Back in 2013, as part of a list of ways in which I wanted to improve my handbell technique, I wrote:

• Make friends with more coursing orders. It was said of the mathematician Srinivasa Ramanujan, by his collaborator John Littlewood, that "every positive integer is one of his personal friends". When conducting, I find that it takes significant concentration to remember the coursing order, except for a few old friends such as 52436, 54326, 32546, 65324 etc. In those cases I can remember which coursing order we are in, without having to remember what that coursing order is. I feel that if I could add more coursing orders to this list, I would find conducting easier.

Prompted by calling Mark Davies' 5056 of Bristol, this article is about friendly coursing orders, which are worth remembering because they produce desirable 4-bell runs in many methods and therefore appear in a lot of compositions. They also contain patterns that make them easy to remember. I will stick to in-course coursing orders, meaning those that can be reached from the plain without using singles. Including out-of-course coursing orders would add another 19 to the list (if I have counted correctly).

So, here goes, dividing the list into several categories according to structure.

1. 5-6 at home: 53246, 52436, 54326.
   These coursing orders are the foundation of everything and we can start learning them by calling 120s of Plain Bob Doubles (although usually that would not be on handbells!). They also occur in the standard calling of Plain Bob Minor. A lot of compositions finish with three homes, giving the coursing orders 52436 and 54326 after whichever part of the plain course hasn't been rung already. These three coursing orders produce xxxx5678 roll-ups at or near course ends (assuming a major method), and often at a couple of other points in the course, e.g. in Yorkshire just before the tenor becomes 6th place bell and just after the tenor becomes 7th place bell.
2. 5-6 at home, reversed: 64235, 62345, 63425.
   In these coursing orders, 2-3-4 are in out-of-course sequences. They produce xxxx6578 roll-ups in major. Many compositions include these coursing orders in a block of three homes part-way through; for royal or maximus this is often around the half-way point.
3. xxxx2345 roll-ups: 24536, 62453, 35426, 63542.
   Notice the pattern: four consecutive bells occurring in ascending then descending pairs. The 6 can be at the beginning or end of the coursing order, so it's possible to move from one to another by calling a before.  The xxxx2345 roll-ups occur during the course in the same pattern as xxxx5678 roll-ups, and they provide an easy audible check. If the coursing order is 2453 then the roll-ups are at handstroke, and if the coursing order is 3542 they are at backstroke. These coursing orders are also encountered early in a conducting career, as 2453 and 3542 both occur in the standard calling of Plain Bob Minor.
4. xxxx3456 roll-ups: 35642, 23564, 46532, 24653.
   These coursing orders have a similar pattern to the previous group.
5. xxxx5432 roll-ups: 53246, 65324, 42356, 64235.
   Again similar, but now we have descending then ascending pairs.
6. xxxx6543 roll-ups: 64352, 26435, 53462, 25346.
   Similar again.
7. xxxx7654 roll-ups: 54632.
   Writing the 7 at the beginning of the coursing order, 7546, shows the familiar pattern of descending then ascending pairs. These roll-ups occur at handstroke. In a composition with the tenors fixed, there won't be 7654s at backstroke, or 4567s. Calling Middle then Home from 54632 produces rounds, and if a composition finishes in this way it's an aid to learning because the end is familiar.
8. 5-6 or 6-5 at the end of the coursing order: 23456, 34256, 42356, 32465, 24365, 43265.
   In many methods, these coursing orders produce xxxx5678 or xxxx6578 roll-ups, respectively, at other positions than those produced by 53246 etc. I don't know whether this terminology is standard, but Roger Bailey used to call them "incidental roll-ups". In some major methods, for example Yorkshire and Bristol, they also produce xxxx8765 or xxxx8756 roll-ups respectively. The reversed roll-ups can also occur on the front, especially in Bristol because it's a double method: 5678xxxx and so on - this also applies to the earlier groups.
9. 5-6 or 6-5 at the beginning of the coursing order: 56342, 56423, 56234, 65324, 65243, 65432.
   These work in a similar way to the previous group.

I said I was going to describe 31 coursing orders, but adding up the totals from the 9 groups above gives 35. That's because four coursing orders appear in two groups each: 42356, 64235, 53246, 65324. This can be understood by noting, for example, that the plain course contains xxxx5678 roll-ups and xxxx5432 roll-ups, covering two of the groups.

Some of the coursing orders are memorable in more than one way. For example, the cyclic rotations of the plain course: 53246, 65324, 46532, 24653, 32465. They can be remembered in that way, and some compositions link them all together in a block of five befores, but also they all occur in various groups because of the roll-ups that they produce. Similarly for the cyclic rotations of 64235. Other examples are 25346, which would occur in a block of three wrongs from the plain course, and 53462, which would occur in a block of three middles from the plain course. Others contain useful mnemonic patterns: 23456 and 65432 are obvious examples.

Coming back to the Mark Davies 5056 of Bristol, and linking with the idea of learning the composition by its coursing orders, that composition contains 25 of these 31 friendly coursing orders and only 6 that are not on the list. Moreover, in most cases, each coursing order is rung for a good chunk of a course because the idea is to take maximum advantage of the music. This means that the coursing order changes relatively infrequently, and that also helps to cement each one in the memory. In contrast, just after Christmas I conducted (on tower bells) an unsuccessful attempt for a 10-part peal composition of the core seven surprise major by Don Morrison. It has an attractive structure but it contains 50 coursing orders and each part has a block of 4 bobs at consecutive leads, so the coursing order changes frequently. I found it much harder to keep track of (although that's not why we lost the peal).