Musical Permutation Group!

Rounds
Ringing usually starts with bells being rung in rounds. If you are ringing two bells, then the position in the ringing order for those two bells never changes when in rounds.

1  2  3  4  5  6 

1  2  3  4  5  6 

1  2  3  4  5  6 

1  2  3  4  5  6 

1  2  3  4  5  6 

1  2  3  4  5  6 

Plain Hunting
The next pattern usually taught is the plain hunting pattern. Consider 6 handbells. In rounds, the bells would ring in the positions numbered as above.

The next simplest thing is for each bell to change place with its neighbor. The following lines show the number of the bell and the position gives its ringing location. An X is below the pairs of bells switching places or permuting.

1   2   3   4   5   6 

  X       X       X   

2   1   4   3   6   5 

      X       X       

2   4   1   6   3   5 

  X       X       X   

4   2   6   1   5   3 

      X       X       

4   6   2   5   1   3 

  X       X      X    

6   4   5   2   3   1 

      X       X       

6   5   4   3   2   1 

  X       X      X    

5   6   3   4   1   2 

      X       X       

5   3   6   1   4   2 

  X       X       X   

3   5   1   6   2   4 

      X       X       

3   1   5   2   6   4 

  X       X       X   

1   3   2   5   4   6 

      X       X       

1   2   3   4   5   6 

And so we end up back where we started.