm-up exercises before more serious stuff, or ... as chill-out sessions after some furious number passing.

Eight clubs fast/slow ultimate/ultimate feed

Everybody juggles an ultimate pattern: no selfs, only passes. But the feeder and the feedees follow different rhythms.

The feeder - on the middle line, in the diagram above - is on the fast side: he (or she, of course) juggles on a standard ultimate rhythm and makes only outside passes along the sequence: Cross, Cross, Straight, Straight, or in other words: R to J1R, L to J3L, R to J1L, L to J3R.

The feedees are on the slow side: they juggle twice slower than the feeder, as if doing one side of the 2-passers 5-clubs ultimate pattern on a rather quiet pace. This huge amount of time for the feedees between the passes can (must?) be put to good use to insert and improvise fancy variations: flourishes, pirouettes, additional throws such as Self+Handacross between passes, box variations: passing with the "wrong" hand while simultaneaously freeing the "correct" hand with a handacross, ...

Starting position: The feeder has 2 clubs in each hand, the feedees have 1 club in each hand.

Siteswap description: < (- , -) (2 , 3p2x) (- , -) (3p2 , 2) | (- , 3p1x) (3p3x , -) (- , 3p1) (3p3 , -) | (2 , 3p2) (- , -) (3p2x , 2) (- , -) >

Eight-clubs slow/fast ultimate/4-count feed

A reasonably simple pattern and a very nice one to watch. In this pattern, the usual triangle position of the jugglers is stretched to a straight line, the feeder J2 stands in the middle with J1 on his right.

The first feedee J1 is doing 4-count right-handed while the second feedee J3 is doing 4-count left-handed out of phase with J1, meaning that J3 will start throwing passes 2 beats after J1.

The feeder is now on the slow side of the pattern and he makes only passes on a very slow pace, but he will do them behind the back or under the arms for more fun and visual effect.

(Don't be abashed by the backwards going arrows, they simply mean that the feeder's hands remain empty for one beat after he has passed.)

The sequence of passes for the feeder is as follows: 1. throw behind the back with left and catch with the right, 2. pause, 3. throw behind the back with right and catch with the left, 4. pause.

Notice that the rest beats of the feeder allow him to indulge in fancy swinging movements between the catching and throwing positions. Also, the feeder might turn a half-pirouette now and then, resulting in normal outside passes and catches (try it, it really isn't difficult).

Needless to say, the feedees can try to throw all their usual 4-count tricks ...

Starting position: The feeder has 1 club in each hand, feedee J1 has 2 clubs in the right and 1 in the left, feedee J3 has 2 clubs in the left hand and 1 in the right.

Variation: Both feedees pass with the right hand making life for the feeder (slightly) more difficult.

Siteswap description: < (- , 3p2) (3 , -) (- , 3) (3 , -) | (3p1x, -) (0 , 1x) (- , 3p3x) (1x , 0) | (3 , -) (- , 3) (3p2 , -) (- , 3) >

Nine-clubs feeds

The nine-clubs shower feed is certainly the most popular passing pattern for 3 jugglers, be they beginners or advanced. And for good reasons: it really is a wonderful pattern! The only drawback of the shower feed is that it is strictly right-handed ... In my opinion, a passing session cannot be complete and really fulfilling without a few ambidextrous patterns. Come on: bring some relief to your left shoulder and give them a try!

Changing roles in the Nine-clubs PPS feed

The nine-clubs PPS feed has been already addressed in Kaskade 59. Here I would only like to mention that it is both feasible and entertaining to change roles on the fly in this pattern now and then.

One feedee wants to move to the feeder's side, making the other feedee the new feeder. How does it work?

One solution goes like this:
Assume that J3 , the feedee on the left of the feeder J2 , is also the "second" feedee, i.e. the feedee who receives the _second_ pass of the feeder. Now, J3 wants to move to J2's side, making J1 the new feeder, he will do this as follows: on his right hand pass beat, J3 begins to walk towards his new position on the (left) side of J2, catches the incoming club in the left hand, while still walking and turning leftwards in order to face J1, and throws the club back to J1 on his normal left hand pass beat.

So the entire move lasts for 3 beats. During this period J3 can either stop throwing selfs (and therefore manage 2 clubs in the left hand for a short while) or keep on juggling normally, throwing his two selfs (I find it easier this way).
Naturally, the ex-feeder J2 will have to stop passing to J3 : he will shift from PPS to PSS without transition.
While J1, the new feeder, will have to convert his first self into a pass to J3, shifting from PSS to PPS without transition.

The sequence of throws is summed up in the causal diagram:

Try it! Hilarity and drops guaranteed on first tries!

Remarks:
With every switch the hand order of the feeder's passes is exchanged: in the example
above from (RO = right outside, etc ...) RO LO LI RI   to   RI LI LO RO .
Oddly enough, if the "first" feedee wants to move, the transition is less natural. See by yourself!

Siteswap description: < 3p2 3 3 3p2 3 3 3p2 3p3 3 3p2 3p3 3 |
3p1 3p3 3 3p1 3p3 3 3p1 3 3 3p1 3 3 |
3 3p2 3 3 3p2 3 3 3p1 3 3 3p1 3 >

Nine-clubs PPH/3-count feed

An advanced 9-clubs pattern perhaps, since it is a little bit fast. What happens here is that the feeder will do Pass Pass Handacross while the feedees will follow a 3-count rhythm Pass Self Self. What? Pass Pass Handacross instead of Pass Pass Self!? How can it be?? Let us look at the causal diagram:

(the backwards going arrows represent the handacrosses)

Notice three points from the causal diagram:
- from the throw positions, one sees that the pattern is staggered: the feedees' passes are done half a beat after the feeder's
- from the lenghts of the arrows, the (single spin) passes must he higher than the selfs
- finally, note that the feeder's passes are straight while the feedees make crossing passes.

Starting position: The feeder and feedee J1 have 2 clubs in the right hand and 1 in the left, feedee J3 has 2 clubs in the left hand and 1 in the right. Each feedee waits for the feeder's pass to be thrown to him before replying by a pass.

Variation: The feeder makes crossing passes and the feedees make straight passes.

Siteswap description: feedees J1 and J3 delayed by half a beat
< 3.5p2x 3 3 | 3.5p1 3.5p3 1 | 3 3.5p2x 3 >

Nine clubs ultimate feed

A nice pattern, and quite doable if the feeder feels comfortable with 6 clubs ultimate. The feeder always makes inside straight passes. J1 showers left-handed and J3 showers right-handed.

Starting position: The feeder and feedee J3 have 2 clubs in the right hand and 1 in the left, feedee J1 has 2 clubs in the left hand and 1 in the right.

Variation 1: The feeder makes outside passes.
Variation 2: Both feedees pass with the right hand.

Siteswap description: < 3 3p2 | 3p3 3p1 | 3p2 3 >

Nine clubs Alan's Anguish

This pattern is similar to the Eight clubs fast/slow ultimate/ultimate feed examined previously: everybody juggles an ultimate pattern: no selfs, only passes ; but the feeder and the feedees follow different rhythms.
The feeder - on the middle line, in the diagram above - is on the fast side: he juggles on a standard ultimate rhythm and makes only inside passes along the sequence: Cross, Cross, Straight, Straight, starting with J3 on the left, in other words: R to J3R, L to J1L, R to J3L, L to J1R.
The feedees are on the slow side: they juggle twice slower than the feeder, as if doing one side of the 2-passers 5-clubs ultimate pattern on a rather quiet pace. Once you manage to get a reasonably stable pattern, the feedees can try to use the huge amount of time between the passes to insert and improvise fancy variations as in the 8 clubs version. Note that the feedees always pass to the closest feeder's hand, namely J2R for J1 and J2L for J3 .

The pattern differs from the 8 clubs versions in two respects however: the pattern is now staggered and the single spin passes should be higher than usual (say, as in 7 shower in singles). Also ... it is much more difficult!

Starting position: The feeder has 3 clubs in the right hand and 2 clubs in the left, the feedees have 1 club in each hand. Each feedee waits as long as possible before passing back to the feeder.

Siteswap description: feedees J1 and J3 delayed by half a beat
< (2 , 3.5p2x) (- , -) (3.5p2 , 2) (- , -) | (- , 3.5p3x) (3.5p1x , -) (- , 3.5p3) (3.5p1 , -) |
(- , -) (2 , 3.5p2) (- , -) (3.5p2x , 2) >

Ten clubs feeds

A few (low-ceiling) 10-clubs patterns to finish off this passing session.

Ten clubs ultimate feed

A logical follow-up of the 9-clubs ultimate feed ... but actually a completely different pattern! (and also a much more difficult one)

The feeder juggles a (relatively fast) ultimate pattern with outside straight passes. J1 showers right-handed while J3 showers leftt-handed. Both feedees throw crossing passes. The passes of all the jugglers should be high and lofty, and in any case, they should be higher than the selfs of the feedees.

Notice that the causal diagram is divided in 2 independent parts: each hand of the feeder passes 5 clubs with a different feedee (so that each feedee passes back to the hand that feeds him). You can also readily see that the pattern is staggered: the passes of the jugglers alternate along the sequence J2 J1 J2 J3 . The relative lenghts of the arrows clearly indicate that all passes should be higher than the selfs of the feedees.

Starting position: The feeder has 2 clubs in each hand, feedee J1 has 2 clubs in the right hand and 1 club in the left hand, feedee J3 has 2 clubs in the left and 1 in the right. Each feedee waits for the feeder's pass to be thrown to him before replying by a pass.

Remark: This pattern is also know as the gorilla pattern. Guess why!
Tip for the feeder: practice each hand separately (i.e. with only one feedee).
Variation 1: The feeder's hands pass simultaneously. This is what sometimes happens naturally after a while anyway.
Variation 2: The feeder makes outside crossing passes (and the feedees pass straight). I personnaly find this version easier than the true "gorilla".
Variation 3: Both feedees pass with the right hand

Siteswap description: feedees J1 and J3 delayed by half a beat
< 3.5p2x 3 | 3.5p1 3.5p3 | 3 3.5p2x >

Ten clubs shower singles feed

The ten clubs shower feed in doubles is very popular. Surprisingly, the single spin version is almost never seen.

The feeder will essentially do one side of 7-clubs shower in singles ... but with two partners instead of only one. This means that he will juggle on a slightly galopped rhythm, the selfs following quickly the passes, with selfs higher than usual and actually as high as the passes. For the feedees, they have to make lofty single passes to the same height as the feeder's, and certainly higher than the selfs ; moreover the feedees might be slightly galopped as well, the first self quickly following the pass.
The pattern is staggered: the feeder passes first to J1 who will wait as long as possible before passing back, then the feeder passes to J3 who in turn waits before replying.

A remark about the rhythm: in actual practice, the pattern is not as much galopped as the causal diagram suggests ; in order to even the rhythm, most jugglers will keep the clubs in their left hands for a longer time than they keep them in their right hands.

There is a collision problem here between the feeder's pass to J3 (on the left) and the incoming pass of J1: make sure that J1's passes are long and high enough.

Starting position: The feeder has 2 clubs in each hand, each feedee has 2 clubs in the right hand and 1 club in the left. Each feedee waits for the feeder's pass to be thrown to him before replying by a pass.

Variation: Switch back and forth from the the standard double spin version of the pattern to this single spin version.

Remark: In case of a drop, the pattern will rapidly settle down to a standard 9-clubs shower feed. It is possible to kick up the dropped club back into the pattern as follows: move the club on your right foot, then, on your (last - if you are a feedee) self beat, throw a lofty single pass with the left hand while simultaneously kicking up the dropped club to your right hand. Everybody will feel quite hurried for a few throws. Good luck!

Siteswap description: too tedious ;-)

Ten clubs sync shower feed

The last pattern is really advanced for the feeder. Essentially, he will do one side of 8-clubs shower in singles, passing a lofty single with the right hand while simultaneously throwing a same height single self from the left hand.

Both feedees juggle a right-handed shower pattern with passes and selfs as high as the feeder's (they should try to juggle as sloooow as possible ...).

Starting position: The feeder has 2 clubs in each hand, the feedees both have 2 clubs in the right hand and 1 club in the left hand.

Siteswap description: < (- , 3p2) (3 , -) | (3* , 3p1*) (3* , 3p3*) | (3 , -) (- , 3p2) >

Author: JiBe

introduction: remembering 6 clubs passing

With 6 clubs, the base of most passing patterns is two jugglers juggling a solo 3 club cascade synchronously. They're doing some singles and alternate right and left hand throws. Let's write that as: - RH self: S - LH self: S - RH self: S        etc... so each juggler's sequence is SSSSSS....

J1: SSSSS J2: SSSSS

So what happens when J1 decides to throw a pass to J2? For instance, J1 throws a single pass from his RH to J2's LH. Then: J1 now has one less club in his pattern. He now needs to get another club back, and J2 is the only supplier available at the moment. J2 sees a 4th club arriving in his cascade. He has to get rid of a club by passing it to J1 in order to keep going. In fact, J1's pass arrives in his LH at the same time than his RH self. Thus he needs to pass instead doing this RH left, which is at the same time than J1's pass.

J1 passes to J2 --> problems

Solution: J2 passes at the same time

J1 and J2 throw synchronously (as passes or selfs) with their RH and LH alternatively.
Selfs (noted S) are crossing singles (RH -> LH or LH -> RH)
Passes (noted P) are tramline singles (RH -> LH or LH -> RH)
The rhythms are symetric (symetric passing patterns) and synchronous: if J1 does S, then J2 does S -- if J1 does P, then J2 does P.

What happens with 8 clubs?

We're going to do exactly the same thing. The base is now 2 jugglers juggling a solo 4 club fountain in doubles. We can juggle exactly the same patterns than with 6 clubs, but some of the rules change:

Selfs (noted by S) are straight doubles (RH -> RH or LH -> LH)
Passes (noted by P) are crossing doubles (RH -> RH or LH -> LH)

There is no more single-pass or single-self !

Example 1 - basic patterns

Once the theory is known, there is not much more to say, except:

These patterns are collision prone because both jugglers are passing crossing passes at the same time. See the collision page for assistance!.
In 4-count (PSSS), you pass and receive from the same hand. Each club you receive is the one you're going to throw back. In usual 6 and 7 club patterns, this happens in a 3-count.

Here are a few patterns you can try:

4-count (PSSS)

3-count or PSS (and the 6-count) are detailed here.

1-count or ultimate (P). Also worth trying in singles.

PPS (to be mastered before example 2)

and the chocolate bar (PPSS) !

Example 2 - Mild Madness

I haven't tried this yet, however JoePass! can do it perfectly :-) , and I think it might be possible to do 1 or 2 cycles if you can already do the above PPS and have understood well 6 club Mild Madness.

Here's how it goes:
J1 (top line in the diagram) throws crossing passes, J2 throws straight passes
We don't have (as in mild madness) a pass-zip, rather a double-zip (the double being a self).
In fact, it's worse than that; because when you receive a pass at the 'wrong' end, you have to throw a crossing self double followed by a zip (or at the same time as the zip).
The full cycle is in fact: PPS PPScZ, which means:
Pass, Pass, Double Self - Pass, Pass, Crossing Double Self, Zip
The causal diagram for a full cycle shows all this.

8 clubs Mild Madness

Author: JiBe
Credits: original idea by Brendan Brolly

Thanks to Tarim for clarifying some things for us on this matter in Rotterdam.  Also, feel free to take a look at the articles posted on this subject at rec.juggling in 1994 (there's one in particular by Tarim that is interesting because it expands the theory to include other rhythms and feeds, which I will do here one day).

This theory, whose application lies essentially in 6- and 7-club ultimate, says the following:

To pass 6 (or 7) clubs in ultimate is somewhat like juggling 4 (or 5, respectively) alone, horizontally, from the point of view of one of the two jugglers.

Thus one could try to derive traditional siteswap figures using the following rules.  The numbers can be written in BN (Brendan notation), since the pattern doesn't follow the classic rules of siteswap. With 4- and 5-ball solo patterns as a starting point, one may be inspired to find corresponding passing patterns.

So that's from the passer's point of view. 

For the one who's catching the passes, just one tip:  throw only when you have to.  To clarify, wait until a pass arrives (in the case of doubles and triples) to empty your hand (by throwing).  

Classic examples in 6 ultimate

The corresponding passes are in red.  Note that the top juggler, who receives the passes, waits each time until the last possible moment to throw, the pauses shown by blue arrows.  

 

BN : 53 siteswap : <3p 3p 2 3p 3p ...| 3p 4p 3 3p 3p ...> Written out : double-self

BN : 534 (continuous) siteswap : <3p 2 3p| 4p 3 3p> Written out : double, self, pass, double, self, pass,... Note : this becomes almost  PPS

BN : 552 siteswap : <3p 3p 2 3p 3p ...| 3p 4p 4p 2 3p...> Written out : double, double, pause

BN : 5551 siteswap : <3p 3p 2 3p 3p 3p...| 3p 4p 4p 4p 1 3p...> Written out : double, double, double, hand-across

BN : 55550 siteswap : <3p 3p 2 3p 3p 3p...| 3p 4p 4p 4p 4p 0 ...> written out : double, double, double, double, empty hand

BN : 633 siteswap : <3p 3p 2 2 3p ...| 3p 5p 3 3 3p...> Written out : triple, self, self

Try also 6451, 64514 (continuous) and all siteswaps that come to mind.

---

Classic examples in 7 ultimate

BN : 64 Written out : double pass, double self

BN : 663 Written out : double pass, double pass, self

BN : 744 Written out : triple pass, self, self

Try also 6662, 66661, 97531 (???), 66771661 (or the continuous version: 66{771}661, you'll see) and all siteswaps that come to mind.

Author: JiBe
Credits: causal diagrams were invented by Martin Frost

Introduction

Siteswaps for passing

A passing siteswap consists of two sets of numbers (N for one side, M for the other) between brackets: '<...>' and separated by ' | '.

Each of the sequences describes the throws of one juggler.  By default, these are integers, as in a solo siteswap (but you will see that this is not always true).  A throw that is a pass will be indicated by a p after the number (ex.:  3p for a normal single self). When you get to the end of the sequence, go back to the beginning as in solo siteswaps (instead of writing "a b c a b c a b c a b c ..." we settle for "a b c").
  If the sequence is especially long, it may be separated into 2 (or more) parts in the following format:
<N1 N2 | M1 M2>
<N3 N4 | M3 M4>

When the two jugglers do exactly the same thing (at the same time or staggered), the rhythm is called symmetrical (Christophe's "symmetrical passing patterns").  Thus sometimes we only need to write one sequence.
  Ex.: 5p 3 3 3 instead of <5p 3 3 3 | 3 3 5p 3>

For those who know nothing about solo siteswaps, take a look at the recommended sites posted on the links page.

Causal diagrams

A two-person causal diagram is made up of two lines.  Each line represents one of the jugglers.  On these lines are written the letters R and L, which represent the two hands of each juggler:

• R = Right hand
• L = Left hand

Next, we add arrows between the letters (hands), which represent a throw, whether a self (staying on the same line) or a pass (crossing lines).

Time progresses from left to right, from which it follows that the arrows point toward the right:  first one throws and then one catches.  That explains the alternation of L's and R's on each line; in a normal juggling pattern, one's hands throw one after the other.

For each circle (letter), there will be an arrow coming in and another arrow going out, i.e. one incoming pass and one outgoing pass (cf. the examples below; the first explanatory diagram don't show this because it is not a complete diagram).  This illustrates the fact that one must throw a club in order to be able to receive another.  The incoming club is the cause of the next throw.

Different types of arrows and what the numbers mean

The explanations given here follow (for now) the normal rules of siteswap, which state:

• an odd throw (1, 3, 5..., i.e. handacross, singles, triples) go from Right Hand to Left Hand (or RH to LH). This is shown by R->L or L->R (pass or self) arrows.
• an even throw (2, 4, 6..., i.e. doubles, quadruples, etc.) go from Right Hand to Right Hand (or LH to LH).  This is shown by R->R or L->L arrows.

Beware however, contrary to the ladder diagrams, the arrows do not lead to the time when the same club will be thrown again.  The arrow points at the moment when the club is caught (if it had been thrown there), combined with the moment when another club is thrown to take its place.

Passes

<3p .....| .....>	A single pass (single spin) that goes straight across (R to L)
<4p .....| .....>	Double pass
<5p .....| .....>	Triple pass (it's easy to imagine what quadruple passes would look like...)

Classic selfs (3, 4, 5...)

<3 .....| .....>	Normal single self.
<4 .....| .....>	A double (which then comes back to the hand that threw it).
<5 .....| .....>	A triple self (changing hands)

Bizarre selfs (0, 1, 2)

<3p 2 .....| 4p .....>	Keep one club in hand (the arrow won't always be drawn). When no club arrives for a given hand, one may hold the club for another beat.  That's a chance to do a flourish, thumb twirl...
<3p 1 .....| 3p .....>	A handacross.  The arrow goes backward (back in time)!!!  That's because this handacross is the cause of the previous throw: you have to free the right hand for catching it.
<3p 3p 3 0 | ..... >	An empty hand (no need to throw).  Again, the arrow goes back in time: in order for the hand to be empty, one must have made an earlier throw with the same hand.  That's the cause that makes it possible to catch the incoming club.

Some examples

4-count or every other

<3p 3 3 3 | 3p 3 3 3>

This is the most common pattern (every other).  The jugglers pass at the same time and always with the right hand.  There are 3 selfs between each pass.

3-count with a 441

<3p 3 3 3p 4 4p 1| 3p 3 3 3p 3 3>

Waltz:  jugglers pass at the same time and alternate between right and left hands.

Here one of the jugglers, upon receiving a pass does:  - self double (4) - crossing double pass (4p) - handacross (1, the arrow pointing left)

2-count with doubles and triples

<3p 3 3p 2 3p 3 3p 3| 3p 3 4 4 5 3 0 3>

 

Here, the bottom juggler does the traditional right-left-triple in 2-count.

The first double, thrown at the same time as a regular pass, arrives late (a double takes longer to get there than a single).  The top juggler therefore has a pause (a 2) with his left hand (which otherwise would have received a regular pass).

When someone throws a triple, there is no pass coming to the right hand, which will then be empty two counts later (at which point the arrow goes backward: a 0).

Standard 7 clubs in 2-count

<4p 3 | 3 4p>

Here you will begin to grumble, and with good reason: why are 4's (doubles, all the passes) not made as crossing passes (R to R or L to L, as before)?

It's because the two jugglers are no longer doing exactly the same thing at the same time.  The R's of the top juggler correspond to the bottom juggler's L's.  There is a staggered start, which is not indicated by siteswap notation (on Joepass! you would enter it as "#jugglerStartLeft 2").

Crossing 7 clubs in 2-count

<4p 3 | 3 4p>

This is crossing 7 clubs in 2-count which follows the rules stated above.  The jugglers throw with the same hand at the same time, but one of them must make left-handed passes.

Staggered starts

You have seen in the previous examples that the two jugglers don't always throw with the same hand at the same time.  According to the time delay between both their right (or left) hands, I categorize rhythms into three families (not counting hurries or 'galloped patterns').

Siteswap does not take staggered starts into account.  Therefore, sometimes there are several ways to juggle certain sequences (cf. <4p 3 | 3 4p> in the examples above).
Be also aware that the new rules stated under are valid only for passes. Selfs throws will always follow the usual rules.

Family 1 : Delay=0

This includes 4-count, 3-count, 2-count, 1-count with 6 clubs, 4-count or crossing 2-count with 7 clubs...

 
In this family, the standard siteswap rules apply:
- even passes (4, 6... i.e. doubles, quadruples...) cross:  R->R or L->L
- odd passes (3, 5... i.e. singles, triples) go straight across:  R->L or L->R.

Family 2 : Delay=1 count

For example, 2-count or compressed mesopotamia with 7 clubs.

 
Note that the 1-count delay means that when A throws with the RH, B throws with the LH.  In this family, the standard siteswap rules are reversed:
- even passes (4, 6... i.e. doubles, quadruples...) go straight across: R->L or L->R
- odd passes (3, 5... i.e. singles, triples...) cross: R->R or L->L

Family 3 : Delay=0.5 count

These are essentially 7-club patterns-- 3-count, ultimate--but also some with 6 clubs--whynot?--as well as 8 and more.

 
In this family, the rules change completely; since the delay is no longer a whole number, neither are the passes.  The passes are now written as 3.5p, 4.5p, 5.5p...
In practice, you may choose to do either doubles or singles for 3.5p (which is between 3 and 4 - I know, you could've figured that out on your own).

A second new element is that in this case, one juggler makes all crossing passes, while the other makes all straight passes (without changing the numbers).  Thus we have: If N (=3.5p for example) is a crossing pass for J1, it is straight for J2.  And N+1 (4.5p in this case) is therefore a straight pass for J1.

A special siteswap notation may be applied to these patterns: 4-handed siteswaps.

I know that some people won't agree with this classification system.  However, if the diagrams are new for you, this may be less confusing.
FYI, some points to consider:

Properties

Siteswap : properties

The total number of clubs equals:
(average of the numbers in the two sequences)*(number of jugglers).

For example, for <3p 4 4 1 | 3p 3 3 3 > :
average = (3+4+4+1+3+3+3+3)/8 = 3 (24/8)
and the number of clubs = 6 (3*2, i.e. 3 clubs per juggler).

One could also calculate the number of clubs juggled by each juggler (with his corresponding sequence) as in normal siteswaps.  When doing this, one often ends up with numbers like 3.5 clubs per juggler (for regular 7 clubs).

Causal diagrams : properties

In order to calculate the number of clubs in a causal diagram, we must first find (and define this notion) the number of causal lines present in the diagram.  In the example below, the three causal lines are clearly shown (one blue, one green, one red).  This should be enough to understand the concept of causal lines.  One may also make a vertical line and count the number of arrows that it crosses, but in this case arrows that go from right to left (hand-across and empty hand) should be counted as negative.

So we have:  number of clubs = ( number of lines ) + ( total number of hands).
In the case of 2-person passing patterns, there are 4 hands.

Here: number of clubs = 3 + 4 = 7 (it's a popcorn with 7 clubs).

In short, the lines represent the number of objects in the air at a given time, as opposed to those which jugglers hold in their hands (which is how we get the formula).

Moving on

Hurries

A hurry is often defined as throwing twice in a row with the same hand.  This often happens because someone catches the club in the "wrong" hand.

Here I've shown the hurries in green, breaking the alternation of RLRLRL... by sometimes having 2 R or 2 L in a row.

Multiplexes

Here I've tried to represent a duplex in a 2-count pattern (6 clubs).  The bottom juggler catches two clubs in his right hand and throws them back two counts later.  

The diagram's ambiguity comes from the fact that one line (the red one) is broken. We should agree on a way of dealing with this, perhaps by introducing a new arrow (like the dotted one) in the diagrams.  

Various self patterns

If desired, one may add an extra line to show self patterns which necessitate, for example (as is the case here for columns) synchronous throws.  Note that the line (red loop) thus created does not intervene in the calculation of the number of clubs in the pattern (we have simply created a problem for ourselfs by throwing a club even though nothing forced us to do so). 

Note: Most jugglers do this pattern by throwing synchronous doubles, handacross, pass (not synchronous doubles, hand-across, self, pass).  When making a clear diagram, you can see that theoretically that triples should be thrown, but by taking some liberties in throw height, it still works with doubles.

Kickups

A kickup is the action of picking up and "throwing" (in a self or a pass) a club with one's foot.  A circle with an F (for Foot) suffices for this type of diagram.  In this case, you create a new line since you add another club to the pattern.

Thus you can play with the diagrams, doing what you want with them.  Feel free to take some initiative!

More jugglers

Adding jugglers is simple, both for the diagrams and for siteswaps.  In the diagrams, all you have to do is add a line for each new juggler.

For siteswap, you add a sequence of numbers for each juggler (still using a '|' (pipe) to separate each juggler).  On the other hand, you must identify which juggler should receive which passes, so we write 3p1 to note a pass thrown to juggler number 1 (The jugglers need to be numbered first).

Classic feed

<3 3 3p2 3 | 3p3 3 3p1 3| 3p2 3 3 3>

Line with a turn

<3p2 3 5p3 2 2 3 ...| 3p3 3 3 4p1 2 3 ...| 3p1 3 3 3 3p2 3 ...>

Author: JiBe

Diagonal collisions: RH->RH and RH->RH (or LH->LH and LH->LH)

Diagonal collisions 2: RH->RH and LH->LH

		To avoid this, you have to agree that the person who throws with the right hand (R to R) will throw their pass from the outside (from as far right as possible) and the one who throws left-handed passes will throw from the inside (from the centre).  The diagrams on the left will give you an idea.  An example of a such a pattern is Brendan's Folly.
With collision	Without collision

Head-on collision: RH->LH and LH->RH

		This type of problem is rather difficult to resolve and is only relevant to certain barbaric patterns (e.g. compressed Mesopotamia).  In theory, one must create imaginary corridors, the two jugglers slightly offset from one another (see diagrams); in practice, it's still hard to do!
With collision	Without collision

Author: JiBe

Reminder:
The context is that of patterns that can be put into classic siteswap notation, in which one's hands throw one after the other.

Consequences, examples, and other aspects of the problem:

• The simplest example (in solo juggling) is the following:
  In a 3-club cascade, throw a single from the RH to the RH (in other words, go into a round of two in one hand, in singles).  In classic siteswap notation, you would throw a double (3333 423 33).  Throwing a single makes the club come down one count sooner and forces you to throw one count sooner.
• Often (but not always), it's because a club arrives one count sooner (coming as a pass or a self) that one must throw one count sooner.
• Often (but not always), this means someone will have to throw twice in a row from the same hand.  Right-Right-Left-Left-Right... This property (which applies quite often) is sometimes given as a definition; however, it is neither necessary nor sufficient.
• There exists a notation in which you simply add a star after the number which signifies a hurry throw.  Going back to the first example: when the double is changed to a single, 333 423 333 becomes: 33 3x 3* 333.
    The 2 gets skipped, and the 4 is replaced by a 3x (a 3 followed by an x to specify that it doesn't cross).  The star indicates that there is a hurry, and therefore that it's the same hand that threw the 3x.

All that was to give you an idea of the principle; to be able to go on to discover your own passing patterns.
In passing, to create a hurry (we will later see how to get out of them using various passes), one throws a crossing pass which otherwise should have been straight pass (or vice versa).

Let's take a classic 4-count, for example:

	Classic 4-count: < 3p 3 3 3 | 3p 3 3 3>
	With a hurry on the last pass: < 3px 3 3 3 | 3p 3* 3 3 >

The bottom juggler makes their last pass a crossing single (in blue, R to R).  The hurry (in red) comes from the fact that the top juggler makes a pass with their right hand at the same time.  They must free their right hand right afterward in order to receive the crossing pass.  It's easy to see that the alternation between Right and Left (RLRLRL) is broken--we have RLRL RR LRLR.

Thus we can create new patterns based upon most classic patterns; all that needs to happen is for one juggler to cross all his passes that he previously threw straight across.  The two jugglers can then continue on with the same rhythm.  In the example above, the top juggler starts a 4-count left-handed cycle after the hurry.

Continuous 4-count with a hurry: <3px 3 3 3 3px 3* 3 3 | 3p 3* 3 3 3p 3 3 3>

 
Thus we get a pattern with one juggler who crosses all their passes (in blue).  The two jugglers alternate 2 cycles of left-handed 4-count and then 2 cycles of right-handed 4-count.  The hurry (in red) switches from one juggler to the other.