Here are the basics of change-ringing:

• The rows are changed continuously; every handstroke and every backstroke has the bells in a different order.
• Each bell sounds once, and once only in every row.
• Repetitions of rows are normally avoided until all available rows have been used. On six bells, 720 different rows are possible. They take about 15 minutes to ring on handbells, about 25 minutes on tower bells (handbells are usually rung faster than tower bells). 
• On six bells, it’s normal to swap all three adjacent pairs, or failing that, two pairs simultaneously. Swapping just one pair is considered undesirable because the ringing sounds too static.

The simplest thing you can do from rounds is to swap all three pairs:

                                                                            123456
       Swap 3 pairs (1&2, 3&4, 5&6)                   214365     

If you do that again, then this happens:

                                                                            123456
    Swap 3 pairs (1&2, 3&4, 5&6)                      214365    
     Swap 3 pairs (2&1, 4&3, 6&5)                     123456      

We’ve repeated a row already! In fact, it has come round after only 2 of the 720 possible changes. That’s no good!

The next most simple thing to do is to swap the two internal pairs (the bells on the inside of the row), so let’s do that to get our next row:

                                                                           123456
      Swap 3 pairs  (1&2, 3&4, 5&6)                  214365   
       Swap 2 pairs (1&4, 3&6)                           241635   

Now we can swap all three pairs again, then the two internal pairs,  then all three pairs, then the two internal pairs and so on, like this:

                                                                           123456
    Swap 3 pairs                                                 214365   
    Swap 2 pairs                                                 241635   
    Swap 3 pairs                                                 426153   
     Swap 2 pairs                                                462513  
      etc                                                                645231  
                                                                           654321   
                                                                           563412   
                                                                           536142   
                                                                           351624   
                                                                           315264   
                                                                           132546   
                                                                           123456   

After 12 rows, we arrive back in rounds. This little block is called ‘Plain Hunt’ and it forms the basis of all change ringing on all numbers of bells. To get Plain Hunt on a different (even) number of bells you follow exactly the same principle: swap all the pairs, then swap all the internal pairs alternately until it comes round (after twice as many rows as there are bells; for instance, on 8 bells, Plain Hunt is 2 × 8 = 16 rows long). See if you can write out Plain Hunt on 8. Squared paper is useful!

Can you see why this principle doesn’t quite work on an odd number of bells and how you can adapt it to get Plain Hunt to work on an odd number of bells? See if you can work out what Plain Hunt on 5 would look like. There are TWO likely solutions to this exercise. Can you find both? They should both be 10 changes long.

Ringing an odd number of bells is much more common on tower bells than it is on handbells. In the next lesson, I'll say more about Plain Hunt on six, aimed mainly at those learning handbells. The one after that will deal with Plain Hunt on five bells, for those setting out on tower bells.