Coursing Order

David Pipe and Mark Davies both referred to coursing order in their recent webinars, so I just wanted to explain a bit more about this concept, which is not only vital in conducting and composing, but can help at every level of ringing. And in fact you probably use it already, even if you don't give it that name.

We have talked before about coursing pairs (in the context of ringing handbells) and the concept of course bells and after bells comes in Learning the Ropes level 3. The basic ideas are easiest to spot in Plain Hunt, but apply in some ways in most methods. Looking, for example, at the 4th, it leads after the 2nd leads and it lies behind after the 2nd does. So the 2nd is the 4th's course bell. And we can see that the 5th leads after the 4th and lies behind after the 4th. So the 5th is the 4th's after bell. And the 4th is the 5th's course bell.

We can continue this sequence, looking at the order in which the bells lead (and lie behind); after the 2nd is the 4th, then the 5th, then the 3rd, then the treble, then the 2nd, then the 4th... And we see that the order keeps going round the same sequence; 2 4 5 3 1 2 4 5 3 1 2...; in a never-ending cycle. We can write that the coursing order is 24531. Or, equally, we could write 53124, or 31245; because it's a cycle, we can start anywhere within it.

Or we can look at the bells followed as one hunts up to the back or down to the front. For instance, looking at the 4th again, it follows 5312 on the way up and 5312 again on the way down. We can see that this is the order that the bells come in the coursing order, after the 4th.

Similarly, we can use the coursing order to predict which bells another bell would follow. Let's try it for the 3rd. We had the coursing order 24531, but we recall that it is a cycle, so we know it extends to 2 4 5 3 1 2 4 5 3 1. Starting from the 3rd, we get 1245. Checking in the method, we see our prediction is correct:

As with most patterns in bell-ringing, this can be used to help you ring the method, but it can also help the conductor keep people right, as they know which order they ought to meet the bells.

So, what about Plain Bob Doubles? Let's look to see who the 2nd follows in a plain course:

Note that I have concentrated on the plain hunt parts, as that's where you actually pass bells, so each order on the way up or down is a sequence of the 4 other bells. The 3-4 dodges are essentially a bit of "treading water" before getting on with the hunting. And the 4 blows behind is another little "rest" while the 3rd and 4th dodge underneath you. So we get:

The interesting thing here is that you pass the other working bells in the same order every time; it's always 4, then 5, then 3, but the treble can be anywhere in the sequence. That shouldn't be a surprise; you know that the same bell (the 4th, who is your after bell) always takes you off the lead - except when the treble does, which is a signal to you to make Seconds.

And here's another example of patterns working both ways; you are (hopefully) familiar with using where you see the treble as a reminder of which work you have to do next. For example, seeing the treble when you are just reaching the back tells you that your next piece of work in 3-4 down. But, conversely, if I'm conducting and I know my next work is 3-4 down, I know that I will meet the treble in 5ths place, so the coursing order (from the 2nd) will be 4531.

So you can see that, from the point of view of the coursing order, all the working bells stay in the same place relative to each other, while the treble moves through the pattern. So, if we ignore the treble's place, this pattern 453 will sum up the whole of the plain course of Plain Bob Doubles for the 2nd, which is much less to remember than the list of changing coursing orders listed above. This is why, when David and Mark were talking about coursing orders, they never included the treble.

So the coursing order for Plain Bob Doubles (and for a lot of other Doubles methods) is usually stated as being 2453. As we said above, it is a cycle of bells, so we can predict the order in which the 5th (for instance) will see the bells. Starting from 5 in the coursing order, we get 5324. And this is often written (5)324 or just 324, as the ringer of the 5th can (hopefully) remember which bell they are ringing themself and only needs to know about the other bells. We can see below that this is correct; the 5th always pass the other working bells in the order 324. For instance, the first piece of work for the 5th in the plain course is 3-4 up, so they know they will pass the treble in 2-3 (i.e. going from 2nds place to 3rds place), so the order will be 3124 (dodging with the 2nd on the way up).

Next, in order to conduct or compose, we need to think about what happens at a Bob.

If you're feeling particularly bored by the lockdown, feel free to write out a 120 of Plain Bob Doubles, with the 2nd unaffected (i.e. calling a Bob each time the 2nd is doing 4 blows behind) and look to see what happens to the coursing order. It's good practice, but here's what you ought to find.

We know the coursing order starts off, in a plain course, as (2)453. After the first Bob, we find the coursing order becomes (2)534. The other three bells have been rearranged; 4 has moved to the end of the coursing order, while 5 and 3 have each shuffled one place left. This pattern of rearrangement is summarised in the phrase that David used, that any order ABC becomes BCA; A has been moved to the end, while B and C have each moved one position to the left.

At the next Bob, we find that (2)534 is transformed to (2)345. The pattern of movement is the same; if the starting pattern is ABC, then A is 5, B is 3 and C is 4. So the outcome, BCA, is 345.

Another Bob transforms the coursing order (2)345 to (2)453. And we recognised this as the coursing order of the plain course, so, having called three bobs, we will get back to rounds. Hopefully, it's not a surprise that it took three bobs to get back to rounds, as we have been swapping three bells around at each bob. In summary, the coursing orders were:

Now let's try another bell unaffected. How about if we were calling from the 4th? We know the coursing order in the plain course is (4)532. Rearranging 532 in the same way as before at each Bob gives:

Another time, I may well write some more about the codes for calling positions (Wrong, Home, Middle and so on, often abbreviated W, H and M) and how touches can be written out, but for now, let's finish by seeing how this BCA transposition was used by David and Mark in their talks.

David was looking at calling Plain Bob Minor. The coursing order for the plain course is 65324. David looked at a calling from the point of view of the tenor, which is how things are usually done. However, it was commented in the chat that conductors might not always be wanting to ring a heavy bell, so, for variety I shall give my example as being called from the 3rd. Remembering 65324 is a cycle, the initial coursing order from the point of view of the 3rd is (3)2465.

David's touch of 120 changes had a call every time the observation bell was dodging in 5-6. Unlike the Plain Bob Doubles example, where there are only three other bells, who must all be affected by the bob, here three bells are affected, but one other bell (who is the one dodging with you) will be unaffected.

The initial coursing order is 2465.
At the 5-6 down, you must be dodging with the 2nd, as you can see from the coursing order that this is your after bell. So 465 are the bells to be rearranged, using ABC → BCA. 465 becomes 654. The coursing order is now 2654.
The next Bob is at 5-6 up, where you dodge with the 4th, leaving 265 affected. And 265 → 652. So we get coursing order 6524.
5-6 down again just affects the final three bells in the coursing order, i.e. 524, which becomes 245.
And the 5-6 up again affects the first three bells in the coursing order: 624 → 246, giving coursing order 2465, which we recognise as being back in the plain course. So we confidently call "That's All" as we do 3-4 up.

Mark used Bristol Surprise Major for his example. The coursing order for the plain course is 8753246. But because he was doing everything from the tenor's point of view, and with the 7th coursing the 8th throughout ("tenors together" was his phrase), he only looked at the bells affected by the calls, he used the initial coursing order 53246. Except that he wasn't bothered about 2 and 3, so just used dots for them. I will keep them in, for clarity.

We just need to know which three bells in the coursing order are affected at each call. Wrong (W) affects the first three, Home (H) affects the middle set of three and Middle (M) affects the last three. I have highlighted the bells affected at each call below.

Starting coursing order 53246
2H means two Homes; the first changes 324 to 243 52436
The second home also affects the same three bells 54326
2M is two Middles, firstly 326 → 263... 54263
...then 263 → 632. 54632
Another Home, affecting 463 56342
Two more Middles; 342 becomes 423... 56423
... then 423 becomes 234 56234
Two more Homes, each affecting 623... 52364
... to end up as 236 and then 362 53624
Then a Wrong, meaning the 5th is affected for the first time 36524
A Middle is next 36245
And two Wrongs; first 362 → 623... 62345
... and 623 → 236 23645
A Home affects 364 26435
Then, although shown as H, the next call was a Middle 26354
And finally a Wrong 63254

So 3 and 2 are back to their home places in the coursing order, but 4, 5 and 6 have been swapped round. That means that we haven't got rounds yet, but doing the whole lot three times will get them back to where they started. The coursing orders at the part ends are 63254, 43265 and 65324.

Amazing what you can do just with a single pattern ABC → BCA.