Existing Juggling Notation Systems
Table of Contents
What toss juggling notation systems are already out there, and how do they compare?
What do they describe, and what do they not describe?
This article mixes personal opinions with personal observations, but in the conclusions at the bottom we will hopefully find some objective truths about the differences between these notation systems.
If you know of any useful systems that are not listed here, please do contact me.
This article was updated on 22-02-2022 to include Multisynchronous, Joachim Voigt club ladders, Music swap, 491 patterns for the solo juggler, Le Corps Jonglé, S-Notation, Labanotation, George Gillson diagrams, and Aidan notation.
Update 21-06-2022: Note that this list only includes systems that already existed at the time this research started. The 3 systems that came out of this research, namely dNote, Improved Body Trick Notation (IMBO) and Rhythmic Catches (RC) are not included. You can find information on those in their links, especially the latter two are worth reading about as they improve upon all the systems described here.
Siteswaps were invented in the 1980’s and is without a doubt the most commonly used juggling notation system.
For those unfamiliar with it, there is a good explanation video of siteswaps by Numberphile.
Siteswaps define the order in which objects are handled. This is typically translated to throw heights. For example, if ball A and ball B are thrown after each other at the same height, they will also come down in the order AB. But if A is thrown much higher than B, B could come down before A, and their order is now swapped: BA.
Timing and height of throws are often assumed from siteswaps. People treat beats to have equal spacing, and a
5 throw is typically seen as higher than a
I personally get frustrated with those assumptions, there is much more to juggling than equal spaced beats. I’ve had fun finding all 3 permutations of the pattern
441 over 4 beats using 2 single beat throws and one double beat throw.
Jugglers are much more aware that siteswap does not describe spacing: Siteswap will never tell you from where an object is thrown. Therefor you will hear jugglers say things like ‘lets do
423 with the
3 thrown under the leg’.
Despite its limitations, siteswaps are amazing and have completely transformed juggling. This deserves a post of its own.
Siteswaps without any of the extensions listed below is sometimes referred to as “vanilla siteswaps”.
Siteswaps can also be translated to state diagrams.
Recommended viewing & reading:
- Siteswaps DVD (now free online!) by Gandini Juggling
- Siteswap fundamentals by Thom Wall
Synchronous siteswap and multiplexes⌗
In 1990 Jack Boyce extended siteswap with notation for multiplexing, synch juggling and passing1. The former 2 are commonplace among jugglers, the latter is mostly interesting for simulation software.
Despite it being commonplace, not everybody thinks that is system is elegant.
As a side note, Jack is also the originator of juggling state diagrams.
In theory siteswaps could describe a pattern with any number of hands, instead of the default order
RL you’d just interpret it as order
AR BR AL BL for jugglers A and B. This is typically called global siteswap. This also assumes that the jugglers throw asynchronously with each other, their throws are never at the same moment in time.
To make those patterns more readable, you can also have local siteswap, siteswap as interpreted by each individual juggler. If you halve each number, and then take every other number (looping around once) you get the local siteswap. This may include half numbers such as
2.5. Confusingly, a
2.5 throw in a standard 4 handed siteswap can go either straight across or crossed across, depending on which of the 2 jugglers throws it.
It is possible to have both (or multiple) jugglers juggle synchronously too. In this case you have to notate which throws are passing throws, and from the throw height it can be deduced which hand they go to (depending on which hand the other juggler started with). These local patterns may look like
3p3 (a 6 prop 2 count) or for more than 2 jugglers something like
3p1 3p2 3 as you have to also notate which juggler you’re throwing to. If the pattern is asymmetrical, the siteswap becomes even more complex as each juggler will need a unique siteswap. For example,
<3p3|3|3p1><3|3|3><3p2|3p1|3><3|3|3> is a way to write a “3 person 9 prop feed” in Juggling Lab.
Local siteswap notation is often associated with Prechac, which is a system to transform siteswaps into symmetrical or staggered symmetrical passing patterns. Writing down asymmetrical local siteswap is rare, probably because it is lengthy and causal diagrams would be easier to read.
A great resource for creating symmetrical passing patterns is prechacthis.org.
Another (unrelated to siteswaps) notation system sometimes used for passing is a Box Diagram
Hand Siteswap Sequence⌗
Regular siteswaps describe the way objects swap order. But you could use a system that describes the hand order too. This was documented by Mahit Warhadpande, who explains it in this video. Also known as hss. I discovered later that hss is also documented in The Mathematics Of Juggling by Burkard Polster in 2003.
The same rules that apply to siteswap can be applied to hss, any valid 2 ball siteswap is a valid 2 hand hss, for 3 ball siteswaps you need 3 hands. The only exception is that you can’t have a
0 in hss unless there is a
0 on the same beat in the siteswap as well.
The default hss that we use for vanilla siteswap is
2, which means that the hands alternate. But if you were to add the hss
123 which translates to
RLL to the siteswap
3, you’d get something which can’t be expressed in regular siteswaps (but it looks similar to ss:
Multisynchronous & Yet another tweaked form of siteswap⌗
In order to mix vanilla siteswaps with multiplexes and synchronous siteswaps, Frédéric Roudaut suggests the term Multisynchronous.
The concepts and syntax are outlined in an article from Miika Toukola called “Yet Another Tweaked Form of Siteswap”. It suggests new syntax such as the use of the
* in the middle of a siteswap sequence to make the next throw by the same hand as the previous throw, and the
! to indicate that the next throw is made on the same beat as the previous one.
With this there is no longer a need for special syntax for synch siteswaps as
(4,4) can now be written as
4!40, nor there is need for multiplex notation as
 can now be written as
I am not convinced this contributes to the clarity of the pattern, but surely there was a need for some extra syntax to make transitions between synch and asynch possible.
- Siteswaps define the order of object interaction.
They do not describe:
- Rhythm or timing
- Where a ball is thrown or caught
- What body parts are used
- How props interact with each other
Or basically anything else. Juggling is so much more! Which is why we find many more notation systems.
Siteswap pros & cons⌗
Personal opinions incoming:
- Patterns that are hard to imagine can be generated or calculated
- Siteswaps are relatively intuitive to juggle, because of the connection ‘higher number is higher throw’.
- Patterns can be categorized into families, example.
- It’s not hard to come up with new variations of a trick within a family.
- A pattern can be applied on any amount of hands
- A pattern can be applied on any body move or special catch
- Very minimal format, pattern consists only of a short string of numbers, eg
- Widely used
- There are many tools to generate, verify, modify, simulate or otherwise play with siteswaps. See siteswap.org
- Can’t easily tell a valid siteswap from an invalid siteswap
- It’s difficult to describe transitions between synch and asynch.
- It can be difficult to tell what siteswap someone is juggling if the beats are not regular.
- Adding an extra catch site makes patterns hard to read. A pattern for 2 hands and one elbow must be read differently than a pattern for 2 hands, which is so confusing that almost nobody does this (we’ll see examples in Generalised Siteswap)
- It’s difficult to write down starts and stops, as you have to get into multiplex notation.
Ladder diagrams describe the timing of objects moving from one interaction site (eg hands) to another. Every line represents an object.
They can be easily created from siteswaps, and some of siteswaps development was inspired by ladder diagrams2 but it can be much more precise as also the time of a catch can be denoted in a ladder diagram, not just the throw. In the Juggling Lab software the timing of a trick can be modified by altering the ladder diagram.
Ladder diagrams pros & cons⌗
- Can easily be expanded to include extra interaction sites, such as an elbow, without getting harder to read.
- Can deal with starts, stops, multiplexes, synch patterns, without making the system more complex
- Very intuitive to read, is typically used as a method to explain the slightly more difficult siteswaps.
- Translating a video of a trick to a ladder diagram is easy and straightforward (and can be done to find out the pattern siteswap)
- Harder to read when there are more than 2 interaction sites (hands), as lines cross over.
- Reading and writing a ladder diagram takes more time than a siteswap.
- There is no standard way to convert a ladder diagram into a text string, making the diagrams harder to share. This is especially true for the timing part on the chart.
A variation of the ladder diagram is the causal diagram. Here not every prop is shown but rather which throws cause which other throws. I find them harder to explain than a ladder diagram, but because the diagrams have far fewer lines they are much simpler to draw and read once you understand the system.
They are used a lot when notating multi person passing, as describing patterns with 6 or more objects is much more convenient with causal diagrams than with ladder diagrams.
Typically dwell time is not shown in a causal diagram, but I came across this visualization from Jaco Stuifbergen which includes them.
Joachim Voigt club ladders⌗
In Kaskade magazine 253 Joachim Voigt proposes some extensions on ladder diagrams for club juggling. They consist of symbols drawn onto the throw paths which signify things such as the amount of spin a club has in the air or if body tricks are being made like backcrosses or under the leg throws.
Ben Beever describes his system of layering pattern attributes on top of siteswaps in his Guide to Juggling Patterns. He abbreviates it as “GS notation”.
These layers are: Throw time, siteswap, throw site (which body part), throw position (the position of that body part), catch site, catch position, catch type(claw, fork), spin, minimum air time. This is similar to the layers that Denis Paumier suggests in the Siteswap DVD2.
For these layers Ben comes up with a series of abbreviations, for example in a throw site you could write down
FR for “foot, right” or
OC for “on chin”. Also he offers extra information such as an approximate throw difficulty or catch difficulty for a certain throw position, or maximum throw height from a certain body part.
The layers are represented in a matrix, time horizontally and all the layers vertically.
This system, notates every hand at every beat. That is fine for synchronous patterns but convoluted for asynchronous patterns. For each of those beats it describes which hand and which beat a prop goes to.
This notation was designed by Ed Carstens for the juggling program JugglePro4, which can be found here (good luck running it on modern hardware, I gave up.).
Beatmap was invented by Luke Burrage5. It describes every hand on every beat, and it describes dwell time, which allow it to make timing patterns that are more complex than you typically find in siteswaps. It does not distinguish between synch and asynch patterns, which make it much more convenient than siteswaps if you want to transition between those. However if you only juggle asynch, it could contain a lot of redundancy.
It is easy to add an extra interaction site, and possible to add extra instructions such as a body position. Each extra instruction gets its own column and the column types are described in a ‘key’.
Beatmap is similar to Multi Hand Notation in that both systems describe each hand on every beat. It is also very similar to what Luna Harran describes as Polyrhythmic notation.
Also known as propswap and described by Adam Chalcraft as generators2. Adam suggests it was first invented by Colin Wright. It is not to be confused with prop swap as described by Craig Quat for the Juggle Board, which is a different notation system.
For every prop it is written how many unique props are thrown before this prop is thrown again. This results in the following properties:
Every siteswap translates to one unique stack sequence, and vise a versa, of equal length. The highest number in a stack sequence describes the amount of balls. Any sequence of numbers is a valid stack sequence.
Stack is not very practical as it is hard to work out what throws to make from a stack sequence, but it does have interesting mathematical properties. For example, stack can be used to determine the amount of possible patterns with a given length and prop count.
Alan Blim offers a version of siteswap that sits in between vanilla siteswap and Beatmap. A
3 in siteswap is called a
1 in music swap, as it takes only 1 beat to arrive. A music swap
3 is typically followed by 2 beats of no throws, but if the next throw is marked to start earlier with a negative number it can still be thrown immediately.
3,3(-2),3(-2) then refers to a 3 ball flash, which would be expressed as
55500 in siteswaps.
This notation does not distinguish between crossing or non crossing throws, it only specifies throw height and timing. Thus, patterns like musicswap
12 become possible which is a 3 beat pattern consisting of 2 throws. To write the crossed version of that pattern in siteswap would be something like
(1x,3)!4x1x (this would work in Juggling Lab), which is clearly much more complicated to express (but also contains the information about the crossing).
More information about music swap can be found here.
491 patterns for the solo juggler⌗
In the book “491 patterns for the solo juggler”, Martin Probert describes a new matrix based notation system. I have not been able to obtain a copy of this book, but in Kaskade magazine 226 the system is also explained by the author.
In this system a 3 ball height is referred to as
1, 4 ball as
2, etc, and it is noted separately if a throw is a cascade throw (crossing) or a fountain throw (straight). Also it is noted which hand makes the throw.
For example, a 4 ball half shower (siteswap
53)looks like this:
R L 3 1 c c
In the examples in the article all the patterns repeat the hand order
RL and also all the even throws are fountain throws and all the odd ones cascade throws. I therefor do not understand the added value of these extra layers, it effectively functions as a variation on vanilla siteswap, but with
n=n-2 for each number
n in the sequence.
It is possible that in the book more details of the system are explained which justify these layers. The book was written in 1990, which was only a year after a first paper on siteswaps were published, so this was likely not common knowledge at the time.
Body Trick Notation⌗
Invented by Denis Paumier in 20017. Also known as bodymove.
Body Trick Notation (BTN) describes the pathways a prop can take around the body using a topological model of a juggler. It assumes that a path always starts and ends at the front of the body, but even tricks like “blind behind the back” could be described if you pretend the ball is taken to the front after every catch.
In order to notate these pats BTN has a name for every ‘hole’ in the jugglers body plane:
BOL for between the legs,
AC for the hole between head and arm and
AL for the hole between arm and leg.
OP is prefixed if a hole is on the opposite side of the previous hole or else the throwing hand. You end up with pronounceable sequences like
ALOPAC which could be interpreted as backcrosses. This system can be combined with siteswaps to form patterns like 3ALOPAC33 which is a 3 ball cascade with one backcross.
Limiting the juggler to these 5 holes seems like a fair way to describe all pathways, but in order to describe body tricks well it would possibly need to be expanded with a way to describe throw site and catch site, as the pathways can be interpreted into multiple tricks. For example, the pattern
ALBOL could describe a throw made under the leg and then caught, or a normal throw being made and caught under the leg. Typically jugglers distinguish those two as different body tricks, but with BTN there is no way to distinguish them.
I dislike the use of AC & AL and BOL and OP, too many similar letters. I would prefer a system that is easier to read. Also, the use of ‘opposite’ means that it will be harder to describe a throw that does not come from a right or left body part, for example a prop that leaves from the mouth. This is rare, but not unthinkable.
Frédéric Roudaut has noticed that there might also be too few holes8, for example an “ass catch” which is normally thrown straight over the head rather than one of the 2 shoulders.
Nonetheless Frédéric did make good BTN pattern viewer, using recorded footage for many possible paths.
Symbolics for Objects and Juggler Planes⌗
The Symbolics for Objects and Juggler Planes, abbreviated as SOJUP, is a system designed by Frédéric Roudaut in 2011. It was designed to make it possible to implement complex body throws in juggling software.
It describes paths around the body, taking inspiration from the topology in Body Trick Notation, but it also describes the throw and catch location of a prop, and the objects path in relation to the space.
To describe throws a series of symbols are used which can be combined or layered on top of each other to give very precise definitions of a body trick. The symbols are in part inspired by symbols from the book Le Corps Jonglé by Frédéric Durand and Thierry Pavelak.
Space around the juggler is divided into a 2x2x2 cube. A circular symbol denotes from which direction we are currently viewing that cube, and a number (0 - 2) lets us know which depth layer of the cube is being described. Then objects and pathways are drawn on top of a 2d representation of that cube. A black object denotes an object being held or thrown, a white object one that is in the air or being caught. Some times a pentagram is added to describe the topology of a throw similar to Body Trick Notation.
On top of that, this system also adds a symbol to describes the rotation of an object. The rotation angles are similar to those as in Rotation Notation, but unlike in Rotation Notation the direction of the object is not noted. For symmetrical objects like clubs, rings and hats this is actually no issue at all as the direction can be assumed from the spin axis, but it takes away the ability to tell in which direction an object is pointing. Also, some letters can be added to distinguish different types of rotations:
R for rotations in a throw,
Rs for swinging and
Rm for other manipulations, which might need to be further specified. The direction of spin is denoted with a
-. To understand the direction you need to follow the logic explained in Frédéric’s article on Planes and Axis of the Juggler and Rotations of Objects.
It is suggested to use this system in conjunction with siteswaps, and the author offers some suggestions on how to mix the two: A certain body throw description is to be applied to each proceeding siteswap until a new body throw is denoted.
At last, the viewing angle can be dictated with a symbol, the system allows you to note down whether it should be viewed from the front, side, top, etc.
Some downsides are that because the juggler model can be seen from multiple different angles, it can take a moment to work out what throw is being described exactly. Also there is a lot of redundant information in many of the throws. At last, because of its graphic style it can be difficult to describe this notation and its tricks in a verbal language.
On the plus side, this model is very complete when it comes to tricks with positions around the body.
Points Stratégiques du Corps Jonglé⌗
In 2012 Frédéric Roudaut wrote an article about the strategical points on the jugglers body.
It describes a series of English abbreviations for body parts that could be used to either balance, catch, or interact, or a combination of those 3, with objects. For example the catch point ‘hand’ is abbreviated as
LH, and the teeth as
Mt (Mouth Teeth).
He notes that the list is not exhaustive, but to find more possible balance points one could for example try to describe it with a point on a path between two listed points. Also, catching points can be created artificially by combining 2 body parts such as an elbow and a knee and clamping an object between those, there is no notation suggested for this.
To distinguish between a balance and a grip or interaction, one can prefix a point with
int- so that
bal-H will be read as a balance on the hand.
Frédéric concludes that this notation system could be useful for simulation software, which is something I might indeed try.
Le Corps Jonglé⌗
Le Corps Jonglé is a beautiful book written by Frederic Durand and Thierry Pavelak, published in 1999. It discusses many possible considerations one can do when relating juggling to the body, and for all their ideas they suggest some icons or graphics to convey or notate these ideas. In the end of the book the graphics are combined to form what seem to be juggling patterns, but it is unclear to me how the combination of graphics are to be read.
There are icons to describe the following features of a juggling trick:
- From which direction we’re looking at the juggler
- On which plane the juggling takes place
- At what distance and height the juggling takes place in relationship to the body
- To a limited extend in which pose the juggler is
- At which point on the body the objects make contact
- At which point an object may have contact on the feet
- The various ways a ball can connect with the hands
- The various ways a ball can be thrown or caught
It is an in depth exploration of the various possibilities of juggling around the body, but does very little to consider the combination of such possibilities. Also the graphics are relatively complex yet at the same time not very precise in what they describe, making them hard to use for actually writing and reading juggling.
In the Jugglers Hand Book by Bear Stone, published in 1983, we find one of the earliest examples of juggling notation.
I have not been able to obtain the book, but Jack Boyce was kind enough to share some pages with me.
The system uses simple graphics to represent the juggler and their hands. Multiple graphics in a column are used to display the positions of multiple balls. For example in a 3 ball cascade you have a graphic to represent a ball in the right hand, a graphic to represent a ball in the left hand, and a graphic to represent a ball in mid air. Multiple graphics in a row are used to represent different moments in time, and each row tracks one object.
Variations of the hand symbol can be used to indicate that a ball is being clawed or caught with another body part.
Because a symbol is needed for each ball at each moment in time, writing out a complete pattern can take up a lot of space, but this can probably be simplified if all the repetitions are removed.
Labanotation is a system for notating dance9, and can be written with a lot of detail about each movement. So much so that you can even use it to describe juggling.
I obtained the book “Advanced Labanotation: Handling of Objects, Props” by Ann Hutchingson Guest and Joukje Kolff. The book describes many symbols and their usage within the Laban system to describe how dancers might interact with props, ranging from small hand props to furniture, clothes and even imaginary objects. Extra symbols can be used to describe movement qualities such as “with force” to turn something like a touch into a punch or slap.
Unlike with most juggling notation systems, there is much more emphasis on the quality of connection with the object. One can indicate nearness to an object, addressing it, enclosing it, touching it, grasping it, supporting it, penetrating it, and more.
As Laban scores movement over time there are very accurate ways to indicate how long an object relationship should be, ranging from momentous to continuous.
Using drawings of the prop one can indicate where the prop is to be touched, which is especially useful for larger props such as chairs. Also, labanotation allows you to be precise about what body part is touching, for example which fingers are involved in the action. Objects can be connected to different body parts at once, or connected to other objects or the floor, or other performers.
At the core of labanotation sits a system to show direction, so of course this can be applied to objects too. For example a stick can be pointing up/down, left/right, forward/backwards, and diagonal in between any combination of these. With a drawing of the object it can be indicated which part of the prop is doing the pointing. By showing the rotation of the object and the rotation of the wrist and hand it can be worked out how an object is to be grasped. There are also rotation symbols that can show relative motion, such as “rotate the prop for a half spin on the frontal plane”.
An object that is not connected to a performer nor to the ground must be in the air, so juggling can be displayed. Although one can draw exactly which body parts connect with the prop at which time, there is probably too much information in a laban score to make it really useful for notating juggling tricks. Nonetheless a score for juggling with 2 balls has been included in the book9.
The book goes on to give examples and descriptions of many different props a dancer might use, such as skipping rope, a hoop, umbrella, a pillow, and many many more.
The book credits Maria Szentpal and Albrecht Knust for laying the groundwork of the prop handling notation in Laban.
Musical notation style⌗
Graphic Juggling Notation⌗
This system was developed by Rauli Katajavuori. Ideas for it started in 199610 but it got published first in 201611. The original document that explains the notation can be found on the website of Sirkus Supianen.
Siteswaps are denoted as heights on a score similar to a musical score. A square defines a right handed throw, a circle a left hand. Pattern like
423 can be described by a square on between line 2 and 3, a circle between line 1 and 2 and a square on line 3, written next to each other from left to right. In order to make this pattern repeat it would have to be written down twice, once for the left hand and once for the right hand.
There is syntax for synchronous siteswaps and multiplexes.
Spacing on the horizontal axis allows to denote some variations in timing.
Inside and outside throws are denoted with a filled or open shape.
Graphic Juggling Notation includes a form of Body Trick Notation, but it is represented graphically with 2 little arms on each square or circle, each arm representing a hole. Also this system does not use the “opposite” notation from BTN, it always assumes we see the juggler from the front. Multiple arms can be added if the object makes multiple rotations around the body in one throw.
It is an interesting attempt at displaying siteswaps and BTN graphically, but the characters can get quite complex to draw and read. A trick that is complex to describe in siteswap will be at least as complex to describe in GJS, and potentially it contains a lot of redundant information if the pattern is of an odd length but repeating.
Harmonic Throws has been developed by Jonathan Lardillier since 2016 and was published in 2019. It is designed to help jugglers choreograph and work collaborate with other jugglers or musicians by being able to exchange diagrams. Information can be found on the website of l’Expedition. There is also a booklet written about the system and its background by Cyrille Roussial.
The notation consists of 3 layers that work together: The grid which describes the balls and timing, the space which describes the path around the body and the reach which describes the position and movement of the body. At last there is a key that describes the starting position.
The key describes the amount of objects in each hand, and which hand will start the sequence.
The grid does not use siteswap, but it introduces its own beat and number based notation system. Similar to Graphic Juggling Notation, a higher noted throw means that it will take more beats to come down. A throw height 3 (which noted as a circle on the second line) is caught 2 beats later, as also the beat that the prop is released is counted. So a prop can be thrown at beat 1, flying at 2, caught at beat 3, making it height 3. This is the first system we come across that denotes the catching time.
The grid can be either in right or in left mode, in right mode every odd numbered beat is executed by the right hand by default. There are symbols to switch between right and left handed mode.
An object that is thrown crossed is a closed circle, a ball that is thrown straight as an open circle. There are extra symbols possible to denote catches if they are claw catches.
Synch throws are not drawn synchronously in time, they are spaced out as normal but connected by a line.
On the grid you can also mark if a throw is made on the inside or outside.
I like how the grid is removed from the assumptions of siteswaps, and it encourages a style that includes starts and stops.
The space uses a system called TAC, which is Body Trick Notation, but different names and a graphical representation.
OPAL are translated to
BO. I think that is a good choice because it is shorter. However, the choice to abbreviate a
tiTO path to
tT seems rather confusing to me, and is hard to read and write. There is also a graphical symbol for each combination, which may be easier to remember for some, but as the letters are already very short I don’t think it is very useful.
“The reach” is my translation of “la portée”, perhaps there is a better name for it.
In my opinion this is one of the most interesting and unique aspects of Harmonic throws. The reach describes the body of the juggler using a simplified version of Benesh notation, which was originally developed for dance. It describes movements pose to pose, so the exact path between poses needs to be filled in by the performer. However, in combination with the space it becomes possible to describe tricks around the body fairly accurately. There are symbols for the head, body, elbows, hands, knees and feet, which are drawn as a kind of stick figure seen from the front, with variations of the symbols to describe if they are on the front, middle or back plane. An extra symbol denotes a crossed hand or leg so that the two hands don’t get confused. Only the relevant body parts need to be drawn, so for most tricks you don’t need to draw the whole body.
This system is great for it’s expressiveness, but doesn’t convert easily to a verbal language.
Harmonic throws seems to favor balls, as there is no rotation notation but there are special catching instructions which are most useful for balls.
Overall I enjoy how the system seems to encourage to move away from ‘tricks’ and instead think about sequences of moves.
Mills Mess State Transition Diagram⌗
Invented by Mike Day to work out how to reverse a Mills Mess pattern2, in 199212. It is often abbreviated as MMSTD.
It denotes the state of the hands which can be crossed over or under or uncrossed, and right can be about to throw or left can be about to throw. A total of 6 states.
There are paths that take you from one state to the other, which can involve inside or outside throws. The paths assume that left and right alternate, as is typical in siteswaps.
Only ‘natural’ feeling paths are included, there are paths that are physically possible but not included in the notation. However, it is not difficult to use the same notation for unnatural paths, as explored here.
The states can be written as
Ul for “uncrossed, left hand” or
Rr for “Right over left, right hand”. The original text notation for paths was to write an underscore over outside throws, but as this requires 2 lines for a pattern and is hard to write in a text document Frédéric Roudaut suggests
-x->. The pattern “mills mess” could become
Ur -o-> Rl -x-> Rr -x-> Ul -o-> Lr -x-> Ll -x->.
SOU is a simplification of the Mills Mess State Transition Diagram system. It was designed by Frédéric Roudaut in 2007. Here is the original article.
S stands for Side, arms uncrossed.
O is Over, arms crossed describing the top hand.
U is Under, crossed bottom hand.
Inside throws are noted with an
i and outside with
o. Siteswap can be added to this, a 3 ball cascade becomes
Chops can be denoted as
3Ui. This pattern is considered invalid in the original MMSTD unless you were to write it with siteswap
522 as the path does not exist.
Doing away with the R and L notation makes this system more suitable for siteswaps than MMSTD.
Pretzel Hand comes from Steve Bags who conceived it in 2020. Here is the original article.
It uses letters to describe the throw position using a system very similar to MMSTD, but it is different in that it also denotes the catch position.
Also with a
/ character you can describe on which side of the body the first throw peaks. A
: is used to denote that we’re throwing from the opposite side of the body. A cascade can look like this:
i\ Uu : Uu
Mills mess is written as
o\ Ru Ul Ll : Lu Ur Rr and here you can see the catch sites being applied to give a tad more detail about how the pattern is executed.
George Gillson Diagrams⌗
George Gillson invented a simple diagram to explain tricks like “mills mess”, which he then used in his book “Beyond the Cascade”13. I managed to get a copy of the book to study the diagrams. Many tricks were also republished in the Kaskade magazine, making sure that many jugglers have learnt from these diagrams.
The diagram displays two hands and all balls as seen from the jugglers perspective. Each ball is assigned a number. Arrows are used to indicate where a ball or hand is going next, and multiple diagrams are shown for multiple moments in time in a trick. Sometimes the next hand position is indicated with a dashed line.
Variations or rotations of the hand symbol are used to indicate different types of holding the ball.
In the book there are explanations of tricks around the body such as backcrosses and shoulder throws, but these could not be understood from the diagrams alone, one needs the accompanying text for these to make sense. However, tricks that take place in front of the body such as “mills mess” could be well understood, possibly even without being explained how the system works, from the diagrams alone.
This system was designed by Varkor to describe the orientation and rotation of juggling props.
It describes the prop alignment and direction at the moment of the throw, and it describes the axis the prop rotates around in flight, and the amount of rotations.
It can only describe rotation in 1 axis at a time, which makes it quite simple to use and understand. I am actually surprised by its simplicity, I had worried it would be complex and unusable but now this makes me want to pick up some clubs!
I got my information from the juggle wiki, the original document appears to be offline and I am unable to reach Varkor. There is a bunch of relevant discussion about its publication on rec.juggling.
Aidan notation is a system for specific club passing patterns. Although it could be used for other passing tricks, it is most suitable for patterns in which there is passing and club intercepting.
For each juggler there is a score which indicates whether the juggler is throwing a pass or a self on each beat of the pattern. A manipulator has a score that indicates when they are carrying a club, substituting a club, or intercepting a club. Whenever an intercept takes place, the person passing becomes the manipulator. At the end of the sequence there can be an indication which roles the passers take on next.
The system is explained here, and on YouTube there is a nice talk about how the system came to be and why a domain specific language like Aidan notation can be so powerful and valuable.
Among other things, the Aidan notation was used to discover all 27 variations of the scrambled V.
Here is a table listing different features.
You can also view the table here in a spreadsheet, which is recommended as it is much easier to view than the two tables below.
|Up to the year 2000||Labannotation for prop handling||Siteswap||Ladder diagram||S-Notation||Causal Diagram||Stack Notation||Synch and multiplex siteswap||491 Patterns for the Solo Juggler||George Gillson Diagrams||Multi Hand Notation||Joachim Voigt club ladders||Mills Mess State Transition Diagram||Le Corps Jonglé|
|Object interaction order||✔||~||✔||✔||~||✔||✔||~||✔||✔|
|Object position to objects||~||✔||✔||~|
|Throwing and catching styles||✔||✔||✔|
|Object position to body||✔||✔|
|Object interaction with body||✔||✔|
|Object path around body||~||~||~|
|Ball air time||✔|
|Contact points on the body||✔||~|
|Object pointing direction||✔|
|Simpler than its precursors||✔||✔||✔||✔||✔||✔||✔||~|
|Year of origin||~1976||1981||1981||1983||1984||1985- 1996?||1990||1990||1990||1991||1992||1992||1999|
|Originator||Rudulf Laban, Maria Szentpal, Albrecht Knust||Paul Klimek||Claude Shannon or Paul Klimek||Bear Stone||Mike Day||Colin Wright||Jack Boyce||Martin Probert||George Gillson||Ed Carsten||Joachim Voigt||Mike Day||Frédéric Durand, Thierry Pavelak|
|From the year 2000 onwards||Generalised siteswap||Body Throw Notation||Music Swap||Beatmap||SOU||Symbolics for Objects and Juggler Planes||Points Stratégiques du Corps Jonglé||Rotation Notation||Aidan notation||Graphic Juggling Notation||Harmonic Throws||Pretzel Hand|
|Object interaction order||✔||✔||✔||✔||✔||✔||✔||✔|
|Object position to objects||~||~||~||~||~||~|
|Throwing and catching styles||✔|
|Object position to body||~||✔||~||✔||~|
|Object interaction with body||✔||✔|
|Object path around body||✔||✔||✔||✔|
|Ball air time||✔||~||✔|
|Contact points on the body||✔|
|Object pointing direction||~||✔|
|Simpler than its precursors||✔||~||✔||✔||✔||✔||~||~|
|Year of origin||2000||2001||2004||2007||2011||2012||2012||2014||2016||2019||2020|
|Originator||Ben Beever||Denis Paumier||Alan Blim||Luke Burrage||Frédéric Roudaut||Frédéric Roudaut||Frédéric Roudaut||Varkor||Aidan Burns||Rauli Katajavuori||Jonathan Lardillier||Steve Bags|
Whoa, something stands out here. Laban for objects came way before the first juggling specific notation systems, and is able to perform in all the categories I made up. Yet at the same time, as far as I know it has not been explored to notate tricks by jugglers at all. To me this suggests that the best system is not the one with the most features, but the one that can give the most relevant information in the simplest way possible.
The bottom category “simpler than its precursors” is my attempt to highlight those systems that manage to be a simpler system without loosing too much detail in the categories they describe.
Siteswaps DVD (now free online!) by Gandini Juggling ↩︎
Voigt, J. (1992, March). Juggling on Paper. Kaskade, 25, 16–17. ↩︎
Probert, M. (1991, June). Playing with Patterns. Kaskade, 22, 18–17. ↩︎
Guest, A. H., & Kolff, J. (2002). Advanced Labanotation, Issue 8, Handling of Objects, Props. Dance Books Ltd. ↩︎
Gillson, G. (1990). Beyond the Cascade. Ugly Juggling. ↩︎