# Siteswap

Siteswap 53145305520

With siteswap refers to a type of notation of juggling patterns (similar to the notes when playing a musical instrument) using number sequences. The word is used both as a name for the notation and for patterns described in this way.

The siteswap notation only describes the "order" in which the juggled objects are thrown. Siteswaps do not contain any information on arm movements or rhythm. So there are many ways to juggle a single siteswap. There are many juggling tricks , such as Statue of Liberty, Windmill, MillsMess or Chops and many more, all of which - like the basic pattern Kaskade - have the siteswap "3", although they are juggled completely differently, while selected, more difficult or more complex siteswaps (e.g. B. " 531 ", " 441"," 336 "etc.) are already in their basic form considered independent juggling tricks. A siteswap also does not specify the number of hands with which the pattern is juggled. Not every juggling pattern can be noted in siteswaps. For example, a juggler can briefly hold a ball while juggling and continue to catch and throw balls with the same hand. Such and many other patterns are not possible with this notation without extended spellings.

## notation

A siteswap consists of a series of numbers , such as "5 3 1". To make the notation easier, the numbers are usually written as digits one after the other, numbers from 10 are assigned to letters. This convention comes from the notation of hexadecimal numbers . Each digit (or letter) stands for a throw and indicates how many throws it will later be caught again. This results in the flight duration and throwing height "relative" to the other throws. The actual throwing height and flight time (which are mutually physically and directly dependent) are practically free and different depending on the juggler, rhythm, built-in delays or accelerations or depending on the freedom of the pattern, as long as the siteswap is adhered to.

The following digits have a special meaning:

• 0 - no throw, empty, empty once.
You can use this hand to do other things while juggling, e.g. B. hang this hand or snap your finger .
• 1 - The juggling device is handed over directly (mostly to the other hand) almost without throwing it. A "zip" is used in technical jargon.
• 2 - Hold, stay. Some juggling patterns require that the trapped object be held for one or more bars. A throw from left to left or right to right in just two bars - that is, while the other hand is on the throw - stays where it is. With a little practice or with some multiplexes (multiple throws, see below) you can also juggle low “thrown 2's”. Even then, the object remains in the same hand once.

From 3 upwards, the digits indicate correct throws, whereby the odd 3, 5, 7, 9, ... normally (if you are not juggling with crossed arms) land in the other hand (or throwing point), the even 4, 6 , 8, ... usually in the same hand that threw it.

To interpret a siteswap, you only need to know two things:

• All drop points alternately throw one object each in a fixed order.
• The pattern is read from left to right and a number is assigned to each throw. The number indicates how many throws the object that has just been thrown will be thrown again later. The patterns are to be understood periodically: after the last throw, the first one follows again.

"Drop points" is kept very general here, as Siteswap has long since ceased to be used only for two-handed patterns. Also diabolo players (a cord is thrown off) and registration (eg., Four hands on two people) use siteswap. From now on, however, this article assumes that only two hands are involved.

### example

Siteswap 3b 531.gif

From the siteswap notation "531" one can see that the throwing pattern described below will occur. (We decide to use balls and start with the right hand.) Here is a detailed description of the effects of the 5 , 3 and 1 for the consecutively numbered bar starts (1..7) ; the balls may be yellow, red, and blue. Since the hands take turns throwing, we immediately know that the right hand throws in all odd bars and the left always throws in even bars:

1. right hand: 5 ; This means that the yellow ball is thrown so high that it is thrown again exactly five bars later - in bar 6. There it is the turn of the left hand, so it does not have to be thrown straight up, but cross the middle of the body. How high it is thrown depends solely on the requirement that bars 2–5 must run first.
2. left hand: 3 ; that is, the red ball is only thrown so high that it can be thrown with the right hand after the next three bars (i.e. in bar 5). So this litter is significantly lower than the first.
3. right hand: 1 ; the blue ball has to be thrown again in the next bar, i.e. before the red ball, which is currently in the air as 3 from bar 2. To do this, it must be thrown very low - as a rule, this throw is handed over rather than thrown.
4. left hand: 5 ; The siteswap "531" has now been run through once and from here on it is reversed with the other hand. The passage was done in such a way that it is run through again starting with the blue ball, that is, we now throw the blue ball we just received from bar 3 above as high as we did the yellow ball from bar 1, so that after the now the next five bars (i.e. in bar No. 9) can be started again.
5. right hand: 3 ; Here we have just caught the red ball that was thrown at bar 2, and we throw it back so high that it is thrown with the left hand after the next three bars (i.e. in 8).
6. left hand: 1 ; Here we have just caught the yellow ball that was thrown at bar 1, and now we are throwing it directly to the right hand using the shortest possible route, so that it can be thrown again immediately at bar 7.
7. etc. ... (from here the text of bar 1 applies again)

### Clock and throwing height

With normal, constant juggling speed with two hands (about 140 throws / minute with a 3 or 4 ball juggling) you can assign exactly one height to each digit. A number then corresponds to the throw in the "simplest" basic pattern with this number of objects. This can be seen, for example, from the fact that in siteswap "3" all objects are thrown equally and there is only one type of litter. However, since the bar length does not change anything on the throw if other numbers are next to it, a "3" is always this type of throw if you are juggling at the same speed.

In practice, if you have more objects you go to a faster pace. In addition, siteswaps are rarely thrown at a fixed rate - the sequence of numbers only indicates the sequence of the litters, the bars are very different in length. The most prominent example of this is the shower “51” - there is almost always a strong gallop, the 1 thrown directly after the 5, with a longer break after the 1.

## Further considerations

### Object number: checksum rule

A nice side effect: Because a siteswap pattern is nothing more than distributing a certain number of balls between two hands in time, the average of a sequence is exactly the number of balls that you have available. Using the example of “531”: The cross sum is 9, divided by 3 (length of the sequence) results in 3 (number of balls). This side effect can be used to clarify in advance whether it is even possible to throw a certain siteswap (but it is only a necessary criterion, not sufficient, see juggling ability). The siteswap "532", for example, is not possible because the checksum 10 divided by the length of the sequence 3 does not result in a whole number.

### Juggling ability

But even if this calculation results in an integer, that can be an indication of the juggling ability of the pattern, but that is not yet proof of this. So is z. For example, the pattern "534" can be juggled (checksum 12, sequence 3, resulting in 4 objects), the siteswap "543", on the other hand, is not possible, although the calculation still works out. After checking as above, a problem arises: Bar 1: Ball 1 is thrown and after 5 bars, i.e. in bar 6, it is back to the turn. Measure 2: Ball 2 is thrown and after 4 measures, i.e. in measure 6, it is again your turn. The siteswap notation only allows for one throw per bar - in bar 6 there are now two balls in the hand at the same time - that is not possible without adding "multiplex throws" to the notation (see below).

Two numbers A and B within a siteswap notation must not be any distance apart. Let us assume that A comes before B, then the number of bars it takes after A until B is thrown cannot be equal to the difference AB.

### Get in

Some patterns cannot be started straight away from the basic pattern of the corresponding number of objects. The state that is present with each throw of the basic pattern is called the "ground state". In order to get into the siteswap pattern correctly, you need a so-called get-in sequence, and to get out again afterwards you need a get-out sequence. If a siteswap needs these sequences, it is called "excited". For the Shower 51 , for example, you need such transition throws: z. B. With a 4 you get from the cascade to the shower, and with a 2 you get back to the basic pattern. A seamless combination of cascade and shower (… 33 3 5 1 51…) is not a valid juggling pattern. - the bold digits collide. With the transition throws (… 33 4 5151… 5151 2 33…) the pattern can be juggled as a whole.

### Trajectories and rotation

An interesting aspect of siteswaps are the often different paths that the objects take through the pattern: In the animated example described above (531), the blue and yellow balls with the 5s and 1s alternate during the red ball only makes all 3-s. With the right or a suitable siteswap, different trajectories can be assigned for different objects (of different sizes, different types or only different colors). Also, when learning a trick that initially appears complicated and confusing, it can be very helpful to know a ball in the siteswap that always flies the same (relative) height. In 4b-345 e.g. B. only one ball makes all 3's; then two other balls each make the following 4 and 5 throws to the same side (on the other side the third other ball is ready for the next 4 after the change of side). Having a color-conspicuous ball made these 3-s, which initiate the change of sides, makes the pattern even more transparent and easier to learn.

## Extensions of the notation

The notation can by no means describe all patterns. The two rules mentioned above allow a very compact representation of certain patterns, but are simultaneously subject to two restrictions

1. Only one object is thrown at a time. Throwing two things from one hand at the same time ("multiplex") is so easy that even non-jugglers can do it just like throwing synchronously with both hands.
2. The order in which hands or other throwers take turns is fixed.

In addition, passing patterns noted as four-handed siteswaps are often not visual - patterns in which several people throw at the same time are quite common.

### Synchronous throwing

Both hands throw at the same time, for example (6x, 4x). The numbers for the left and right hand are in brackets, separated by a comma. "X" stands for "crossing", ie the ball is thrown to the other hand, without an x ​​the throw goes back to the same hand.

Examples:

• (6x, 4x) Synchronous 5 ball half shower
• (6x, 4) (4.6x)
• (6x, 4) (4.2x) (4.6x) (2x, 4), see animation on the right

### Multiplex throws

It is possible to throw 2 or more balls from one hand at the same time. All numbers that a hand throws at the same time are enclosed in square brackets, e.g. B. [43] (ie one ball is thrown as “4”, the other as “3”). Now it is also allowed for two balls to land in one hand - this is even a prerequisite for being able to throw a multiplex later. Example animation on the left: 3-ball cascade with juggled "5", 4 balls, siteswap: [53] 3333.

### Passing

Four-handed siteswaps are very popular in some circles. In contrast to the solo juggling siteswaps, the numbers here are twice as large. A distinction is made between the global siteswap, which can theoretically also be juggled with two hands, and the local siteswap, which states what each individual juggler has to throw. In the global siteswap, the four hands of the two jugglers are counted alternately: after the right hand of juggler 1, the right hand of juggler 2, then the left hand of juggler 1 and then the left hand of juggler 2. If both jugglers throw at the same time, so that If synchronous notation were necessary, the four-handed siteswaps are not used. Instead, one often writes a separate siteswap for each juggler and gives throws that go to others with a "p" (passport). If there are more than two jugglers, it is not clear to which of the fellow jugglers the pass is going. As a rule, the jugglers are then numbered and after the “p” comes the name of the destination, e.g. B. "3 pC" as a pass to the juggler, which is marked with "C". Since not all registerers have to throw at the same time, but can also be shifted by fractions of bars, passing patterns are not limited to whole numbers.

Examples:

• 3p 3 3 - Three-Count, "Waltz" - all jugglers throw at the same time.
• 5 3 3,5p 3 3 - "5-count popcorn" - the jugglers are offset by half a bar, see animation on the right. The four-handed siteswap for this is local: a 6 7 6 6 (a stands for 10) or global: 7 a 6 6 6 or a 6 6 6 7.

## software

There are a large number of freely available programs for almost every operating system to display siteswaps. Many also offer the ability to set the movements of your hand to perform complicated tricks such as B. to represent the Mills Mess .

• Juggling Lab is an open source program written in Java that supports various siteswap syntaxes. As an applet, it can be built into websites to animate tricks.
• Jaggle is a Java applet and animates the patterns in 3D graphics and has several predefined patterns. The tricks can also be played backwards in the animation, this simplifies learning.
• Jongl is available for many operating systems and can also animate passing patterns with various objects such as clubs, balls and rings. The program not only shows the objects, but also the jugglers in 3D.
• JavaMaster is an applet written in Java, which has a large trick list and can also display siteswaps.
• Joepass! mainly focuses on passing patterns, but can also represent normal siteswaps. The software is available for Windows and Macintosh .