We rang a peal of cyclic spliced maximus in the tower recently, which is beyond what I can ring on handbells at the moment although while learning the methods I did try ringing two bells on Mabel with varying success. I find that practising on handbells is a good test of whether I know methods thoroughly.
The cyclic maximus was David Pipe's "cyclic six" composition. A few years ago I produced a quarter peal composition of major with a similar structure, which I would like to ring on handbells but haven't got around to putting on the agenda yet. When it comes to cyclic compositions, it's a curious fact that the same idea can often find its natural length as either a quarter of major or a peal of maximus. As well as generating lots of music in the form of runs of consecutive bells, the cyclic six composition has some interesting structural features when rung on tower bells and even more when rung on handbells. My quarter peal of "cyclic four" has the same features, so I'll use it to explain them on a smaller scale.
Here's the composition:
1288 Spliced Major (4m) Simon J. Gay 12345678 ---------- N 14263857 A 13527486 H 16482735 H 15738264 A 18674523 N 17856342 O 18735264 O 17823456 ---------- 7 part. 448 Norwich Surprise, Hull Surprise; 336 Albany Little Treble Place; 56 Oxford Differential Little Bob; 41 changes of method; all the work.
Now for the key features. First, the cyclic part end: 17823456. This generates different runs in each part. For example, 5678s in the first part become 4567s, 3456s and 2345s in other parts; also 8234s, 7823s and 6782s, which are not so musical.
Next, the main methods, which are Norwich, Albany and Hull, form a palindromic block. The most important methods here are Norwich and Hull, which both produce 4-bell runs at the back. In the first lead of Norwich these are 5678s in the triple dodges at the beginning and end of the lead. In the second lead of Norwich, when the tenor is 2nd place bell, they are 5432s. In the first lead of Hull, when the tenor is 7th place bell, there are 5678s in the double dodges at the beginning and end of the lead. In the second lead of Hull, when the tenor is 4th place bell, the runs are 5432s.
The third method is chosen for its place bell order, so that it fits between the desired leads of Norwich and Hull. It needs to have Cambridge place bell order but with an 8th place lead end (because the other methods are 8th place and we have to avoid lead heads repeating with lead ends). I constructed a method with a simple structure and a shorter lead, so that the quarter doesn't become too long; also it matches the style of the cyclic six maximus in which not all the methods have a treble dodging path. The method hasn't been rung and named, but I provisionally call it Albany. The idea is to have the treble doing treble bob up to 6th place, with all the other bells doing treble bob hunting up to 8th place except for a triple dodge in 7-8 across the half lead. To avoid falseness, all the bells including the treble ring Kent places in 3-4.
That sequence of six leads produces the lead end 17856342. To get to the cyclic part end 17823456 we use a "link" method, which is a feature of the cyclic six maximus and several other cyclic compositions. The method, again not yet rung and named, is Oxford Differential Little Bob, and two leads of it are rung. In the same way that Kent Little Bob is like Bastow with Kent places in 3-4, Oxford Differential Little Bob is like Bastow with Oxford places in 3-4. It's "differential" because not all the place bells are part of the same sequence. 2nd and 3rd place bells swap with each other, and the other 5 shuffle round. The effect is that two leads bring 7 and 8 back to 2nd and 3rd place bells where they were, and the other bells move from 56342 to 23456.
A notable feature of the composition, shared with the cyclic six maximus, is that in each part there are two bells that alternately ring the symmetrical place bells (the "pivot" bells) in each method. In the first part of the quarter, these are 2 and 8. In the first lead of Norwich, 2 is 2nd place bell, which is the pivot. In the first lead of Albany, 8 is 6th place bell, which is the pivot. In the first lead of Hull, 2 is 4th place bell, which is the pivot. In the second lead of Hull, 8 is 4th place bell; in the second lead of Albany, 2 is 6th place bell; in the second lead of Norwich, 8 is 2nd place bell.
In the maximus composition, I think this alternation of pivot bells is part of the design in order to produce lots of musical runs. Roughly speaking, when the tenor is a pivot bell it tends to stay near one end of the change and the little bells are working together at the other end of the change, producing runs. Similarly, when the 2 is a pivot bell, there tend to be runs of big bells at the opposite end of the change. That's not the whole story because in the maximus methods there are usually runs at both ends of the change, big bells and little bells, within a single lead. The major composition has fewer runs overall and I chose the methods for simplicity rather than maximal music, but I think the principal of the alternating pivot bells is valid.
If we think about what the handbell pairs do throughout the composition, there are some further interesting features. The first is that all the pairs do the same work as each other during the whole composition. This is simply because of the cyclic part ends. For example, 7-8 are in 5-6 at the beginning of one part and in 3-4 at the beginning of another part, and similarly for the other handbell pairs.
How much time does a handbell pair spend in each position? There aren't any bobs or singles, so a pair is in the same position for the whole of a part (not including the leads of Oxford DLB). If starting as 7th and 8th place bells, or as 2nd and 3rd place bells, the position is coursing. If starting as 6th and 7th place bells, or as 3rd and 4th place bells, the position is 3-4. If starting as 5th and 6th place bells, or as 4th and 5th place bells, the position is 5-6. There is one more starting position, which is 2nd and 8th place bells, and that is also the 5-6 position. So overall there are equal amounts of the coursing and 3-4 positions, and a slight excess of the 5-6 position. For the maximus composition it's similar, with equal amounts of each position except for an excess of the 7-8 position.
Because of the palindromic structure of each part, the whole composition is also a palindrome. This means that whenever a handbell pair rings a particular pair of place bells in one of the methods, it also rings the reverse of those place bells in the same method, in the opposite half of a different part. This is for the same reason as ringing a pair of place bells and later their reverses when ringing a plain course of a single method.
It also turns out that each handbell pair rings the symmetrical lead in each position (3-4, 5-6, 7-8) in every method. Actually the symmetrical leads are all rung twice, because of the point above about ringing the reverse every pair of place bells that is rung. Ringing all the symmetrical leads doesn't follow from the palindromic structure; it depends on the specific sequence of methods. It's a consequence of the alternating pivot bells. When the 2nd is a pivot bell, all the handbell pairs are ringing symmetrical leads in their home positions. As we work through the parts, every handbell pair gets symmetrical leads in all the other positions. When the 8th is a pivot bell, the symmetrical leads are rung by 6-7, 4-5 and 2-3, and all the handbell pairs also get into all those positions during the composition.
There's even more. Considering a particular handbell pair, in most of the parts that pair rings alternately a symmetrical lead and some other lead. The exception is the part in which the pair rings 2nd and 8th place bells at the beginning of the part, because that's the part in which the bells take turns to be pivot bells and therefore there are no symmetrical leads. This is a nice feature because although the symmetrical leads are not necessarily the easiest (e.g. when ringing 7-8 to Yorkshire Major, the symmetrical lead is often found to be the trickiest), if you get to the half lead successfully you can be confident of ringing the second half of the lead.
If we compare my quarter with David Pipe's peal, the obvious difference in structure is that my link method (two leads of Oxford DLB) comes at the end of the part, whereas David's link method (one lead of Slinky) comes at the beginning of the part. I expect it would be possible to produce a major composition with a link method at the beginning of the part, but I found it easier to start with Norwich and its runs in the first lead and work from there.