Introduction

In Siteswap and Rhythm: Problems (part 1) we discussed reasons why siteswap might not be suitable for rhythmic juggling. In this part 2 we consider some existing solutions such as using a special form of synchronous siteswap or a rhythmic notation like Harmonic Throws.

I will also present a new system: Rhythmic catches.

Half beat synch siteswaps

One possible solution to “fix” siteswaps is by sticking to the assumption that throws should be spaced evenly, but then alter how we write down our tricks. For example, if we tried to write down our optimal 441), we could interpret it as a 2 beat synchronous pattern. In that case we would write it as (4,2)(2x,4)*.

Writing it as a 3 beat rhythm with a gap is slightly more difficult as we get into “half synch beats” (marked with a ! in Juggling Lab), but it could be done for example as (4,0)!(1,3x)!1x*.

When I enter the sequence (4,0)!(1,3x)!1x* in Juggling Lab it is certainly closer to how I personally juggle the 441 trick compared to how when you enter 441 into the software. But is that extra bit of precision worth the much more complex notation?

(4,0)!(1,3x)!1x*
(4,0)!(1,3x)!1x* in Juggling Lab
441
441 in Juggling Lab

Harmonic Throws

Harmonic Throws is a system which uses a rhythmic notation system. Throws and catches are on the same time grid, more on that later. Normally the rhythm is displayed graphically, but for the purpose of this article we can translate throws with numbers to represent how many beats they span. The numbers reflect the amount of beats that a throw spans, not the amount of beats that a ball is in the air. So a normal siteswap (SS) SS3 throw which takes 1 beat to arrive is written in harmonic throws (HT) as a HT2. A SS1 is written as HT1 as both the throw and catch take place on 1 single beat.

Sadly, harmonic throws is not often used to notate basic siteswap patterns, so I have no reference of what SS441 in harmonic throws would look like. I would probably write the catches spaced evenly version as some form of HT3(1,3)0, with the 0 representing “no throw” and the (a,b) representing to hands throwing at once. However, this version assumes “perfect exchanges”, beats in which a throw and a catch happens in the same hand at the same time, which is of course not practically possible.

I’m not sure if it is a rule, but I have noticed that Harmonic Throws choreographies typically avoid these kind of theoretical collisions.

Since harmonic throws has throws and catches on the same time grid where they could happen at the same time it is difficult to write juggling as it is typically performed, as normally throw and catch rhythms are slightly offset by about a third of a beat (as a result of optimal dwell time). Most Harmonic Throw choreographies that I’ve seen try to solve this by having throws and catches spaced at least 1 beat apart so that a perfect exchange never needs to be performed. However, this leads to longer empty hand times, which means that the balls need to be thrown higher. This may make for perfect musical juggling as both the throws and the catches can be aligned to an even rhythm, but it does not make juggling easy. Therefor harmonic throws is not very suitable for notating juggling tricks, but only for very specific (rhythm dependent) juggling choreographies. Translating SS441 to harmonic throws without throws and catches happening at the same moment could not be done if you assume that the second 4 and the 1 are done on the same beat, as the 1 lands at the same time as the 4 is thrown. In 441 one could argue that you perhaps have to juggle it differently, with both the 4’s released before the 1 gets thrown, but a pattern like the box would still be impossible to notate without theoretical collisions.

Rhythmic Catches

NOTE: This version of Rhythmic Catches explained below is outdated. For the new and improved version, you can read the explanation in this post. The next sections (benefits and issues) may still be relevant, even though they use older syntax.

I propose a solution: Rhythmic Catches (RC). Similar to the system in harmonic throws, but with one major difference: It is not exactly noted when the throws are made, only when catches are made. Also, the system is not graphical, and uses different numbering.

A number designates the amount of beats later that an object will be caught. For example, an RC1 will take one beat. However, it is allowed to throw it any time between “beat 0” and “beat -1”. So the amount of time that the ball could be in the air is actually between 1 and 2, depending how early it is being caught. A normal throw RC1 with normal dwell time will usually be in the air for about 1.6 beats. Note that the throw has to be made between beat 0 and -1, it is not allowed to throw on 0 or -1 as this would allow for confusion. For example if you do two 1 throws after each other it may be unclear whether you are throwing 2 different balls, or twice the same ball. As soon as the first ball arrives, you might be throwing it again as that would be beat 0 of the second throw. This is not allowed, instead there is special notation to deal with hits or slaps.

The absence of a throw is written as -.

As per the siteswap convention, odd throws cross and even throws are straight, unless there is an x behind the number, then they do the opposite. So for example 2x- is a high 3 ball cascade.

Throws will be made alternating left and right, but if a * is placed in between throws the same hand operates again. So for example RC2x2x* (which is a variation of SS552 but with slightly different timing) would have the hand order RLLRRLLR.... Unlike with siteswaps an * can also be written in the middle of a pattern, for example 2x2x*22 is a valid pattern too, with the hand order RLLRLRRLRLLRLRRL....

Throws that are made on the same beat are written in brackets and separated with a comma, for example (2,2). In brackets we don’t assume that the left number is the left hand and the right number is the right hand like in siteswaps, instead the left right order continues from the number sequence. So in the pattern 112-(2,3)-* the hand order when starting on the right is RLR(LR)

The SS441 pattern with catches spaced evenly could now be written as RC2(2,0x)-

Also, rhythmical tricks like a galloping cascade are now easier to write. SS(1x,3)!4x1x could now be written as RC12x-

As a bonus feature, I propose a symbol to deal with hits or slaps. If an incoming ball is hit it means that it is thrown and caught at the same instant, which is not allowed according to our rules above. Therefore we will note a hit with a + symbol in front of the number, which suggests that we “add” airtime to it. So 11 are two throws with 2 balls, but 1+1 means that one ball is being thrown, and one beat later it is being hit. This will be useful when trying to describe patterns such as these. However, in the current version of rhythm notation there is not yet a way to reference other body parts.

Multiplexes can be tricky, in SS[33]33 you’re typically not expected to catch the [33]s at the exact same time. However, with the rule that the number in RC defines the landing beat, it is hard to read the equivalent RC[11]11 as anything other than a perfect squeeze catch. To solve for this I suggest that a ~ suffixed behind a number means “landing earlier; some time between the previous beat and this beat”. Like this we can write RC[1~1]11 to indicate that the first multiplexed ball lands just before beat 1 and the second multiplexed ball exactly on beat 1. Even when writing RC[11~1~]11 both 1~ throws don’t need to land at the same time, they can both land at any moment between beat 0 and 1. This feature also means that when someone writes a finishing collect like RC210 and there are no ~s, we assume that it is intended as a squeeze catch. A ~ can even be suffixed to a 0, it would have to land before the beat but since it can be thrown from on any moment since beat -1, it is for example possible to throw on -0.8 and catch on -0.5.

If a throw is made by the hand that catches the ~ throw, it can be assumed that the throw is still made before the catch and not the other way around. So if ~1 arrives at beat 0.5, then the next throw has to be made between beat 0 and 0.5, not between 0 and 1 as usual.

Rhythmic Catches benefits

In Rhythmic Catches, similar to Harmonic throws, you don’t need to notate holds. This could make notating patterns with a lot of holding such as this sequence easier to notate, but also in patterns that transition from asynch to synch there are typically some confusing SS1x holds which no longer need to be written down.

This is on top of the obvious benefits such as being able to write rhythmical juggling. With rhythmical juggling you can easily write patterns such as galloped patterns, be specific about how you want your SS441 catches timed, throw any 3 beat pattern into a 4 beat rhythm, or fix juggling to music.

Rhythmic Catches clarifies that rhythmical juggling is mostly about the catches, and that the throw timing follows from that, despite the throws of course coming first.

It allows you to write down hits or slaps and it has notation for squeeze catches and non squeeze catch collects.

And at last, it allows you to write SS441 with the catches spaced evenly which is RC2(2,0x)-, or the “optimal” SS441 which is RC 2~(2,0x)-.

Rhythmic Catches issues

This system can still not represent the different speeds of different patterns, so it will not be suitable for all choreographing purposes.

There is also no solution for all polyrhythm patterns, but possibly the system could be extended to include polyrhythm with a decimal point. Perhaps “4 over 5” could be written something like RC(2,2.4)2 2.4 2 2.4 2 2.4 2*, but the details of this notation would have to be worked out further.

The system is vague about when to throw and specific about when to catch, but then allows to modify the catch timing with the ~ to make it vague too. One could argue that in non musical/rhythmical juggling there is no place for a metronome and perhaps by default everything should be made vague. My argument would then be that siteswap is a non rhythmical system, yet there seems to be a huge desire to apply it in a rhythmical fashion. This is an attempt to approach juggling the other way around.

Also, there need not necessarily be a rule that all beats are evenly spaced. Perhaps all of this could be interpreted with an uneven rhythm, like a swing rhythm or syncopation in music.