Four, five, six, seven

At the Glasgow practice last week we had a visit from Chris Field, who rings in Nottingham and is a friend of Peter's from university. He is also a handbell ringer, but he wasn't in Glasgow long enough for us to arrange any handbell ringing. He told me about a style of rule-based or pattern-based ringing that bands he rings with in the East Midlands have been trying. As we had a handbell day yesterday, this new idea was ideal for something to try in the evening.

The composition Chris explained is called 4, 5, 6, 7. What does this mean? 4 means plain hunting in the front four places while the bells at the back dodge in pairs. 5 means plain hunting at the back, from 5th place upwards, while the bells on the front dodge in pairs. 6 means plain hunting in the front six places and dodging above, and 7 means plain hunting at the back from 7th place upwards, with dodging below.

The composition 4, 5, 6, 7 works on any number of bells from 8 upwards. For each number, you ring half a course of plain hunting so that the hunting bells become reversed. Here's how it works on 10.

Starting from rounds, ring 4 until the front four are reversed:


Then ring 5 until the back six are reversed:


Then ring 6 until the bells in the front six places are reversed:


Then ring 7 until the bells in the back four places are reversed:


which is a cyclic part end, with the pairs kept together.

Repeat four more times.

Here's how it looks overall, with one part per column and the lines shown for 9-10 (diagram from CompLib). It has rotational symmetry, which is nice. M4 and so on are just because CompLib doesn't allow a numerical method abbreviation.

4567 Royal

It takes a little while to get into it, but it's fun. Every time the pattern changes, all the pairs are back together, which is a big hint for conducting (I called it like spliced, announcing the next number when necessary).

The same idea works on 12 (just that the 5 and 7 involve bigger blocks of hunting and last longer) and on 8 (in that case 7 just swaps the bells in 7th and 8th places by hunting in the back two places). We rang all of them.

As a warm-up on 8 we rang 4, 5, 8 repeated (8 means plain hunting on all 8, for 8 changes to reverse the whole row).

It turns out that on n bells the total length is n squared (exercise!). To ring it on 6, just call 4, 5, 6 (no need for the 7).

I think Chris said he had been ringing it on tower bells, but it's the kind of thing that's much easier in hand. It could be seen as a development from the "kaleidoscope" ringing found in the ART materials, or as a tiny step towards David Pipe's "particles" composition of cyclic spliced maximus.

Many other compositions are possible. There's no need to always ring half a course of plain hunting at a time, and then you can mix the bells up more. Clearly you can reproduce any right-place method whose place notation only has one internal place at a time. For example, on minor, a plain course of Little Bob is 6 (for two changes), 4 (for two changes), 6 (for two changes), 2 (for two changes), repeated four more times. That's just another way of writing the place notation. I like the scheme of half courses though, so that the pairs keep coming back together. An interesting question is exactly how many of the possible rows you can get in this style. For ringing interest, I think the ideal would be to alternate odd and even numbers as much as possible, so that pairs don't get stuck dodging for too long. I will have to see if I can find a quarter peal composition.