Multi-hand notation (MHN) is a juggling notation system invented by Ed Carstens.
In this notation system a pattern is written as a matrix, where each row corresponds to the throws made by a certain hand (or a certain juggler), and each column corresponds to a beat in the pattern (a point in time when throws can be made).
Each element in the matrix is an ordered pair representing a throw made by a certain hand at a certain time. The numbers in the pair indicate what time and what hand the object will be in when it's caught (relative to where it is when it's thrown).
The first entry in the ordered pair designates which hand the object is thrown to: Whatever number is the first number in the pair, go that many rows down in the matrix to get to the destination hand. When a hand throws to itself, this number will be 0, and when it throws to a hand represented in a higher position in the matrix, the number will be negative.
The second entry in the ordered pair is the number of beats later the object will be thrown again. A 0 represents an empty hand, and in jugglable patterns it can only be directed to the same hand that threw it, so if the second number in an ordered pair is 0, the first must also be 0. (0,1) means an object stays in the same hand until the next beat.
A simplified version of the notation replaces each ordered pair with a letter showing which hand (or juggler) to throw to and a number, with no parentheses. Throws are separated with commas.
( 1,3) ( 1,1) (-1,1) (-1,3)
6 object 4-count:
( 3,2) ( 0,1) (1,2) ( 0,1) ( 0,1) (-1,2) (0,1) (-1,2) (-1,2) ( 0,1) (1,2) ( 0,1) ( 0,1) (-1,2) (0,1) (-1,2)
D2,A1,B2,A1 B1,A2,B1,A2 B2,C1,D2,C1 D1,C2,D1,C2
3-person feed, written in a simpler version of MHN, where the rows represent jugglers instead of individual hands:
( 1,3) (0,3) ( 0,3) (0,3) (-1,3) (0,3) ( 1,3) (0,3) ( 0,3) (0,3) (-1,3) (0,3)
B3,A3,A3,A3 A3,B3,C3,B3 C3,C3,B3,C3