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Mhn and Causals: Hurried patterns

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.

The standard definition of a hurry is a situation where a juggler has to throw twice in a row from the same hand.
This definition obviously assumes an underlying rhythm of the standard async siteswap category: a hurry occurs when one deviates from the hand pattern RL to enter a different async hand pattern such as RRLL as in the following example:

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:

3x3* sync: (2 , 4)(2 , 4x)(4 , 2)(4x , 2)
1x5 sync: (0 , 2)(2 , 8x)(2 , 0)(8x , 2)
4x* sync: (0 , 6x)(6x , 0)

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:

sync: <(2 , 4px) (4px , 2x) (4x , 2) (2 , 4px) (4px , 2) (2 , 4x) % |
(2 , 4p) (4p , 2) (2 , 4x) (4p , 2) (2x , 4p) (2 , 4x) % >
One must admit however that he sync notation is somewhat heavy and not very intuitive.
The numbers do not immediately refer to the throw heights used in practise and the connection between ordinary unhurried patterns - written in mhn - and related hurried patterns - written in sync notation - is obscured by the use of different notations.

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:

3x3* mhn*: (- , 3x)(1x , 3*)(3x , -)(3* , 1x)
4x* mhn*: (0 , 4x*)(4x* , 0)
Mild Madness mhn*: <(- , 3p)(3p , 2x*)(3* , -)(- , 3p)(3p , -)(- , 3) % |
(- , 3px )(3px , -)(- , 3)(3px , -)(2x* , 3px)(- , 3*) %>

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

<(- , 3p)(3p , 2x*)(3* , -)(- , 3p)(3p , -)(- , 3) % | (- , 3px)(3px , -)(- , 3)(3px , -)(2x* , 3px)(- , 3*) %>
is not too difficult to decipher: the two passers juggle the sequence Pass, Pass-Handacross, Self, Pass, Pass, Self, out of phase with each other ; one juggler passes straight singles while the other passes crossing singles.

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:

mhn sync
s , s >= 3 2s-2 x if s odd ; 2s-2 if s even
sx , s >= 3 2s-2 if s odd ; 2s-2 x if s even
2 2
2x 2x
1 0x
1x 2
0 0
- 2

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.

mhn*: (0 , 3x)(0 , 3x*)(0 , 3*)(0 , -)(- , 3)%

sync: (0 , 4)(0 , 4)(0 , 4x)(0 , 2)(2 , 4x)%

4 doubles/singles switch

mhn*: (4 , 4)(- , -)(4 , 4)(- , -)(3x , 3x)(3x* , 3x*)(3x* , 3x*)(4* , 4*)(- , -)

sync: (6 , 6)(2 , 2)(6 , 6)(2 , 2)(4 , 4)(4 , 4)(4 , 4)(6 , 6)(2 , 2)

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.

mhn*: (3x* , 3x*)(0 , 3*)(3x* , 3x*)(3* , 0)

Alternating shuffle

mhn*: (- , 3*)(2x , 3*)(3* , -)(3* , 2x)

A nice trick

Two versions:

mhn: (4 , 4)(1* , -)(0 , 4)(- , -)%

mhn: (4 , 4)(2x* , 0)(0 , 4*)(- , -)%

A 4 objects 4 count tennis

mhn*: (- , 4x)(4x , -)(4* , 1x)(- , 4) %

Passing patterns

A nice 3 count trick

With the handacross behind the back

mhn*: <(3px* , 0) (4* , 4*) (2x* , 0) (0 , 3px*) (4* , 4*) (0 , 2x*) |
(- , 3p) (3 , -) (- , 3) (3p , -) (- , 3) (3 , -) >

sync: <(4p , 0) (6 , 6) (2x , 0) (0 , 4p) (6 , 6) (0 , 2x) |
(2 , 4px) (4x , 2) (2 , 4x) (4px , 2) (2 , 4x) (4x , 2) >

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.

mhn*: <(4p* , 3p) (0 , -) (- , 3) (3p , 4p*) (- , 0) (3 , -) |
(- , 3p) (3p , -) (- , 3) (3p , -) (- , 3p) (3 , -)>

sync: <(6p , 4px) (0 , 2) (2 , 4x) (4px , 6p) (2 , 0) (4x , 2) |
(2 , 4px) (4px , 2) (2 , 4x) (4px , 2) (2 , 4px) (4x , 2)>

async/sync ultimate

J1 forces the rhythm to change without throwing doubles.

mhn*: <(- , 3p) (3p , -) (3p* , 3p) (0 , -) (3p , 3p) (3p* , -) (0 , 3p) (3p , -) |
(- , 3p) (3p , -) (- , 3p) (3p , 3p*) (- , -) (3p , 3p) (- , 3p*) (3p , -) >

sync: <(2 , 4px) (4px , 2) (4px , 4px) (0 , 2) (4px , 4px) (4px , 2) (0 , 4px) (4px , 2) |
(2 , 4px) (4px , 2) (2 , 4px) (4px , 4px) (2 , 2) (4px , 4px) (2 , 4px) (4px , 2) >

Martin's ultimate

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

sync: <(2 , 4px) (4px , 2x) (4px , 2) (2 , 4px) % |
(2 , 4p) (4p , 2) (2 , 4p) (4p , 2x) % >

Oddities

0 sync shower!

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

mhn: (1* , 1*)

Akward 1 shower

mhn: (1* , 2x*)

Fast 2 shower

mhn: (2x* , 2x*)