Before we can start change-ringing, we need some basic principles:

• 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 not allowed 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
      214365      swap 3 (!2, 34, 56)

If you do that again, then this happens:

      123456
      214365      swap 3 (12, 34, 56)
      123456      swap 3 (21, 43, 65)

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, so let’s do that to get our next row:

     123456
     214365     swap 3 (12, 34, 56)
     241635     swap 2 (14, 36)

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
     214365   swap 3 (12, 34, 56)
     241635   swap 2 (14, 36)
     426153   swap 3 (24, 16, 35)
     462513   swap 2 (26, 15)
     645231   swap 3 etc
     654321   swap 2
     563412   swap 3
     536142   swap 2
     351624   swap 3
     315264   swap 2
     132546   swap 3
     123456   swap 2

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!

Another little exercise: 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.

Finally, here’s another difference between tower bell ringing and handbell ringing: ringing an odd number of bells is much more common on tower bells than it is on handbells. I’ll explain why some other time, but for that reason, and for the foreseeable future, I’m only going to deal with ringing an even number of bells; six in fact, as we said at the outset.

Answers to the exercises next time……