Welcome to this blog. Here I present my thesis about juggling notation, titled:

Tricky throws and pretty patterns: improving upon 40 years of juggling notation

This thesis consists of many individual blog posts. Some are core to this thesis, some can be seen as appendix, and some can be considered as scribbles in my personal notebook. To guide you through the good stuff, this page summarizes my findings, introduces you to my new notation systems Rhythmic Catches (RC) and Improved Body Throw Notation (IMBO), and links you to the relevant posts.

Have fun reading!

Daniel Simu

Much like music can be represented on paper as sheet music, so too can juggling tricks be represented by juggling notation. Jugglers use notation to record, instruct, or otherwise communicate juggling with both peers and software, but notation is also a particularly useful tool to analyze tricks and generate new ones. However, the existing notation systems are often also limiting, confusing, or hard to use.

To improve upon the 25 different juggling notation systems that I have identified, I designed two new systems: A pattern notation called Rhythmic Catches which can be used in place of the popular but limiting system Siteswaps, and a throw notation called IMBO which can be used in place of the clever but ambiguous system Body Trick Notation.

To evaluate these new systems I analyzed the features of ball juggling tricks from expert contemporary jugglers. I found that many of these features, such as tosses and catches with body parts other than hands, are hard or impossible to describe with existing systems but often within reach for my new ones. Also I created a list of 22 common 3 ball tricks which I transcribed in 8 different notation systems, and argue that my new systems are the most suitable ones to represent these tricks.

Not only do I conclude that Rhythmic Catches and IMBO can indeed be used to elegantly describe a wider range of patterns than previously possible, also these systems would be suitable to use in future juggling simulators.

If you’re are a juggler like me, you have likely heard about or made use of a juggling notation system called siteswap. It’s a beautiful and simple mathematical system that represents throws with numbers, and it can be used to write down juggling patterns. I have used siteswap a lot, for example to create new tricks and choreographies. It serves as the basis of almost all juggling simulation software that I know of, and the invention of siteswap in the early 80s¹ has in my opinion revolutionized juggling.

Despite it’s value and success, I have also always found it limiting. Siteswap does not describe anything but the order in which objects are handled. It does not describe pathways around the body, interactions with the body, and it gets progressively more difficult to use when more than two hands are involved in the juggling.

Frustrated by these limitations I have always been looking for other notation systems that could describe juggling better. Such a system could be used to record juggling, to instruct other jugglers, to communicate about juggling, to understand juggling better, to simulate juggling, to generate new patterns, far beyond what we already can with siteswap. However, the systems that I have found were often either under-developed, hard to use, ambiguous or only applicable to a very small niche of tricks.

By getting a deeper understanding of the existing juggling notation systems, and by reading about dance and music notation, I will attempt to improve upon the existing systems and create new ones. The newly designed notation systems needs to be able to deal with many features of juggling that are difficult or even impossible to describe with the current systems.

I will evaluate these new systems by using them to describe simple and complex juggling patterns, and by comparing the new systems to other existing ones.

The process of researching, designing and evaluating will be done in a somewhat informal manner, namely by writing informal standalone blog posts.

In this thesis overview I will link to posts that contribute to the chapters in this page.

For example, if you would like more introduction I would like to refer you to the post:

• Why do we notate juggling?

Publicly accessible information about juggling is scattered in books, blog-posts, videos and web forums, and there are only very few articles published about the practice of juggling that hold up to academic standards.

From what I could find online, in books, and in magazines I compiled a list of about 25 existing juggling notation systems. I have briefly described each of them, and created a table which sorts them by their origin date and compares their features. My understanding of these systems has become the basis of my new systems. You can find all this in the article:

• Existing Juggling Notation Systems

I have also had a brief look at dance notation, music notation, and the lessons we can learn from these. This gave insight in different ways to categorize notation systems, and what different applications they may have.

• Dance notation
• Music notation

At last there was also a bit of historical research, particularly about the invention of siteswaps in the early 80s. This article contains some random notes I took when watching the interviews on the Gandini Siteswaps DVD.

• Observations from the siteswaps DVD

Inspired by the various notation systems I have studied I quickly built a siteswap alternative that could deal with multiple manipulators, in an attempt to be less confusing and containing less redundant information than the alternatives. I called this system dNote.

• dNote, a siteswap extension

Similarly, I also extended Body Trick Notation in an attempt to make it’s throws less ambiguous. This is called IMBO.

• Improved Body Trick Notation (IMBO)

After these newly designed systems I analyzed ball juggling tricks from contemporary jugglers in an attempt to discover difficult to describe juggling trick features.

• Analyzing Ball Juggling Tricks

Through this analysis, and my own observations whilst thinking about dNote, I realized there were two more issues I wanted to tackle. The first being the juggling rhythm, as siteswap poses some interesting challenges when trying to apply it in the real world. The second of these articles introduces an early version of a new notation system called Rhythmic Catches.

• Siteswap and rhythm: Problems (part 1)
• Siteswap and rhythm: solutions (part 2)

Resulting this analysis of siteswap and rhythm, I concluded that it was more valuable for me to continue with a rhythm based notation system.

• Siteswap based vs rhythm based pattern notation

The second issue I still wanted to tackle was inside and outside throws. These turned out to be harder to define than I had expected.

• Inside & outside

With all these new insights I was able to construct a final version of Rhythmic Catches. For this final version I used a list of body points for easier abbreviations.

• Rhythmic Catches (RC)
• Interaction points on the body

But how did these new systems hold up compared to the existing ones? I wished to test my systems on a standard list of tricks, but there was no such list yet. Therefor I created one.

• Daniel’s 3 ball trick list

With some help, I transcribed all the 22 tricks on the list into 8 different juggling notation systems, so that I could then evaluate their differences.

• Standard tricks transcribed into 8 notation systems
• Notation Comparison Evaluations

Also, I tried once again to describe the tricks from the earlier post about Analyzing Ball Juggling Tricks, but this time using only Rhythmic Catches and IMBO.

• Notating tricky tricks

So, how about it, are Rhythmic Catches and IMBO any good? Partially this has already been answered by the comparison evaluations, but in this post I summarize all that there is to say about it. I finally lay out a bunch of the goals that have been in my head during all of this process, I evaluate the systems with an external list of goals for good notation systems, and I even provide some anecdotes about how Rhythmic Catches and IMBO have already been useful to me. To make a long answer short: I think they’re pretty good.

• Evaluating Rhythmic Catches and IMBO

A lot can be said about my improvised methods. Are they any good? They certainly are not free of bias. Coming up with the methods, the goals, the tests and the systems has been an organic process rather than a systematic one. There is not a single proven method for coming up with good notation systems that I’m aware of, the best I can do is to try and be rigorous and honest and to report about every step of the process. This is also why this thesis is in this blog format.

So with method, how sure can one be that these new systems contribute to how jugglers will be able to use notation in the future?

For starters, I know I will have a use for it, see the anecdotes in Evaluating Rhythmic Catches and IMBO.

I strongly believe that still very few jugglers understand the relationship between throws, catches and rhythms as it is so difficult to realize what your hands do out of habit, as I wrote about in the conclusion of the Siteswap and Rhythm: Problems. I think that even for jugglers who have no interest in juggling notation, learning the foundations of Rhythmic Catches will allow them to have a much better understanding of the juggling rhythm.

It’s funny how things seem obvious in hindsight, when they were nearly imperceptible at the time. When I started with this research I had no system to accurately describing tricks around the body other than with words and names. But then when the idea was sparked for marking not only the hole but also the moment of catching and throwing in relationship with the holes in IMBO, it seemed so obvious that I can’t imagine not thinking about these holes any more. This does not mean that IMBO is without issues, as I discuss in the issues section of Improved Body Trick Notation, but I have a feeling that this concept will trickle into the knowledge base of the juggling community in the following years. There is even some evidence that supports this suggestion, which is that Harmonic Throws v2 will use a nearly identical concept, as I discuss in the comparison with Harmonic Throws in the Evaluation of Rhythmic Catches and IMBO.

Siteswaps gave jugglers a large understanding of patterns, in solo juggling these are almost always limited to just two hands. As far as I am aware, Rhythmic Catches is the simplest and most effective notation to describe patterns that interact with multiple body parts such as the 4b elbow trap, the elbow zip in out, or even monkey juggling. I expect that now that these kinds of patterns can be understood separate from their individual moves, it will be much easier to work out variations that use different manipulation sites, different timings, or both.

Of course it should also be possible to generate patterns like these, using Rhythmic Catches and IMBO. I hope to see this in future research, just like I hope to see the simulation of such patterns. This page will be updated in the near future with a link to an article about the woes of creating juggling simulators, and also with a link to an article about future research.

Until Rhythmic Catches and IMBO are used by a larger amount of jugglers than just me, it will be difficult to tell exactly how valuable they can be. And until there is also a solid system to support prop orientations, as I discuss in Evaluating Rhythmic Catches and IMBO, these current systems are far from being able to describe all toss juggling.

But considering the desire for such systems, as I discuss in the notating juggling section of Why do we notate juggling?, and considering that Rhythmic Catches and IMBO outperform all of the other multi feature notation systems as shown in the comparing support for various trick aspects section of the Notation Comparison Evaluations, I think there is a very good chance it will prove itself useful in the future.

Although the notation systems are functional, they may still be improved or expanded upon in the future, and I invite anyone to take part in this. I discuss the desire to improve Rhythmic Catches in the future section of Rhythmic Catches.

At last, I have attempted to list all the limitations of Rhythmic Catches and IMBO that I am aware of:

• Limitations of Rhythmic Catches and IMBO

And I discuss my desires for future research:

• Future Research

This research has been successful in creating useful toss juggling notation systems that can be used to write down juggling tricks or choreographies, with more detail or less effort than existing systems. I propose Rhythmic Catches as a “pattern” notation and IMBO as a “throw” notation, which can be combined to represent most ball juggling tricks.

The Evaluation of Rhythmic Catches and IMBO concludes that these new notation systems manage to achieve all their goals, such as being able to describe tricks around and with the body with elegance in a way that improves upon existing notation systems.

In the Siteswap based vs rhythm based pattern notation I conclude that a rhythm based system can be more specific and more elegant than a siteswap based one, which further justifies the invention of Rhythmic Catches.

These new systems build upon the existing notation systems that we have identified, and were formed after detailed analysis of juggling rhythms and object pathways.

From the evaluations we learn that they are in many aspects better than the previously existing systems.

This research was conducted in 2022 as part of the Media Technology Masters degree program at Leiden University.

I had an incredible amount of feedback and support from my first supervisor Dr. Rob Saunders, and my second supervisor and juggling expert Owen Reynolds.

In the process of writing I was lucky to be able to share thoughts with many fellow juggling notation experts, but in particular this thesis would not have been the same without the help of Jack Boyce and his software Juggling Lab and Jonathan Lardillier and his notation system Harmonic Throws.

Most of the colorful header images were kindly created by Yara Valente. The other images and animations inside the posts are created by myself.

See the individual articles for their references.

All the articles and their chapters can be found in the archive.

The references used on this page are below the line:

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1. Gandini, S. (Director), (2006). Siteswaps[dvd]. Media Circus. ↩︎