What do the / and + characters mean?

Siteswap transition generator

These two characters are used in transitions between asynchronous and synchronous siteswaps.

/ = rhythm change

The / character is used to show the change in rhythm either from asynchronous to synchronous or synchronous to asynchronous.

For example in the following sequence the 4, 5 and 3+ are thrown asynchronously. Everything else is thrown synchronously.

4 53+/ (6x,4)(2,4x)

Where the / appears will be dictated by when props thrown from the initial pattern are received. We cannot change rhythm until at least all-2 of the props have been received.

+ = plus one beat extra

The + character is used to show the previous throw must be thrown one beat higher to enable a change in rhythm. I use + because the alternative method of increasing the throw value changes the destination hand of the throw and blurs the distinction between what part of the transition is asynchronous and what part is synchronous.

If we start off in an asynchronous rhythm:

To shift into a synchronous rhythm we can delay all left hand (or all right hand) throws by one beat:

To shift back into an asynchronous rhythm we can delay all right hand (or all left hand) throws again by one beat:

Consider two jugglers side by side, one juggling 4 and the other juggling (4,4). All throws are thrown to the same height and both right hands are throwing at the same time.

The synchronous juggler's left hand is throwing one beat later than the asynchronous juggler's left hand.

To transition from an asynchronous to a synchronous rhythm all throws made before the rhythm change that land in one of the hands after the rhythm change need to be thrown with an extra beat of air time to land at the correct point. Which hand depends on the destination pattern's rhythm and starting hand as shown in the following table.

For example transitioning from an asynchronous to a synchronous pattern that starts with the left hand, all throws that land in the left hand need to be received one beat later:

You could also use - to indicate throws made with less air time to achieve the same effect. However, I think throwing higher and waiting is more practical than throwing lower and hurrying so for the sake of keeping complexity to a minimum I've decided to only use + in the Siteswap transition generator.